Scattering of a high-order Bessel beam by a spheroidal particle

NASA Astrophysics Data System (ADS)

Han, Lu

2018-05-01

Within the framework of generalized Lorenz-Mie theory (GLMT), scattering from a homogeneous spheroidal particle illuminated by a high-order Bessel beam is formulated analytically. The high-order Bessel beam is expanded in terms of spheroidal vector wave functions, where the spheroidal beam shape coefficients (BSCs) are computed conveniently using an intrinsic method. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident Bessel beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by nonspherical particles and particle manipulation applications using Bessel beams.

Dispersion and Attenuation Due to Scattering from Heterogeneities of the Frame Bulk Modulus of a Poroelastic Medium

DTIC Science & Technology

2010-02-19

attenuation is a function of the Hurst exponent which characterizes the fractal het- erogeneity. Muller and Gurevich15,16 used statistical smoothing of...modified Bessel function of the third kind, Γ denotes the gamma function, and ν is the Hurst coefficient which is assumed to be 0 < ν ≤ 1. The three...The Hurst coefficient, ν, is ν = 0.1 (long-dashed line), ν = 0.5 (short-dashed line), and ν = 0.9 (long-short dashed line). In (a) the sound speed

Development and Testing of a Multiple Frequency Continuous Wave Radar for Target Detection and Classification

DTIC Science & Technology

2007-03-01

1 2’ VIH " 1 ’ 󈧏) (34) where is the modified Bessel function of zero order. Here is the conditional variance and is the conditional probability...10, the probability of detection is the area under the signal-plus-noise curve above the detection threshold co M vF (V 2+ A2)]10 ( vAPd= fnp~ju,( vIH

Bessel functions in mass action modeling of memories and remembrances

NASA Astrophysics Data System (ADS)

Freeman, Walter J.; Capolupo, Antonio; Kozma, Robert; Olivares del Campo, Andrés; Vitiello, Giuseppe

2015-10-01

Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory.

Optical trapping forces of a focused azimuthally polarized Bessel-Gaussian beam on a double-layered sphere

NASA Astrophysics Data System (ADS)

Wu, F. P.; Zhang, B.; Liu, Z. L.; Tang, Y.; Zhang, N.

2017-12-01

We calculate the trapping forces exerted by a highly focused Bessel-Gaussian beam on a double-layered sphere by means of vector diffraction integral, T-matrix method and Maxwell stress tensor integral. The Bessel-Gaussian beam is azimuthally polarized. Numerical results predicate that the double-layered sphere with air core can be stably trapped in three-dimensions. The trapping forces and efficiencies are dependent on the refraction index and size of the inner core. The trapping efficiency can be optimized by choosing the refraction indices of the inner core and outer layer. Our computational method can be easily modified for other laser beams and particles with arbitrary geometries and multilayers.

Laplace approximation for Bessel functions of matrix argument

NASA Astrophysics Data System (ADS)

Butler, Ronald W.; Wood, Andrew T. A.

2003-06-01

We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A[nu]; matrix Bessel B[nu]; and the type II confluent hypergeometric function of matrix argument, [Psi]. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A[nu], B[nu] and [Psi] given here, together with the Laplace approximations to the matrix argument functions 1F1 and 2F1 presented in Butler and Wood (Laplace approximations to hyper-geometric functions with matrix argument, Ann. Statist. (2002)), satisfy all the important confluence relations and symmetry relations enjoyed by the original functions.

An Investigation of the Pareto Distribution as a Model for High Grazing Angle Clutter

DTIC Science & Technology

2011-03-01

radar detection schemes under controlled conditions. Complicated clutter models result in mathematical difficulties in the determination of optimal and...a population [7]. It has been used in the modelling of actuarial data; an example is in excess of loss quotations in insurance [8]. Its usefulness as...UNCLASSIFIED modified Bessel functions, making it difficult to employ in radar detection schemes. The Pareto Distribution is amenable to mathematical

Bessel Weighted Asymmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avakian, Harut; Gamberg, Leonard; Rossi, Patrizia

We review the concept of Bessel weighted asymmetries for semi-inclusive deep inelastic scattering and focus on the cross section in Fourier space, conjugate to the outgoing hadron’s transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized partonmore » model. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy and hard scale Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.« less

A bivariate gamma probability distribution with application to gust modeling. [for the ascent flight of the space shuttle

NASA Technical Reports Server (NTRS)

Smith, O. E.; Adelfang, S. I.; Tubbs, J. D.

1982-01-01

A five-parameter gamma distribution (BGD) having two shape parameters, two location parameters, and a correlation parameter is investigated. This general BGD is expressed as a double series and as a single series of the modified Bessel function. It reduces to the known special case for equal shape parameters. Practical functions for computer evaluations for the general BGD and for special cases are presented. Applications to wind gust modeling for the ascent flight of the space shuttle are illustrated.

A linear model of population dynamics

NASA Astrophysics Data System (ADS)

Lushnikov, A. A.; Kagan, A. I.

2016-08-01

The Malthus process of population growth is reformulated in terms of the probability w(n,t) to find exactly n individuals at time t assuming that both the birth and the death rates are linear functions of the population size. The master equation for w(n,t) is solved exactly. It is shown that w(n,t) strongly deviates from the Poisson distribution and is expressed in terms either of Laguerre’s polynomials or a modified Bessel function. The latter expression allows for considerable simplifications of the asymptotic analysis of w(n,t).

Elementary functions in thermodynamic Bethe ansatz

NASA Astrophysics Data System (ADS)

Suzuki, J.

2015-05-01

Some years ago, Fendley found an explicit solution to the thermodynamic Bethe ansatz (TBA) equation for an N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek explicit solutions for other super-potential cases utilizing the idea from the ODE/IM correspondence. We find that the TBA equations, corresponding to a wider class of super-potentials, admit solutions in terms of elementary functions such as modified Bessel functions and confluent hyper-geometric series. Based on talks given at ‘Infinite Analysis 2014’ (Tokyo, 2014) and at ‘Integrable lattice models and quantum field theories’ (Bad Honnef, 2014).

Metasurface-assisted orbital angular momentum carrying Bessel-Gaussian Laser: proposal and simulation.

PubMed

Zhou, Nan; Wang, Jian

2018-05-23

Bessel-Gaussian beams have distinct properties of suppressed diffraction divergence and self-reconstruction. In this paper, we propose and simulate metasurface-assisted orbital angular momentum (OAM) carrying Bessel-Gaussian laser. The laser can be regarded as a Fabry-Perot cavity formed by one partially transparent output plane mirror and the other metasurface-based reflector mirror. The gain medium of Nd:YVO 4 enables the lasing wavelength at 1064 nm with a 808 nm laser serving as the pump. The sub-wavelength structure of metasurface facilitates flexible spatial light manipulation. The compact metasurface-based reflector provides combined phase functions of an axicon and a spherical mirror. By appropriately selecting the size of output mirror and inserting mode-selection element in the laser cavity, different orders of OAM-carrying Bessel-Gaussian lasing modes are achievable. The lasing Bessel-Gaussian 0 , Bessel-Gaussian 01 + , Bessel-Gaussian 02 + and Bessel-Gaussian 03 + modes have high fidelities of ~0.889, ~0.889, ~0.881 and ~0.879, respectively. The metasurface fabrication tolerance and the dependence of threshold power and output lasing power on the length of gain medium, beam radius of pump and transmittance of output mirror are also discussed. The obtained results show successful implementation of metasurface-assisted OAM-carrying Bessel-Gaussian laser with favorable performance. The metasurface-assisted OAM-carrying Bessel-Gaussian laser may find wide OAM-enabled communication and non-communication applications.

Trellis Coding of Non-coherent Multiple Symbol Full Response M-ary CPFSK with Modulation Index 1/M

NASA Technical Reports Server (NTRS)

Lee, H.; Divsalar, D.; Weber, C.

1994-01-01

This paper introduces a trellis coded modulation (TCM) scheme for non-coherent multiple full response M-ary CPFSK with modulation index 1/M. A proper branch metric for the trellis decoder is obtained by employing a simple approximation of the modified Bessel function for large signal to noise ratio (SNR). Pairwise error probability of coded sequences is evaluated by applying a linear approximation to the Rician random variable.

Inspection system calibration methods

DOEpatents

Deason, Vance A.; Telschow, Kenneth L.

2004-12-28

An inspection system calibration method includes producing two sideband signals of a first wavefront; interfering the two sideband signals in a photorefractive material, producing an output signal therefrom having a frequency and a magnitude; and producing a phase modulated operational signal having a frequency different from the output signal frequency, a magnitude, and a phase modulation amplitude. The method includes determining a ratio of the operational signal magnitude to the output signal magnitude, determining a ratio of a 1st order Bessel function of the operational signal phase modulation amplitude to a 0th order Bessel function of the operational signal phase modulation amplitude, and comparing the magnitude ratio to the Bessel function ratio.

Generation of nondiffracting Bessel beam using digital micromirror device.

PubMed

Gong, Lei; Ren, Yu-Xuan; Xue, Guo-Sheng; Wang, Qian-Chang; Zhou, Jin-Hua; Zhong, Min-Cheng; Wang, Zi-Qiang; Li, Yin-Mei

2013-07-01

We experimentally demonstrated Bessel-like beams utilizing digital micromirror device (DMD). DMD with images imitating the equivalent axicon can shape the collimated Gaussian beam into Bessel beam. We reconstructed the 3D spatial field of the generated beam through a stack of measured cross-sectional images. The output beams have the profile of Bessel function after intensity modulation, and the beams extend at least 50 mm while the lateral dimension of the spot remains nearly invariant. Furthermore, the self-healing property has also been investigated, and all the experimental results agree well with simulated results numerically calculated through beam propagation method. Our observations demonstrate that the DMD offers a simple and efficient method to generate Bessel beams with distinct nondiffracting and self-reconstruction behaviors. The generated Bessel beams will potentially expand the applications to the optical manipulation and high-resolution fluorescence imaging owing to the unique nondiffracting property.

Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.

Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.

Studies of Transverse Momentum Dependent Parton Distributions and Bessel Weighting

NASA Astrophysics Data System (ADS)

Gamberg, Leonard

2015-04-01

We present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. Advantages of employing Bessel weighting are that transverse momentum weighted asymmetries provide a means to disentangle the convolutions in the cross section in a model independent way. The resulting compact expressions immediately connect to work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions. As a test case, we apply the procedure to studies of the double longitudinal spin asymmetry in SIDIS using a dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. Using a fully differential cross section for the process, the effect of four momentum conservation is analyzed using various input models for transverse momentum distributions and fragmentation functions. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations. Bessel weighting provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs. Work is supported by the U.S. Department of Energy under Contract No. DE-FG02-07ER41460.

Studies of Transverse Momentum Dependent Parton Distributions and Bessel Weighting

NASA Astrophysics Data System (ADS)

Gamberg, Leonard

2015-10-01

We present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. Advantages of employing Bessel weighting are that transverse momentum weighted asymmetries provide a means to disentangle the convolutions in the cross section in a model independent way. The resulting compact expressions immediately connect to work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions. As a test case, we apply the procedure to studies of the double longitudinal spin asymmetry in SIDIS using a dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. Using a fully differential cross section for the process, the effect of four momentum conservation is analyzed using various input models for transverse momentum distributions and fragmentation functions. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations. Bessel weighting provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs. Work is supported by the U.S. Department of Energy under Contract No. DE-FG02-07ER41460.

Physical Applications of a Simple Approximation of Bessel Functions of Integer Order

ERIC Educational Resources Information Center

Barsan, V.; Cojocaru, S.

2007-01-01

Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

PubMed

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

Boundary Layers Induced by Three-Dimensional Vortex Loops

DTIC Science & Technology

1993-12-01

obtained analytically (see Appendix B) and are given by =-2 Oz,(sin0 -)I- k IK(I IckI) - sKo (Y I k ) Cosa, (2.35) 1= -2 1 k Oq IIJ~ G=2 -’(cosO-y’)lkl...F- Ko (o Ipl) 279Ul I 280 p = if’, and similarly U a E(g) = 2(g 2 + a2)3/2 ** F = IPI K(a Ipl) 3 where K0, K, are the modified Bessel functions of

Bessel beam fluorescence lifetime tomography of live embryos (Conference Presentation)

NASA Astrophysics Data System (ADS)

Xu, Dongli; Peng, Leilei

2016-03-01

Optical tomography allows isotropic 3D imaging of embryos. Scanning-laser optical tomography (SLOT) has superior light collecting efficiency than wide-field optical tomography, making it ideal for fluorescence imaging of live embryos. We previously reported an imaging system that combines SLOT with a novel Fourier-multiplexed fluorescence lifetime imaging (FmFLIM) technique named FmFLIM-SLOT. FmFLIM-SLOT performs multiplexed FLIM-FRET readout of multiple FRET sensors in live embryos. Here we report a recent effort on improving the spatial resolution of the FmFLIM-SLOT system in order to image complex biochemical processes in live embryos at the cellular level. Optical tomography has to compromise between resolution and the depth of view. In SLOT, the commonly-used focused Gaussian beam diverges quickly from the focal plane, making it impossible to achieve high resolution imaging in a large volume specimen. We thus introduce Bessel beam laser-scanning tomography, which illuminates the sample with a spatial-light-modulator-generated Bessel beam that has an extended focal depth. The Bessel beam is scanned across the whole specimen. Fluorescence projection images are acquired at equal angular intervals as the sample rotates. Reconstruction artifacts due to annular-rings of the Bessel beam are removed by a modified 3D filtered back projection algorithm. Furthermore, in combination of Fourier-multiplexing fluorescence lifetime imaging (FmFLIM) method, the Bessel FmFLIM-SLOT system is capable of perform 3D lifetime imaging of live embryos at cellular resolution. The system is applied to in-vivo imaging of transgenic Zebrafish embryos. Results prove that Bessel FmFLIM-SLOT is a promising imaging method in development biology research.

A symmetric integral identity for Bessel functions with applications to integral geometry

NASA Astrophysics Data System (ADS)

Salman, Yehonatan

2017-12-01

In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.

Asymptotics of Determinants of Bessel Operators

NASA Astrophysics Data System (ADS)

Basor, Estelle L.; Ehrhardt, Torsten

For aL∞(+)∩L1(+) the truncated Bessel operator Bτ(a) is the integral operator acting on L2[0,τ] with the kernel where Jν stands for the Bessel function with ν>-1. In this paper we determine the asymptotics of the determinant det(I+Bτ(a)) as τ-->∞ for sufficiently smooth functions a for which a(x)≠1 for all x[0,∞). The asymptotic formula is of the form det(I+Bτ(a)) GτE with certain constants G and E, and thus similar to the well-known Szegö-Akhiezer-Kac formula for truncated Wiener-Hopf determinants.

On a method for generating inequalities for the zeros of certain functions

NASA Astrophysics Data System (ADS)

Gatteschi, Luigi; Giordano, Carla

2007-10-01

In this paper we describe a general procedure which yields inequalities satisfied by the zeros of a given function. The method requires the knowledge of a two-term approximation of the function with bound for the error term. The method was successfully applied many years ago [L. Gatteschi, On the zeros of certain functions with application to Bessel functions, Nederl. Akad. Wetensch. Proc. Ser. 55(3)(1952), Indag. Math. 14(1952) 224-229] and more recently too [L. Gatteschi and C. Giordano, Error bounds for McMahon's asymptotic approximations of the zeros of the Bessel functions, Integral Transform Special Functions, 10(2000) 41-56], to the zeros of the Bessel functions of the first kind. Here, we present the results of the application of the method to get inequalities satisfied by the zeros of the derivative of the function . This function plays an important role in the asymptotic study of the stationary points of the solutions of certain differential equations.

Monotonic sequences related to zeros of Bessel functions

NASA Astrophysics Data System (ADS)

Lorch, Lee; Muldoon, Martin

2008-12-01

In the course of their work on Salem numbers and uniform distribution modulo 1, A. Akiyama and Y. Tanigawa proved some inequalities concerning the values of the Bessel function J 0 at multiples of π, i.e., at the zeros of J 1/2. This raises the question of inequalities and monotonicity properties for the sequences of values of one cylinder function at the zeros of another such function. Here we derive such results by differential equations methods.

Electromagnetic scattering by a uniaxial anisotropic sphere located in an off-axis Bessel beam.

PubMed

Qu, Tan; Wu, Zhen-Sen; Shang, Qing-Chao; Li, Zheng-Jun; Bai, Lu

2013-08-01

Electromagnetic scattering of a zero-order Bessel beam by an anisotropic spherical particle in the off-axis configuration is investigated. Based on the spherical vector wave functions, the expansion expression of the zero-order Bessel beam is derived, and its convergence is numerically discussed in detail. Utilizing the tangential continuity of the electromagnetic fields, the expressions of scattering coefficients are given. The effects of the conical angle of the wave vector components of the zero-order Bessel beam, the ratio of the radius of the sphere to the central spot radius of the zero-order Bessel beam, the shift of the beam waist center position along both the x and y axes, the permittivity and permeability tensor elements, and the loss of the sphere on the radar cross section (RCS) are numerically analyzed. It is revealed that the maximum RCS appears in the conical direction or neighboring direction when the sphere is illuminated by a zero-order Bessel beam. Furthermore, the RCS will decrease and the symmetry is broken with the shift of the beam waist center.

Construction of normal-regular decisions of Bessel typed special system

NASA Astrophysics Data System (ADS)

Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.

2017-09-01

Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.

Studies of transverse momentum dependent parton distributions and Bessel weighting

DOE PAGES

Aghasyan, M.; Avakian, H.; De Sanctis, E.; ...

2015-03-01

In this paper we present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. Using a fully differential cross section for the process, the effect of four momentum conservation is analyzed using various input models for transverse momentum distributions and fragmentation functions. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Montemore » Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy/Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.« less

Studies of transverse momentum dependent parton distributions and Bessel weighting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aghasyan, M.; Avakian, H.; De Sanctis, E.

In this paper we present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. Using a fully differential cross section for the process, the effect of four momentum conservation is analyzed using various input models for transverse momentum distributions and fragmentation functions. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Montemore » Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy/Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.« less

Transverse circular-polarized Bessel beam generation by inward cylindrical aperture distribution.

PubMed

Pavone, S C; Ettorre, M; Casaletti, M; Albani, M

2016-05-16

In this paper the focusing capability of a radiating aperture implementing an inward cylindrical traveling wave tangential electric field distribution directed along a fixed polarization unit vector is investigated. In particular, it is shown that such an aperture distribution generates a non-diffractive Bessel beam whose transverse component (with respect to the normal of the radiating aperture) of the electric field takes the form of a zero-th order Bessel function. As a practical implementation of the theoretical analysis, a circular-polarized Bessel beam launcher, made by a radial parallel plate waveguide loaded with several slot pairs, arranged on a spiral pattern, is designed and optimized. The proposed launcher performance agrees with the theoretical model and exhibits an excellent polarization purity.

A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

NASA Astrophysics Data System (ADS)

Parand, K.; Nikarya, M.

2017-11-01

In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

Light-sheet microscopy by confocal line scanning of dual-Bessel beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Pengfei; Phipps, Mary Elizabeth; Goodwin, Peter Marvin

Here, we have developed a light-sheet microscope that uses confocal scanning of dual-Bessel beams for illumination. A digital micromirror device (DMD) is placed in the intermediate image plane of the objective used to collect fluorescence and is programmed with two lines of pixels in the “on” state such that the DMD functions as a spatial filter to reject the out-of-focus background generated by the side-lobes of the Bessel beams. The optical sectioning and out-of-focus background rejection capabilities of this microscope were demonstrated by imaging of fluorescently stained actin in human A431 cells. The dual-Bessel beam system enables twice as manymore » photons to be detected per imaging scan, which is useful for low light applications (e.g., single-molecule localization) or imaging at high speed with a superior signal to noise. While demonstrated for two Bessel beams, this approach is scalable to a larger number of beams.« less

Light-sheet microscopy by confocal line scanning of dual-Bessel beams

DOE PAGES

Zhang, Pengfei; Phipps, Mary Elizabeth; Goodwin, Peter Marvin; ...

2016-10-25

Here, we have developed a light-sheet microscope that uses confocal scanning of dual-Bessel beams for illumination. A digital micromirror device (DMD) is placed in the intermediate image plane of the objective used to collect fluorescence and is programmed with two lines of pixels in the “on” state such that the DMD functions as a spatial filter to reject the out-of-focus background generated by the side-lobes of the Bessel beams. The optical sectioning and out-of-focus background rejection capabilities of this microscope were demonstrated by imaging of fluorescently stained actin in human A431 cells. The dual-Bessel beam system enables twice as manymore » photons to be detected per imaging scan, which is useful for low light applications (e.g., single-molecule localization) or imaging at high speed with a superior signal to noise. While demonstrated for two Bessel beams, this approach is scalable to a larger number of beams.« less

Hierarchical Type Stability Criteria for Delayed Neural Networks via Canonical Bessel-Legendre Inequalities.

PubMed

Zhang, Xian-Ming; Han, Qing-Long; Zeng, Zhigang

2018-05-01

This paper is concerned with global asymptotic stability of delayed neural networks. Notice that a Bessel-Legendre inequality plays a key role in deriving less conservative stability criteria for delayed neural networks. However, this inequality is in the form of Legendre polynomials and the integral interval is fixed on . As a result, the application scope of the Bessel-Legendre inequality is limited. This paper aims to develop the Bessel-Legendre inequality method so that less conservative stability criteria are expected. First, by introducing a canonical orthogonal polynomial sequel, a canonical Bessel-Legendre inequality and its affine version are established, which are not explicitly in the form of Legendre polynomials. Moreover, the integral interval is shifted to a general one . Second, by introducing a proper augmented Lyapunov-Krasovskii functional, which is tailored for the canonical Bessel-Legendre inequality, some sufficient conditions on global asymptotic stability are formulated for neural networks with constant delays and neural networks with time-varying delays, respectively. These conditions are proven to have a hierarchical feature: the higher level of hierarchy, the less conservatism of the stability criterion. Finally, three numerical examples are given to illustrate the efficiency of the proposed stability criteria.

Integrating products of Bessel functions with an additional exponential or rational factor

NASA Astrophysics Data System (ADS)

Van Deun, Joris; Cools, Ronald

2008-04-01

We provide two MATLAB programs to compute integrals of the form ex∏i=1kJν_i(ax)dxand 0∞xr+x∏i=1kJν_i(ax)dx with Jν_i(x) the Bessel function of the first kind and (real) order ν. The parameter m is a real number such that ∑ν+m>-1 (to assure integrability near zero), r is real and the numbers c and a are all strictly positive. The program can deliver accurate error estimates. Program summaryProgram title: BESSELINTR, BESSELINTC Catalogue identifier: AEAH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1601 No. of bytes in distributed program, including test data, etc.: 13 161 Distribution format: tar.gz Programming language: Matlab (version ⩾6.5), Octave (version ⩾2.1.69) Computer: All supporting Matlab or Octave Operating system: All supporting Matlab or Octave RAM: For k Bessel functions our program needs approximately ( 500+140k) double precision variables Classification: 4.11 Nature of problem: The problem consists in integrating an arbitrary product of Bessel functions with an additional rational or exponential factor over a semi-infinite interval. Difficulties arise from the irregular oscillatory behaviour and the possible slow decay of the integrand, which prevents truncation at a finite point. Solution method: The interval of integration is split into a finite and infinite part. The integral over the finite part is computed using Gauss-Legendre quadrature. The integrand on the infinite part is approximated using asymptotic expansions and this approximation is integrated exactly with the aid of the upper incomplete gamma function. In the case where a rational factor is present, this factor is first expanded in a Taylor series around infinity. Restrictions: Some (and eventually all) numerical accuracy is lost when one or more of the parameters r,c,a or v grow very large, or when r becomes small. Running time: Less than 0.02 s for a simple problem (two Bessel functions, small parameters), a few seconds for a more complex problem (more than six Bessel functions, large parameters), in Matlab 7.4 (R2007a) on a 2.4 GHz AMD Opteron Processor 250. References:J. Van Deun, R. Cools, Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions, ACM Trans. Math. Software 32 (4) (2006) 580-596.

Generation of low-divergence laser beams

DOEpatents

Kronberg, James W.

1993-01-01

Apparatus for transforming a conventional beam of coherent light, having a Gaussian energy distribution and relatively high divergence, into a beam in which the energy distribution approximates a single, non-zero-order Bessel function and which therefore has much lower divergence. The apparatus comprises a zone plate having transmitting and reflecting zones defined by the pattern of light interference produced by the combination of a beam of coherent light with a Gaussian energy distribution and one having such a Bessel distribution. The interference pattern between the two beams is a concentric array of multiple annuli, and is preferably recorded as a hologram. The hologram is then used to form the transmitting and reflecting zones by photo-etching portions of a reflecting layer deposited on a plate made of a transmitting material. A Bessel beam, containing approximately 50% of the energy of the incident beam, is produced by passing a Gaussian beam through such a Bessel zone plate. The reflected beam, also containing approximately 50% of the incident beam energy and having a Bessel energy distribution, can be redirected in the same direction and parallel to the transmitted beam. Alternatively, a filter similar to the Bessel zone plate can be placed within the resonator cavity of a conventional laser system having a front mirror and a rear mirror, preferably axially aligned with the mirrors and just inside the front mirror to generate Bessel energy distribution light beams at the laser source.

Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model

NASA Astrophysics Data System (ADS)

Wang, Jia Jie; Han, Yi Ping; Chang, Jiao Yong; Chen, Zhu Yang

2018-02-01

Within the framework of generalized Lorenz-Mie theory (GLMT), an eccentrically stratified dielectric sphere model illuminated by an arbitrarily incident Bessel beam is applied to investigate the scattering characteristics of a single nucleated biological cell. The Bessel beam propagating in an arbitrary direction is expanded in terms of vector spherical wave functions (VSWFs), where the beam shape coefficients (BSCs) are calculated rigorously in a closed analytical form. The effects of the half-cone angle of Bessel beam, the location of the particle in the beam, the size ratio of nucleus to cell, and the location of the nucleus inside the cell on the scattering properties of a nucleated cell are analyzed. The results provide useful references for optical diagnostic and imaging of particle having nucleated structure.

Generation of low-divergence laser beams

DOEpatents

Kronberg, J.W.

1993-09-14

Apparatus for transforming a conventional beam of coherent light, having a Gaussian energy distribution and relatively high divergence, into a beam in which the energy distribution approximates a single, non-zero-order Bessel function and which therefore has much lower divergence. The apparatus comprises a zone plate having transmitting and reflecting zones defined by the pattern of light interference produced by the combination of a beam of coherent light with a Gaussian energy distribution and one having such a Bessel distribution. The interference pattern between the two beams is a concentric array of multiple annuli, and is preferably recorded as a hologram. The hologram is then used to form the transmitting and reflecting zones by photo-etching portions of a reflecting layer deposited on a plate made of a transmitting material. A Bessel beam, containing approximately 50% of the energy of the incident beam, is produced by passing a Gaussian beam through such a Bessel zone plate. The reflected beam, also containing approximately 50% of the incident beam energy and having a Bessel energy distribution, can be redirected in the same direction and parallel to the transmitted beam. Alternatively, a filter similar to the Bessel zone plate can be placed within the resonator cavity of a conventional laser system having a front mirror and a rear mirror, preferably axially aligned with the mirrors and just inside the front mirror to generate Bessel energy distribution light beams at the laser source. 11 figures.

Calculation of Rayleigh type sums for zeros of the equation arising in spectral problem

NASA Astrophysics Data System (ADS)

Kostin, A. B.; Sherstyukov, V. B.

2017-12-01

For zeros of the equation (arising in the oblique derivative problem) μ J n ‧ ( μ ) cos α + i n J n ( μ ) sin α = 0 , μ ∈ ℂ , with parameters n ∈ ℤ, α ∈ [-π/2, π/2] and the Bessel function Jn (μ) special summation relationships are proved. The obtained results are consistent with the theory of well-known Rayleigh sums calculating by zeros of the Bessel function.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorbachev, D V; Ivanov, V I

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles.

Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2015-12-01

Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ = π / 2) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β and order m of the Bessel vortex beam, as well as the dimensionless size parameter kr0. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz') waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ = 0) and backward (θ = π) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.

Wavefront shaping with an electrowetting liquid lens using surface harmonics (Conference Presentation)

NASA Astrophysics Data System (ADS)

Strauch, Matthias; Konijnenberg, Sander; Shao, Yifeng; Urbach, H. Paul

2017-02-01

Liquid lenses are used to correct for low order wavefront aberrations. Electrowetting liquid lenses can nowadays control defocus and astigmatism effectively, so they start being used for ophthalmology applications. To increase the performance and applicability, we introduce a new driving mechanism to create, detect and correct higher order aberrations using standing waves on the liquid interface. The speed of a liquid lens is in general limited, because the liquid surface cannot follow fast voltage changes, while providing a spherical surface. Surface waves are created instead and with them undesired aberrations. We try to control those surface waves to turn them into an effective wavefront shaping tool. We introduce a model, which treats the liquid lens as a circular vibrating membrane with adjusted boundary conditions. Similar to tunable acoustic gradient (TAG) lenses, the nature of the surface modes are predicted to be Bessel functions. Since Bessel functions are a full set of orthogonal basis functions any surface can be created as a linear combination of different Bessel functions. The model was investigated experimentally in two setups. First the point spread functions were studied and compared to a simulation of the intensity distribution created by Fresnel propagated Bessel surfaces. Second the wavefronts were measured directly using a spatial light modulator. The surface resonance frequencies confirm the predictions made by the model as well as the wavefront measurements. By superposition of known surface modes, it is possible to create new surface shapes, which can be used to simulate and measure the human eye.

Analytical study on the self-healing property of Bessel beam

NASA Astrophysics Data System (ADS)

Chu, X.

2012-10-01

With the help of Babinet principle, an analytical expression for the self-healing of Bessel beam is derived by using the Gaussian absorption function to describe the obstacle. Based on the analytical expression, the self-healing properties of Bessel beam are studied. It shows that Bessel beam has the ability to reconstruct its beam shape disturbed by an obstacle. However, during the self-healing process, not only the intensity of the beam behind the obstacle but also the other part will be affected by the obstruction. Meanwhile, the highlight spot, which intensity is larger than that without the obstacle will appear, and the size and strength of the highlight spot is determined by the size of the obstacle. From the change of Poynting vector and Babinet principle, the physical interpretations for the self-healing ability, the effects of the obstruction on the other part and the appearance of highlight spot are given.

A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nash, Patrick L.

2008-01-10

Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation {delta}{sub perpendicular} {sup FDA} of 1/r ({partial_derivative})/({partial_derivative}r) r({partial_derivative})/({partial_derivative}r) that possesses an associated exact unitary representation of e{sup i/2{lambda}}{sup {delta}{sub perpendicular}{sup FDA}}. The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown tomore » be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium.« less

High resolution multiplexed functional imaging in live embryos (Conference Presentation)

NASA Astrophysics Data System (ADS)

Xu, Dongli; Zhou, Weibin; Peng, Leilei

2017-02-01

Fourier multiplexed fluorescence lifetime imaging (FmFLIM) scanning laser optical tomography (FmFLIM-SLOT) combines FmFLIM and Scanning laser optical tomography (SLOT) to perform multiplexed 3D FLIM imaging of live embryos. The system had demonstrate multiplexed functional imaging of zebrafish embryos genetically express Foster Resonant Energy Transfer (FRET) sensors. However, previous system has a 20 micron resolution because the focused Gaussian beam diverges quickly from the focused plane, makes it difficult to achieve high resolution imaging over a long projection depth. Here, we present a high-resolution FmFLIM-SLOT system with achromatic Bessel beam, which achieves 3 micron resolution in 3D deep tissue imaging. In Bessel-FmFLIM-SLOT, multiple laser excitation lines are firstly intensity modulated by a Michelson interferometer with a spinning polygon mirror optical delay line, which enables Fourier multiplexed multi-channel lifetime measurements. Then, a spatial light modulator and a prism are used to transform the modulated Gaussian laser beam to an achromatic Bessel beam. The achromatic Bessel beam scans across the whole specimen with equal angular intervals as sample rotated. After tomography reconstruction and the frequency domain lifetime analysis method, both the 3D intensity and lifetime image of multiple excitation-emission can be obtained. Using Bessel-FmFLIM-SLOT system, we performed cellular-resolution FLIM tomography imaging of live zebrafish embryo. Genetically expressed FRET sensors in these embryo will allow non-invasive observation of multiple biochemical processes in vivo.

Hipergeometric solutions to some nonhomogeneous equations of fractional order

NASA Astrophysics Data System (ADS)

Olivares, Jorge; Martin, Pablo; Maass, Fernando

2017-12-01

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 < alpha < 1. Caputo definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

Spectrum analysis of radar life signal in the three kinds of theoretical models

NASA Astrophysics Data System (ADS)

Yang, X. F.; Ma, J. F.; Wang, D.

2017-02-01

In the single frequency continuous wave radar life detection system, based on the Doppler effect, the theory model of radar life signal is expressed by the real function, and there is a phenomenon that can't be confirmed by the experiment. When the phase generated by the distance between the measured object and the radar measuring head is л of integer times, the main frequency spectrum of life signal (respiration and heartbeat) is not existed in radar life signal. If this phase is л/2 of odd times, the main frequency spectrum of breath and heartbeat frequency is the strongest. In this paper, we use the Doppler effect as the basic theory, using three different mathematical expressions——real function, complex exponential function and Bessel's function expansion form. They are used to establish the theoretical model of radar life signal. Simulation analysis revealed that the Bessel expansion form theoretical model solve the problem of real function form. Compared with the theoretical model of the complex exponential function, the derived spectral line is greatly reduced in the theoretical model of Bessel expansion form, which is more consistent with the actual situation.

Bessel beam CARS of axially structured samples

NASA Astrophysics Data System (ADS)

Heuke, Sandro; Zheng, Juanjuan; Akimov, Denis; Heintzmann, Rainer; Schmitt, Michael; Popp, Jürgen

2015-06-01

We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer functions, the underling resolving power of axially structured geometries is investigated. It is found that through the non-linearity of the CARS process in combination with the folded illumination geometry continuous phase-matching is achieved starting from homogeneous samples up to spatial sample frequencies at twice of the pumping electric field wave. The experimental and analytical findings are modeled by the implementation of the Debye Integral and scalar Green function approach. Finally, the goal of reconstructing an axially layered sample is demonstrated on the basis of the numerically simulated modulus and phase of the anti-Stokes far-field radiation pattern.

Bessel beam CARS of axially structured samples.

PubMed

Heuke, Sandro; Zheng, Juanjuan; Akimov, Denis; Heintzmann, Rainer; Schmitt, Michael; Popp, Jürgen

2015-06-05

We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer functions, the underling resolving power of axially structured geometries is investigated. It is found that through the non-linearity of the CARS process in combination with the folded illumination geometry continuous phase-matching is achieved starting from homogeneous samples up to spatial sample frequencies at twice of the pumping electric field wave. The experimental and analytical findings are modeled by the implementation of the Debye Integral and scalar Green function approach. Finally, the goal of reconstructing an axially layered sample is demonstrated on the basis of the numerically simulated modulus and phase of the anti-Stokes far-field radiation pattern.

Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves.

PubMed

Mitri, F G

2017-02-01

The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto-fluidics would benefit from the results of the present investigation. Copyright © 2016 Elsevier B.V. All rights reserved.

USAF Summer Faculty Research Program. 1980. Research Reports. Volume I.

DTIC Science & Technology

1980-10-01

dt C f(t)e e. ( 1 ) Equation (10) is seen to be of the form of a sum of terms , each of which gives the absorption of an individual line with a strength...t4,8k2T 2 + 3(T+T 2) 12 kT( +"T + + 1 -- - (27) 4! TT2 12 In terms of the spectral moments, Eq. (17): t2 ReC(t) = 1 -- M(28)2 2 4! M4+* (8 with the result...Lorentzian profile and K is the modified 1 Bessel function of the second kind. The emission term rif(W+) is extremely small compared to the absorption

WGM-Resonator/Tapered-Waveguide White-Light Sensor Optics

NASA Technical Reports Server (NTRS)

Stekalov, Dmitry; Maleki, Lute; Matsko, Andrey; Savchenkov, Anatoliy; Iltchenko, Vladimir

2007-01-01

Theoretical and experimental investigations have demonstrated the feasibility of compact white-light sensor optics consisting of unitary combinations of (1) low-profile whispering-gallery-mode (WGM) resonators and (2) tapered rod optical waveguides. These sensors are highly wavelength-dispersive and are expected to be especially useful in biochemical applications for measuring absorption spectra of liquids. These sensor optics exploit the properties of a special class of non-diffracting light beams that are denoted Bessel beams because their amplitudes are proportional to Bessel functions of the radii from their central axes. High-order Bessel beams can have large values of angular momentum. In a sensor optic of this type, a low-profile WGM resonator that supports modes having large angular momenta is used to generate high-order Bessel beams. As used here, "low-profile" signifies that the WGM resonator is an integral part of the rod optical waveguide but has a radius slightly different from that of the adjacent part(s).

Scattering of a longitudinal Bessel beam by a sphere embedded in an isotropic elastic solid.

PubMed

Leão-Neto, J P; Lopes, J H; Silva, G T

2017-11-01

The scattering of a longitudinal Bessel beam of arbitrary order by a sphere embedded in an isotropic solid matrix is theoretically analyzed. The spherical inclusion can be made of a viscoelastic, elastic, or fluid-filled isotropic material. In the analysis, the absorbing, scattering, and extinction efficiency factors are obtained, e.g., the corresponding power per characteristic beam intensity per sphere's cross-section area. Furthermore, the extended optical theorem, which expresses the extinction efficiency in terms of an integral of the longitudinal scattering function is derived. Several features of zeroth- and first-order Bessel beams scattering in solids are illustrated considering a polymer adhesive (cured) sphere embedded in a stainless steel matrix. For instance, omnidirectional scattering can be achieved by choosing specific values of the half-cone angle of the Bessel beam, which is the beam's geometrical parameter. Additionally, it is demonstrated that mode suppression leads to lower absorption inside the inclusion when compared to plane wave scattering results.

Instability of low viscosity elliptic jets with varying aspect ratio

NASA Astrophysics Data System (ADS)

Kulkarni, Varun

2011-11-01

In this work an analytical description of capillary instability of liquid elliptic jets with varying aspect ratio is presented. Linear stability analysis in the long wave approximation with negligible gravitational effects is employed. Elliptic cylindrical coordinate system is used and perturbation velocity potential substituted in the Laplace equation to yield Mathieu and Modified Mathieu differential equations. The dispersion relation for elliptical orifices of any aspect ratio is derived and validated for axisymmetric disturbances with m = 0, in the limit of aspect ratio, μ = 1 , i.e. the case of a circular jet. As Mathieu functions and Modified Mathieu function solutions converge to Bessel's functions in this limit the Rayleigh-Plateau instability criterion is met. Also, stability of solutions corresponding to asymmetric disturbances for the kink mode, m = 1 and flute modes corresponding to m >= 2 is discussed. Experimental data from earlier works is used to compare observations made for elliptical orifices with μ ≠ 1 . This novel approach aims at generalizing the results pertaining to cylindrical jets with circular cross section leading to better understanding of breakup in liquid jets of various geometries.

Beam wander characteristics of flat-topped, dark hollow, cos and cosh-Gaussian, J0- and I0- Bessel Gaussian beams propagating in turbulent atmosphere: a review

NASA Astrophysics Data System (ADS)

Eyyuboğlu, Halil T.; Baykal, Yahya; Çil, Celal Z.; Korotkova, Olga; Cai, Yangjian

2010-02-01

In this paper we review our work done in the evaluations of the root mean square (rms) beam wander characteristics of the flat-topped, dark hollow, cos-and cosh Gaussian, J0-Bessel Gaussian and the I0-Bessel Gaussian beams in atmospheric turbulence. Our formulation is based on the wave-treatment approach, where not only the beam sizes but the source beam profiles are taken into account as well. In this approach the first and the second statistical moments are obtained from the Rytov series under weak atmospheric turbulence conditions and the beam size are determined as a function of the propagation distance. It is found that after propagating in atmospheric turbulence, under certain conditions, the collimated flat-topped, dark hollow, cos- and cosh Gaussian, J0-Bessel Gaussian and the I0-Bessel Gaussian beams have smaller rms beam wander compared to that of the Gaussian beam. The beam wander of these beams are analyzed against the propagation distance, source spot sizes, and against specific beam parameters related to the individual beam such as the relative amplitude factors of the constituent beams, the flatness parameters, the beam orders, the displacement parameters, the width parameters, and are compared against the corresponding Gaussian beam.

F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements

NASA Astrophysics Data System (ADS)

Karney, C. F. F.; Deakin, R. E.

2010-08-01

Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3 cm over distances in excess of 1000 km (and the method remains accurate for geodesics that encircle the Earth). Despite the use of logarithms, Bessel's numerical methods are surprisingly up-to-date: he writes out his series in a form that allows them to be extended to any order and he carries out a rather detailed analysis of the numerical errors. Bessel's derivation and tables were extensively used throughout the nineteenth century and many twentieth century works continued to refer to ``Bessel's method''. However, over time, the attributions to Bessel have become diluted as authors cite more recent works. This trend accelerated with the introduction of electronic calculators when Bessel's algorithms were thought to be too complex and simpler less accurate ones were substituted (these approximate algorithms are still in widespread use). However, now that floating-point hardware is fast and accurate, it is these later algorithms that often seem outdated, while Bessel's are easily adapted for implementation on modern computers.

Extracting Micro-Doppler Radar Signatures from Rotating Targets Using Fourier-Bessel Transform and Time-Frequency Analysis

DTIC Science & Technology

2014-10-16

Time-Frequency analysis, Short-Time Fourier Transform, Wigner Ville Distribution, Fourier Bessel Transform, Fractional Fourier Transform. I...INTRODUCTION Most widely used time-frequency transforms are short-time Fourier Transform (STFT) and Wigner Ville distribution (WVD). In STFT, time and...frequency resolutions are limited by the size of window function used in calculating STFT. For mono-component signals, WVD gives the best time and frequency

Coupling coefficients for tensor product representations of quantum SU(2)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

2014-10-15

We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

Fast calculation of the line-spread-function by transversal directions decoupling

NASA Astrophysics Data System (ADS)

Parravicini, Jacopo; Tartara, Luca; Hasani, Elton; Tomaselli, Alessandra

2016-07-01

We propose a simplified method to calculate the optical spread function of a paradigmatic system constituted by a pupil-lens with a line-shaped illumination (‘line-spread-function’). Our approach is based on decoupling the two transversal directions of the beam and treating the propagation by means of the Fourier optics formalism. This requires simpler calculations with respect to the more usual Bessel-function-based method. The model is discussed and compared with standard calculation methods by carrying out computer simulations. The proposed approach is found to be much faster than the Bessel-function-based one (CPU time ≲ 5% of the standard method), while the results of the two methods present a very good mutual agreement.

Scattering of acoustic evanescent waves by circular cylinders: Partial wave series solution

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2002-05-01

Evanescent acoustical waves occur in a variety of situations such as when sound is incident on a fluid interface beyond the critical angle and when flexural waves on a plate are subsonic with respect to the surrounding fluid. The scattering by circular cylinders at normal incidence was calculated to give insight into the consequences on the scattering of the evanescence of the incident wave. To analyze the scattering, it is necessary to express the incident wave using a modified expansion involving cylindrical functions. For plane evanescent waves, the expansion becomes a double summation with products of modified and ordinary Bessel functions. The resulting modified series is found for the scattering by a fluid cylinder in an unbounded medium. The perfectly soft and rigid cases are also examined. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on the transverse coordinate. The associated exponential dependence of the scattering on the location of a scatterer was previously demonstrated [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].

A coupled analytical model for hydrostatic response of 1-3 piezocomposites.

PubMed

Rajapakse, Nimal; Chen, Yue

2008-08-01

This study presents a fully coupled analysis of a unit cell of a 1-3 piezocomposite under hydrostatic loading. The governing equations for coupled axisymmetric electroelastic field of a transversely isotropic piezoelectric medium and a transversely isotropic elastic medium are used. A reduced form of the analytical general solutions expressed in terms of series of modified Bessel functions of the first and second kind are used. The solution of the boundary-value problem corresponding to a unit cell is presented. The effective properties of a 1-3 piezocomposite are obtained for different fiber volume fractions, polymer and piezoceramic properties, and fiber aspect ratios. Comparisons with previously reported simplified and uncoupled models are made.

Generation of arbitrary order Bessel beams via 3D printed axicons at the terahertz frequency range.

PubMed

Wei, Xuli; Liu, Changming; Niu, Liting; Zhang, Zhongqi; Wang, Kejia; Yang, Zhengang; Liu, Jinsong

2015-12-20

We present the generation of arbitrary order Bessel beams at 0.3 THz through the implementation of suitably designed axicons based on 3D printing technology. The helical axicons, which possess thickness gradients in both radial and azimuthal directions, can convert the incident Gaussian beam into a high-order Bessel beam with spiral phase structure. The evolution of the generated Bessel beams are characterized experimentally with a three-dimensional field scanner. Moreover, the topological charges carried by the high-order Bessel beams are determined by the fork-like interferograms. This 3D-printing-based Bessel beam generation technique is useful not only for THz imaging systems with zero-order Bessel beams but also for future orbital-angular-momentum-based THz free-space communication with higher-order Bessel beams.

Slowing of Bessel light beam group velocity

NASA Astrophysics Data System (ADS)

Alfano, Robert R.; Nolan, Daniel A.

2016-02-01

Bessel light beams experience diffraction-limited propagation. A different basic spatial property of a Bessel beam is reported and investigated. It is shown a Bessel beam is a natural waveguide causing its group velocity can be subluminal (slower than the speed of light) when the optical frequency ω approaches a critical frequency ωc. A free space dispersion relation for a Bessel beam, the dependence of its wave number on its angular frequency, is developed from which the Bessel beam's subluminal group velocity is derived. It is shown under reasonable laboratory conditions that a Bessel light beam has associated parameters that allow slowing near a critical frequency. The application of Bessel beams with 1 μm spot size to slow down 100 ps to 200 ps over 1 cm length for a natural optical buffer in free space is presented.

A theorem regarding roots of the zero-order Bessel function of the first kind

NASA Technical Reports Server (NTRS)

Lin, X.-A.; Agrawal, O. P.

1993-01-01

This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.

Pedagogical Implications in the Thermal Analysis of Uniform Annular Fins: Alternative Analytic Solutions by Series.

ERIC Educational Resources Information Center

Campo, Antonio; Rodriguez, Franklin

1998-01-01

Presents two alternative computational procedures for solving the modified Bessel equation of zero order: the Frobenius method, and the power series method coupled with a curve fit. Students in heat transfer courses can benefit from these alternative procedures; a course on ordinary differential equations is the only mathematical background that…

Ultrafast Bessel beams: advanced tools for laser materials processing

NASA Astrophysics Data System (ADS)

Stoian, Razvan; Bhuyan, Manoj K.; Zhang, Guodong; Cheng, Guanghua; Meyer, Remy; Courvoisier, Francois

2018-05-01

Ultrafast Bessel beams demonstrate a significant capacity of structuring transparent materials with a high degree of accuracy and exceptional aspect ratio. The ability to localize energy on the nanometer scale (bypassing the 100-nm milestone) makes them ideal tools for advanced laser nanoscale processing on surfaces and in the bulk. This allows to generate and combine micron and nano-sized features into hybrid structures that show novel functionalities. Their high aspect ratio and the accurate location can equally drive an efficient material modification and processing strategy on large dimensions. We review, here, the main concepts of generating and using Bessel non-diffractive beams and their remarkable features, discuss general characteristics of their interaction with matter in ablation and material modification regimes, and advocate their use for obtaining hybrid micro and nanoscale structures in two and three dimensions (2D and 3D) performing complex functions. High-throughput applications are indicated. The example list ranges from surface nanostructuring and laser cutting to ultrafast laser welding and the fabrication of 3D photonic systems embedded in the volume.

Experiments with BECs in a Painted Potential: Atom SQUID, Matter Wave Bessel Beams, and Matter Wave Circuits

NASA Astrophysics Data System (ADS)

Boshier, Malcolm; Ryu, Changhyun; Blackburn, Paul; Blinova, Alina; Henderson, Kevin

2014-05-01

The painted potential is a time-averaged optical dipole potential which is able to create arbitrary and dynamic two dimensional potentials for Bose Einstein condensates (BECs). This poster reports three recent experiments using this technique. First, we have realized the dc atom SQUID geometry of a BEC in a toroidal trap with two Josephson junctions. We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. Second, we have used free expansion of a rotating toroidal BEC to create matter wave Bessel beams, which are of interest because perfect Bessel beams (plane waves with amplitude profiles described by Bessel functions) propagate without diffraction. Third, we have realized the basic circuit elements necessary to create complex matter wave circuits. We launch BECs at arbitrary velocity along straight waveguides, propagate them around curved waveguides and stadium-shaped waveguide traps, and split them coherently at y-junctions that can also act as switches. Supported by LANL/LDRD.

Low-frequency acousto-optic backscattering of Bessel light beams

NASA Astrophysics Data System (ADS)

Khilo, Nikolai A.; Belyi, Vladimir N.; Khilo, Petr A.; Kazak, Nikolai S.

2018-05-01

The use of Bessel light beams, as well as Bessel acoustic beams, substantially enhances the capabilities of acousto-optic methods for control of optical field. We present a theoretical study of the process of optical Bessel beams conversion by means of backward acousto-optic scattering on a Bessel acoustic field in a transversely isotropic crystal. It is shown that, with an appropriate choice of Bessel beams parameters, the backscattering in visible spectral range can be realized at relatively low acoustic frequencies less than one gigahertz. Under conditions of phase matching and transverse spatial synchronism, the efficiency of backscattering is sufficiently high, which is interesting, for example, for construction of acousto-optic spectral analyzers.

Negative values of quasidistributions and quantum wave and number statistics

NASA Astrophysics Data System (ADS)

Peřina, J.; Křepelka, J.

2018-04-01

We consider nonclassical wave and number quantum statistics, and perform a decomposition of quasidistributions for nonlinear optical down-conversion processes using Bessel functions. We show that negative values of the quasidistribution do not directly represent probabilities; however, they directly influence measurable number statistics. Negative terms in the decomposition related to the nonclassical behavior with negative amplitudes of probability can be interpreted as positive amplitudes of probability in the negative orthogonal Bessel basis, whereas positive amplitudes of probability in the positive basis describe classical cases. However, probabilities are positive in all cases, including negative values of quasidistributions. Negative and positive contributions of decompositions to quasidistributions are estimated. The approach can be adapted to quantum coherence functions.

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

PubMed

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

High-power Bessel beams with orbital angular momentum in the terahertz range

NASA Astrophysics Data System (ADS)

Choporova, Yu. Yu.; Knyazev, B. A.; Kulipanov, G. N.; Pavelyev, V. S.; Scheglov, M. A.; Vinokurov, N. A.; Volodkin, B. O.; Zhabin, V. N.

2017-08-01

In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of ±1 and ±2 formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at f =5.6 MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about L /r ≈190 and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, "diffraction-free" propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by π , the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 μ m in our case), the BPAs can form the beams at incident radiation with any wavelength, albeit with a reduced diffraction efficiency, and their cross section is the same for any wavelength.

Asymmetric skew Bessel processes and their applications to finance

NASA Astrophysics Data System (ADS)

Decamps, Marc; Goovaerts, Marc; Schoutens, Wim

2006-02-01

In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order Bessel processes are then discussed as well as invariance properties. We call this family of diffusions asymmetric skew Bessel processes in opposition to skew Bessel processes as defined in Barlow et al. [On Walsh's Brownian motions, Seminaire de Probabilities XXIII, Lecture Notes in Mathematics, vol. 1372, Springer, Berlin, New York, 1989, pp. 275-293]. We present factorizations involving (asymmetric skew) Bessel processes with random time. Finally, applications to the valuation of perpetuities and Asian options are proposed.

Generation of a spiral wave using amplitude masks

NASA Astrophysics Data System (ADS)

Anguiano-Morales, Marcelino; Salas-Peimbert, Didia P.; Trujillo-Schiaffino, Gerardo

2011-09-01

Optical beams of Bessel-type whose transverse intensity profile remains unchanged under free-space propagation are called nondiffracting beams. Experimentally, Durnin used an annular slit on the focal plane of a convergent lens to generate a Bessel beam. However, this configuration is only one of many that can be used to generate nondiffracting beams. The method can be modified in order to generate a required phase distribution in the beam. In this work, we propose a simple and effective method to generate spiral beams whose intensity remains invariant during propagation using amplitude masks. Laser beams with spiral phase, i.e., vortex beams have attracted great interest because of their possible use in different applications for areas ranging from laser technologies, medicine, and microbiology to the production of light tweezers and optical traps. We present a study of spiral structures generated by the interference between two incomplete annular beams.

Acoustical radiation torque and force for spheres and Bessel beam extinction efficiency

NASA Astrophysics Data System (ADS)

Marston, Philip L.; Zhang, Likun

2014-11-01

The scattering of optical and acoustical beams is relevant to the levitation and manipulation of drops. Here we examine theoretical developments in the acoustical case. We previously showed how the optical theorem for extinction can be extended to invariant beams. The example of a sphere in a Bessel beam facilitates the direct comparison with a circular disc computed using Babinet's principle and the Kirchhoff approximation. In related work, by considering traveling or standing wave first-order vortex beams we previously showed that the radiation torque is the ratio of the absorbed power and the radian acoustic frequency. By modifying the scattering to account for the viscosity of the surrounding fluid in the analysis of the absorbed power, approximations for radiation torque and force are obtained at long wavelengths in special cases and these can be compared with results published elsewhere.

Morse oscillator propagator in the high temperature limit II: Quantum dynamics and spectroscopy

NASA Astrophysics Data System (ADS)

Toutounji, Mohamad

2018-04-01

This paper is a continuation of Paper I (Toutounji, 2017) of which motivation was testing the applicability of Morse oscillator propagator whose analytical form was derived by Duru (1983). This is because the Morse oscillator propagator was reported (Duru, 1983) in a triple-integral form of a functional of modified Bessel function of the first kind, which considerably limits its applicability. For this reason, I was prompted to find a regime under which Morse oscillator propagator may be simplified and hence be expressed in a closed-form. This was well accomplished in Paper I. Because Morse oscillator is of central importance and widely used in modelling vibrations, its propagator applicability will be extended to applications in quantum dynamics and spectroscopy as will be reported in this paper using the off-diagonal propagator of Morse oscillator whose analytical form is derived.

Non-free gas of dipoles of non-singular screw dislocations and the shear modulus near the melting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malyshev, Cyril, E-mail: malyshev@pdmi.ras.ru

2014-12-15

The behavior of the shear modulus caused by proliferation of dipoles of non-singular screw dislocations with finite-sized core is considered. The representation of two-dimensional Coulomb gas with smoothed-out coupling is used, and the stress–stress correlation function is calculated. A convolution integral expressed in terms of the modified Bessel function K{sub 0} is derived in order to obtain the shear modulus in approximation of interacting dipoles. Implications are demonstrated for the shear modulus near the melting transition which are due to the singularityless character of the dislocations. - Highlights: • Thermodynamics of dipoles of non-singular screw dislocations is studied below themore » melting. • The renormalization of the shear modulus is obtained for interacting dipoles. • Dependence of the shear modulus on the system scales is presented near the melting.« less

Vectorial diffraction properties of THz vortex Bessel beams.

PubMed

Wu, Zhen; Wang, Xinke; Sun, Wenfeng; Feng, Shengfei; Han, Peng; Ye, Jiasheng; Yu, Yue; Zhang, Yan

2018-01-22

A vortex Bessel beam combines the merits of an optical vortex and a Bessel beam, including a spiral wave front and a non-diffractive feature, which has immense application potentials in optical trapping, optical fabrication, optical communications, and so on. Here, linearly and circularly polarized vortex Bessel beams in the terahertz (THz) frequency range are generated by utilizing a THz quarter wave plate, a spiral phase plate, and Teflon axicons with different opening angles. Taking advantage of a THz focal-plane imaging system, vectorial diffraction properties of the THz vortex Bessel beams are comprehensively characterized and discussed, including the transverse (Ex, Ey) and longitudinal (Ez) polarization components. The experimental phenomena are accurately simulated by adopting the vectorial Rayleigh diffraction integral. By varying the opening angle of the axicon, the characteristic parameters of these THz vortex Bessel beams are exhibited and compared, including the light spot size, the diffraction-free range, and the phase evolution process. This work provides the precise experimental and theoretical bases for the comprehension and application of a THz vortex Bessel beam.

Scintillation analysis of truncated Bessel beams via numerical turbulence propagation simulation.

PubMed

Eyyuboğlu, Halil T; Voelz, David; Xiao, Xifeng

2013-11-20

Scintillation aspects of truncated Bessel beams propagated through atmospheric turbulence are investigated using a numerical wave optics random phase screen simulation method. On-axis, aperture averaged scintillation and scintillation relative to a classical Gaussian beam of equal source power and scintillation per unit received power are evaluated. It is found that in almost all circumstances studied, the zeroth-order Bessel beam will deliver the lowest scintillation. Low aperture averaged scintillation levels are also observed for the fourth-order Bessel beam truncated by a narrower source window. When assessed relative to the scintillation of a Gaussian beam of equal source power, Bessel beams generally have less scintillation, particularly at small receiver aperture sizes and small beam orders. Upon including in this relative performance measure the criteria of per unit received power, this advantageous position of Bessel beams mostly disappears, but zeroth- and first-order Bessel beams continue to offer some advantage for relatively smaller aperture sizes, larger source powers, larger source plane dimensions, and intermediate propagation lengths.

Mean intensity of the vortex Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this work the question of stability of the vortex Bessel-Gaussian optical beams formed in turbulent atmosphere is theoretically considered. The detailed analysis of features of spatial structure of distribution of mean intensity of vortex Bessel-Gaussian optical beams in turbulent atmosphere are analyzed. The quantitative criterion of possibility of formation of vortex Bessel-Gaussian optical beams in turbulent atmosphere is derived. It is shown that stability of the form of a vortex Bessel-Gaussian optical beam during propagation in turbulent atmosphere increases with increase of value of a topological charge of this optical beam.

Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves.

PubMed

Alzahrani, Mohammed A; Gauthier, Robert C

2015-10-05

Maxwell's vector wave equations are solved for dielectric configurations that match the symmetry of a spherical computational domain. The electric or magnetic field components and the inverse of the dielectric profile are series expansion defined using basis functions composed of the lowest order spherical Bessel function, polar angle single index dependant Legendre polynomials and azimuthal complex exponential (BLF). The series expressions and non-traditional form of the basis functions result in an eigenvalue matrix formulation of Maxwell's equations that are relatively compact and accurately solvable on a desktop PC. The BLF matrix returns the frequencies and field profiles for steady states modes. The key steps leading to the matrix populating expressions are provided. The validity of the numerical technique is confirmed by comparing the results of computations to those published using complementary techniques.

Precise analytic approximations for the Bessel function J1 (x)

NASA Astrophysics Data System (ADS)

Maass, Fernando; Martin, Pablo

2018-03-01

Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.

PubMed

Mitri, Farid G

2015-10-01

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (θ = π) in the near field and the backscattering form function in the far field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) because of the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3-D directivity patterns illustrate the near- and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.

On the JWKB solution of the uniformly lengthening pendulum via change of independent variable in the Bessel's equation

NASA Astrophysics Data System (ADS)

Deniz, Coşkun

2017-01-01

Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel's equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel's equation into the normal form `via the suggested change of independent variable'. JWKB approximation of the first-order Bessel functions ( ν=1) of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders ( ν=0 and 2) by the recursion relations. The required initial values are also being studied and a quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully.

Engineering the on-axis intensity of Bessel beam by a feedback tuning loop

NASA Astrophysics Data System (ADS)

Li, Runze; Yu, Xianghua; Yang, Yanlong; Peng, Tong; Yao, Baoli; Zhang, Chunmin; Ye, Tong

2018-02-01

The Bessel beam belongs to a typical class of non-diffractive optical fields that are characterized by their invariant focal profiles along the propagation direction. However, ideal Bessel beams only rigorously exist in theory; Bessel beams generated in the lab are quasi-Bessel beams with finite focal extensions and varying intensity profiles along the propagation axis. The ability to engineer the on-axis intensity profile to the desired shape is essential for many applications. Here we demonstrate an iterative optimization-based approach to engineering the on-axis intensity of Bessel beams. The genetic algorithm is used to demonstrate this approach. Starting with a traditional axicon phase mask, in the design process, the computed on-axis beam profile is fed into a feedback tuning loop of an iterative optimization process, which searches for an optimal radial phase distribution that can generate a generalized Bessel beam with the desired onaxis intensity profile. The experimental implementation involves a fine-tuning process that adjusts the originally targeted profile so that the optimization process can optimize the phase mask to yield an improved on-axis profile. Our proposed method has been demonstrated in engineering several zeroth-order Bessel beams with customized on-axis profiles. High accuracy and high energy throughput merit its use in many applications.

Terahertz plasmonic Bessel beamformer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Monnai, Yasuaki; Shinoda, Hiroyuki; Jahn, David

We experimentally demonstrate terahertz Bessel beamforming based on the concept of plasmonics. The proposed planar structure is made of concentric metallic grooves with a subwavelength spacing that couple to a point source to create tightly confined surface waves or spoof surface plasmon polaritons. Concentric scatterers periodically incorporated at a wavelength scale allow for launching the surface waves into free space to define a Bessel beam. The Bessel beam defined at 0.29 THz has been characterized through terahertz time-domain spectroscopy. This approach is capable of generating Bessel beams with planar structures as opposed to bulky axicon lenses and can be readily integratedmore » with solid-state terahertz sources.« less

Diffraction of Nondiverging Bessel Beams by Fork-Shaped and Rectilinear Grating

NASA Astrophysics Data System (ADS)

Janicijevic, Ljiljana; Topuzoski, Suzana

2007-04-01

We present an investigation about Fresnel diffraction of Bessel beams, propagating as nondiverging within a distance Ln, with or without phase singularities, by rectilinear and fork-shaped gratings. The common general transmission function of these gratings is defined and specialized for three different cases: binary amplitude gratings, amplitude holograms and their phase versions. Solving the Fresnel diffraction integral in cylindrical coordinates, we obtain analytical expressions for the diffracted wave amplitude for all types of proposed gratings, and make conclusions about the existence of phase singularities and corresponding topological charges in the created by the gratings beams of different diffraction orders.

Force Density Function Relationships in 2-D Granular Media

NASA Technical Reports Server (NTRS)

Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.

2004-01-01

An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms

PROPOSED SIAM PROBLEM

DOE Office of Scientific and Technical Information (OSTI.GOV)

BAILEY, DAVID H.; BORWEIN, JONATHAN M.

A recent paper by the present authors, together with mathematical physicists David Broadhurst and M. Larry Glasser, explored Bessel moment integrals, namely definite integrals of the general form {integral}{sub 0}{sup {infinity}} t{sup m}f{sup n}(t) dt, where the function f(t) is one of the classical Bessel functions. In that paper, numerous previously unknown analytic evaluations were obtained, using a combination of analytic methods together with some fairly high-powered numerical computations, often performed on highly parallel computers. In several instances, while we were able to numerically discover what appears to be a solid analytic identity, based on extremely high-precision numerical computations, wemore » were unable to find a rigorous proof. Thus we present here a brief list of some of these unproven but numerically confirmed identities.« less

Invited Article: Refined analysis of synchrotron radiation for NIST's SURF III facility

NASA Astrophysics Data System (ADS)

Shirley, Eric L.; Furst, Mitchell; Arp, Uwe

2018-04-01

We have developed a new method for the exact calculation of synchrotron radiation for the National Institute of Standards and Technology Synchrotron Ultraviolet Radiation Facility, SURF III. Instead of using the Schwinger formula, which is only an approximation, we develop formulae based on Graf's addition theorem for Bessel functions and accurate asymptotic expansions for Hankel functions and Bessel functions. By measuring the radiation intensity profile at two distances from the storage ring, we also confirm an apparent vertical emittance that is consistent with the vertical betatron oscillations that are intentionally introduced to extend beam lifetime by spreading the electron beam spatially. Finally, we determine how much diffraction by beamline apertures enhances the spectral irradiance at an integrating sphere entrance port at the end station. This should eliminate small but treatable components of the uncertainty budget that one should consider when using SURF III or similar synchrotrons as standard, calculable sources of ultraviolet and other radiation.

Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.

PubMed

Lukin, Igor P

2016-04-20

The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.

Control of the formation of vortex Bessel beams in uniaxial crystals by varying the beam divergence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paranin, V D; Karpeev, S V; Khonina, S N

The transformation of zero-order Bessel beams into a second-order vortex Bessel beam in CaCO3 and LiNbO3 crystals is experimentally studied, and a possibility of controlling the beam transformation by changing the wavefront curvature of the illumi-nating beam is shown. A quasi-periodic nature of the Bessel beam transformation in a crystal while illuminating the diffraction axi-con by a convergent beam is observed (laser beams)

Propagation of Bessel-X pulses in a hybrid photonic crystal

NASA Astrophysics Data System (ADS)

Chung, K. B.

2018-05-01

We report the propagation of Bessel-X pulses in a two-dimensional hybrid photonic crystal, investigated by the finite-difference time-domain method, in which broadband super-collimation and the propagation of self-collimated ultrashort pulses were reported. We first show the propagation of Bessel-X pulses in two-dimensional free space, whose transverse branches diverge rapidly with propagation. We then show that Bessel-X pulses propagate with their transverse and longitudinal shapes almost unchanged in the hybrid photonic crystal.

Focusing of concentric piecewise vector Bessel-Gaussian beam

NASA Astrophysics Data System (ADS)

Li, Jinsong; Fang, Ying; Zhou, Shenghua; Ye, Youxiang

2010-12-01

The focusing properties of a concentric piecewise vector Bessel-Gaussian beam are investigated in this paper. The beam consists of three portions: the center circular portion and outer annular portion are radially polarized, while the inner annular portion is generalized polarized with tunable polarized angle. Numerical simulations show that the evolution of focal pattern is altered considerably with different Bessel parameters in the Bessel term of the vector Bessel-Gaussian beam. The polarized angle also affects the focal pattern remarkably. Some interesting focal patterns may appear, such as two-peak, dark hollow focus; ring focus; spherical shell focus; cylindrical shell focus; and multi-ring-peak focus, and transverse focal switch occurs with increasing polarized angle of the inner annular portion, which may be used in optical manipulation.

Generation of high-order Bessel vortex beam carrying orbital angular momentum using multilayer amplitude-phase-modulated surfaces in radiofrequency domain

NASA Astrophysics Data System (ADS)

Kou, Na; Yu, Shixing; Li, Long

2017-01-01

A high-order Bessel vortex beam carrying orbital angular momentum (OAM) is generated by using multilayer amplitude-phase-modulated surfaces (APMSs) at 10 GHz. The APMS transmitarray is composed of four-layer conformal square-loop (FCSL) surfaces with both amplitude and phase modulation. The APMS can transform a quasi-spherical wave emitted from the feeding source into a pseudo non-diffractive high-order Bessel vortex beam with OAM. The APMS for a second-order Bessel beam carrying OAM in the n = 2 mode is designed, fabricated, and measured. Full-wave simulation and measurement results confirm that Bessel vortex beams with OAM can be effectively generated using the proposed APMS transmitarray.

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com

2015-07-20

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity,more » the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.« less

Complex plane integration in the modelling of electromagnetic fields in layered media: part 1. Application to a very large loop

NASA Astrophysics Data System (ADS)

Silva, Valdelírio da Silva e.; Régis, Cícero; Howard, Allen Q., Jr.

2014-02-01

This paper analyses the details of a procedure for the numerical integration of Hankel transforms in the calculation of the electromagnetic fields generated by a large horizontal loop over a 1D earth. The method performs the integration by deforming the integration path into the complex plane and applying Cauchy's theorem on a modified version of the integrand. The modification is the replacement of the Bessel functions J0 and J1 by the Hankel functions H_0^{(1)} and H_1^{(1)} respectively. The integration in the complex plane takes advantage of the exponentially decaying behaviour of the Hankel functions, allowing calculation on very small segments, instead of the infinite line of the original improper integrals. A crucial point in this problem is the location of the poles. The companion paper shows two methods to estimate the pole locations. We have used this method to calculate the fields of very large loops. Our results show that this method allows the estimation of the integrals with fewer evaluations of the integrand functions than other methods.

Acoustic radiation force of a Bessel beam on a porous sphere.

PubMed

Azarpeyvand, Mahdi

2012-06-01

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.

Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams.

PubMed

Dennis, Mark R; Ring, James D

2013-09-01

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wave packets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator that interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ko, L.F.

Calculations for the two-point correlation functions in the scaling limit for two statistical models are presented. In Part I, the Ising model with a linear defect is studied for T < T/sub c/ and T > T/sub c/. The transfer matrix method of Onsager and Kaufman is used. The energy-density correlation is given by functions related to the modified Bessel functions. The dispersion expansion for the spin-spin correlation functions are derived. The dominant behavior for large separations at T not equal to T/sub c/ is extracted. It is shown that these expansions lead to systems of Fredholm integral equations. Inmore » Part II, the electric correlation function of the eight-vertex model for T < T/sub c/ is studied. The eight vertex model decouples to two independent Ising models when the four spin coupling vanishes. To first order in the four-spin coupling, the electric correlation function is related to a three-point function of the Ising model. This relation is systematically investigated and the full dispersion expansion (to first order in four-spin coupling) is obtained. The results is a new kind of structure which, unlike those of many solvable models, is apparently not expressible in terms of linear integral equations.« less

Simplified Generation of High-Angular-Momentum Light Beams

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Maleki, Lute; Matsko, Andrey; Strekalov, Dmitry; Grudinin, Ivan

2007-01-01

A simplified method of generating a beam of light having a relatively high value of angular momentum (see figure) involves the use of a compact apparatus consisting mainly of a laser, a whispering- gallery-mode (WGM) resonator, and optical fibers. The method also can be used to generate a Bessel beam. ( Bessel beam denotes a member of a class of non-diffracting beams, so named because their amplitudes are proportional to Bessel functions of the radii from their central axes. High-order Bessel beams can have high values of angular momentum.) High-angular-momentum light beams are used in some applications in biology and nanotechnology, wherein they are known for their ability to apply torque to make microscopic objects rotate. High-angular-momentum light beams could also be used to increase bandwidths of fiber-optic communication systems. The present simplified method of generating a high-angular-momentum light beam was conceived as an alternative to prior such methods, which are complicated and require optical setups that include, variously, holograms, modulating Fabry-Perot cavities, or special microstructures. The present simplified method exploits a combination of the complex structure of the electromagnetic field inside a WGM resonator, total internal reflection in the WGM resonator, and the electromagnetic modes supported by an optical fiber. The optical fiber used to extract light from the WGM resonator is made of fused quartz. The output end of this fiber is polished flat and perpendicular to the fiber axis. The input end of this fiber is cut on a slant and placed very close to the WGM resonator at an appropriate position and orientation. To excite the resonant whispering- gallery modes, light is introduced into the WGM resonator via another optical fiber that is part of a pigtailed fiber-optic coupler. Light extracted from the WGM resonator is transformed into a high-angular- momentum beam inside the extraction optical fiber and this beam is emitted from the polished flat output end. By adjusting the geometry of this apparatus, it is possible to generate a variety of optical beams characterized by a wide range of parameters. These beams generally have high angular momenta and can be of either Bessel or Bessel-related types.

Higher-order harmonics of general limited diffraction Bessel beams

NASA Astrophysics Data System (ADS)

Ding, De-Sheng; Huang, Jin-Huang

2016-12-01

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).

Optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays

NASA Astrophysics Data System (ADS)

Luo, Zhi; Yin, Kai; Dong, Xinran; Duan, Ji’an

2018-05-01

A numerical algorithm, modelling the transformation from a Gaussian beam to a Bessel beam, is presented for the purpose to study the optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays (CMLAs). By applying the numerical algorithm to simulate the spatial intensity distribution behind the axicon under different defects of a rotund-apex and different diameter ratios of an incident beam to the axicon, we find that the diffraction effects formed by the axicon edge can be almost eliminated when the diameter ratio is less than 1:2, but the spatial intensity distribution is disturbed dramatically even a few tens of microns deviation of the apex, especially for the front part of the axicon-generated Bessel beam. Fortunately, the lateral intensity profile in the rear part still maintains a desirable Bessel curve. Therefore, the rear part of the Bessel area and the less than 1:2 diameter ratio are the optimal choice for employing an axicon-generated Bessel beam to implement surface microstructures fabrication. Furthermore, by applying the optimal conditions to direct writing microstructures on fused silica with a femtosecond (fs) laser, a large area close-packed CMLA is fabricated. The CMLA presents high quality and uniformity and its optical performance is also demonstrated.

Sound radiation quantities arising from a resilient circular radiator.

PubMed

Aarts, Ronald M; Janssen, Augustus J E M

2009-10-01

Power series expansions in ka are derived for the pressure at the edge of a radiator, the reaction force on the radiator, and the total radiated power arising from a harmonically excited, resilient, flat, circular radiator of radius a in an infinite baffle. The velocity profiles on the radiator are either Stenzel functions (1-(sigma/a)2)n, with sigma the radial coordinate on the radiator, or linear combinations of Zernike functions Pn(2(sigma/a)2-1), with Pn the Legendre polynomial of degree n. Both sets of functions give rise, via King's integral for the pressure, to integrals for the quantities of interest involving the product of two Bessel functions. These integrals have a power series expansion and allow an expression in terms of Bessel functions of the first kind and Struve functions. Consequently, many of the results in [M. Greenspan, J. Acoust. Soc. Am. 65, 608-621 (1979)] are generalized and treated in a unified manner. A foreseen application is for loudspeakers. The relation between the radiated power in the near-field on one hand and in the far field on the other is highlighted.

Positional Accuracy in Optical Trap-Assisted Nanolithography

NASA Astrophysics Data System (ADS)

Arnold, Craig B.; McLeod, Euan

2009-03-01

The ability to directly print patterns on size scales below 100 nm is important for many applications where the production or repair of high resolution and density features are important. Laser-based direct-write methods have the benefit of quickly and easily being able to modify and create structures on existing devices, but feature sizes are conventionally limited by diffraction. In this presentation, we show how to overcome this limit with a new method of probe-based near-field nanopatterning in which we employ a CW laser to optically trap and manipulate dispersed microspheres against a substrate using a 2-d Bessel beam optical trap. A secondary, pulsed nanosecond laser at 355 nm is directed through the bead and used to modify the surface below the microsphere, taking advantage of the near-field enhancement in order to produce materials modification with feature sizes under 100 nm. Here, we analyze the 3-d positioning accuracy of the microsphere through analytic modeling as a function of experimental parameters. The model is verified in all directions for our experimental conditions and is used to predict the conditions required for improved positional accuracy.

A Broadband Bessel Beam Launcher Using Metamaterial Lens

PubMed Central

Qing Qi, Mei; Tang, Wen Xuan; Cui, Tie Jun

2015-01-01

An approach of generating broadband Bessel beams is presented. The broadband Bessel beams are produced by a gradient index (GRIN) metamaterial lens illuminated by broadband waveguide antenna. The metamaterial lens is constructed with multi-layered structure and each layer is composed of GRIN metamaterials. The metamaterials are designed as dielectric plates printed with metallic patterns in the center region and drilled by air holes near the edge, which operate in wide band. The metamaterial lens serves as a convertor which transforms the spherical beams emitted from feed into conical beams. The conical beams form quasi-Bessel beams in the near-field region. The aperture diameter of the GRIN lens is much larger than the operating wavelength to guarantee the transformation. In principle, this kind of metamaterial lens can produce Bessel beams at arbitrary distance by designing the refractive-index distribution. To verify the approach, we have designed, fabricated and tested a metamaterial lens. Full-wave simulation and experiment results have proved that the generated Bessel beams can be maintained in distance larger than 1 meter within a ranging from 12 GHz to 18 GHz. PMID:26122861

A Broadband Bessel Beam Launcher Using Metamaterial Lens.

PubMed

Qi, Mei Qing; Tang, Wen Xuan; Cui, Tie Jun

2015-06-30

An approach of generating broadband Bessel beams is presented. The broadband Bessel beams are produced by a gradient index (GRIN) metamaterial lens illuminated by broadband waveguide antenna. The metamaterial lens is constructed with multi-layered structure and each layer is composed of GRIN metamaterials. The metamaterials are designed as dielectric plates printed with metallic patterns in the center region and drilled by air holes near the edge, which operate in wide band. The metamaterial lens serves as a convertor which transforms the spherical beams emitted from feed into conical beams. The conical beams form quasi-Bessel beams in the near-field region. The aperture diameter of the GRIN lens is much larger than the operating wavelength to guarantee the transformation. In principle, this kind of metamaterial lens can produce Bessel beams at arbitrary distance by designing the refractive-index distribution. To verify the approach, we have designed, fabricated and tested a metamaterial lens. Full-wave simulation and experiment results have proved that the generated Bessel beams can be maintained in distance larger than 1 meter within a ranging from 12 GHz to 18 GHz.

Helicon waves in uniform plasmas. IV. Bessel beams, Gendrin beams, and helicons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urrutia, J. M.; Stenzel, R. L.

Electromagnetic waves in the low frequency whistler mode regime are investigated experimentally and by digital data superposition. The radiation from a novel circular antenna array is shown to produce highly collimated helicon beams in a uniform unbounded plasma. The differences to Bessel beams in free space are remarked upon. Low divergence beams arise from the parallel group velocity of whistlers with phase velocity either along the guide field or at the Gendrin angle. Waves with angular momentum are produced by phasing the array in the circular direction. The differences in the field topologies for positive and negative modes numbers aremore » shown. It is also shown that in uniform plasmas, the radial amplitude profile of the waves depends on the antenna field topology. Thus, there are no helicon “eigenmodes” with radial Bessel function profiles in uniform plasmas. It is pointed out that phase measurements in helicon devices indicate radial wave propagation which is inconsistent with helicon eigenmode theory based on paraxial wave propagation. Trivelpiece-Gould modes also exist in uniform unbounded plasmas.« less

Second-harmonic generation of practical Bessel beams

NASA Astrophysics Data System (ADS)

Huang, Jin H.; Ding, Desheng; Hsu, Yin-Sung

2009-11-01

A fast Gaussian expansion approach is used to investigate fundamental and second-harmonic generation in practical Bessel beams of finite aperture. The analysis is based on the integral solutions of the KZK equation under the quasilinear approximation. The influence of the medium's attenuation on the beam profile is considered. Analysis results show that the absorption parameter has a significant effect on the far-field beam profile of the second harmonic. Under certain circumstances, the second harmonic of a practical Bessel beam still has the main properties of an ideal Bessel beam of infinite aperture when it propagates within its depth of field.

Laser scanning stereomicroscopy for fast volumetric imaging with two-photon excitation and scanned Bessel beams

NASA Astrophysics Data System (ADS)

Yang, Yanlong; Zhou, Xing; Li, Runze; Van Horn, Mark; Peng, Tong; Lei, Ming; Wu, Di; Chen, Xun; Yao, Baoli; Ye, Tong

2015-03-01

Bessel beams have been used in many applications due to their unique optical properties of maintaining their intensity profiles unchanged during propagation. In imaging applications, Bessel beams have been successfully used to provide extended focuses for volumetric imaging and uniformed illumination plane in light-sheet microscopy. Coupled with two-photon excitation, Bessel beams have been successfully used in realizing fluorescence projected volumetric imaging. We demonstrated previously a stereoscopic solution-two-photon fluorescence stereomicroscopy (TPFSM)-for recovering the depth information in volumetric imaging with Bessel beams. In TPFSM, tilted Bessel beams were used to generate stereoscopic images on a laser scanning two-photon fluorescence microscope; upon post image processing we could successfully provide 3D perception of acquired volume images by wearing anaglyph 3D glasses. However, tilted Bessel beams were generated by shifting either an axicon or an objective laterally; the slow imaging speed and severe aberrations made it hard to use in real-time volume imaging. In this article, we report recent improvements of TPFSM with newly designed scanner and imaging software, which allows 3D stereoscopic imaging without moving any of the optical components on the setup. This improvement has dramatically improved focusing qualities and imaging speed so that the TPFSM can be performed potentially in real-time to provide 3D visualization in scattering media without post image processing.

Higher-order harmonics of limited diffraction Bessel beams

PubMed

Ding; Lu

2000-03-01

We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.

Bessel beams with spatial oscillating polarization

PubMed Central

Fu, Shiyao; Zhang, Shikun; Gao, Chunqing

2016-01-01

Bessel beams are widely used in optical metrology mainly because of their large Rayleigh range (focal length). Radial/azimuthal polarization of such beams is of interest in the fields of material processing, plasma absorption or communication. In this paper an experimental set-up is presented, which generates a Bessel-type vector beam with a spatial polarization, oscillating along the optical axis, when propagating in free space. A first holographic axicon (HA) HA1 produces a normal, linearly polarized Bessel beam, which by a second HA2 is converted into the spatial oscillating polarized beam. The theory is briefly discussed, the set-up and the experimental results are presented in detail. PMID:27488174

Adaptive free-space optical communications through turbulence using self-healing Bessel beams

PubMed Central

Li, Shuhui; Wang, Jian

2017-01-01

We present a scheme to realize obstruction- and turbulence-tolerant free-space orbital angular momentum (OAM) multiplexing link by using self-healing Bessel beams accompanied by adaptive compensation techniques. Compensation of multiple 16-ary quadrature amplitude modulation (16-QAM) data carrying Bessel beams through emulated atmospheric turbulence and obstructions is demonstrated. The obtained experimental results indicate that the compensation scheme can effectively reduce the inter-channel crosstalk, improve the bit-error rate (BER) performance, and recuperate the nondiffracting property of Bessel beams. The proposed scheme might be used in future high-capacity OAM links which are affected by atmospheric turbulence and obstructions. PMID:28230076

High-dimensional structured light coding/decoding for free-space optical communications free of obstructions.

PubMed

Du, Jing; Wang, Jian

2015-11-01

Bessel beams carrying orbital angular momentum (OAM) with helical phase fronts exp(ilφ)(l=0;±1;±2;…), where φ is the azimuthal angle and l corresponds to the topological number, are orthogonal with each other. This feature of Bessel beams provides a new dimension to code/decode data information on the OAM state of light, and the theoretical infinity of topological number enables possible high-dimensional structured light coding/decoding for free-space optical communications. Moreover, Bessel beams are nondiffracting beams having the ability to recover by themselves in the face of obstructions, which is important for free-space optical communications relying on line-of-sight operation. By utilizing the OAM and nondiffracting characteristics of Bessel beams, we experimentally demonstrate 12 m distance obstruction-free optical m-ary coding/decoding using visible Bessel beams in a free-space optical communication system. We also study the bit error rate (BER) performance of hexadecimal and 32-ary coding/decoding based on Bessel beams with different topological numbers. After receiving 500 symbols at the receiver side, a zero BER of hexadecimal coding/decoding is observed when the obstruction is placed along the propagation path of light.

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

NASA Technical Reports Server (NTRS)

Campbell, Joel

2007-01-01

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

KTX circuit model and discharge waveform prediction

NASA Astrophysics Data System (ADS)

Bai, Wei; Lan, T.; Mao, W. Z.; You, W.; Li, H.; Liu, A. D.; Xie, J. L.; Wan, S. D.; Liu, W. D.; Yang, L.; Fu, P.; Xiao, C. J.; Ding, W. X.

2013-10-01

The Keda Torus eXperiment (KTX) is a constructing reversed field pinch (RFP) device in University of Science and Technology of China. The KTX power supply system includes the Ohmic heating, field shaping and toroidal power supply systems, which produce the Ohmic field, equilibrium field and toroidal field, respectively. The detailed circuit model will be introduced in this poster. Another purpose is to predict its discharge waveforms using the modified Bessel function mode (MBFM), which describes the evolution of plasma current and magnetic flux in RFP base on Taylor theory. Furthermore, the power supply requirements of external field shaping winding are also predicted in the model, which will be very helpful for the design of plasma equilibrium controlling system. Supported by ITER-China program (No. 2011GB106000), NNSFC (Nos. 10990210, 10990211, 10335060 and 10905057), CPSF (No. 20080440104), YIF (No. WK2030040019) and KIPCAS (No. kjcx-yw-n28).

The SMM model as a boundary value problem using the discrete diffusion equation.

PubMed

Campbell, Joel

2007-12-01

A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Calculation of the second term of the exact Green's function of the diffusion equation for diffusion-controlled chemical reactions

NASA Astrophysics Data System (ADS)

Plante, Ianik

2016-01-01

The exact Green's function of the diffusion equation (GFDE) is often considered to be the gold standard for the simulation of partially diffusion-controlled reactions. As the GFDE with angular dependency is quite complex, the radial GFDE is more often used. Indeed, the exact GFDE is expressed as a Legendre expansion, the coefficients of which are given in terms of an integral comprising Bessel functions. This integral does not seem to have been evaluated analytically in existing literature. While the integral can be evaluated numerically, the Bessel functions make the integral oscillate and convergence is difficult to obtain. Therefore it would be of great interest to evaluate the integral analytically. The first term was evaluated previously, and was found to be equal to the radial GFDE. In this work, the second term of this expansion was evaluated. As this work has shown that the first two terms of the Legendre polynomial expansion can be calculated analytically, it raises the question of the possibility that an analytical solution exists for the other terms.

Conformal mapping for the Helmholtz equation: acoustic wave scattering by a two dimensional inclusion with irregular shape in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala G; Khoo, Boo Cheong; Han, Feng; Liu, Dian Kui

2012-02-01

The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid. © 2012 Acoustical Society of America

Generation of multiple Bessel beams for a biophotonics workstation.

PubMed

Cizmár, T; Kollárová, V; Tsampoula, X; Gunn-Moore, F; Sibbett, W; Bouchal, Z; Dholakia, K

2008-09-01

We present a simple method using an axicon and spatial light modulator to create multiple parallel Bessel beams and precisely control their individual positions in three dimensions. This technique is tested as an alternative to classical holographic beam shaping commonly used now in optical tweezers. Various applications of precise control of multiple Bessel beams are demonstrated within a single microscope giving rise to new methods for three-dimensional positional control of trapped particles or active sorting of micro-objects as well as "focus-free" photoporation of living cells. Overall this concept is termed a 'biophotonics workstation' where users may readily trap, sort and porate material using Bessel light modes in a microscope.

A Comparison of Propagation Between Apertured Bessel and Gaussian beams

NASA Astrophysics Data System (ADS)

Lin, Mei; Yu, Yanzhong

2009-04-01

A true Bessel beam is a family of diffraction-free beams. Thus the most interesting and attractive characteristic of such beam is non-diffracting propagation. In optics, the comparisons of maximum propagation distance had been done between Bessel and Gaussian beams by Durnin and Sprangle, respectively. However, the results obtained by them are conflict due to the difference between their criteria. Because Bessel beams have many potential applications in millimeter wave bands, therefore, it is necessary and significant that the comparison is carried out at these bands. A new contrast criterion at millimeter wavelengths is proposed in our paper. Under this criterion, the numerical results are presented and a new conclusion is drawn.

Tailoring femtosecond 1.5-μm Bessel beams for manufacturing high-aspect-ratio through-silicon vias

NASA Astrophysics Data System (ADS)

He, Fei; Yu, Junjie; Tan, Yuanxin; Chu, Wei; Zhou, Changhe; Cheng, Ya; Sugioka, Koji

2017-01-01

Three-dimensional integrated circuits (3D ICs) are an attractive replacement for conventional 2D ICs as high-performance, low-power-consumption, and small-footprint microelectronic devices. However, one of the major remaining challenges is the manufacture of high-aspect-ratio through-silicon vias (TSVs), which is a crucial technology for the assembly of 3D Si ICs. Here, we present the fabrication of high-quality TSVs using a femtosecond (fs) 1.5-μm Bessel beam. To eliminate the severe ablation caused by the sidelobes of a conventional Bessel beam, a fs Bessel beam is tailored using a specially designed binary phase plate. We demonstrate that the tailored fs Bessel beam can be used to fabricate a 2D array of approximately ∅10-μm TSVs on a 100-μm-thick Si substrate without any sidelobe damage, suggesting potential application in the 3D assembly of 3D Si ICs.

Tailoring femtosecond 1.5-μm Bessel beams for manufacturing high-aspect-ratio through-silicon vias.

PubMed

He, Fei; Yu, Junjie; Tan, Yuanxin; Chu, Wei; Zhou, Changhe; Cheng, Ya; Sugioka, Koji

2017-01-18

Three-dimensional integrated circuits (3D ICs) are an attractive replacement for conventional 2D ICs as high-performance, low-power-consumption, and small-footprint microelectronic devices. However, one of the major remaining challenges is the manufacture of high-aspect-ratio through-silicon vias (TSVs), which is a crucial technology for the assembly of 3D Si ICs. Here, we present the fabrication of high-quality TSVs using a femtosecond (fs) 1.5-μm Bessel beam. To eliminate the severe ablation caused by the sidelobes of a conventional Bessel beam, a fs Bessel beam is tailored using a specially designed binary phase plate. We demonstrate that the tailored fs Bessel beam can be used to fabricate a 2D array of approximately ∅10-μm TSVs on a 100-μm-thick Si substrate without any sidelobe damage, suggesting potential application in the 3D assembly of 3D Si ICs.

Power-Scalable Blue-Green Bessel Beams

DTIC Science & Technology

2016-02-23

19b. TELEPHONE NUMBER (Include area code) 02/23/2016 Final Technical JAN 2011 - DEC 2013 Power-Scalable Blue -Green Bessel Beams Siddharth Ramachandran...fiber lasers, non-traditional emission wavelengths, high-power blue -green tunabel lasers U U U SAR 11 Siddharth Ramachandran 617-353-9811 1 Power...Scalable Blue -Green Bessel Beams Siddharth Ramachandran Photonics Center, Boston University, 8 Saint Mary’s Street, Boston, MA 02215 phone: (617) 353

Bessel beam OCM for analysis of global ischemia in mouse brain

NASA Astrophysics Data System (ADS)

Rapolu, Mounika; Dolezyczek, Hubert; Tamborski, Szymon; Malinowska, Monika; Wilczynski, Grzegorz; Szkulmowski, Maciej; Wojtkowski, Maciej

2017-07-01

We present the in-vivo imaging of the global mouse brain ischemia using Bessel beam optical coherence microscopy. This method allows to monitor changes in brain structure with extra control of blood flow during the process of artery occlusion. The results show the capability and sensitivity of OCM system with Bessel beam to analyze brain plasticity after severe injury within a period of 8 days.

Frequency-radial duality based photoacoustic image reconstruction.

PubMed

Akramus Salehin, S M; Abhayapala, Thushara D

2012-07-01

Photoacoustic image reconstruction algorithms are usually slow due to the large sizes of data that are processed. This paper proposes a method for exact photoacoustic reconstruction for the spherical geometry in the limiting case of a continuous aperture and infinite measurement bandwidth that is faster than existing methods namely (1) backprojection method and (2) the Norton-Linzer method [S. J. Norton and M. Linzer, "Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solution for plane, cylindrical and spherical apertures," Biomedical Engineering, IEEE Trans. BME 28, 202-220 (1981)]. The initial pressure distribution is expanded using a spherical Fourier Bessel series. The proposed method estimates the Fourier Bessel coefficients and subsequently recovers the pressure distribution. A concept of frequency-radial duality is introduced that separates the information from the different radial basis functions by using frequencies corresponding to the Bessel zeros. This approach provides a means to analyze the information obtained given a measurement bandwidth. Using order analysis and numerical experiments, the proposed method is shown to be faster than both the backprojection and the Norton-Linzer methods. Further, the reconstructed images using the proposed methodology were of similar quality to the Norton-Linzer method and were better than the approximate backprojection method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chillara, Vamshi Krishna; Pantea, Cristian; Sinha, Dipen N.

Here, we numerically investigate the resonance and vibration characteristics of radial modes of laterally stiffened piezoelectric disc transducers. Lateral stiffening is modeled using a spring and vibration characteristics of the piezo-disc are investigated with increasing lateral stiffness. It is found that the resonant frequency response of the radial modes follows an asymptotic behavior approaching that of a clamped disc with increasing lateral stiffness. The radial mode vibration pattern of the discs is also found to be affected by lateral stiffness. While the vibration pattern of a free disc corresponds to a Bessel function, laterally stiffened discs show edge-effects where theymore » depart from the Bessel-like behavior. In addition, a fully clamped piezo-disc is found to have an extra side-lobe when compared to a free disc. Ultrasonic beam profiles generated from radial modes of laterally stiffened discs are numerically investigated. It is found that the free piezo-disc generates a Bessel beam that has multiple side-lobes. Increasing the lateral stiffness results in a significant reduction of side-lobes in the beam profile. This technique of generating a collimated beam with side-lobe reduction finds significant applications in imaging through concrete, drilling mud, and other highly attenuating materials.« less

Mixed boundary-value problem for an orthotropic rectangular strip with variable coefficients of elasticity

NASA Astrophysics Data System (ADS)

Sargsyan, M. Z.; Poghosyan, H. M.

2018-04-01

A dynamical problem for a rectangular strip with variable coefficients of elasticity is solved by an asymptotic method. It is assumed that the strip is orthotropic, the elasticity coefficients are exponential functions of y, and mixed boundary conditions are posed. The solution of the inner problem is obtained using Bessel functions.

Optical analysis of time-averaged multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens.

PubMed

McLeod, Euan; Arnold, Craig B

2008-07-10

Current methods for generating Bessel beams are limited to fixed beam sizes or, in the case of conventional adaptive optics, relatively long switching times between beam shapes. We analyze the multiscale Bessel beams created using an alternative rapidly switchable device: a tunable acoustic gradient index (TAG) lens. The shape of the beams and their nondiffracting, self-healing characteristics are studied experimentally and explained theoretically using both geometric and Fourier optics. By adjusting the electrical driving signal, we can tune the ring spacings, the size of the central spot, and the working distance of the lens. The results presented here will enable researchers to employ dynamic Bessel beams generated by TAG lenses.

Generating millimeter-wave Bessel beam with orbital angular momentum using reflective-type metasurface inherently integrated with source

NASA Astrophysics Data System (ADS)

Shen, Yizhu; Yang, Jiawei; Meng, Hongfu; Dou, Wenbin; Hu, Sanming

2018-04-01

Metasurfaces, orbital angular momenta (OAM), and non-diffractive Bessel beams have been attracting worldwide research. Combining the benefits of these three promising techniques, this paper proposes a metasurface-based reflective-type approach to generate a first-order Bessel beam carrying OAM. To validate this approach, a millimeter-wave metasurface is analyzed, designed, fabricated, and measured. Experimental results agree well with simulation. Moreover, this reflective-type metasurface, generating a Bessel beam with OAM, is inherently integrated with a planar feeding source in the same single-layer printed circuit board. Therefore, the proposed design features low profile, low cost, easy integration with front-end active circuits, and no alignment error between the feeding source and the metasurface.

Analytic Description of Critical Point Nuclei in a Spherical-Axially Deformed Shape Phase Transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iachello, F.

2001-07-30

An approximate solution at the critical point of the spherical to axially deformed shape phase transition in nuclei is presented. The eigenvalues of the Hamiltonian are expressed in terms of zeros of Bessel functions of irrational order.

Using special functions to model the propagation of airborne diseases

NASA Astrophysics Data System (ADS)

Bolaños, Daniela

2014-06-01

Some special functions of the mathematical physics are using to obtain a mathematical model of the propagation of airborne diseases. In particular we study the propagation of tuberculosis in closed rooms and we model the propagation using the error function and the Bessel function. In the model, infected individual emit pathogens to the environment and this infect others individuals who absorb it. The evolution in time of the concentration of pathogens in the environment is computed in terms of error functions. The evolution in time of the number of susceptible individuals is expressed by a differential equation that contains the error function and it is solved numerically for different parametric simulations. The evolution in time of the number of infected individuals is plotted for each numerical simulation. On the other hand, the spatial distribution of the pathogen around the source of infection is represented by the Bessel function K0. The spatial and temporal distribution of the number of infected individuals is computed and plotted for some numerical simulations. All computations were made using software Computer algebra, specifically Maple. It is expected that the analytical results that we obtained allow the design of treatment rooms and ventilation systems that reduce the risk of spread of tuberculosis.

Talbot self-imaging phenomenon under Bessel beam illumination

NASA Astrophysics Data System (ADS)

Chakraborty, Rijuparna; Chowdhury, Subhajit Dutta; Chakraborty, Ajoy Kumar

2018-06-01

In this paper, we report the results of our theoretical studies on the phenomenon of self-imaging of periodic object under the illumination of zero-order Bessel beam. Our theoretical analysis indicates that the self-images are visible only after the walk-off distance of the Bessel beam used. It is also observed that the self-images bend around the optical axis of the setup. Besides, the present study justifies the importance of the conditions stipulated by Montgomery.

Axial and transverse acoustic radiation forces on a fluid sphere placed arbitrarily in Bessel beam standing wave tweezers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitri, F.G., E-mail: mitri@chevron.com

The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to anmore » equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves.« less

Ince's limits for confluent and double-confluent Heun equations

NASA Astrophysics Data System (ADS)

Bonorino Figueiredo, B. D.

2005-11-01

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and converges for ∣z∣>∣z0∣, where z0 denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when z0 tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schrödinger equation for inverse fourth- and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.

Luigi Gatteschi's work on asymptotics of special functions and their zeros

NASA Astrophysics Data System (ADS)

Gautschi, Walter; Giordano, Carla

2008-12-01

A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form. This work is reviewed here, and organized along methodological lines.

3-dimensional dark traps for low refractive index bio-cells using a single optical fiber Bessel beam.

PubMed

Zhang, Yu; Tang, Xiaoyun; Zhang, Yaxun; Su, Wenjie; Liu, Zhihai; Yang, Xinghua; Zhang, Jianzhong; Yang, Jun; Oh, Kyunghwan; Yuan, Libo

2018-06-15

We proposed and experimentally demonstrated 3-dimensional dark traps for low refractive index bio-cells using a single optical fiber Bessel beam. The Bessel beam was produced by concatenating single-mode fiber and a step index multimode fiber, which was then focused by a high refractive index glass microsphere integrated on the fiber end facet. The focused Bessel beam provided two dark fields along the axial direction, where stable trapping of low refractive index bio-cells was realized in a high refractive index liquid bath. The all-fiber and seamlessly integrated structure of the proposed scheme can find ample potential as a micro-optical probe in in situ characterization and manipulation of multiple bio-cells with refractive indices lower than that of the liquid bath.

Nonparaxial fractional Bessel and Bessel-Gauss auto-focusing light-sheet pincers and their higher-order spatial derivatives

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-05-01

Nonparaxial fractional electromagnetic Bessel and Bessel-Gauss auto-focusing light-sheet solutions and their spatial derivatives are synthesized stemming from the angular spectrum decomposition in plane waves. The propagation characteristics of these transverse electric-polarized light-sheets are analyzed by computing the radiated component of the incident electric field. Tight bending of the beam along curved trajectories and slit openings are observed, which could offer unique features and potential applications in the development of improved methods and devices in light-sheet tweezers for particle manipulation applications and dynamics in opto-fluidics, particle sizing and imaging to name a few examples. Moreover, computations of the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solutions.

Stable source reconstruction from a finite number of measurements in the multi-frequency inverse source problem

NASA Astrophysics Data System (ADS)

Karamehmedović, Mirza; Kirkeby, Adrian; Knudsen, Kim

2018-06-01

We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the source. We study the problem in a certain finite dimensional setting: from measurements made at a finite set of frequencies we uniquely determine and reconstruct sources in a subspace spanned by finitely many Fourier–Bessel functions. Further, we obtain a constructive criterion for identifying a minimal set of measurement frequencies sufficient for reconstruction, and under an additional, mild assumption, the reconstruction method is shown to be stable. Our analysis is based on a singular value decomposition of the source-to-measurement forward operators and the distribution of positive zeros of the Bessel functions of the first kind. The reconstruction method is implemented numerically and our theoretical findings are supported by numerical experiments.

Simulation of 2D Waves in Circular Membrane Using Excel Spreadsheet with Visual Basic for Teaching Activity

NASA Astrophysics Data System (ADS)

Eso, R.; Safiuddin, L. O.; Agusu, L.; Arfa, L. M. R. F.

2018-04-01

We propose a teaching instrument demonstrating the circular membrane waves using the excel interactive spreadsheets with the Visual Basic for Application (VBA) programming. It is based on the analytic solution of circular membrane waves involving Bessel function. The vibration modes and frequencies are determined by using Bessel approximation and initial conditions. The 3D perspective based on the spreadsheets functions and facilities has been explored to show the 3D moving objects in transitional or rotational processes. This instrument is very useful both in teaching activity and learning process of wave physics. Visualizing of the vibration of waves in the circular membrane which is showing a very clear manner of m and n vibration modes of the wave in a certain frequency has been compared and matched to the experimental result using resonance method. The peak of deflection varies in time if the initial condition was working and have the same pattern with matlab simulation in zero initial velocity

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating.

PubMed

George, Jineesh; Ebenezer, D D; Bhattacharyya, S K

2010-10-01

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.

Characteristic impedance of a microchannel with two immiscible microfluids

NASA Astrophysics Data System (ADS)

Jaramillo Raquejo, Daniela

2014-05-01

Consider the case of a microcapillary of radius R with two microfluidic immiscible. The micro-capillary region 0 < r < R1 is occupied by the microfluidic less dense and less viscous; while the microcapillary region R1 <0 < R is occupied by the microfluidic more dense and more viscous. Determine the characteristic impedance of the microcapillary in this case when both microfluidics are driven by the same pressure gradient as the boundary condition at the wall of the microcapillary is of the non-Newtonian slip. The Navier Stokes equation is solved for both microfluidic methods using the Laplace transform. The velocity profiles are expressed in terms of Bessel functions. Similarly, the characteristic impedance of the microcapillary is expressed by a complex formula Bessel functions. Obtain the analytical results are important for designing engineering microdevices with applications in pharmaceutical, food engineering, nanotechnology and biotechnology in general in particular. For future research it is interesting to consider the case of boundary conditions with memory effects.

Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems

DTIC Science & Technology

2014-10-13

function and wide band Fast multipole methods for Hankel waves. (2) a new linear scaling discontinuous Galerkin density functional theory, which provide a...inflow boundary condition for Wigner quantum transport equations. Also, a book titled "Computational Methods for Electromagnetic Phenomena...equationsin layered media with FMM for Bessel functions , Science China Mathematics, (12 2013): 2561. doi: TOTAL: 6 Number of Papers published in peer

A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fonseca, Julio; Del-Castillo-Negrete, Diego B.; Sokolov, Igor M.

2016-08-25

Here, a statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic driftwaves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K 0, becomes K 0J 0(more » $$\\hat{p}$$), where J 0 is the zeroth-order Bessel function and $$\\hat{p}$$ s the Larmor radius. Assuming a Maxwellian probability density function (pdf) for $$\\hat{p}$$ , we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturba- tion amplitude K 0J 0($$\\hat{p}$$). Using these results, we compute the probability of loss of confinement (i.e., global chaos), P c provides an upper bound for the escape rate, and that P t rovides a good estimate of the particle trapping rate. Lastly. the analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.« less

Measurements of the evaporation and hygroscopic response of single fine-mode aerosol particles using a Bessel beam optical trap.

PubMed

Cotterell, Michael I; Mason, Bernard J; Carruthers, Antonia E; Walker, Jim S; Orr-Ewing, Andrew J; Reid, Jonathan P

2014-02-07

A single horizontally-propagating zeroth order Bessel laser beam with a counter-propagating gas flow was used to confine single fine-mode aerosol particles over extended periods of time, during which process measurements were performed. Particle sizes were measured by the analysis of the angular variation of light scattered at 532 nm by a particle in the Bessel beam, using either a probe beam at 405 nm or 633 nm. The vapour pressures of glycerol and 1,2,6-hexanetriol particles were determined to be 7.5 ± 2.6 mPa and 0.20 ± 0.02 mPa respectively. The lower volatility of hexanetriol allowed better definition of the trapping environment relative humidity profile over the measurement time period, thus higher precision measurements were obtained compared to those for glycerol. The size evolution of a hexanetriol particle, as well as its refractive index at wavelengths 532 nm and 405 nm, were determined by modelling its position along the Bessel beam propagation length while collecting phase functions with the 405 nm probe beam. Measurements of the hygroscopic growth of sodium chloride and ammonium sulfate have been performed on particles as small as 350 nm in radius, with growth curves well described by widely used equilibrium state models. These are the smallest particles for which single-particle hygroscopicity has been measured and represent the first measurements of hygroscopicity on fine mode and near-accumulation mode aerosols, the size regimes bearing the most atmospheric relevance in terms of loading, light extinction and scattering. Finally, the technique is contrasted with other single particle and ensemble methods, and limitations are assessed.

Orthogonal fast spherical Bessel transform on uniform grid

NASA Astrophysics Data System (ADS)

Serov, Vladislav V.

2017-07-01

We propose an algorithm for the orthogonal fast discrete spherical Bessel transform on a uniform grid. Our approach is based upon the spherical Bessel transform factorization into the two subsequent orthogonal transforms, namely the fast Fourier transform and the orthogonal transform founded on the derivatives of the discrete Legendre orthogonal polynomials. The method utility is illustrated by its implementation for the problem of a two-atomic molecule in a time-dependent external field simulating the one utilized in the attosecond streaking technique.

Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence.

PubMed

Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E

2014-06-10

The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.

A high-Strehl low-resolution optical imager (BESSEL): Detection of a 0.7 λ/ D separation binary from the ground

NASA Astrophysics Data System (ADS)

Peters, Mary Anne; Close, Laird M.; Rademacher, Matt; Stalcup, Tom; Swartzlander, Grover A.; Ford, Erin; Abdul-Malik, Rukiah S.

2008-07-01

We have constructed a high-speed image stabilization system, BESSEL, which mounts to the 8-in. refractive telescope coupled to the ray white telescope at steward observatory. The high-speed tip/tilt mirror platform is controlled by an Andor electron multiplication EMCCD enabling wavefront correction at a rate exceeding 1 kHz. BESSEL achieves on-sky Strehl ratios of 98-99% at λ = 800 nm when the telescope aperture is stopped down to half the Fried parameter (typically D = 25.4 mm, where D is the diameter of the effective telescope aperture). Utilizing high Strehls and the technique of roll subtraction enabled BESSEL to resolve the binary, ADS 10418AB (more commonly known as α Her), with separation of only 0.71 λ/ D and a delta magnitude of ˜3 mag at 800 nm. In addition, Arcturus was observed with BESSEL to explore a relatively untested region of Strehl versus D/ r0 parameter space in the optical, specifically at small (˜0.5 D/ r0). We find that in this regime space quality, very high Strehl (˜99%), optical imaging can be obtained from the ground when D/ r0 < 0.5 as one approaches the inner scale of turbulence. Because of BESSEL's demonstrated high Strehls, it is an ideal platform for inexpensive, initial, on-sky characterization of space-based coronagraphs, for which it will be used in the near future.

Radial modes of laterally stiffened piezoelectric disc transducers for ultrasonic collimated beam generation

DOE PAGES

Chillara, Vamshi Krishna; Pantea, Cristian; Sinha, Dipen N.

2017-07-15

Here, we numerically investigate the resonance and vibration characteristics of radial modes of laterally stiffened piezoelectric disc transducers. Lateral stiffening is modeled using a spring and vibration characteristics of the piezo-disc are investigated with increasing lateral stiffness. It is found that the resonant frequency response of the radial modes follows an asymptotic behavior approaching that of a clamped disc with increasing lateral stiffness. The radial mode vibration pattern of the discs is also found to be affected by lateral stiffness. While the vibration pattern of a free disc corresponds to a Bessel function, laterally stiffened discs show edge-effects where theymore » depart from the Bessel-like behavior. In addition, a fully clamped piezo-disc is found to have an extra side-lobe when compared to a free disc. Ultrasonic beam profiles generated from radial modes of laterally stiffened discs are numerically investigated. It is found that the free piezo-disc generates a Bessel beam that has multiple side-lobes. Increasing the lateral stiffness results in a significant reduction of side-lobes in the beam profile. This technique of generating a collimated beam with side-lobe reduction finds significant applications in imaging through concrete, drilling mud, and other highly attenuating materials.« less

Low-frequency ultrasonic Bessel-like collimated beam generation from radial modes of piezoelectric transducers

DOE PAGES

Chillara, Vamshi Krishna; Pantea, Cristian; Sinha, Dipen N.

2017-02-06

We present a very simple approach to generate a collimated ultrasonic beam that exploits the natural Bessel-like vibration pattern of the radial modes of a piezoelectric disc with lateral clamping. This eliminates the need for the conventional annular Bessel pattern of the electrodes with individual electrode excitation on the piezo-disc, thus simplifying the transducer design. Numerical and experimental studies are carried out to investigate the Bessel-like vibration patterns of these radial modes showing an excellent agreement between these two studies. Measured ultrasonic beam- pro les in water from the radial modes con rm the profile to be a Bessel beam.more » Collimated beam generation from radial modes is investigated using a coupled electromechanical finite-element model. It is found that clamping the lateral edges of piezoelectric transducers results in a high-degree of collimation with practically no side-lobes similar to a parametric array beam. Ultrasonic beam- profile measurements in water with both free and clamped piezoelectric transducer are presented. The collimated beam generation using the present technique of using the laterally clamped radial modes finds significant applications in low-frequency imaging through highly attenuating materials.« less

Mode-Division-Multiplexing of Multiple Bessel-Gaussian Beams Carrying Orbital-Angular-Momentum for Obstruction-Tolerant Free-Space Optical and Millimetre-Wave Communication Links.

PubMed

Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P J; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J; Ashrafi, Solyman; Molisch, Andreas F; Tur, Moshe; Willner, Alan E

2016-03-01

We experimentally investigate the potential of using 'self-healing' Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.

Mode-Division-Multiplexing of Multiple Bessel-Gaussian Beams Carrying Orbital-Angular-Momentum for Obstruction-Tolerant Free-Space Optical and Millimetre-Wave Communication Links

PubMed Central

Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P. J.; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J.; Ashrafi, Solyman; Molisch, Andreas F.; Tur, Moshe; Willner, Alan E.

2016-01-01

We experimentally investigate the potential of using ‘self-healing’ Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively. PMID:26926068

Improved fixation quality provided by a Bessel beacon in an adaptive optics system.

PubMed

Lambert, Andrew J; Daly, Elizabeth M; Dainty, Christopher J

2013-07-01

We investigate whether a structured probe beam that creates the beacon for use in a retinal imaging adaptive optics system can provide useful side effects. In particular we investigate whether a Bessel beam that is seen by the subject as a set of concentric rings has a dampening effect on fixation variations of the subject under observation. This calming effect would allow longer periods of observation, particularly for patients with abnormal fixation. An experimental adaptive optics system developed for retinal imaging is used to monitor the fluctuations in aberrations for artificial and human subjects. The probe beam is alternated between a traditional beacon and one provided by a Bessel beam created by SLM. Time-frequency analysis is used to indicate the differences in power and time variation during fixation depending on whether the Bessel beam or the traditional beacon is employed. Comparison is made with the response for an artificial eye to discount systemic variations. Significant evidence is accrued to indicate the reduced fluctuations in fixation when the Bessel beam is employed to create the beacon. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.

Low-frequency ultrasonic Bessel-like collimated beam generation from radial modes of piezoelectric transducers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chillara, Vamshi Krishna; Pantea, Cristian; Sinha, Dipen N.

We present a very simple approach to generate a collimated ultrasonic beam that exploits the natural Bessel-like vibration pattern of the radial modes of a piezoelectric disc with lateral clamping. This eliminates the need for the conventional annular Bessel pattern of the electrodes with individual electrode excitation on the piezo-disc, thus simplifying the transducer design. Numerical and experimental studies are carried out to investigate the Bessel-like vibration patterns of these radial modes showing an excellent agreement between these two studies. Measured ultrasonic beam- pro les in water from the radial modes con rm the profile to be a Bessel beam.more » Collimated beam generation from radial modes is investigated using a coupled electromechanical finite-element model. It is found that clamping the lateral edges of piezoelectric transducers results in a high-degree of collimation with practically no side-lobes similar to a parametric array beam. Ultrasonic beam- profile measurements in water with both free and clamped piezoelectric transducer are presented. The collimated beam generation using the present technique of using the laterally clamped radial modes finds significant applications in low-frequency imaging through highly attenuating materials.« less

Multi-Mode Analysis of Dual Ridged Waveguide Systems for Material Characterization

DTIC Science & Technology

2015-09-17

characterization is the process of determining the dielectric, magnetic, and magnetoelectric properties of a material. For simple (i.e., linear ...field expressions in terms of elementary functions (sines, cosines, exponentials and Bessel functions) and corresponding propagation constants of the...with material parameters 0 and µ0. • The MUT is simple ( linear , isotropic, homogeneous), and the sample has a uniform thickness. • The waveguide

The Shock and Vibration Digest. Volume 18, Number 6

DTIC Science & Technology

1986-06-01

linear, quadratic, or cubic. Bessel function Reed [124] reported a method for computing solutions were obtained for a truncated pyramid amplitudes of a...86-1198 A. Ragab, Chung C. Fu Seismic Analysis of a Large LMFBR with Flu- Cairo Univ., Giza , Egypt . . *. id-Structure Imteractions Computers Struc

Optical pulling force on a magneto-dielectric Rayleigh sphere in Bessel tractor polarized beams

NASA Astrophysics Data System (ADS)

Mitri, F. G.; Li, R. X.; Yang, R. P.; Guo, L. X.; Ding, C. Y.

2016-11-01

The optical radiation force induced by Bessel (vortex) beams on a magneto-dielectric subwavelength sphere is investigated with particular emphasis on the beam polarization and order l (or topological charge). The analysis is focused on identifying the regions and some of the conditions to achieve retrograde motion of the sphere centered on the axis of wave propagation of the incident beam, or shifted off-axially. Exact non-paraxial analytical solutions are established, and computations for linear, circular, radial, azimuthal and mixed polarizations of the individual plane wave components forming the Bessel (vortex) beams by means of the angular spectrum decomposition method (ASDM) illustrate the theory with particular emphasis on the tractor (i.e. reversal) behavior of the force. This effect results in the pulling of the magneto-dielectric sphere against the forward linear momentum density flux associated with the incoming waves. Should some conditions related to the choice of the beam parameters as well as the permittivity and permeability of the sphere be met, the optical force vanishes and reverses sign. Moreover, the beam polarization is shown to affect differently the axial negative pulling force for either the zeroth- or the first-order Bessel beam. When the sphere is centered on the beam‧s axis, the axial force component is always negative for the zeroth-order Bessel beam except for the radial and azimuthal polarization configurations. Nonetheless, for the first-order Bessel beam, the axial force is negative for the radial polarization case only. Additional tractor beam effects arise when the sphere departs from the center of the beam. It is also demonstrated that the tractor beam effect arises from the force component originating from the cross-interaction between the electric and magnetic dipoles. Potential applications are in particle manipulation, optical levitation, tractor beam tweezers, and other emergent technologies using polarized Bessel beams on a small (Rayleigh) magneto-dielectric particle.

Spatial characterization of Bessel-like beams for strong-field physics.

PubMed

Summers, Adam M; Yu, Xiaoming; Wang, Xinya; Raoul, Maxime; Nelson, Josh; Todd, Daniel; Zigo, Stefan; Lei, Shuting; Trallero-Herrero, Carlos A

2017-02-06

We present a compact, simple design for the generation and tuning of both the spot size and effective focal length of Bessel-like beams. In particular, this setup provides an important tool for the use of Bessel-like beams with high-power, femtosecond laser systems. Using a shallow angle axicon in conjunction with a spherical lens, we show that it is possible to focus Bessel-like modes to comparable focal spot sizes to sharp axicons while maintaining a long effective focal length. The resulting focal profiles are characterized in detail using an accurate high dynamic range imaging technique. Quantitatively, we introduce a metric (R_0.8) which defines the spot-size containing 80% of the total energy. Our setup overcomes the typical compromise between long working distances and small spot sizes. This is particularly relevant for strong-field physics where most experiments must operate in vacuum.

Limitations to laser machining of silicon using femtosecond micro-Bessel beams in the infrared

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grojo, David, E-mail: grojo@lp3.univ-mrs.fr; Mouskeftaras, Alexandros; Delaporte, Philippe

We produce and characterize high-angle femtosecond Bessel beams at 1300-nm wavelength leading to nonlinearly ionized plasma micro-channels in both glass and silicon. With microjoule pulse energy, we demonstrate controlled through-modifications in 150-μm glass substrates. In silicon, strong two-photon absorption leads to larger damages at the front surface but also a clamping of the intensity inside the bulk at a level of ≈4 × 10{sup 11 }W cm{sup −2} which is below the threshold for volume and rear surface modification. We show that the intensity clamping is associated with a strong degradation of the Bessel-like profile. The observations highlight that the inherent limitation tomore » ultrafast energy deposition inside semiconductors with Gaussian focusing [Mouskeftaras et al., Appl. Phys. Lett. 105, 191103 (2014)] applies also for high-angle Bessel beams.« less

Formation of high-order acoustic Bessel beams by spiral diffraction gratings

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Picó, R.; Sánchez-Morcillo, V.; Romero-García, V.; García-Raffi, L. M.; Staliunas, K.

2016-11-01

The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically, and experimentally reported in this paper. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow for obtaining Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.

Free convection flow of some fractional nanofluids over a moving vertical plate with uniform heat flux and heat source

NASA Astrophysics Data System (ADS)

Azhar, Waqas Ali; Vieru, Dumitru; Fetecau, Constantin

2017-08-01

Free convection flow of some water based fractional nanofluids over a moving infinite vertical plate with uniform heat flux and heat source is analytically and graphically studied. Exact solutions for dimensionless temperature and velocity fields, Nusselt numbers, and skin friction coefficients are established in integral form in terms of modified Bessel functions of the first kind. These solutions satisfy all imposed initial and boundary conditions and reduce to the similar solutions for ordinary nanofluids when the fractional parameters tend to one. Furthermore, they reduce to the known solutions from the literature when the plate is fixed and the heat source is absent. The influence of fractional parameters on heat transfer and fluid motion is graphically underlined and discussed. The enhancement of heat transfer in such flows is higher for fractional nanofluids in comparison with ordinary nanofluids. Moreover, the use of fractional models allows us to choose the fractional parameters in order to get a very good agreement between experimental and theoretical results.

A mathematical description of a growing cell colony based on the mechanical bidomain model

NASA Astrophysics Data System (ADS)

Auddya, Debabrata; Roth, Bradley J.

2017-03-01

The mechanical bidomain model is used to describe a colony of cells growing on a substrate. Analytical expressions are derived for the intracellular and extracellular displacements. Mechanotransduction events are driven by the difference between the displacements in the two spaces, corresponding to the force acting on integrins. The equation for the displacement consists of two terms: one proportional to the radius that is the same in the intracellular and extracellular spaces (the monodomain term) and one that is proportional to a modified Bessel function that is responsible for mechanotransduction (the bidomain term). The model predicts that mechanotransduction occurs within a few length constants of the colony’s edge, and an expression for the length constant contains the intracellular and extracellular shear moduli and the spring constant of the integrins coupling the two spaces. The model predictions are qualitatively consistent with experiments on human embryonic stem cell colonies, in which differentiation is localized near the edge.

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Analytical model of contamination during the drying of cylinders of jamonable muscle

NASA Astrophysics Data System (ADS)

Montoya Arroyave, Isabel

2014-05-01

For a cylinder of jamonable muscle of radius R and length much greater than R; considering that the internal resistance to the transfer of water is much greater than the external and that the internal resistance is one certain function of the distance to the axis; the distribution of the punctual moisture in the jamonable cylinder is analytically computed in terms of the Bessel's functions. During the process of drying and salted the jamonable cylinder is sensitive to contaminate with bacterium and protozoa that come from the environment. An analytical model of contamination is presents using the diffusion equation with sources and sinks, which is solve by the method of the Laplace transform, the Bromwich integral, the residue theorem and some special functions like Bessel and Heun. The critical times intervals of drying and salted are computed in order to obtain the minimum possible contamination. It is assumed that both external moisture and contaminants decrease exponentially with time. Contaminants profiles are plotted and discussed some possible techniques of contaminants detection. All computations are executed using Computer Algebra, specifically Maple. It is said that the results are important for the food industry and it is suggested some future research lines.

Using the Chebychev expansion in quantum transport calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popescu, Bogdan; Rahman, Hasan; Kleinekathöfer, Ulrich, E-mail: u.kleinekathoefer@jacobs-university.de

2015-04-21

Irradiation by laser pulses and a fluctuating surrounding liquid environment can, for example, lead to time-dependent effects in the transport through molecular junctions. From the theoretical point of view, time-dependent theories of quantum transport are still challenging. In one of these existing transport theories, the energy-dependent coupling between molecule and leads is decomposed into Lorentzian functions. This trick has successfully been combined with quantum master approaches, hierarchical formalisms, and non-equilibrium Green’s functions. The drawback of this approach is, however, its serious limitation to certain forms of the molecule-lead coupling and to higher temperatures. Tian and Chen [J. Chem. Phys. 137,more » 204114 (2012)] recently employed a Chebychev expansion to circumvent some of these latter problems. Here, we report on a similar approach also based on the Chebychev expansion but leading to a different set of coupled differential equations using the fact that a derivative of a zeroth-order Bessel function can again be given in terms of Bessel functions. Test calculations show the excellent numerical accuracy and stability of the presented formalism. The time span for which this Chebychev expansion scheme is valid without any restrictions on the form of the spectral density or temperature can be determined a priori.« less

Raman conversion in intense femtosecond Bessel beams in air

NASA Astrophysics Data System (ADS)

Scheller, Maik; Chen, Xi; Ariunbold, Gombojav O.; Born, Norman; Moloney, Jerome; Kolesik, Miroslav; Polynkin, Pavel

2014-05-01

We demonstrate experimentally that bright and nearly collimated radiation can be efficiently generated in air pumped by an intense femtosecond Bessel beam. We show that this nonlinear conversion process is driven by the rotational Raman response of air molecules. Under optimum conditions, the conversion efficiency from the Bessel pump into the on-axis propagating beam exceeds 15% and is limited by the onset of intensity clamping and plasma refraction on the beam axis. Our experimental findings are in excellent agreement with numerical simulations based on the standard model for the ultrafast nonlinear response of air.

Comparison between broadband Bessel beam launchers based on either Bessel or Hankel aperture distribution for millimeter wave short pulse generation.

PubMed

Pavone, Santi C; Mazzinghi, Agnese; Freni, Angelo; Albani, Matteo

2017-08-07

In this paper, a comparison is presented between Bessel beam launchers at millimeter waves based on either a cylindrical standing wave (CSW) or a cylindrical inward traveling wave (CITW) aperture distribution. It is theoretically shown that CITW launchers are better suited for the generation of electromagnetic short pulses because they maintain their performances over a larger bandwidth than those realizing a CSW aperture distribution. Moreover, the wavenumber dispersion of both the launchers is evaluated both theoretically and numerically. To this end, two planar Bessel beam launchers, one enforcing a CSW and the other enforcing a CITW aperture distribution, are designed at millimeter waves with a center operating frequency of f¯=60GHz and analyzed in the bandwidth 50 - 70 GHz by using an in-house developed numerical code to solve Maxwell's equations based on the method of moments. It is shown that a monochromatic Bessel beam can be efficiently generated by both the launchers over a wide fractional bandwidth. Finally, we investigate the generation of limited-diffractive electromagnetic pulses at millimeter waves, up to a certain non-diffractive range. Namely, it is shown that by feeding the launcher with a Gaussian short pulse, a spatially confined electromagnetic pulse can be efficiently generated in front of the launcher.

Conversion of isotropic fluorescence into a long-range non-diverging beam

NASA Astrophysics Data System (ADS)

Zhang, Douguo; Zhu, Liangfu; Chen, Junxue; Wang, Ruxue; Wang, Pei; Ming, Hai; Badugu, Ramachandram; Rosenfeld, Mary; Zhan, Qiwen; Kuang, Cuifang; Liu, Xu; Lakowicz, Joseph R.

2018-04-01

Fluorescent samples typically emit isotropically in all directions. Large lenses and other optical components are needed to capture a significant fraction of the emission, and complex confocal microscopes are required for high resolution focal-plane imaging. It is known that Bessel beams have remarkable properties of being able to travel over long distances, over 1000 times the wavelength, without diverging, and hence are called non-diffracting beams. In previous reports the Bessel beams were formed by an incident light source, typically with plane-wave illumination on a circular aperture. It was not known if Bessel beams could form from fluorescent light sources. We demonstrate transformation of the emission from fluorescent polystyrene spheres (FPS) into non-diverging beams which propagate up to 130 mm (13 cm) along the optical axis with a constant diameter. This is accomplished using a planar metal film, with no nanoscale features in the X-Y plane, using surface plasmon-coupled emission. Using samples which contain many FPS in the field-of-view, we demonstrate that an independent Bessel beam can be generated from any location on the metal film. The extremely long non-diffracted propagation distances, and self-healing properties of Bessel beams, offer new opportunities in fluorescence sensing and imaging.

A High Frequency Model of Cascade Noise

NASA Technical Reports Server (NTRS)

Envia, Edmane

1998-01-01

Closed form asymptotic expressions for computing high frequency noise generated by an annular cascade in an infinite duct containing a uniform flow are presented. There are two new elements in this work. First, the annular duct mode representation does not rely on the often-used Bessel function expansion resulting in simpler expressions for both the radial eigenvalues and eigenfunctions of the duct. In particular, the new representation provides an explicit approximate formula for the radial eigenvalues obviating the need for solutions of the transcendental annular duct eigenvalue equation. Also, the radial eigenfunctions are represented in terms of exponentials eliminating the numerical problems associated with generating the Bessel functions on a computer. The second new element is the construction of an unsteady response model for an annular cascade. The new construction satisfies the boundary conditions on both the cascade and duct walls simultaneously adding a new level of realism to the noise calculations. Preliminary results which demonstrate the effectiveness of the new elements are presented. A discussion of the utility of the asymptotic formulas for calculating cascade discrete tone as well as broadband noise is also included.

The magnetic particle in a box: Analytic and micromagnetic analysis of probe-localized spin wave modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adur, Rohan, E-mail: adur@physics.osu.edu; Du, Chunhui; Manuilov, Sergei A.

2015-05-07

The dipole field from a probe magnet can be used to localize a discrete spectrum of standing spin wave modes in a continuous ferromagnetic thin film without lithographic modification to the film. Obtaining the resonance field for a localized mode is not trivial due to the effect of the confined and inhomogeneous magnetization precession. We compare the results of micromagnetic and analytic methods to find the resonance field of localized modes in a ferromagnetic thin film, and investigate the accuracy of these methods by comparing with a numerical minimization technique that assumes Bessel function modes with pinned boundary conditions. Wemore » find that the micromagnetic technique, while computationally more intensive, reveals that the true magnetization profiles of localized modes are similar to Bessel functions with gradually decaying dynamic magnetization at the mode edges. We also find that an analytic solution, which is simple to implement and computationally much faster than other methods, accurately describes the resonance field of localized modes when exchange fields are negligible, and demonstrating the accessibility of localized mode analysis.« less

Scattering of plane evanescent waves by buried cylinders: Modeling the coupling to guided waves and resonances

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2003-04-01

The coupling of sound to buried targets can be associated with acoustic evanescent waves when the sea bottom is smooth. To understand the excitation of guided waves on buried fluid cylinders and shells by acoustic evanescent waves and the associated target resonances, the two-dimensional partial wave series for the scattering is found for normal incidence in an unbounded medium. The shell formulation uses the simplifications of thin-shell dynamics. The expansion of the incident wave becomes a double summation with products of modified and ordinary Bessel functions [P. L. Marston, J. Acoust. Soc. Am. 111, 2378 (2002)]. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on depth. Some consequences of this imbalance of partial-wave amplitudes are given by modifying previous ray theory for the scattering [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 97, 777-783 (1995)]. The exponential dependence of the scattering on the location of a scatterer was previously demonstrated in air [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].

Acoustic radiation force on an air bubble and soft fluid spheres in ideal liquids: example of a high-order Bessel beam of quasi-standing waves.

PubMed

Mitri, F G

2009-04-01

The partial wave series for the scattering of a high-order Bessel beam (HOBB) of acoustic quasi-standing waves by an air bubble and fluid spheres immersed in water and centered on the axis of the beam is applied to the calculation of the acoustic radiation force. A HOBB refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Radiation force examples obtained through numerical evaluation of the radiation force function are computed for an air bubble, a hexane, a red blood and mercury fluid spheres in water. The examples were selected to illustrate conditions having progressive, standing and quasi-standing waves with appropriate selection of the waves' amplitude ratio. An especially noteworthy result is the lack of a specific vibrational mode contribution to the radiation force determined by appropriate selection of the HOBB parameters.

Near-field spectral shift of a zero-order Bessel beam scattered from a spherical particle

NASA Astrophysics Data System (ADS)

Chen, Feinan; Li, Jia; Belafhal, Abdelmajid; Chafiq, Abdelghani; Sun, Xiaobing

2018-06-01

Within the accuracy of the first-order Born approximation, expressions are derived for the near-zone spectrum of a zero-order Bessel beam scattered from a spherical particle whose correlation function satisfies a Gaussian distribution. The dependence of the spectral shift and spectral switch of the scattered field on the effective size of the scattering potential (ESSP) are determined by numerical simulations. It is shown that the spectral shift of the scattered field does not occur along the longitudinal propagation direction. Furthermore, when the medium’s ESSP is comparable with the central wavelength of the beam, the spectrum of the scattered field loses the Gaussian distribution and exhibits a blue shift as the reference point sufficiently far away from central origin. These results may have prospective applications in guiding tiny particles when the near-zone spectrums of scattered beams are captured and analyzed.

Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitri, F.G., E-mail: F.G.Mitri@ieee.org; Li, R.X., E-mail: rxli@mail.xidian.edu.cn; Collaborative Innovation Center of Information Sensing and Understanding, Xidian University, Xi’an 710071

A complete description of vector Bessel (vortex) beams in the context of the generalized Lorenz–Mie theory (GLMT) for the electromagnetic (EM) resonance scattering by a dielectric sphere is presented, using the method of separation of variables and the subtraction of a non-resonant background (corresponding to a perfectly conducting sphere of the same size) from the standard Mie scattering coefficients. Unlike the conventional results of standard optical radiation, the resonance scattering of a dielectric sphere in air in the field of EM Bessel beams is examined and demonstrated with particular emphasis on the EM field’s polarization and beam order (or topologicalmore » charge). Linear, circular, radial, azimuthal polarizations as well as unpolarized Bessel vortex beams are considered. The conditions required for the resonance scattering are analyzed, stemming from the vectorial description of the EM field using the angular spectrum decomposition, the derivation of the beam-shape coefficients (BSCs) using the integral localized approximation (ILA) and Neumann–Graf’s addition theorem, and the determination of the scattering coefficients of the sphere using Debye series. In contrast with the standard scattering theory, the resonance method presented here allows the quantitative description of the scattering using Debye series by separating diffraction effects from the external and internal reflections from the sphere. Furthermore, the analysis is extended to include rainbow formation in Bessel beams and the derivation of a generalized formula for the deviation angle of high-order rainbows. Potential applications for this analysis include Bessel beam-based laser imaging spectroscopy, atom cooling and quantum optics, electromagnetic instrumentation and profilometry, optical tweezers and tractor beams, to name a few emerging areas of research.« less

Gaussian vs. Bessel light-sheets: performance analysis in live large sample imaging

NASA Astrophysics Data System (ADS)

Reidt, Sascha L.; Correia, Ricardo B. C.; Donnachie, Mark; Weijer, Cornelis J.; MacDonald, Michael P.

2017-08-01

Lightsheet fluorescence microscopy (LSFM) has rapidly progressed in the past decade from an emerging technology into an established methodology. This progress has largely been driven by its suitability to developmental biology, where it is able to give excellent spatial-temporal resolution over relatively large fields of view with good contrast and low phototoxicity. In many respects it is superseding confocal microscopy. However, it is no magic bullet and still struggles to image deeply in more highly scattering samples. Many solutions to this challenge have been presented, including, Airy and Bessel illumination, 2-photon operation and deconvolution techniques. In this work, we show a comparison between a simple but effective Gaussian beam illumination and Bessel illumination for imaging in chicken embryos. Whilst Bessel illumination is shown to be of benefit when a greater depth of field is required, it is not possible to see any benefits for imaging into the highly scattering tissue of the chick embryo.

A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency

NASA Astrophysics Data System (ADS)

Liu, Xiaodong

2017-08-01

A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functional decays like the bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functional continuously depends on the scattering amplitude, this further implies that the novel sampling method is extremely stable with respect to errors in the data. Different to the classical sampling method such as the linear sampling method or the factorization method, from the numerical point of view, the novel indicator takes its maximum near the boundary of the underlying target and decays like the bessel functions as the sampling points go away from the boundary. The numerical simulations also show that the proposed sampling method can deal with multiple multiscale case, even the different components are close to each other.

Oscillatory slip flow past a spherical inclusion embedded in a Brinkman medium

NASA Astrophysics Data System (ADS)

Palaniappan, D.

2016-11-01

Non-steady flow past an impermeable sphere embedded in a porous medium is investigated based on Brinkman model with Navier slip conditions. Exact analytic solution for the stream-function - involving modified Bessel function of the second kind - describing the slow oscillatory flow around a rigid spherical inclusion is obtained in the limit of low-Reynolds-number. The key parameters such as the frequency of oscillation λ, the permeability constant δ, and the slip coefficient ξ control the flow fields and physical quantities in the entire flow domain. Local streamlines for fixed times demonstrate the variations in flow patterns. Closed form expressions for the tangential velocity profile, wall shear stress, and the force acting on the sphere are computed and compared with the existing results. It is noted that the slip parameter in the range 0 <= ξ <= 0 . 5 has a significant effect in reducing the stress and force. The steady-state velocity overshoot behavior in the vicinity of the sphere is re-iterated. In the limit of large permeability, Darcy (potential) flow is recovered outside a boundary layer. The results are of some interest in predicting maximum wall stress and pressure drop associated with biological models in fibrous media.

Voigt equivalent widths and spectral-bin single-line transmittances: Exact expansions and the MODTRAN®5 implementation

NASA Astrophysics Data System (ADS)

Berk, Alexander

2013-03-01

Exact expansions for Voigt line-shape total, line-tail and spectral bin equivalent widths and for Voigt finite spectral bin single-line transmittances have been derived in terms of optical depth dependent exponentially-scaled modified Bessel functions of integer order and optical depth independent Fourier integral coefficients. The series are convergent for the full range of Voigt line-shapes, from pure Doppler to pure Lorentzian. In the Lorentz limit, the expansion reduces to the Ladenburg and Reiche function for the total equivalent width. Analytic expressions are derived for the first 8 Fourier coefficients for pure Lorentzian lines, for pure Doppler lines and for Voigt lines with at most moderate Doppler dependence. A strong-line limit sum rule on the Fourier coefficients is enforced to define an additional Fourier coefficient and to optimize convergence of the truncated expansion. The moderate Doppler dependence scenario is applicable to and has been implemented in the MODTRAN5 atmospheric band model radiative transfer software. Finite-bin transmittances computed with the truncated expansions reduce transmittance residuals compared to the former Rodgers-Williams equivalent width based approach by ∼2 orders of magnitude.

GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography.

PubMed

Xu, Daguang; Huang, Yong; Kang, Jin U

2014-06-16

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

Extension of filament propagation in water with Bessel-Gaussian beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaya, G.; Sayrac, M.; Boran, Y.

We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.

THz computed tomography system with zero-order Bessel beam

NASA Astrophysics Data System (ADS)

Niu, Liting; Wu, Qiao; Wang, Kejia; Liu, Jinsong; Yang, Zhengang

2018-01-01

Terahertz (THz) waves can penetrate many optically opaque dielectric materials such as plastics, ceramics and colorants. It is effective to reveal the internal structures of these materials. We have built a THz Computed Tomography (CT) system with 0.3 THz zero-order Bessel beam to improve the depth of focus of this imaging system for the non-diffraction property of Bessel beam. The THz CT system has been used to detect a paper cup with a metal rod inside. Finally, the acquired projection data have been processed by the filtered back-projection algorithm and the reconstructed image of the sample has been obtained.

On nonsingular potentials of Cox-Thompson inversion scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palmai, Tamas; Apagyi, Barnabas

2010-02-15

We establish a condition for obtaining nonsingular potentials using the Cox-Thompson inverse scattering method with one phase shift. The anomalous singularities of the potentials are avoided by maintaining unique solutions of the underlying Regge-Newton integral equation for the transformation kernel. As a by-product, new inequality sequences of zeros of Bessel functions are discovered.

Computational Diffusion Magnetic Resonance Imaging Based on Time-Dependent Bloch NMR Flow Equation and Bessel Functions.

PubMed

Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I

2016-04-01

Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it possible to distinguish cancerous cells from normal cells. A typical example of liver distinguished from gray matter, white matter and kidney is demonstrated. Bessel functions and properties are specifically needed to show the direct effect of the instantaneous velocity on the NMR signal originating from normal and abnormal tissues.

Pre-correction of distorted Bessel-Gauss beams without wavefront detection

NASA Astrophysics Data System (ADS)

Fu, Shiyao; Wang, Tonglu; Zhang, Zheyuan; Zhai, Yanwang; Gao, Chunqing

2017-12-01

By utilizing the property of the phase's rapid solution of the Gerchberg-Saxton algorithm, we experimentally demonstrate a scheme to correct distorted Bessel-Gauss beams resulting from inhomogeneous media as weak turbulent atmosphere with good performance. A probe Gaussian beam is employed and propagates coaxially with the Bessel-Gauss modes through the turbulence. No wavefront sensor but a matrix detector is used to capture the probe Gaussian beams, and then, the correction phase mask is computed through inputting such probe beam into the Gerchberg-Saxton algorithm. The experimental results indicate that both single and multiplexed BG beams can be corrected well, in terms of the improvement in mode purity and the mitigation of interchannel cross talk.

Single-shot high aspect ratio bulk nanostructuring of fused silica using chirp-controlled ultrafast laser Bessel beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhuyan, M. K.; Velpula, P. K.; Colombier, J. P.

2014-01-13

We report single-shot, high aspect ratio nanovoid fabrication in bulk fused silica using zeroth order chirp-controlled ultrafast laser Bessel beams. We identify a unique laser pulse length and energy dependence of the physical characteristics of machined structures over which nanovoids of diameter in the range 200–400 nm and aspect ratios exceeding 1000 can be fabricated. A mechanism based on the axial energy deposition of nonlinear ultrashort Bessel beams and subsequent material densification or rarefaction in fused silica is proposed, intricating the non-diffractive nature with the diffusing character of laser-generated free carriers. Fluid flow through nanochannel is also demonstrated.

Bessel beam transformation in c-cuts of uniaxial crystals by varying the source wavelength

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paranin, V. D.

Transformation of Bessel beam of a zero order to Bessel beam of the second order in c-cut of CaCO{sub 3} crystal is experimentally investigated. Possibility of output beam control at changing of wavelength and using of a diffraction axicon is shown. Full transformation of beams at changing of wavelength Δλ=1.5 nanometers is received at initial wavelength λ=637.5 nanometers for a crystal of CaCO{sub 3} with 15 mm long and a diffraction axicon with period of 2 microns. The theoretical value of necessary wavelength changing is Δλ=1.7 nanometers that is according with experimental results.

Matrix Sturm-Liouville equation with a Bessel-type singularity on a finite interval

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia

2017-03-01

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

PubMed

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

NASA Astrophysics Data System (ADS)

Guarnieri, F.; Moon, W.; Wettlaufer, J. S.

2017-09-01

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with a negative constant drift, described by a Fokker-Planck equation with a potential V (x ) =-[b ln(x ) +a x ] , for b >0 and a <0 . The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process that has been extensively studied for its applications in physics, biology, and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schrödinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a constant negative drift. We conclude with a comparison to other analytical methods and with numerical solutions.

Observation of the asymmetric Bessel beams with arbitrary orientation using a digital micromirror device.

PubMed

Gong, Lei; Qiu, Xing-Ze; Ren, Yu-Xuan; Zhu, Hui-Qing; Liu, Wei-Wei; Zhou, Jin-Hua; Zhong, Min-Cheng; Chu, Xiu-Xiang; Li, Yin-Mei

2014-11-03

Recently, V. V. Kotlyar et al. [Opt. Lett.39, 2395 (2014)] have theoretically proposed a novel kind of three-parameter diffraction-free beam with a crescent profile, namely, the asymmetric Bessel (aB) beam. The asymmetry degree of such nonparaxial modes was shown to depend on a nonnegative real parameter c. We present a more generalized asymmetric Bessel mode in which the parameter c is a complex constant. This parameter controls not only the asymmetry degree of the mode but also the orientation of the optical crescent, and affects the energy distribution and orbital angular momentum (OAM) of the beam. As a proof of concept, the high-quality generation of asymmetric Bessel-Gauss beams was demonstrated with the super-pixel method using a digital micromirror device (DMD). We investigated the near-field properties as well as the far field features of such beams, and the experimental observations were in good agreement with the theoretical predictions. Additionally, we provided an effective way to control the beam's asymmetry and orientation, which may find potential applications in light-sheet microscopy and optical manipulation.

MRS3D: 3D Spherical Wavelet Transform on the Sphere

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2011-12-01

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.

Acoustic manipulation: Bessel beams and active carriers

NASA Astrophysics Data System (ADS)

Rajabi, Majid; Mojahed, Alireza

2017-10-01

In this paper, we address the interaction of zero-order acoustic Bessel beams as an acoustic manipulation tool, with an active spherical shell, as a carrier in drug, agent, or material delivery systems, in order to investigate the controllability of exerted acoustic radiation force as the driver. The active body is comprised of a spherical elastic shell stimulated in its monopole mode of vibrations with the same frequency as the incident wave field via an internally bonded and spatially uniformly excited piezoelectric actuator. The main aim of this work is to examine the performance of a nondiffracting and self-reconstructing zero-order Bessel beam to obtain the full manipulability condition of active carriers in comparison with the case of a plane wave field. The results unveil some unique potentials of the Bessel beams in the company of active carriers, with emphasis on the consumed power of the actuation system. This paper will widen the path toward the single-beam robust acoustic manipulation techniques and may lead to the prospect of combined tweezers and fields, with applications in delivery systems, microswimmers, and trapper designs.

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam

NASA Astrophysics Data System (ADS)

F, Khannous; A, A. A. Ebrahim; A, Belafhal

2016-04-01

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.

Dexterous ultrasonic levitation of millimeter-sized objects in air.

PubMed

Seah, Sue Ann; Drinkwater, Bruce W; Carter, Tom; Malkin, Rob; Subramanian, Sriram

2014-07-01

Acoustic levitation in air has applications in contactless handling and processing. Here a first-order Bessel function-shaped acoustic field, generated using an 8-element circular array operating at 40 kHz, traps millimeter-sized objects against gravity. The device can manipulate objects in a vertical plane over a few millimeters with an accuracy of ± 0.09 mm.

Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series

DTIC Science & Technology

2014-10-16

at the same angle to the horizontal, so that the two ramps form a V-shape. In the absence of rolling friction or air drag , the ball rolls a distance...Marichev, Integrals and Series Volume 2: Special Functions, translated by N.M. Queen (Gordon & Breach, New York, 1986). [9] V. Méndez, C. Sans, D

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Degroote, M.; Henderson, T. M.; Zhao, J.

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero.more » Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.« less

Effect of turbulence on the dissipation of the space-charge wave in a bounded turbulent plasma column

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 15588

The dispersion relation and the dissipation process of the space-charge wave propagating in a bounded plasma such as a cylindrical waveguide are investigated by employing the longitudinal dielectric permittivity that contains the diffusivity based on the Dupree theory of turbulent plasma. We derived the dispersion relation for space-charge wave in terms of the radius of cylindrical waveguide and the roots of the Bessel function of the first kind which appears as the boundary condition. We find that the wave frequency for a lower-order root of the Bessel function is higher than that of a higher-order root. We also find thatmore » the dissipation is greatest for the lowest-order root, but it is suppressed significantly as the order of the root increases. The wave frequency and the dissipation process are enhanced as the radius of cylindrical waveguide increases. However, they are always smaller than the case of bulk plasma. We find that the diffusivity of turbulent plasma would enhance the damping of space-charge waves, especially, in the range of small wave number. For a large wave number, the diffusivity has little effect on the damping.« less

Fabrication of microchannels in fused silica using femtosecond Bessel beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yashunin, D. A., E-mail: yashuninda@yandex.ru; Nizhny Novgorod State Technical University, 24 Minin St., Nizhny Novgorod 603950; Malkov, Yu. A.

Extended birefringent waveguiding microchannels up to 15 mm long were created inside fused silica by single-pulse irradiation with femtosecond Bessel beams. The birefringent refractive index change of 2–4 × 10{sup −4} is attributed to residual mechanical stress. The microchannels were chemically etched in KOH solution to produce 15 mm long microcapillaries with smooth walls and a high aspect ratio of 1:250. Bessel beams provide higher speed of material processing compared to conventional multipulse femtosecond laser micromachining techniques and permit simple control of the optical axis direction of the birefringent waveguides, which is important for practical applications [Corrielli et al., “Rotated waveplates inmore » integrated waveguide optics,” Nat. Commun. 5, 4249 (2014)].« less

A three-dimensional semi-analytical solution for predicting drug release through the orifice of a spherical device.

PubMed

Simon, Laurent; Ospina, Juan

2016-07-25

Three-dimensional solute transport was investigated for a spherical device with a release hole. The governing equation was derived using the Fick's second law. A mixed Neumann-Dirichlet condition was imposed at the boundary to represent diffusion through a small region on the surface of the device. The cumulative percentage of drug released was calculated in the Laplace domain and represented by the first term of an infinite series of Legendre and modified Bessel functions of the first kind. Application of the Zakian algorithm yielded the time-domain closed-form expression. The first-order solution closely matched a numerical solution generated by Mathematica(®). The proposed method allowed computation of the characteristic time. A larger surface pore resulted in a smaller effective time constant. The agreement between the numerical solution and the semi-analytical method improved noticeably as the size of the orifice increased. It took four time constants for the device to release approximately ninety-eight of its drug content. Copyright © 2016 Elsevier B.V. All rights reserved.

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 4: Computer user's manual for UAAP turboprop aeroacoustic code

NASA Astrophysics Data System (ADS)

Menthe, R. W.; McColgan, C. J.; Ladden, R. M.

1991-05-01

The Unified AeroAcoustic Program (UAAP) code calculates the airloads on a single rotation prop-fan, or propeller, and couples these airloads with an acoustic radiation theory, to provide estimates of near-field or far-field noise levels. The steady airloads can also be used to calculate the nonuniform velocity components in the propeller wake. The airloads are calculated using a three dimensional compressible panel method which considers the effects of thin, cambered, multiple blades which may be highly swept. These airloads may be either steady or unsteady. The acoustic model uses the blade thickness distribution and the steady or unsteady aerodynamic loads to calculate the acoustic radiation. The users manual for the UAAP code is divided into five sections: general code description; input description; output description; system description; and error codes. The user must have access to IMSL10 libraries (MATH and SFUN) for numerous calls made for Bessel functions and matrix inversion. For plotted output users must modify the dummy calls to plotting routines included in the code to system-specific calls appropriate to the user's installation.

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 4: Computer user's manual for UAAP turboprop aeroacoustic code

NASA Technical Reports Server (NTRS)

Menthe, R. W.; Mccolgan, C. J.; Ladden, R. M.

1991-01-01

The Unified AeroAcoustic Program (UAAP) code calculates the airloads on a single rotation prop-fan, or propeller, and couples these airloads with an acoustic radiation theory, to provide estimates of near-field or far-field noise levels. The steady airloads can also be used to calculate the nonuniform velocity components in the propeller wake. The airloads are calculated using a three dimensional compressible panel method which considers the effects of thin, cambered, multiple blades which may be highly swept. These airloads may be either steady or unsteady. The acoustic model uses the blade thickness distribution and the steady or unsteady aerodynamic loads to calculate the acoustic radiation. The users manual for the UAAP code is divided into five sections: general code description; input description; output description; system description; and error codes. The user must have access to IMSL10 libraries (MATH and SFUN) for numerous calls made for Bessel functions and matrix inversion. For plotted output users must modify the dummy calls to plotting routines included in the code to system-specific calls appropriate to the user's installation.

G0-WISHART Distribution Based Classification from Polarimetric SAR Images

NASA Astrophysics Data System (ADS)

Hu, G. C.; Zhao, Q. H.

2017-09-01

Enormous scientific and technical developments have been carried out to further improve the remote sensing for decades, particularly Polarimetric Synthetic Aperture Radar(PolSAR) technique, so classification method based on PolSAR images has getted much more attention from scholars and related department around the world. The multilook polarmetric G0-Wishart model is a more flexible model which describe homogeneous, heterogeneous and extremely heterogeneous regions in the image. Moreover, the polarmetric G0-Wishart distribution dose not include the modified Bessel function of the second kind. It is a kind of simple statistical distribution model with less parameter. To prove its feasibility, a process of classification has been tested with the full-polarized Synthetic Aperture Radar (SAR) image by the method. First, apply multilook polarimetric SAR data process and speckle filter to reduce speckle influence for classification result. Initially classify the image into sixteen classes by H/A/α decomposition. Using the ICM algorithm to classify feature based on the G0-Wshart distance. Qualitative and quantitative results show that the proposed method can classify polaimetric SAR data effectively and efficiently.

Complex Analysis and Related Topics. Proceedings of the Conference held in Amsterdam on 27 - 29 January 1993

DTIC Science & Technology

1993-01-29

Bessel functions and Jacobi functions (cf. [2]). References [1] R. Askey & J. Wilson, Some basic hypergeometric orthogonal polynomials that gen- eralize...1; 1] can be treated as a part of general theory of T-systems (see [81 for that theory and [7] for some aspects of the Chebyshev polynomials theory...waves in elastic media. It has been known for some time that these multiplicities sometimes occur for topological reasons and are present generically , see

Dynamics of submicron aerosol droplets in a robust optical trap formed by multiple Bessel beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thanopulos, Ioannis; Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Athens 11635; Luckhaus, David

In this paper, we model the three-dimensional escape dynamics of single submicron-sized aerosol droplets in optical multiple Bessel beam traps. Trapping in counter-propagating Bessel beams (CPBBs) is compared with a newly proposed quadruple Bessel beam (QBB) trap, which consists of two perpendicularly arranged CPBB traps. Calculations are performed for perfectly and imperfectly aligned traps. Mie-theory and finite-difference time-domain methods are used to calculate the optical forces. The droplet escape kinetics are obtained from the solution of the Langevin equation using a Verlet algorithm. Provided the traps are perfectly aligned, the calculations indicate very long lifetimes for droplets trapped either inmore » the CPBB or in the QBB trap. However, minor misalignments that are hard to control experimentally already severely diminish the stability of the CPBB trap. By contrast, such minor misalignments hardly affect the extended droplet lifetimes in a QBB trap. The QBB trap is found to be a stable, robust optical trap, which should enable the experimental investigation of submicron droplets with radii down to 100 nm. Optical binding between two droplets and its potential role in preventing coagulation when loading a CPBB trap is briefly addressed.« less

Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation

NASA Astrophysics Data System (ADS)

Vuillemin, Nelly; Mahou, Pierre; Débarre, Delphine; Gacoin, Thierry; Tharaux, Pierre-Louis; Schanne-Klein, Marie-Claire; Supatto, Willy; Beaurepaire, Emmanuel

2016-07-01

Second-harmonic generation (SHG) is the most specific label-free indicator of collagen accumulation in widespread pathologies such as fibrosis, and SHG-based measurements hold important potential for biomedical analyses. However, efficient collagen SHG scoring in histological slides is hampered by the limited depth-of-field of usual nonlinear microscopes relying on focused Gaussian beam excitation. In this work we analyze theoretically and experimentally the use of Bessel beam excitation to address this issue. Focused Bessel beams can provide an axially extended excitation volume for nonlinear microscopy while preserving lateral resolution. We show that shaping the focal volume has consequences on signal level and scattering directionality in the case of coherent signals (such as SHG) which significantly differ from the case of incoherent signals (two-photon excited fluorescence, 2PEF). We demonstrate extended-depth SHG-2PEF imaging of fibrotic mouse kidney histological slides. Finally, we show that Bessel beam excitation combined with spatial filtering of the harmonic light in wave vector space can be used to probe collagen accumulation more efficiently than the usual Gaussian excitation scheme. These results open the way to SHG-based histological diagnoses.

Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation

PubMed Central

Vuillemin, Nelly; Mahou, Pierre; Débarre, Delphine; Gacoin, Thierry; Tharaux, Pierre-Louis; Schanne-Klein, Marie-Claire; Supatto, Willy; Beaurepaire, Emmanuel

2016-01-01

Second-harmonic generation (SHG) is the most specific label-free indicator of collagen accumulation in widespread pathologies such as fibrosis, and SHG-based measurements hold important potential for biomedical analyses. However, efficient collagen SHG scoring in histological slides is hampered by the limited depth-of-field of usual nonlinear microscopes relying on focused Gaussian beam excitation. In this work we analyze theoretically and experimentally the use of Bessel beam excitation to address this issue. Focused Bessel beams can provide an axially extended excitation volume for nonlinear microscopy while preserving lateral resolution. We show that shaping the focal volume has consequences on signal level and scattering directionality in the case of coherent signals (such as SHG) which significantly differ from the case of incoherent signals (two-photon excited fluorescence, 2PEF). We demonstrate extended-depth SHG-2PEF imaging of fibrotic mouse kidney histological slides. Finally, we show that Bessel beam excitation combined with spatial filtering of the harmonic light in wave vector space can be used to probe collagen accumulation more efficiently than the usual Gaussian excitation scheme. These results open the way to SHG-based histological diagnoses. PMID:27435390

Synthesis of generalized surface plasmon beams

NASA Astrophysics Data System (ADS)

Martinez-Niconoff, G.; Munoz-Lopez, J.; Martinez-Vara, P.

2009-08-01

Surface plasmon modes can be considered as the analogous to plane waves for homogeneous media. The extension to partially coherent surface plasmon beams is obtained by means of the incoherent superposition of the interference between surface plasmon modes whose profile is controlled associating a probability density function to the structural parameters implicit in their representation. We show computational simulations for cosine, Bessel, gaussian and dark hollow surface plasmon beams.

Strong-field ionization with twisted laser pulses

NASA Astrophysics Data System (ADS)

Paufler, Willi; Böning, Birger; Fritzsche, Stephan

2018-04-01

We apply quantum trajectory Monte Carlo computations in order to model strong-field ionization of atoms by twisted Bessel pulses and calculate photoelectron momentum distributions (PEMD). Since Bessel beams can be considered as an infinite superposition of circularly polarized plane waves with the same helicity, whose wave vectors lie on a cone, we compared the PEMD of such Bessel pulses to those of a circularly polarized pulse. We focus on the momentum distributions in propagation direction of the pulse and show how these momentum distributions are affected by experimental accessible parameters, such as the opening angle of the beam or the impact parameter of the atom with regard to the beam axis. In particular, we show that we can find higher momenta of the photoelectrons, if the opening angle is increased.

Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams

NASA Astrophysics Data System (ADS)

Milione, Giovanni; Dudley, Angela; Nguyen, Thien An; Chakraborty, Ougni; Karimi, Ebrahim; Forbes, Andrew; Alfano, Robert R.

2015-03-01

We experimentally measured the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams. Radially and azimuthally polarized vector Bessel beams were experimentally generated via a digital version of Durnin's method, using a spatial light modulator in concert with a liquid crystal q-plate. As a proof of principle, their intensities and spatially inhomogeneous states of polarization were experimentally measured using Stokes polarimetry as they propagated through two disparate obstructions. It was found, similar to their intensities, that their spatially inhomogeneous states of polarization self-healed. The self-healing can be understood via geometric optics, i.e., the interference of the unobstructed conical rays in the shadow region of the obstruction, and may have applications in, for example, optical trapping.

Laser controlled deposition of metal microstructures via nondiffracting Bessel beam illumination

NASA Astrophysics Data System (ADS)

Drampyan, Rafael; Leonov, Nikita; Vartanyan, Tigran

2016-04-01

The technique of the laser controlled deposition of sodium and rubidium deposits on the sapphire substrate is presented. The metals were deposited on the clean sapphire substrate from the vapor phase contained in the evacuated and sealed cell. We use an axicon to produce a non-diffracting Bessel beam out of the beam got from the cw diode laser with 200 mW power at the wavelength of 532 nm. After 30 minutes of the laser-controlled deposition the substrates were examined in the optical microscope. The obtained metal deposits form the sharp-cut circles with the pitch of 10 μm, coincident with the tens of dark rings of the Bessel beam. Reduction of the laser power leads to the build up of the continuous metal film over the whole substrate.

Problems of the theory of the consolidation solved in the special functions

NASA Astrophysics Data System (ADS)

Dasibekov, Azhibek; Abzhapbarov, Azimkhan; Duisebayeva, Peruza; Polatbek, Aigul

2016-08-01

The soil, which deformation modulus is continuously increased with depth is called continuously heterogeneous. In this paper, this heterogeneity is presented in the form of: E =Em(α+β z ) m (α >0 ,Em>0 ,α +βz>0 ), wher Em, α, β, m are experimental parameters. On the basis of this dependence the consolidation problems of elastic and elastically creeping inhomogeneous soils are solved in relation to the restricted area of the consolidation. These solutions make it possible to calculate the values of the pore pressure, the amount of the main stresses and vertical displacements of upper surface points of the condensed inhomogeneous soil mass. In these solutions for highly compressed water-saturated clay soils is also taken into account that at the initial time the part of loading, instantly enclosed load q to the soil which is equal in value of the structural strength of the compression pstr, is immediately perceived by a matrix. In addition, Darcy's law is broken, i.e. the initial gradient of pressure is considered. The resulting calculation formulas are presented as a combination of Bessel functions of the first and second kinds. Taking into account that currently one can define any values of the Bessel functions, it is possible to calculate the pressure in the pore fluids and predict the speed of sediments of the compacting mass.

Pump-probe imaging of the fs-ps-ns dynamics during femtosecond laser Bessel beam drilling in PMMA.

PubMed

Yu, Yanwu; Jiang, Lan; Cao, Qiang; Xia, Bo; Wang, Qingsong; Lu, Yongfeng

2015-12-14

A pump-probe shadowgraph imaging technique was used to reveal the femtosecond-picosecond-nanosecond multitimescale fundamentals of high-quality, high-aspect-ratio (up to 287:1) microhole drilling in poly-methyl-meth-acrylate (PMMA) by a single-shot femtosecond laser Bessel beam. The propagation of Bessel beam in PMMA (at 1.98 × 10⁸ m/s) and it induced cylindrical pressure wave expansion (at 3000-3950 m/s in radius) were observed during drilling processes. Also, it was unexpectedly found that the expansion of the cylindrical pressure wave in PMMA showed a linear relation with time and was insensitive to the laser energy fluctuation, quite different from the case in air. It was assumed that the energy insensitivity was due to the anisotropy of wave expansion in PMMA and the ambient air.

Particle confinement by a radially polarized laser Bessel beam

NASA Astrophysics Data System (ADS)

Laredo, Gilad; Kimura, Wayne D.; Schächter, Levi

2017-03-01

The stable trajectory of a charged particle in an external guiding field is an essential condition for its acceleration or for forcing it to generate radiation. Examples of possible guiding devices include a solenoidal magnetic field or permanent periodic magnet in klystrons, a wiggler in free-electron lasers, the lattice of any accelerator, and finally the crystal lattice for the case of channeling radiation. We demonstrate that the trajectory of a point-charge in a radially polarized laser Bessel beam may be stable similarly to the case of a positron that bounces back and forth in the potential well generated by two adjacent atomic planes. While in the case of channeling radiation, the transverse motion is controlled by a harmonic oscillator equation, for a Bessel beam the transverse motion is controlled by the Mathieu equation. Some characteristics of the motion are presented.

MUSIC-type imaging of small perfectly conducting cracks with an unknown frequency

NASA Astrophysics Data System (ADS)

Park, Won-Kwang

2015-09-01

MUltiple SIgnal Classification (MUSIC) is a famous non-iterative detection algorithm in inverse scattering problems. However, when the applied frequency is unknown, inaccurate locations are identified via MUSIC. This fact has been confirmed through numerical simulations. However, the reason behind this phenomenon has not been investigated theoretically. Motivated by this fact, we identify the structure of MUSIC-type imaging functionals with unknown frequency, by establishing a relationship with Bessel functions of order zero of the first kind. Through this, we can explain why inaccurate results appear.

A necessary condition for applying MUSIC algorithm in limited-view inverse scattering problem

NASA Astrophysics Data System (ADS)

Park, Taehoon; Park, Won-Kwang

2015-09-01

Throughout various results of numerical simulations, it is well-known that MUltiple SIgnal Classification (MUSIC) algorithm can be applied in the limited-view inverse scattering problems. However, the application is somehow heuristic. In this contribution, we identify a necessary condition of MUSIC for imaging of collection of small, perfectly conducting cracks. This is based on the fact that MUSIC imaging functional can be represented as an infinite series of Bessel function of integer order of the first kind. Numerical experiments from noisy synthetic data supports our investigation.

Microcomputer Simulation of a Fourier Approach to Optical Wave Propagation

DTIC Science & Technology

1992-06-01

and transformed input in transform domain). 44 Figure 21. SHFTOUTPUT1 ( inverse transform of product of Bessel filter and transformed input). . . . 44...Figure 22. SHFT OUTPUT2 ( inverse transform of product of ,derivative filter and transformed input).. 45 Figure 23. •tIFT OUTPUT (sum of SHFTOUTPUT1...52 Figure 33. SHFT OUTPUT1 at time slice 1 ( inverse transform of product of Bessel filter and transformed input) .... ............. ... 53

Using axicons for depth discrimination in excitation-emission laser scanning imaging systems

NASA Astrophysics Data System (ADS)

Iglesias, Ignacio

2017-10-01

Besides generating good approximations to zero-order Bessel beams, an axicon lens coupled to a spatial filter can be used to collect light while preserving information on the depth coordinate of the source location. To demonstrate the principle, we describe an experimental excitation-emission fluorescence imaging system that uses an axicon twice: to generate an excitation Bessel beam and to collect the emitted light.

Mechanism of nanosecond laser drilling process of 4H-SiC for through substrate vias

NASA Astrophysics Data System (ADS)

Kim, Byunggi; Iida, Ryoichi; Doan, Duc Hong; Fushinobu, Kazuyoshi

2017-06-01

Role of optical parameters on nanosecond laser drilling of 4H-SiC was experimentally studied. Using ns pulsed Nd:YAG laser, parametric studies on effects of wavelength (1064 nm or 532 nm), beam profile (Gaussian or Bessel), and ambient condition (air or water) were conducted. The wavelengths which have large optical penetration depth were selected as wavefront has to propagate through materials to generate Bessel beam. The experimental results showed that carbonization of SiC surface accelerates thermal ablation of the materials with fluence under the lattice melting threshold. Especially, pattern of side lobes with small fluence was formed by irradiation of Bessel beam. The pattern disturbed penetration of wavefronts through materials. Implementation of water environment was not effective to suppress carbonization and had slight effect on improvement of drilling quality. For this reason, deep drilling with small entrance was not achieved using Bessel beam. Irradiation of 1064 nm Gaussian beam with large fluence led to formation of critical amount of re-solidified silicon due to the large optical penetration depth. Carbonization and silicon formation had a significant effect on unique fluence dependence of drilling depth. Absorption mechanism was studied as well to discuss effect of wavelength on processing characteristics.

Vector-beam solutions of Maxwell's wave equation.

PubMed

Hall, D G

1996-01-01

The Hermite-Gauss and Laguerre-Gauss modes are well-known beam solutions of the scalar Helmholtz equation in the paraxial limit. As such, they describe linearly polarized fields or single Cartesian components of vector fields. The vector wave equation admits, in the paraxial limit, of a family of localized Bessel-Gauss beam solutions that can describe the entire transverse electric field. Two recently reported solutions are members of this family of vector Bessel-Gauss beam modes.

Visualizing polarization singularities in Bessel-Poincaré beams.

PubMed

Shvedov, V; Karpinski, P; Sheng, Y; Chen, X; Zhu, W; Krolikowski, W; Hnatovsky, C

2015-05-04

We demonstrate that an annulus of light whose polarization is linear at each point, but the plane of polarization gradually rotates by π radians can be used to generate Bessel-Poincaré beams. In any transverse plane this beam exhibits concentric rings of polarization singularities in the form of L-lines, where the polarization is purely linear. Although the L-lines are invisible in terms of light intensity variations, we present a simple way to visualize them as dark rings around a sharp peak of intensity in the beam center. To do this we use a segmented polarizer whose transmission axes are oriented differently in each segment. The radius of the first L-line is always smaller than the radius of the central disk of the zero-order Bessel beam that would be produced if the annulus were homogeneously polarized and had no phase circulation along it.

Cellular imaging of deep organ using two-photon Bessel light-sheet nonlinear structured illumination microscopy

PubMed Central

Zhao, Ming; Zhang, Han; Li, Yu; Ashok, Amit; Liang, Rongguang; Zhou, Weibin; Peng, Leilei

2014-01-01

In vivo fluorescent cellular imaging of deep internal organs is highly challenging, because the excitation needs to penetrate through strong scattering tissue and the emission signal is degraded significantly by photon diffusion induced by tissue-scattering. We report that by combining two-photon Bessel light-sheet microscopy with nonlinear structured illumination microscopy (SIM), live samples up to 600 microns wide can be imaged by light-sheet microscopy with 500 microns penetration depth, and diffused background in deep tissue light-sheet imaging can be reduced to obtain clear images at cellular resolution in depth beyond 200 microns. We demonstrate in vivo two-color imaging of pronephric glomeruli and vasculature of zebrafish kidney, whose cellular structures located at the center of the fish body are revealed in high clarity by two-color two-photon Bessel light-sheet SIM. PMID:24876996

Quasi-Bessel beams from asymmetric and astigmatic illumination sources.

PubMed

Müller, Angelina; Wapler, Matthias C; Schwarz, Ulrich T; Reisacher, Markus; Holc, Katarzyna; Ambacher, Oliver; Wallrabe, Ulrike

2016-07-25

We study the spatial intensity distribution and the self-reconstruction of quasi-Bessel beams produced from refractive axicon lenses with edge emitting laser diodes as asymmetric and astigmatic illumination sources. Comparing these to a symmetric mono-mode fiber source, we find that the asymmetry results in a transition of a quasi-Bessel beam into a bow-tie shaped pattern and eventually to a line shaped profile at a larger distance along the optical axis. Furthermore, we analytically estimate and discuss the effects of astigmatism, substrate modes and non-perfect axicons. We find a good agreement between experiment, simulation and analytic considerations. Results include the derivation of a maximal axicon angle related to astigmatism of the illuminating beam, impact of laser diode beam profile imperfections like substrate modes and a longitudinal oscillation of the core intensity and radius caused by a rounded axicon tip.

Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.

PubMed

April, Alexandre

2011-10-01

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

Optically Tuned MM-Wave IMPATT Source.

DTIC Science & Technology

1987-07-01

phase of the work has been extended and generalised. Accuracy of the theory in predicting tuning at the higher oscillator voltage swings has been greatly...Accuracy of the theory in predicting tuning at the higher oscillator voltage swings has been greatly improved by reformulating the Bessel function...voltage modulation and a peak optically injected locking current of 100 pA the predicted ftl locking range would be 540MHz, a practicaUy useful value. 4

Three-dimensional spatially curved local Bessel beams generated by metasurface

NASA Astrophysics Data System (ADS)

Liu, Dawei; Wu, Jiawen; Cheng, Bo; Li, Hongliang

2018-03-01

We propose a reflective metasurface based on an artificial admittance modulation surface to generate three-dimensional spatially curved beams. The phase acquisition utilized to modulate this sinusoidally varying surface admittance combines the enveloping theory of differential geometry and the method for producing two-dimensional Bessel beams. The metasurface is fabricated, and the comparison between the full-wave simulations and experimental results demonstrates good performance of three-dimensional spatially curved beams generated by the metasurface.

Hankel-Bessel laser beams.

PubMed

Kotlyar, Victor V; Kovalev, Alexey A; Soifer, Victor A

2012-05-01

An analytical solution of the scalar Helmholtz equation to describe the propagation of a laser light beam in the positive direction of the optical axis is derived. The complex amplitude of such a beam is found to be in direct proportion to the product of two linearly independent solutions of Kummer's differential equation. Relationships for a particular case of such beams-namely, the Hankel-Bessel (HB) beams-are deduced. The focusing of the HB beams is studied. © 2012 Optical Society of America

Uniform analytic approximation of Wigner rotation matrices

NASA Astrophysics Data System (ADS)

Hoffmann, Scott E.

2018-02-01

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

Music algorithm for imaging of a sound-hard arc in limited-view inverse scattering problem

NASA Astrophysics Data System (ADS)

Park, Won-Kwang

2017-07-01

MUltiple SIgnal Classification (MUSIC) algorithm for a non-iterative imaging of sound-hard arc in limited-view inverse scattering problem is considered. In order to discover mathematical structure of MUSIC, we derive a relationship between MUSIC and an infinite series of Bessel functions of integer order. This structure enables us to examine some properties of MUSIC in limited-view problem. Numerical simulations are performed to support the identified structure of MUSIC.

On the solution of the Helmholtz equation on regions with corners.

PubMed

Serkh, Kirill; Rokhlin, Vladimir

2016-08-16

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

On the solution of the Helmholtz equation on regions with corners

PubMed Central

Serkh, Kirill; Rokhlin, Vladimir

2016-01-01

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples. PMID:27482110

Multicolor 4D Fluorescence Microscopy using Ultrathin Bessel Light Sheets

PubMed Central

Zhao, Teng; Lau, Sze Cheung; Wang, Ying; Su, Yumian; Wang, Hao; Cheng, Aifang; Herrup, Karl; Ip, Nancy Y.; Du, Shengwang; Loy, M. M. T.

2016-01-01

We demonstrate a simple and efficient method for producing ultrathin Bessel (‘non-diffracting’) light sheets of any color using a line-shaped beam and an annulus filter. With this robust and cost-effective technology, we obtained two-color, 3D images of biological samples with lateral/axial resolution of 250 nm/400 nm, and high-speed, 4D volume imaging of 20 μm sized live sample at 1 Hz temporal resolution. PMID:27189786

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2016-10-01

An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas.

A 5mm catheter for constant resolution probing in Fourier domain optical coherence endoscopy

NASA Astrophysics Data System (ADS)

Lee, Kye-Sung; Wu, Lei; Xie, Huikai; Ilegbusi, Olusegun; Costa, Marco; Rolland, Jannick P.

2007-02-01

A 5mm biophotonic catheter was conceived for optical coherence tomography (OCT) with collimation optics, an axicon lens, and custom design imaging optics, yielding a 360 degree scan aimed at imaging within concave structures such as lung lobes. In OCT a large depth of focus is necessary to image a thick sample with a constant high transverse resolution. There are two approaches to achieving constant lateral resolution in OCT: Dynamic focusing or Bessel beam forming. This paper focuses on imaging with Bessel beams. A Bessel beam can be generated in the sample arm of the OCT interferometer when axicon optics is employed instead of a conventional focusing lens. We present a design for a 5mm catheter that combines an axicon lens with imaging optics and the coupling of a MEMS mirror attached to a micromotor that allow 360 degree scanning with a resolution of about 5 microns across a depth of focus of about 1.2mm.

Excitation of multipolar surface plasmon resonance in plasmonic nanoparticles by complex accelerating beams

NASA Astrophysics Data System (ADS)

Yang, Yang; Li, Jiafang; Li, Zhi-Yuan; Chen, Yue-Gang

2015-07-01

In this paper, through a vector-spherical harmonics approach, we investigate the optical spectra of plasmonic Au nanoparticles excited by two special accelerating beams: a non-paraxial Airy beam and a Bessel beam. We systematically analyze the impacts of the beam profile, phase, and helical wave front of the electromagnetic fields on the optical spectrum and the excitation of the surface plasmon resonance (SPR). We find that the high-order phase in the Airy beam would result in strong plasmonic oscillations in the optical spectra, while the cone angle and orbital angular momentum carried by the Bessel beam could be employed to engineer the plasmon modes excited in Au nanoparticles. Furthermore, the optical spectrum excited by a combined Airy-Bessel-Gauss beam is discussed. The study could help to deeply explore new ways to manipulate SPR in metal nanoparticles via the wave front engineering of optical beams for enhancing light-matter interaction and optical sensing performance.

Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces

NASA Astrophysics Data System (ADS)

David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth

2015-04-01

We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.

Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces.

PubMed

David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth

2015-04-21

We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.

Non-contact high resolution Bessel beam probe for diagnostic imaging of cornea and trabecular meshwork region in eye

NASA Astrophysics Data System (ADS)

Murukeshan, V. M.; Jesmond, Hong Xun J.; Shinoj, V. K.; Baskaran, M.; Tin, Aung

2015-07-01

Primary angle closure glaucoma is a major form of disease that causes blindness in Asia and worldwide. In glaucoma, irregularities in the ocular aqueous outflow system cause an elevation in intraocular pressure (IOP) with subsequent death of retinal ganglion cells, resulting in loss of vision. High resolution visualization of the iridocorneal angle region has great diagnostic value in understanding the disease condition which enables monitoring of surgical interventions that decrease IOP. None of the current diagnostic techniques such as goniophotography, ultrasound biomicroscopy (UBM), anterior segment optical coherence tomography (AS-OCT) and RetCam™ can image with molecular specificity and required spatial resolution that can delineate the trabecular meshwork structures. This paper in this context proposes new concepts and methodology using Bessel beams based illumination and imaging for such diagnostic ocular imaging applications. The salient features using Bessel beams instead of the conventional Gaussian beam, and the optimization challenges in configuring the probe system will be illustrated with porcine eye samples.

From education to occupation: the story of Thomas Bessell Kidner.

PubMed

Friedland, Judith; Davids-Brumer, Naomi

2007-02-01

Thomas Bessell Kidner is well-known in the United States as a great contributor to occupational therapy. He is not well-known in Canada despite the fact that his first contributions to the profession were made here between 1900 and 1918. To tell the story of Thomas Bessell Kidner and his impact on occupational therapy. Interpretive biography research methods using archival materials, published papers and family papers. Kidner's work as an organizer of manual training in elementary schools in Nova Scotia and New Brunswick and as Director of Technical Education for Calgary prepared him for his work as Vocational Secretary of the Military Hospitals Commission during World War I. Kidner developed, implemented and oversaw the reeducation program for injured soldiers across Canada. It included bedside occupations, off-ward and curative workshop activities provided by ward aides, as well as industrial training and apprenticeships in the workplace. Kidner's story stimulates us to revisit our profession's early emphasis on return-to-work. Knowing about our past helps occupational therapists to build a stronger identity.

Generalized spheroidal wave equation and limiting cases

NASA Astrophysics Data System (ADS)

Figueiredo, B. D. Bonorino

2007-01-01

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed.

Noise normalization and windowing functions for VALIDAR in wind parameter estimation

NASA Astrophysics Data System (ADS)

Beyon, Jeffrey Y.; Koch, Grady J.; Li, Zhiwen

2006-05-01

The wind parameter estimates from a state-of-the-art 2-μm coherent lidar system located at NASA Langley, Virginia, named VALIDAR (validation lidar), were compared after normalizing the noise by its estimated power spectra via the periodogram and the linear predictive coding (LPC) scheme. The power spectra and the Doppler shift estimates were the main parameter estimates for comparison. Different types of windowing functions were implemented in VALIDAR data processing algorithm and their impact on the wind parameter estimates was observed. Time and frequency independent windowing functions such as Rectangular, Hanning, and Kaiser-Bessel and time and frequency dependent apodized windowing function were compared. The briefing of current nonlinear algorithm development for Doppler shift correction subsequently follows.

Some More Solutions of Burgers' Equation

NASA Astrophysics Data System (ADS)

Kumar, Mukesh; Kumar, Raj

2015-01-01

In this work, similarity solutions of viscous one-dimensional Burgers' equation are attained by using Lie group theory. The symmetry generators are used for constructing Lie symmetries with commuting infinitesimal operators which lead the governing partial differential equation (PDE) to ordinary differential equation (ODE). Most of the constructed solutions are found in terms of Bessel functions which are new as far as authors are aware. Effect of various parameters in the evolutional profile of the solutions are shown graphically and discussed them physically.

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pabst, M., E-mail: M.Pabst@fz-juelich.de

2014-06-14

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10{sup −4} so the Fourier-Bessel series can be approximatedmore » by elementary functions. The time development of the system is characterized by two time constants, τ{sub c} and τ{sub g}. The constant τ{sub c} describes the approach to the stationary state of the total charge and the potential. τ{sub c} is several orders of magnitude smaller than the geometry-dependent constant τ{sub g}, which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.« less

Rapid and efficient formation of propagation invariant shaped laser beams.

PubMed

Chriki, Ronen; Barach, Gilad; Tradosnky, Chene; Smartsev, Slava; Pal, Vishwa; Friesem, Asher A; Davidson, Nir

2018-02-19

A rapid and efficient all-optical method for forming propagation invariant shaped beams by exploiting the optical feedback of a laser cavity is presented. The method is based on the modified degenerate cavity laser (MDCL), which is a highly incoherent cavity laser. The MDCL has a very large number of degrees of freedom (320,000 modes in our system) that can be coupled and controlled, and allows direct access to both the real space and Fourier space of the laser beam. By inserting amplitude masks into the cavity, constraints can be imposed on the laser in order to obtain minimal loss solutions that would optimally lead to a superposition of Bessel-Gauss beams forming a desired shaped beam. The resulting beam maintains its transverse intensity distribution for relatively long propagation distances.

Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping.

PubMed

Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan

2012-02-15

Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.

Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.

PubMed

Porras, Miguel A; Ramos, Francisco

2017-09-01

The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.

Non-linear optical measurements using a scanned, Bessel beam

NASA Astrophysics Data System (ADS)

Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.

2015-03-01

Oftentimes cells are removed from the body for disease diagnosis or cellular research. This typically requires fluorescent labeling followed by sorting with a flow cytometer; however, possible disruption of cellular function or even cell death due to the presence of the label can occur. This may be acceptable for ex vivo applications, but as cells are more frequently moving from the lab to the body, label-free methods of cell sorting are needed to eliminate these issues. This is especially true of the growing field of stem cell research where specialized cells are needed for treatments. Because differentiation processes are not completely efficient, cells must be sorted to eliminate any unwanted cells (i.e. un-differentiated or differentiated into an unwanted cell type). In order to perform label-free measurements, non-linear optics (NLO) have been increasingly utilized for single cell analysis because of their ability to not disrupt cellular function. An optical system was developed for the measurement of NLO in a microfluidic channel similar to a flow cytometer. In order to improve the excitation efficiency of NLO, a scanned Bessel beam was utilized to create a light-sheet across the channel. The system was tested by monitoring twophoton fluorescence from polystyrene microbeads of different sizes. Fluorescence intensity obtained from light-sheet measurements were significantly greater than measurements made using a static Gaussian beam. In addition, the increase in intensity from larger sized beads was more evident for the light-sheet system.

SIG. Signal Processing, Analysis, & Display

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez, J.; Lager, D.; Azevedo, S.

1992-01-22

SIG is a general-purpose signal processing, analysis, and display program. Its main purpose is to perform manipulations on time and frequency-domain signals. However, it has been designed to ultimately accommodate other representations for data such as multiplexed signals and complex matrices. Two user interfaces are provided in SIG; a menu mode for the unfamiliar user and a command mode for more experienced users. In both modes errors are detected as early as possible and are indicated by friendly, meaningful messages. An on-line HELP package is also included. A variety of operations can be performed on time and frequency-domain signals includingmore » operations on the samples of a signal, operations on the entire signal, and operations on two or more signals. Signal processing operations that can be performed are digital filtering (median, Bessel, Butterworth, and Chebychev), ensemble average, resample, auto and cross spectral density, transfer function and impulse response, trend removal, convolution, Fourier transform and inverse window functions (Hamming, Kaiser-Bessel), simulation (ramp, sine, pulsetrain, random), and read/write signals. User definable signal processing algorithms are also featured. SIG has many options including multiple commands per line, command files with arguments, commenting lines, defining commands, and automatic execution for each item in a `repeat` sequence. Graphical operations on signals and spectra include: x-y plots of time signals; real, imaginary, magnitude, and phase plots of spectra; scaling of spectra for continuous or discrete domain; cursor zoom; families of curves; and multiple viewports.« less

SIG. Signal Processing, Analysis, & Display

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez, J.; Lager, D.; Azevedo, S.

1992-01-22

SIG is a general-purpose signal processing, analysis, and display program. Its main purpose is to perform manipulations on time-and frequency-domain signals. However, it has been designed to ultimately accommodate other representations for data such as multiplexed signals and complex matrices. Two user interfaces are provided in SIG - a menu mode for the unfamiliar user and a command mode for more experienced users. In both modes errors are detected as early as possible and are indicated by friendly, meaningful messages. An on-line HELP package is also included. A variety of operations can be performed on time and frequency-domain signals includingmore » operations on the samples of a signal, operations on the entire signal, and operations on two or more signals. Signal processing operations that can be performed are digital filtering (median, Bessel, Butterworth, and Chebychev), ensemble average, resample, auto and cross spectral density, transfer function and impulse response, trend removal, convolution, Fourier transform and inverse window functions (Hamming, Kaiser-Bessel), simulation (ramp, sine, pulsetrain, random), and read/write signals. User definable signal processing algorithms are also featured. SIG has many options including multiple commands per line, command files with arguments, commenting lines, defining commands, and automatic execution for each item in a repeat sequence. Graphical operations on signals and spectra include: x-y plots of time signals; real, imaginary, magnitude, and phase plots of spectra; scaling of spectra for continuous or discrete domain; cursor zoom; families of curves; and multiple viewports.« less

Signal Processing, Analysis, & Display

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lager, Darrell; Azevado, Stephen

1986-06-01

SIG is a general-purpose signal processing, analysis, and display program. Its main purpose is to perform manipulations on time- and frequency-domain signals. However, it has been designed to ultimately accommodate other representations for data such as multiplexed signals and complex matrices. Two user interfaces are provided in SIG - a menu mode for the unfamiliar user and a command mode for more experienced users. In both modes errors are detected as early as possible and are indicated by friendly, meaningful messages. An on-line HELP package is also included. A variety of operations can be performed on time- and frequency-domain signalsmore » including operations on the samples of a signal, operations on the entire signal, and operations on two or more signals. Signal processing operations that can be performed are digital filtering (median, Bessel, Butterworth, and Chebychev), ensemble average, resample, auto and cross spectral density, transfer function and impulse response, trend removal, convolution, Fourier transform and inverse window functions (Hamming, Kaiser-Bessel), simulation (ramp, sine, pulsetrain, random), and read/write signals. User definable signal processing algorithms are also featured. SIG has many options including multiple commands per line, command files with arguments,commenting lines, defining commands, and automatic execution for each item in a repeat sequence. Graphical operations on signals and spectra include: x-y plots of time signals; real, imaginary, magnitude, and phase plots of spectra; scaling of spectra for continuous or discrete domain; cursor zoom; families of curves; and multiple viewports.« less

SIG. Signal Processing, Analysis, & Display

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez, J.; Lager, D.; Azevedo, S.

1992-01-22

SIG is a general-purpose signal processing, analysis, and display program. Its main purpose is to perform manipulations on time- and frequency-domain signals. However, it has been designed to ultimately accommodate other representations for data such as multiplexed signals and complex matrices. Two user interfaces are provided in SIG - a menu mode for the unfamiliar user and a command mode for more experienced users. In both modes errors are detected as early as possible and are indicated by friendly, meaningful messages. An on-line HELP package is also included. A variety of operations can be performed on time- and frequency-domain signalsmore » including operations on the samples of a signal, operations on the entire signal, and operations on two or more signals. Signal processing operations that can be performed are digital filtering (median, Bessel, Butterworth, and Chebychev), ensemble average, resample, auto and cross spectral density, transfer function and impulse response, trend removal, convolution, Fourier transform and inverse window functions (Hamming, Kaiser-Bessel), simulation (ramp, sine, pulsetrain, random), and read/write signals. User definable signal processing algorithms are also featured. SIG has many options including multiple commands per line, command files with arguments,commenting lines, defining commands, and automatic execution for each item in a repeat sequence. Graphical operations on signals and spectra include: x-y plots of time signals; real, imaginary, magnitude, and phase plots of spectra; scaling of spectra for continuous or discrete domain; cursor zoom; families of curves; and multiple viewports.« less

Imaging of trabecular meshwork using Bessel-Gauss light sheet with fluorescence

NASA Astrophysics Data System (ADS)

Jie Jeesmond Hong, Xun; Shinoj, V. K.; Murukeshan, V. M.; Baskaran, M.; Aung, Tin

2017-03-01

Ocular imaging technology that holds promise for both fundamental investigation and clinical detection of glaucoma is still a challenging research area. A direct view of the trabecular meshwork (TM) with high resolution is not generally possible because the iridocorneal angle region is obstructed by the sclera overlap. The best approach to observe the aqueous outflow system (AOS) is therefore to view from the opposite angle. In this research work, we developed two imaging systems for the high resolution ex vivo studies of the AOS inside porcine eye, based on a Gaussian illuminated and a digitally scanned Bessel-Gauss beam light sheet fluorescence configurations. The digitally scanned Bessel-Gauss beam is able to overcome the trade-off between the length and thickness of the Gaussian light sheet to give better imaging performance. It has adequate spatial resolution to resolve critical anatomical structures such as the TM, thereby enabling objective information about the AOS. This non-contact and non-invasive imaging methodology with excellent safety profile is expected to be well received by vision researchers and clinicians in the evaluation and management of glaucoma.

Negative radiation forces and the asymmetry of scattered radiation: spheres in Bessel beams

NASA Astrophysics Data System (ADS)

Marston, Philip L.; Zhang, Likun

2011-11-01

The discovery that acoustical and optical, radiation forces computed on spheres placed on the axis of acoustical and optical Bessel beams may be opposite the direction of beam propagation makes it appropriate to reexamine the relationship between radiation forces and the asymmetry of the scattered radiation. For all of the previously identified acoustical cases in which the force was negative and the scattering pattern was also computed, it was found that the backscattering was suppressed and the forward scattering relatively enhanced (see e.g.). In the present research the acoustic radiation force on an arbitrary isotropic sphere is related to the asymmetry in the scattering and the extinction introduced by the sphere for the case of a helical Bessel beam of arbitrary order. The analysis confirms that conditions are more favorable for generating negative forces when the asymmetry is such that the backscattering is suppressed relative to the forward scattering. It is also found, however, that absorption of power by the sphere gives rise to a positive force contribution, a term which has been neglected in the corresponding optical analysis.

Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces

DOE Office of Scientific and Technical Information (OSTI.GOV)

David, Grégory; Esat, Kıvanç; Hartweg, Sebastian

We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance formore » the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.« less

Radiation torque on an absorptive spherical drop centered on an acoustic helicoidal Bessel beam

NASA Astrophysics Data System (ADS)

Zhang, Likun; Marston, Philip L.

2009-11-01

Circularly polarized electromagnetic waves carry axial angular momentum and analysis shows that the axial radiation torque on an illuminated sphere is proportional to the power absorbed by the sphere [1]. Helicoidal acoustic beams also carry axial angular momentum and absorption of such a beam should also produce an axial radiation torque [2]. In the present work the acoustic radiation torque on solid spheres and spherical drops centered on acoustic helicoidal Bessel beams is examined. The torque is predicted to be proportional to the ratio of the absorbed power to the acoustic frequency. Depending on the beam helicity, the torque is parallel or anti-parallel to the beam axis. The analysis uses a relation between the scattering and the partial wave coefficients for a sphere in a helicoidal Bessel beam. Calculations suggest that beams with a low topological charge are more efficient for generating torques on solid spheres.[4pt] [1] P. L. Marston and J. H. Crichton, Phys. Rev. A. 30, 2508-2516 (1984).[0pt] [2] B. T. Hefner and P. L. Marston, J. Acoust. Soc. Am. 106, 3313-3316 (1999).

Negative radiation forces on spheres illuminated by acoustic Bessel beams.

NASA Astrophysics Data System (ADS)

Marston, Philip L.; Thiessen, David B.

2007-11-01

An analytical solution for the scattering of an acoustic Bessel beam by a sphere centered on the beam has made it possible to explore the way the acoustic radiation force on elastic and fluid spheres depends on beam and material parameters. Situations have been previously noted where, even in the absence of absorption, the radiation force of the beam on the sphere is opposite the direction of beam propagation [1]. In extensions of that work, conditions have been identified for such a force reversal on solid spheres and elastic shells. Negative radiation forces may be useful for manipulation of objects in reduced gravity and of biological cells (with single beam acoustic tweezers). The finite element method (FEM) has been used to evaluate the total acoustic field in the region near the sphere. This makes it possible to evaluate the radiation force from numerical integration of an appropriate projection of the Brillouin radiation stress tensor. FEM and analytical results agree for plane wave and Bessel beam illumination. 1. P. L. Marston, J. Acoust. Soc. Am. 120, 3518-3524 (2006).

Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel.

PubMed

Zhao, Cunlu; Yang, Chun

2013-03-01

EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Simple and efficient LCAO basis sets for the diffuse states in carbon nanostructures.

PubMed

Papior, Nick R; Calogero, Gaetano; Brandbyge, Mads

2018-06-27

We present a simple way to describe the lowest unoccupied diffuse states in carbon nanostructures in density functional theory calculations using a minimal LCAO (linear combination of atomic orbitals) basis set. By comparing plane wave basis calculations, we show how these states can be captured by adding long-range orbitals to the standard LCAO basis sets for the extreme cases of planar sp 2 (graphene) and curved carbon (C 60 ). In particular, using Bessel functions with a long range as additional basis functions retain a minimal basis size. This provides a smaller and simpler atom-centered basis set compared to the standard pseudo-atomic orbitals (PAOs) with multiple polarization orbitals or by adding non-atom-centered states to the basis.

Simple and efficient LCAO basis sets for the diffuse states in carbon nanostructures

NASA Astrophysics Data System (ADS)

Papior, Nick R.; Calogero, Gaetano; Brandbyge, Mads

2018-06-01

We present a simple way to describe the lowest unoccupied diffuse states in carbon nanostructures in density functional theory calculations using a minimal LCAO (linear combination of atomic orbitals) basis set. By comparing plane wave basis calculations, we show how these states can be captured by adding long-range orbitals to the standard LCAO basis sets for the extreme cases of planar sp 2 (graphene) and curved carbon (C60). In particular, using Bessel functions with a long range as additional basis functions retain a minimal basis size. This provides a smaller and simpler atom-centered basis set compared to the standard pseudo-atomic orbitals (PAOs) with multiple polarization orbitals or by adding non-atom-centered states to the basis.

Orientational analysis of planar fibre systems observed as a Poisson shot-noise process.

PubMed

Kärkkäinen, Salme; Lantuéjoul, Christian

2007-10-01

We consider two-dimensional fibrous materials observed as a digital greyscale image. The problem addressed is to estimate the orientation distribution of unobservable thin fibres from a greyscale image modelled by a planar Poisson shot-noise process. The classical stereological approach is not straightforward, because the point intensities of thin fibres along sampling lines may not be observable. For such cases, Kärkkäinen et al. (2001) suggested the use of scaled variograms determined from grey values along sampling lines in several directions. Their method is based on the assumption that the proportion between the scaled variograms and point intensities in all directions of sampling lines is constant. This assumption is proved to be valid asymptotically for Boolean models and dead leaves models, under some regularity conditions. In this work, we derive the scaled variogram and its approximations for a planar Poisson shot-noise process using the modified Bessel function. In the case of reasonable high resolution of the observed image, the scaled variogram has an approximate functional relation to the point intensity, and in the case of high resolution the relation is proportional. As the obtained relations are approximative, they are tested on simulations. The existing orientation analysis method based on the proportional relation is further experimented on images with different resolutions. The new result, the asymptotic proportionality between the scaled variograms and the point intensities for a Poisson shot-noise process, completes the earlier results for the Boolean models and for the dead leaves models.

Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime.

PubMed

Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E

2010-11-08

Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geometrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n|>1 to |n|<1, thus revealing new and interesting trapping properties.

An optical tweezer in asymmetrical vortex Bessel-Gaussian beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotlyar, V. V.; Kovalev, A. A., E-mail: alexeysmr@mail.ru; Porfirev, A. P.

We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.

Scintillation analysis of pseudo-Bessel-Gaussian Schell-mode beams propagating through atmospheric turbulence with wave optics simulation

NASA Astrophysics Data System (ADS)

Zheng, Guo; Wang, Jue; Wang, Lin; Zhou, Muchun; Chen, Yanru; Song, Minmin

2018-03-01

The scintillation index of pseudo-Bessel-Gaussian Schell-mode (PBGSM) beams propagating through atmospheric turbulence is analyzed with the help of wave optics simulation due to the analytic difficulties. It is found that in the strong fluctuation regime, the PBGSM beams are more resistant to the turbulence with the appropriate parameters β and δ . However, the case is contrary in the weak fluctuation regime. Our simulation results indicate that the PBGSM beams may be applied to free-space optical (FSO) communication systems only when the turbulence is strong or the propagation distance is long.

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.

1983-01-01

Use of previously coded and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main progress. The probability distributions provided include the beta, chi-square, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F. Other mathematical functions include the Bessel function, I sub o, gamma and log-gamma functions, error functions, and exponential integral. Auxiliary services include sorting and printer-plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.H.

1980-01-01

Use of previously codes and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main programs. The probability distributions provided include the beta, chisquare, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F tests. Other mathematical functions include the Bessel function I (subzero), gamma and log-gamma functions, error functions and exponential integral. Auxiliary services include sorting and printer plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Optical tractor Bessel polarized beams

NASA Astrophysics Data System (ADS)

Mitri, F. G.; Li, R. X.; Guo, L. X.; Ding, C. Y.

2017-01-01

Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.

Probing neural tissue with airy light-sheet microscopy: investigation of imaging performance at depth within turbid media

NASA Astrophysics Data System (ADS)

Nylk, Jonathan; McCluskey, Kaley; Aggarwal, Sanya; Tello, Javier A.; Dholakia, Kishan

2017-02-01

Light-sheet microscopy (LSM) has received great interest for fluorescent imaging applications in biomedicine as it facilitates three-dimensional visualisation of large sample volumes with high spatiotemporal resolution whilst minimising irradiation of, and photo-damage to the specimen. Despite these advantages, LSM can only visualize superficial layers of turbid tissues, such as mammalian neural tissue. Propagation-invariant light modes have played a key role in the development of high-resolution LSM techniques as they overcome the natural divergence of a Gaussian beam, enabling uniform and thin light-sheets over large distances. Most notably, Bessel and Airy beam-based light-sheet imaging modalities have been demonstrated. In the single-photon excitation regime and in lightly scattering specimens, Airy-LSM has given competitive performance with advanced Bessel-LSM techniques. Airy and Bessel beams share the property of self-healing, the ability of the beam to regenerate its transverse beam profile after propagation around an obstacle. Bessel-LSM techniques have been shown to increase the penetration-depth of the illumination into turbid specimens but this effect has been understudied in biologically relevant tissues, particularly for Airy beams. It is expected that Airy-LSM will give a similar enhancement over Gaussian-LSM. In this paper, we report on the comparison of Airy-LSM and Gaussian-LSM imaging modalities within cleared and non-cleared mouse brain tissue. In particular, we examine image quality versus tissue depth by quantitative spatial Fourier analysis of neural structures in virally transduced fluorescent tissue sections, showing a three-fold enhancement at 50 μm depth into non-cleared tissue with Airy-LSM. Complimentary analysis is performed by resolution measurements in bead-injected tissue sections.

Characterization of microwave plasma in a multicusp using 2D emission based tomography: Bessel modes and wave absorption

NASA Astrophysics Data System (ADS)

Rathore, Kavita; Bhattacharjee, Sudeep; Munshi, Prabhat

2017-06-01

A tomographic method based on the Fourier transform is used for characterizing a microwave plasma in a multicusp (MC), in order to obtain 2D distribution of plasma emissions, plasma (electron) density (Ne) and temperature (Te). The microwave plasma in the MC is characterized as a function of microwave power, gas pressure, and axial distance. The experimentally obtained 2D emission profiles show that the plasma emissions are generated in a circular ring shape. There are usually two bright rings, one at the plasma core and another near the boundary. The experimental results are validated using a numerical code that solves Maxwell's equations inside a waveguide filled with a plasma in a magnetic field, with collisions included. It is inferred that the dark and bright circular ring patterns are a result of superposition of Bessel modes (TE11 and TE21) of the wave electric field inside the plasma filled MC, which are in reasonable agreement with the plasma emission profiles. The tomographically obtained Ne and Te profiles indicate higher densities in the plasma core (˜1010 cm-3) and enhanced electron temperature in the ECR region (˜13 eV), which are in agreement with earlier results using a Langmuir probe and optical emission spectroscopy (OES) diagnostics.

Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging.

PubMed

Thériault, Gabrielle; Cottet, Martin; Castonguay, Annie; McCarthy, Nathalie; De Koninck, Yves

2014-01-01

Two-photon microscopy has revolutionized functional cellular imaging in tissue, but although the highly confined depth of field (DOF) of standard set-ups yields great optical sectioning, it also limits imaging speed in volume samples and ease of use. For this reason, we recently presented a simple and retrofittable modification to the two-photon laser-scanning microscope which extends the DOF through the use of an axicon (conical lens). Here we demonstrate three significant benefits of this technique using biological samples commonly employed in the field of neuroscience. First, we use a sample of neurons grown in culture and move it along the z-axis, showing that a more stable focus is achieved without compromise on transverse resolution. Second, we monitor 3D population dynamics in an acute slice of live mouse cortex, demonstrating that faster volumetric scans can be conducted. Third, we acquire a stereoscopic image of neurons and their dendrites in a fixed sample of mouse cortex, using only two scans instead of the complete stack and calculations required by standard systems. Taken together, these advantages, combined with the ease of integration into pre-existing systems, make the extended depth-of-field imaging based on Bessel beams a strong asset for the field of microscopy and life sciences in general.

Bessel Fourier Orientation Reconstruction (BFOR): An Analytical Diffusion Propagator Reconstruction for Hybrid Diffusion Imaging and Computation of q-Space Indices

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Alexander, Andrew L.

2012-01-01

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier orientation reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA). PMID:22963853

Lommel modes

NASA Astrophysics Data System (ADS)

Kovalev, Alexey A.; Kotlyar, Victor V.

2015-03-01

We study a non-paraxial family of nondiffracting laser beams whose complex amplitude is proportional to an n-th order Lommel function of two variables. These beams are referred to as Lommel modes. Explicit analytical relations for the angular spectrum of plane waves and orbital angular momentum of the Lommel beams have been derived. The even (n=2p) and odd (n=2p+1) Lommel modes are mutually orthogonal, as are the Lommel modes characterized by different projections of the wave vector on the optical axis. At a definite parameter, the Lommel modes change to conventional Bessel beams. Asymmetry of the Lommel modes depends on a complex parameter с, with its modulus in the polar notation defining the intensity pattern in the beam‧s cross-section and the argument defining the angle of rotation of the intensity pattern about the optical axis. If the parameter с is real or purely imaginary, the transverse intensity component of the Lommel modes is specularly symmetric about the Cartesian coordinate axes. Besides, with the modulus of the с parameter increasing from 0 to 1, the orbital angular momentum of the Lommel modes increases from a finite value proportional to the topological charge n to infinity. The orbital angular momentum of the Lommel modes undergoes continuous variations, in contrast to its discrete changes in the Bessel modes.

Analytical description of lateral binding force exerted on bi-sphere induced by high-order Bessel beams

NASA Astrophysics Data System (ADS)

Bai, J.; Wu, Z. S.; Ge, C. X.; Li, Z. J.; Qu, T.; Shang, Q. C.

2018-07-01

Based on the generalized multi-particle Mie equation (GMM) and Electromagnetic Momentum (EM) theory, the lateral binding force (BF) exerted on bi-sphere induced by an arbitrary polarized high-order Bessel beam (HOBB) is investigated with particular emphasis on the half-conical angle of the wave number components and the order (or topological charge) of the beam. The illuminating HOBB with arbitrary polarization angle is described in terms of beam shape coefficients (BSCs) within the framework of generalized Lorenz-Mie theories (GLMT). Utilizing the vector addition theorem of the spherical vector wave functions (SVWFs), the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the bi-sphere is considered. Numerical effects of various parameters such as beam polarization angles, incident wavelengths, particle sizes, material losses and the refractive index, including the cases of weak, moderate, and strong than the surrounding medium are numerically analyzed in detail. The observed dependence of the separation of optically bound particles on the incidence of HOBB is in agreement with earlier theoretical prediction. Accurate investigation of BF induced by HOBB could provide an effective test for further research on BF between more complex particles, which plays an important role in using optical manipulation on particle self-assembly.

Optical theorem for acoustic non-diffracting beams and application to radiation force and torque

PubMed Central

Zhang, Likun; Marston, Philip L.

2013-01-01

Acoustical and optical non-diffracting beams are potentially useful for manipulating particles and larger objects. An extended optical theorem for a non-diffracting beam was given recently in the context of acoustics. The theorem relates the extinction by an object to the scattering at the forward direction of the beam’s plane wave components. Here we use this theorem to examine the extinction cross section of a sphere centered on the axis of the beam, with a non-diffracting Bessel beam as an example. The results are applied to recover the axial radiation force and torque on the sphere by the Bessel beam. PMID:24049681

Optical reprogramming of human somatic cells using ultrashort Bessel-shaped near-infrared femtosecond laser pulses

NASA Astrophysics Data System (ADS)

Uchugonova, Aisada; Breunig, Hans Georg; Batista, Ana; König, Karsten

2015-11-01

We report a virus-free optical approach to human cell reprogramming into induced pluripotent stem cells with low-power nanoporation using ultrashort Bessel-shaped laser pulses. Picojoule near-infrared sub-20 fs laser pulses at a high 85 MHz repetition frequency are employed to generate transient nanopores in the membrane of dermal fibroblasts for the introduction of four transcription factors to induce the reprogramming process. In contrast to conventional approaches which utilize retro- or lentiviruses to deliver genes or transcription factors into the host genome, the laser method is virus-free; hence, the risk of virus-induced cancer generation limiting clinical application is avoided.

Bessel Plasmon-Polaritons at the Boundaries of Metamaterials with Near-Zero Dielectric Constants

NASA Astrophysics Data System (ADS)

Kurilkina, S. N.; Belyi, V. N.; Kazak, N. S.; Binhussain, M. A.

2015-07-01

The conditions for and features of the excitation of Bessel plasmon-polaritons (BPP) are examined at the boundary of a hyperbolic metamaterial with a near-zero dielectric constant made of a dielectric matrix with metal nanorods embedded in it normal to its surface. This material is compared with BPP that have traditional surface plasmons. The effect of the absorption of the metamaterial on the excitation of BPP is studied. The possibility of changes in the direction of the radial energy fl ows in BPP excited at the surface of an isotropic medium, a hyperbolic metamaterial, is demonstrated and the conditions for these changes are determined.

VizieR Online Data Catalog: WASP-22, WASP-41, WASP-42, WASP-55 (Southworth+, 2016)

NASA Astrophysics Data System (ADS)

Southworth, J.; Tregloan-Reed, J.; Andersen, M. I.; Calchi Novati, S.; Ciceri, S.; Colque, J. P.; D'Ago, G.; Dominik, M.; Evans, D. F.; Gu, S.-H.; Herrera-Cordova, A.; Hinse, T. C.; Jorgensen, U. G.; Juncher, D.; Kuffmeier, M.; Mancini, L.; Peixinho, N.; Popovas, A.; Rabus, M.; Skottfelt, J.; Tronsgaard, R.; Unda-Sanzana, E.; Wang, X.-B.; Wertz, O.; Alsubai, K. A.; Andersen, J. M.; Bozza, V.; Bramich, D. M.; Burgdorf, M.; Damerdji, Y.; Diehl, C.; Elyiv, A.; Figuera Jaimes, R.; Haugbolle, T.; Hundertmark, M.; Kains, N.; Kerins, E.; Korhonen, H.; Liebig, C.; Mathiasen, M.; Penny, M. T.; Rahvar, S.; Scarpetta, G.; Schmidt, R. W.; Snodgrass, C.; Starkey, D.; Surdej, J.; Vilela, C.; von Essen, C.; Wang, Y.

2018-05-01

17 light curves of transits of the extrasolar planetary systems WASP-22, WASP-41, WASP-42 and WASP-55 are presented. 13 of the light curves were obtained using the Danish 1.54m telescope at ESO La Silla, Chile, in the Bessell R or Bessell I passbands. The other 4 light curves were obtained using the 84cm telescope at Observatorio Cerro Armazones, Chile, using either an R filter or no filter. The errorbars for each transit have been scaled so the best-fitting model (obtained using the JKTEBOP code) has a reduced chi-squared value of 1.0. (4 data files).

Optimization of laser energy deposition for single-shot high aspect-ratio microstructuring of thick BK7 glass

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garzillo, Valerio; Grigutis, Robertas; Jukna, Vytautas

We investigate the generation of high aspect ratio microstructures across 0.7 mm thick glass by means of single shot Bessel beam laser direct writing. We study the effect on the photoinscription of the cone angle, as well as of the energy and duration of the ultrashort laser pulse. The aim of the study is to optimize the parameters for the writing of a regular microstructure due to index modification along the whole sample thickness. By using a spectrally resolved single pulse transmission diagnostics at the output surface of the glass, we correlate the single shot material modification with observations of themore » absorption in different portions of the retrieved spectra, and with the absence or presence of spectral modulation. Numerical simulations of the evolution of the Bessel pulse intensity and of the energy deposition inside the sample help us interpret the experimental results that suggest to use picosecond pulses for an efficient and more regular energy deposition. Picosecond pulses take advantage of nonlinear plasma absorption and avoid temporal dynamics effects which can compromise the stationarity of the Bessel beam propagation.« less

Bessel light sheet structured illumination microscopy

NASA Astrophysics Data System (ADS)

Noshirvani Allahabadi, Golchehr

Biomedical study researchers using animals to model disease and treatment need fast, deep, noninvasive, and inexpensive multi-channel imaging methods. Traditional fluorescence microscopy meets those criteria to an extent. Specifically, two-photon and confocal microscopy, the two most commonly used methods, are limited in penetration depth, cost, resolution, and field of view. In addition, two-photon microscopy has limited ability in multi-channel imaging. Light sheet microscopy, a fast developing 3D fluorescence imaging method, offers attractive advantages over traditional two-photon and confocal microscopy. Light sheet microscopy is much more applicable for in vivo 3D time-lapsed imaging, owing to its selective illumination of tissue layer, superior speed, low light exposure, high penetration depth, and low levels of photobleaching. However, standard light sheet microscopy using Gaussian beam excitation has two main disadvantages: 1) the field of view (FOV) of light sheet microscopy is limited by the depth of focus of the Gaussian beam. 2) Light-sheet images can be degraded by scattering, which limits the penetration of the excitation beam and blurs emission images in deep tissue layers. While two-sided sheet illumination, which doubles the field of view by illuminating the sample from opposite sides, offers a potential solution, the technique adds complexity and cost to the imaging system. We investigate a new technique to address these limitations: Bessel light sheet microscopy in combination with incoherent nonlinear Structured Illumination Microscopy (SIM). Results demonstrate that, at visible wavelengths, Bessel excitation penetrates up to 250 microns deep in the scattering media with single-side illumination. Bessel light sheet microscope achieves confocal level resolution at a lateral resolution of 0.3 micron and an axial resolution of 1 micron. Incoherent nonlinear SIM further reduces the diffused background in Bessel light sheet images, resulting in confocal quality images in thick tissue. The technique was applied to live transgenic zebra fish tg(kdrl:GFP), and the sub-cellular structure of fish vasculature genetically labeled with GFP was captured in 3D. The superior speed of the microscope enables us to acquire signal from 200 layers of a thick sample in 4 minutes. The compact microscope uses exclusively off-the-shelf components and offers a low-cost imaging solution for studying small animal models or tissue samples.

Elliptic integral evaluations of Bessel moments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

2008-01-06

We record what is known about the closed forms for variousBessel function moments arising in quantum field theory, condensed mattertheory and other parts of mathematical physics. More generally, wedevelop formulae for integrals of products of six or fewer Besselfunctions. In consequence, we are able to discover and prove closed formsfor c(n,k) := Int_0 inf tk K_0 n(t) dt, with integers n = 1, 2, 3, 4 andk greater than or equal to 0, obtaining new results for the even momentsc3,2k and c4,2k . We also derive new closed forms for the odd momentss(n,2k+1) := Int_0 inf t(2k+1) I_0(t) K_0n(t) dt,withmore » n = 3, 4 and fort(n,2k+1) := Int_0 inf t(2k+1) I_02(t) K_0(n-2) dt, with n = 5, relatingthe latter to Green functions on hexagonal, diamond and cubic lattices.We conjecture the values of s(5,2k+1), make substantial progress on theevaluation of c(5,2k+1), s(6,2k+1) and t(6,2k+1) and report more limitedprogress regarding c(5,2k), c(6,2k+1) and c(6,2k). In the process, weobtain 8 conjectural evaluations, each of which has been checked to 1200decimal places. One of these lies deep in 4-dimensional quantum fieldtheory and two are probably provable by delicate combinatorics. Thereremains a hard core of five conjectures whose proofs would be mostinstructive, to mathematicians and physicists alike.« less

Constant-roll tachyon inflation and observational constraints

NASA Astrophysics Data System (ADS)

Gao, Qing; Gong, Yungui; Fei, Qin

2018-05-01

For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio to the first order of epsilon1 by using the method of Bessel function approximation. The derived ns-r results are compared with the observations, we find that only the constant-roll inflation with ηH being a constant is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflation which is consistent with the observations.

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

NASA Astrophysics Data System (ADS)

Conway, John T.; Cohl, Howard S.

2010-06-01

A new method is presented for Fourier decomposition of the Helmholtz Green function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Green function are split into their half advanced + half retarded and half advanced-half retarded components, and closed form solutions for these components are then obtained in terms of a Horn function and a Kampé de Fériet function respectively. Series solutions for the Fourier coefficients are given in terms of associated Legendre functions, Bessel and Hankel functions and a hypergeometric function. These series are derived either from the closed form 2-dimensional hypergeometric solutions or from an integral representation, or from both. A simple closed form far-field solution for the general Fourier coefficient is derived from the Hankel series. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented. Fourth order ordinary differential equations for the Fourier coefficients are also given and discussed briefly.

Laguerre-Gaussian, Hermite-Gaussian, Bessel-Gaussian, and Finite-Energy Airy Beams Carrying Orbital Angular Momentum in Strongly Nonlocal Nonlinear Media

NASA Astrophysics Data System (ADS)

Wu, Zhenkun; Gu, Yuzong

2016-12-01

The propagation of two-dimensional beams is analytically and numerically investigated in strongly nonlocal nonlinear media (SNNM) based on the ABCD matrix. The two-dimensional beams reported in this paper are described by the product of the superposition of generalized Laguerre-Gaussian (LG), Hermite-Gaussian (HG), Bessel-Gaussian (BG), and circular Airy (CA) beams, carrying an orbital angular momentum (OAM). Owing to OAM and the modulation of SNNM, we find that the propagation of these two-dimensional beams exhibits complete rotation and periodic inversion: the spatial intensity profile first extends and then diminishes, and during the propagation the process repeats to form a breath-like phenomenon.

Subwavelength dark hollow focus of spirally polarized axisymmetric Bessel-modulated Gaussian beam

NASA Astrophysics Data System (ADS)

Gao, X. M.; Zhan, Q. F.; Wang, Q.; Yun, M. J.; Guo, H. M.; Zhuang, S. L.

2011-09-01

Dark hollow focus plays an important role in many optical systems. In this paper, dark hollow focal shaping of spirally polarized axisymmetric Bessel-modulated Gaussian beam is investigated by vector diffraction theory in detail. Results show that the dark hollow focus can be altered considerably by beam parameter and spiral parameter that indicates polarization spiral degree. One dark hollow focus and two dark hollow foci pattern may occur for certain spiral parameter, and the transverse size of dark hollow focus can be less than the diffraction limit size of bright focus. In addition, there may also appear two triangle dark hollow foci that are connected by one dark line focus.

High-efficiency generation of Bessel beams with transmissive metasurfaces

NASA Astrophysics Data System (ADS)

Wang, Zhuo; Dong, Shaohua; Luo, Weijie; Jia, Min; Liang, Zhongzhu; He, Qiong; Sun, Shulin; Zhou, Lei

2018-05-01

Circularly polarized Bessel beams (BBs) are important in biomolecule-sensing-related applications, but the available generators are too bulky in size and/or exhibit low efficiencies. Here, we design and fabricate ultra-thin ( ˜λ /6 ) transmissive Pancharatnam-Berry metasurfaces and perform near-field scanning measurements to show that they can generate circularly polarized BBs within a frequency window of 10.7-12.3 GHz. We experimentally demonstrate that the generated BBs exhibit a self-healing effect, illustrating their non-diffraction characteristics. Finally, we employ far-field measurements to demonstrate that the working efficiency of our devices can reach 91%, while the simulated efficiency reaches 92%. All experimental results are in perfect agreement with full-wave simulations.

Wave-optics description of self-healing mechanism in Bessel beams.

PubMed

Aiello, Andrea; Agarwal, Girish S

2014-12-15

Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.

Strehl ratio: a tool for optimizing optical nulls and singularities.

PubMed

Hénault, François

2015-07-01

In this paper a set of radial and azimuthal phase functions are reviewed that have a null Strehl ratio, which is equivalent to generating a central extinction in the image plane of an optical system. The study is conducted in the framework of Fraunhofer scalar diffraction, and is oriented toward practical cases where optical nulls or singularities are produced by deformable mirrors or phase plates. The identified solutions reveal unexpected links with the zeros of type-J Bessel functions of integer order. They include linear azimuthal phase ramps giving birth to an optical vortex, azimuthally modulated phase functions, and circular phase gratings (CPGs). It is found in particular that the CPG radiometric efficiency could be significantly improved by the null Strehl ratio condition. Simple design rules for rescaling and combining the different phase functions are also defined. Finally, the described analytical solutions could also serve as starting points for an automated searching software tool.

Fabrication of nanoparticles and nanostructures using ultrafast laser ablation of silver with Bessel beams

NASA Astrophysics Data System (ADS)

Krishna Podagatlapalli, G.; Hamad, Syed; Ahamad Mohiddon, Md; Venugopal Rao, S.

2015-03-01

Ablation of silver targets immersed in double distilled water (DDW)/acetone was performed with first order, non-diffracting Bessel beams generated by focusing ultrashort Gaussian pulses (~2 and ~40 fs) through an Axicon. The fabricated Ag dispersions were characterized by UV-visible absorption spectroscopy, transmission electron microscopy and the nanostructured Ag targets were characterized by field emission scanning electron microscopy. Ag colloids prepared with ~2 ps laser pulses at various input pulse energies of ~400, ~600, ~800 and ~1000 µJ demonstrated similar localized surface plasmon resonance (LSPR) peaks appearing near 407 nm. Analogous behavior was observed for Ag colloids prepared in acetone and ablated with ~40 fs pulses, wherein the LSPR peak was observed near 412 nm prepared with input energies of ~600, ~800 and ~1000 µJ. Observed parallels in LSPR peaks, average size of NPs, plasmon bandwidths are tentatively explained using cavitation bubble dynamics and simultaneous generation/fragmentation of NPs under the influence of Bessel beam. Fabricated Ag nanostructures in both the cases demonstrated strong enhancement factors (>106) in surface enhanced Raman scattering studies of the explosive molecule CL-20 (2,4,6,8,10,12-Hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane) at 5 μM concentration.

Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Mironov, V. A.; Skobelev, S. A.

2017-01-01

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the "kaleidoscopic" picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.

Optical force on a large sphere illuminated by Bessel beams: comparisons between ray optics method and generalized Lorenz-Mie theory.

PubMed

Song, Shukun; Wang, Neng; Lu, Wanli; Lin, Zhifang

2014-10-01

Optical forces are calculated for a dielectric spherical particle illuminated by a zero-order Bessel beam based on both the generalized Lorenz-Mie theory (GLMT) and the ray optics method (ROM). Particles with positive and negative refractive indices are examined. The peculiar characteristics of the Bessel beam allow for analytical expressions for the beam shape coefficients required in the GLMT as well as a decomposition of optical force into the gradient and the scattering forces irrespective of the particle size, which enable respective comparisons for the gradient and scattering forces between the results obtained from the GLMT and the ROM. Our results demonstrate that the discrepancy between the results obtained from the GLMT and the ROM depends on the particle refractive index n_p, the particle size, and, also, the particle location in the beam field. As the particle size increases, the difference between the results from the GLMT and the ROM shows a general tendency of decreasing, as can be expected, but the change may exhibit oscillatory rather than monotonic behavior. A phase diagram is presented that displays the regime for particle size and refractive index where a specified accuracy can be achieved for optical force by the ROM.

Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, A. A., E-mail: balakin.alexey@yandex.ru; Mironov, V. A.; Skobelev, S. A., E-mail: sk.sa1981@gmail.com

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wavemore » packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.« less

Q{sub 2} evolution of parton distributions at small values of x: Effective scale for combined H1 and ZEUS data on the structure function F{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotikov, A. V., E-mail: kotikov@theor.jinr.ru; Shaikhatdenov, B. G.

2015-06-15

An expression for the structure function F{sub 2} in the form of Bessel functions at small values of the Bjorken variable x is used. This expression was derived for a flat initial condition in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. The argument of the strong coupling constant was chosen in such a way as to annihilate the singular part of the anomalous dimensions in the next-to-leading-order of perturbation theory. This choice, together with the frozen and analytic versions of the strong coupling constant, is used to analyze combined data of the H1 and ZEUS Collaborations obtained recently for the structure functionmore » F{sub 2}.« less

Mathematical models of real geometrical factors in restricted blood vessels for the analysis of CAD (coronary artery diseases) using Legendre, Boubaker and Bessel polynomials.

PubMed

Awojoyogbe, O B; Faromika, O P; Dada, M; Boubaker, Karem; Ojambati, O S

2011-12-01

Most cardiovascular emergencies are directly caused by coronary artery disease. Coronary arteries can become clogged or occluded, leading to damage to the heart muscle supplied by the artery. Modem cardiovascular medicine can certainly be improved by meticulous analysis of geometrical factors closely associated with the degenerative disease that results in narrowing of the coronary arteries. There are, however, inherent difficulties in developing this type of mathematical models to completely describe the real or ideal geometries that are very critical in plaque formation and thickening of the vessel wall. Neither the mathematical models of the blood vessels with arthrosclerosis generated by the heart and blood flow or the NMR/MRI data to construct them are available. In this study, a mathematical formulation for the geometrical factors that are very critical for the understanding of coronary artery disease is presented. Based on the Bloch NMR flow equations, we derive analytical expressions to describe in detail the NMR transverse magnetizations and signals as a function of some NMR flow and geometrical parameters which are invaluable for the analysis of blood flow in restricted blood vessels. The procedure would apply to the situations in which the geometry of the fatty deposits, (plague) on the interior walls of the coronary arteries is spherical. The boundary conditions are introduced based on Bessel, Boubaker and Legendre polynomials.

Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging

PubMed Central

Thériault, Gabrielle; Cottet, Martin; Castonguay, Annie; McCarthy, Nathalie; De Koninck, Yves

2014-01-01

Two-photon microscopy has revolutionized functional cellular imaging in tissue, but although the highly confined depth of field (DOF) of standard set-ups yields great optical sectioning, it also limits imaging speed in volume samples and ease of use. For this reason, we recently presented a simple and retrofittable modification to the two-photon laser-scanning microscope which extends the DOF through the use of an axicon (conical lens). Here we demonstrate three significant benefits of this technique using biological samples commonly employed in the field of neuroscience. First, we use a sample of neurons grown in culture and move it along the z-axis, showing that a more stable focus is achieved without compromise on transverse resolution. Second, we monitor 3D population dynamics in an acute slice of live mouse cortex, demonstrating that faster volumetric scans can be conducted. Third, we acquire a stereoscopic image of neurons and their dendrites in a fixed sample of mouse cortex, using only two scans instead of the complete stack and calculations required by standard systems. Taken together, these advantages, combined with the ease of integration into pre-existing systems, make the extended depth-of-field imaging based on Bessel beams a strong asset for the field of microscopy and life sciences in general. PMID:24904284

Deep skin structural and microcirculation imaging with extended-focus OCT

NASA Astrophysics Data System (ADS)

Blatter, Cedric; Grajciar, Branislav; Huber, Robert; Leitgeb, Rainer A.

2012-02-01

We present an extended focus OCT system for dermatologic applications that maintains high lateral resolution over a large depth range by using Bessel beam illumination. More, Bessel beams exhibit a self-reconstruction property that is particularly useful to avoid shadowing from surface structures such as hairs. High lateral resolution and high-speed measurement, thanks to a rapidly tuning swept source, allows not only for imaging of small skin structures in depth but also for comprehensive visualization of the small capillary network within the human skin in-vivo. We use this information for studying temporal vaso-responses to hypothermia. In contrast to other perfusion imaging methods such as laser Doppler imaging (LDI), OCT gives specific access to vascular responses in different vascular beds in depth.

WGM resonators for studying orbital angular momentum of a photon, and methods

NASA Technical Reports Server (NTRS)

Matsko, Andrey B. (Inventor); Savchenkov, Anatoliy A. (Inventor); Maleki, Lute (Inventor); Strekalov, Dmitry V. (Inventor)

2009-01-01

An optical system, device, and method that are capable of generating high-order Bessel beams and determining the orbital angular momentum of at least one of the photons of a Bessel beam are provided. The optical system and device include a tapered waveguide having an outer surface defined by a diameter that varies along a longitudinal axis of the waveguide from a first end to an opposing second end. The optical system and device include a resonator that is arranged in optical communication with the first end of the tapered waveguide such that an evanescent field emitted from (i) the waveguide can be coupled with the resonator, or (ii) the resonator can be coupled with the waveguide.

On the efficiency of treating singularities in triatomic variational vibrational computations. The vibrational states of H(+)3 up to dissociation.

PubMed

Szidarovszky, Tamás; Császár, Attila G; Czakó, Gábor

2010-08-01

Several techniques of varying efficiency are investigated, which treat all singularities present in the triatomic vibrational kinetic energy operator given in orthogonal internal coordinates of the two distances-one angle type. The strategies are based on the use of a direct-product basis built from one-dimensional discrete variable representation (DVR) bases corresponding to the two distances and orthogonal Legendre polynomials, or the corresponding Legendre-DVR basis, corresponding to the angle. The use of Legendre functions ensures the efficient treatment of the angular singularity. Matrix elements of the singular radial operators are calculated employing DVRs using the quadrature approximation as well as special DVRs satisfying the boundary conditions and thus allowing for the use of exact DVR expressions. Potential optimized (PO) radial DVRs, based on one-dimensional Hamiltonians with potentials obtained by fixing or relaxing the two non-active coordinates, are also studied. The numerical calculations employed Hermite-DVR, spherical-oscillator-DVR, and Bessel-DVR bases as the primitive radial functions. A new analytical formula is given for the determination of the matrix elements of the singular radial operator using the Bessel-DVR basis. The usually claimed failure of the quadrature approximation in certain singular integrals is revisited in one and three dimensions. It is shown that as long as no potential optimization is carried out the quadrature approximation works almost as well as the exact DVR expressions. If wave functions with finite amplitude at the boundary are to be computed, the basis sets need to meet the required boundary conditions. The present numerical results also confirm that PO-DVRs should be constructed employing relaxed potentials and PO-DVRs can be useful for optimizing quadrature points for calculations applying large coordinate intervals and describing large-amplitude motions. The utility and efficiency of the different algorithms is demonstrated by the computation of converged near-dissociation vibrational energy levels for the H molecular ion.

A plasma model for reversed field pinch circuit design

NASA Astrophysics Data System (ADS)

Johnston, J. W.

1981-03-01

A plasma model has been developed for use in the design of circuits for reversed field pinch experiments. The magnetic field is assumed to evolve through a given series of relaxed states with the plasma resistivity specified as a function of time. At any instant the magnetic field configuration is determined by the field energy and the toroidal flux. If the Bessel function model is chosen as the relaxed state then the magnetic helicity can be used as an alternative to the magnetic energy without altering the results. Simulations of discharges on ZETA and ETA BETA II are presented. By suitable choices of the relaxed field configuration and plasma resistivity it is possible to obtain close agreement with the experimental waveforms. Application to the proposed RFX device is discussed.

A method for computing the kernel of the downwash integral equation for arbitrary complex frequencies

NASA Technical Reports Server (NTRS)

Desmarais, R. N.; Rowe, W. S.

1984-01-01

For the design of active controls to stabilize flight vehicles, which requires the use of unsteady aerodynamics that are valid for arbitrary complex frequencies, algorithms are derived for evaluating the nonelementary part of the kernel of the integral equation that relates unsteady pressure to downwash. This part of the kernel is separated into an infinite limit integral that is evaluated using Bessel and Struve functions and into a finite limit integral that is expanded in series and integrated termwise in closed form. The developed series expansions gave reliable answers for all complex reduced frequencies and executed faster than exponential approximations for many pressure stations.

A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers

NASA Astrophysics Data System (ADS)

Belafhal, A.; Ez-zariy, L.; Hricha, Z.

2016-11-01

By means of the expansion of the nondiffracting beams on plane waves with help of the Whittaker integral, an exact analytical expression of the far-field form function of the scattering of the acoustic and optical nondiffracting Lommel beams propagating in a medium containing spherical particles, considered as rigid and single spheres, is investigated in this work. The form function of the scattering of the high order Bessel beam by a rigid and isolated sphere is deduced, from our finding, as a special case. The effects of the wave number-sphere radius product (ka) , the polar angle (φ) , the propagation half-cone angle (β) and the scattering angle (θ) on the far-field form function of the scattered wave have been analyzed and discussed numerically. The numerical results show that the illumination of a rigid sphere by Lommel beams produces asymmetrical scattering.

Walk-off reduction, using an external optical plate and Bessel-Gaussian interaction

NASA Astrophysics Data System (ADS)

Masoume, Mansouri; Mohsen, Askarbioki; Saeed Ghavami, Sabouri; Alireza, Khorsandi

2015-02-01

To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type II KTiOPO4 and type I β-BaB2O4 optical crystals, and the Gaussian output beam of a Q-switched Nd:YAG laser, a simple theoretical model was developed based on a rotatable BK7 plate of variable thickness. By rotating the plate up to 35° along the beam direction, we reduced the walk-off angle up to ˜ 13%. The same phenomenon is predicted by the model, confirming the performance of the model. It is found that, due to the walk-off effect, the intensity profile of the third-harmonic generation beam is slightly degraded. To compensate for the observed phenomena and further reduce the walk-off, we used a combination of a convex lens and an axicon to transform the beam profile of the interacting fundamental and second-harmonic generation waves to the zero-order Bessel-Gaussian form. As a result, the walk-off is decreased to ˜48.81 mrad, providing ˜30% relative reduction. By using the same BK7 plate rotated up to 35° along the third-harmonic beam direction, the walk-off angle is further reduced to 38.9 mrad. Moreover, it is observed that the beam profile of the emerged Bessel-Gaussian third-harmonic generation beam remains unchanged with no degradation.

Implementation of Bessel's method for solar eclipses prediction in the WRF-ARW model

NASA Astrophysics Data System (ADS)

Montornes, Alex; Codina, Bernat; Zack, John W.; Sola, Yolanda

2016-05-01

Solar eclipses are predictable astronomical events that abruptly reduce the incoming solar radiation into the Earth's atmosphere, which frequently results in non-negligible changes in meteorological fields. The meteorological impacts of these events have been analyzed in many studies since the late 1960s. The recent growth in the solar energy industry has greatly increased the interest in providing more detail in the modeling of solar radiation variations in numerical weather prediction (NWP) models for the use in solar resource assessment and forecasting applications. The significant impact of the recent partial and total solar eclipses that occurred in the USA (23 October 2014) and Europe (20 March 2015) on solar power generation have provided additional motivation and interest for including these astronomical events in the current solar parameterizations.Although some studies added solar eclipse episodes within NWP codes in the 1990s and 2000s, they used eclipse parameterizations designed for a particular case study. In contrast to these earlier implementations, this paper documents a new package for the Weather Research and Forecasting-Advanced Research WRF (WRF-ARW) model that can simulate any partial, total or hybrid solar eclipse for the period 1950 to 2050 and is also extensible to a longer period. The algorithm analytically computes the trajectory of the Moon's shadow and the degree of obscuration of the solar disk at each grid point of the domain based on Bessel's method and the Five Millennium Catalog of Solar Eclipses provided by NASA, with a negligible computational time. Then, the incoming radiation is modified accordingly at each grid point of the domain.This contribution is divided in three parts. First, the implementation of Bessel's method is validated for solar eclipses in the period 1950-2050, by comparing the shadow trajectory with values provided by NASA. Latitude and longitude are determined with a bias lower than 5 x 10-3 degrees (i.e., ~ 550 m at the Equator) and are slightly overestimated and underestimated, respectively. The second part includes a validation of the simulated global horizontal irradiance (GHI) for four total solar eclipses with measurements from the Baseline Surface Radiation Network (BSRN). The results show an improvement in mean absolute error (MAE) from 77 to 90 % under cloudless skies. Lower agreement between modeled and measured GHI is observed under cloudy conditions because the effect of clouds is not included in the simulations for a better analysis of the eclipse outcomes. Finally, an introductory discussion of eclipse-induced perturbations in the surface meteorological fields (e.g., temperature, wind speed) is provided by comparing the WRF-eclipse outcomes with control simulations.

Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis.

PubMed

Gutiérrez-Vega, Julio C; Rodríguez-Masegosa, Rodolfo; Chávez-Cerda, Sabino

2003-11-01

A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.

Performance analysis of decode-and-forward dual-hop optical spatial modulation with diversity combiner over atmospheric turbulence

NASA Astrophysics Data System (ADS)

Odeyemi, Kehinde O.; Owolawi, Pius A.; Srivastava, Viranjay M.

2017-11-01

Dual-hops transmission is a growing interest technique that can be used to mitigate against atmospheric turbulence along the Free Space Optical (FSO) communication links. This paper analyzes the performance of Decode-and-Forward (DF) dual-hops FSO systems in-conjunction with spatial modulation and diversity combiners over a Gamma-Gamma atmospheric turbulence channel using heterodyne detection. Maximum Ratio Combiner (MRC), Equal Gain Combiner (EGC) and Selection Combiner (SC) are considered at the relay and destination as mitigation tools to improve the system error performance. Power series expansion of modified Bessel function is used to derive the closed form expression for the end-to-end Average Pairwise Error Probability (APEP) expressions for each of the combiners under study and a tight upper bound on the Average Bit Error Rate (ABER) per hop is given. Thus, the overall end-to-end ABER for the dual-hops FSO system is then evaluated. The numerical results depicted that dual-hops transmission systems outperformed the direct link systems. Moreover, the impact of having the same and different combiners at the relay and destination are also presented. The results also confirm that the combination of dual hops transmission with spatial modulation and diversity combiner significantly improves the systems error rate with the MRC combiner offering an optimal performance with respect to variation in atmospheric turbulence, change in links average received SNR and link range of the system.

Analysis of blood flow with nanoparticles induced by uniform magnetic field through a circular cylinder with fractional Caputo derivatives

NASA Astrophysics Data System (ADS)

Abdullah, M.; Butt, Asma Rashid; Raza, Nauman; Alshomrani, Ali Saleh; Alzahrani, A. K.

2018-01-01

The magneto hydrodynamic blood flow in the presence of magnetic particles through a circular cylinder is investigated. To calculate the impact of externally applied uniform magnetic field, the blood is electrically charged. Initially the fluid and circular cylinder is at rest but at time t =0+ , the cylinder starts to oscillate along its axis with velocity fsin (Ωt) . To obtain the mathematical model of blood flow with fractional derivatives Caputo fractional operator is employed. The solutions for the velocities of blood and magnetic particles are procured semi analytically by using Laplace transformation method. The inverse Laplace transform has been calculated numerically by using MATHCAD computer software. The obtained results of velocities are presented in Laplace domain in terms of modified Bessel function I0 (·) . The obtained results satisfied all imposed initial and boundary conditions. The hybrid technique that is employed here less computational effort and time cost as compared to other techniques used in literature. As the limiting cases of our results the solutions of the flow model with ordinary derivatives has been procured. Finally, the impact of Reynolds number Re, fractional parameter α and Hartmann number Ha is analyzed and portrayed through graphs. It is worthy to pointing out that fractional derivatives brings remarkable differences as compared to ordinary derivatives. It also has been observed that velocity of blood and magnetic particles is weaker under the effect of transverse magnetic field.

Systems of frequency distributions for water and environmental engineering

NASA Astrophysics Data System (ADS)

Singh, Vijay P.

2018-09-01

A wide spectrum of frequency distributions are used in hydrologic, hydraulic, environmental and water resources engineering. These distributions may have different origins, are based on different hypotheses, and belong to different generating systems. Review of literature suggests that different systems of frequency distributions employed in science and engineering in general and environmental and water engineering in particular have been derived using different approaches which include (1) differential equations, (2) distribution elasticity, (3) genetic theory, (4) generating functions, (5) transformations, (6) Bessel function, (7) expansions, and (8) entropy maximization. This paper revisits these systems of distributions and discusses the hypotheses that are used for deriving these systems. It also proposes, based on empirical evidence, another general system of distributions and derives a number of distributions from this general system that are used in environmental and water engineering.

Self-healing of quantum entanglement after an obstruction.

PubMed

McLaren, Melanie; Mhlanga, Thandeka; Padgett, Miles J; Roux, Filippus S; Forbes, Andrew

2014-01-01

Quantum entanglement between photon pairs is fragile and can easily be masked by losses in transmission path and noise in the detection system. When observing the quantum entanglement between the spatial states of photon pairs produced by parametric down-conversion, the presence of an obstruction introduces losses that can mask the correlations associated with the entanglement. Here we show that we can overcome these losses by measuring in the Bessel basis, thus once again revealing the entanglement after propagation beyond the obstruction. We confirm that, for the entanglement of orbital angular momentum, measurement in the Bessel basis is more robust to these losses than measuring in the usually employed Laguerre-Gaussian basis. Our results show that appropriate choice of measurement basis can overcome some limitations of the transmission path, perhaps offering advantages in free-space quantum communication or quantum processing systems.

Reexamination of group velocities of structured light pulses

NASA Astrophysics Data System (ADS)

Saari, Peeter

2018-06-01

Recently, a series of theoretical and experimental papers on free-space propagation of pulsed Laguerre-Gaussian and Bessel beams was published, which reached contradictory and controversial results about group velocities of such pulses. Depending on the measurement scheme, the group velocity can be defined differently. We analyze how different versions of group velocity are related to the measurable travel time (time of flight) of the pulse between input (source) and output (detecting) planes. The analysis is tested on a theoretical model—the Bessel-Gauss pulse whose propagation path exhibits both subluminal and superluminal regions. Our main conclusion from resolving the contradictions in the literature is that different versions of group velocity are appropriate, depending on whether or not the beam is hollow and how the pulse is recorded in the output plane—integrally or with spatial resolution.

A line scanned light-sheet microscope with phase shaped self-reconstructing beams.

PubMed

Fahrbach, Florian O; Rohrbach, Alexander

2010-11-08

We recently demonstrated that Microscopy with Self-Reconstructing Beams (MISERB) increases both image quality and penetration depth of illumination beams in strongly scattering media. Based on the concept of line scanned light-sheet microscopy, we present an add-on module to a standard inverted microscope using a scanned beam that is shaped in phase and amplitude by a spatial light modulator. We explain technical details of the setup as well as of the holograms for the creation, positioning and scaling of static light-sheets, Gaussian beams and Bessel beams. The comparison of images from identical sample areas illuminated by different beams allows a precise assessment of the interconnection between beam shape and image quality. The superior propagation ability of Bessel beams through inhomogeneous media is demonstrated by measurements on various scattering media.

A Generalized Technique in Numerical Integration

NASA Astrophysics Data System (ADS)

Safouhi, Hassan

2018-02-01

Integration by parts is one of the most popular techniques in the analysis of integrals and is one of the simplest methods to generate asymptotic expansions of integral representations. The product of the technique is usually a divergent series formed from evaluating boundary terms; however, sometimes the remaining integral is also evaluated. Due to the successive differentiation and anti-differentiation required to form the series or the remaining integral, the technique is difficult to apply to problems more complicated than the simplest. In this contribution, we explore a generalized and formalized integration by parts to create equivalent representations to some challenging integrals. As a demonstrative archetype, we examine Bessel integrals, Fresnel integrals and Airy functions.

Front-surface fabrication of moderate aspect ratio micro-channels in fused silica by single picosecond Gaussian-Bessel laser pulse

NASA Astrophysics Data System (ADS)

Liu, Xin; Sanner, Nicolas; Sentis, Marc; Stoian, Razvan; Zhao, Wei; Cheng, Guanghua; Utéza, Olivier

2018-02-01

Single-shot Gaussian-Bessel laser beams of 1 ps pulse duration and of 0.9 μm core size and 60 μm depth of focus are used for drilling micro-channels on front side of fused silica in ambient condition. Channels ablated at different pulse energies are fully characterized by AFM and post-processing polishing procedures. We identify experimental energy conditions (typically 1.5 µJ) suitable to fabricate non-tapered channels with mean diameter of 1.2 µm and length of 40 μm while maintaining an utmost quality of the front opening of the channels. In addition, by further applying accurate post-polishing procedure, channels with high surface quality and moderate aspect ratio down to a few units are accessible, which would find interest in the surface micro-structuring of materials, with perspective of further scalability to meta-material specifications.

An integrated single- and two-photon non-diffracting light-sheet microscope

NASA Astrophysics Data System (ADS)

Lau, Sze Cheung; Chiu, Hoi Chun; Zhao, Luwei; Zhao, Teng; Loy, M. M. T.; Du, Shengwang

2018-04-01

We describe a fluorescence optical microscope with both single-photon and two-photon non-diffracting light-sheet excitations for large volume imaging. With a special design to accommodate two different wavelength ranges (visible: 400-700 nm and near infrared: 800-1200 nm), we combine the line-Bessel sheet (LBS, for single-photon excitation) and the scanning Bessel beam (SBB, for two-photon excitation) light sheet together in a single microscope setup. For a transparent thin sample where the scattering can be ignored, the LBS single-photon excitation is the optimal imaging solution. When the light scattering becomes significant for a deep-cell or deep-tissue imaging, we use SBB light-sheet two-photon excitation with a longer wavelength. We achieved nearly identical lateral/axial resolution of about 350/270 nm for both imagings. This integrated light-sheet microscope may have a wide application for live-cell and live-tissue three-dimensional high-speed imaging.

Laser-plasma interactions with a Fourier-Bessel particle-in-cell method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andriyash, Igor A., E-mail: igor.andriyash@gmail.com; LOA, ENSTA ParisTech, CNRS, Ecole polytechnique, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau cedex; Lehe, Remi

A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this domain, the equations are solved analytically in time, and the spatial derivatives are approximated with high accuracy. In contrast to the finite-difference time domain (FDTD) methods, that are used commonly in PIC, the developed method does not produce numerical dispersion and does not involve grid staggering for the electric and magnetic fields. These features are especially valuable in modeling the wakefield acceleration of particles in plasmas.more » The proposed algorithm is implemented in the code PLARES-PIC, and the test simulations of laser plasma interactions are compared to the ones done with the quasi-cylindrical FDTD PIC code CALDER-CIRC.« less

Rayleigh scattering of twisted light by hydrogenlike ions

NASA Astrophysics Data System (ADS)

Peshkov, A. A.; Volotka, A. V.; Surzhykov, A.; Fritzsche, S.

2018-02-01

The elastic Rayleigh scattering of twisted light and, in particular, the polarization (transfer) of the scattered photons have been analyzed within the framework of second-order perturbation theory and Dirac's relativistic equation. Special attention was paid hereby to the scattering on three different atomic targets: single atoms, a mesoscopic (small) target, and a macroscopic (large) target, which are all centered with regard to the beam axis. Detailed calculations of the polarization Stokes parameters were performed for C5 + ions and for twisted Bessel beams. It is shown that the polarization of scattered photons is sensitive to the size of an atomic target and to the helicity, the opening angle, and the projection of the total angular momentum of the incident Bessel beam. These computations indicate more that the Stokes parameters of the (Rayleigh) scattered twisted light may significantly differ from their behavior for an incident plane-wave radiation.

Higher order Riesz transforms associated with Bessel operators

NASA Astrophysics Data System (ADS)

Betancor, Jorge J.; Fariña, Juan C.; Martinez, Teresa; Rodríguez-Mesa, Lourdes

2008-10-01

In this paper we investigate Riesz transforms R μ ( k) of order k≥1 related to the Bessel operator Δμ f( x)=- f”( x)-((2μ+1)/ x) f’( x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every k≥1, R μ ( k) is a principal value operator of strong type ( p, p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ( x)= x 2μ+1 dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R μ ( k) maps L p (ω) into itself and L 1(ω) into L 1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class mathcal{A}p^μ of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman.

Experimental verification of position-dependent angular-momentum selection rules for absorption of twisted light by a bound electron

NASA Astrophysics Data System (ADS)

Afanasev, Andrei; Carlson, Carl E.; Schmiegelow, Christian T.; Schulz, Jonas; Schmidt-Kaler, Ferdinand; Solyanik, Maria

2018-02-01

We analyze the multipole excitation of atoms with twisted light, i.e, by a vortex light field that carries orbital angular momentum. A single trapped 40Ca+ ion serves as a localized and positioned probe of the exciting field. We drive the {S}1/2\\to {D}5/2 transition and observe the relative strengths of different transitions, depending on the ion's transversal position with respect to the center of the vortex light field. On the other hand, transition amplitudes are calculated for a twisted light field in form of a Bessel beam, a Bessel-Gauss and a Laguerre-Gauss mode. Analyzing experimental obtained transition amplitudes we find agreement with the theoretical predictions at a level of better than 3%. Finally, we propose measurement schemes with two-ion crystals to enhance the sensing accuracy of vortex modes in future experiments.

Non-linear optical flow cytometry using a scanned, Bessel beam light-sheet.

PubMed

Collier, Bradley B; Awasthi, Samir; Lieu, Deborah K; Chan, James W

2015-05-29

Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers.

The Effect of Three-Dimensional Freestream Disturbances on the Supersonic Flow Past a Wedge

NASA Technical Reports Server (NTRS)

Duck, Peter W.; Lasseigne, D. Glenn; Hussaini, M. Y.

1997-01-01

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al, through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results are presented for specific classes of freestream disturbances, and the study shows conclusively that the shock is stable to all classes of disturbances (i.e. time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic (loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-Bessel series, valid far downstream of the shock.

Multiaxial Cyclic Thermoplasticity Analysis with Besseling's Subvolume Method

NASA Technical Reports Server (NTRS)

Mcknight, R. L.

1983-01-01

A modification was formulated to Besseling's Subvolume Method to allow it to use multilinear stress-strain curves which are temperature dependent to perform cyclic thermoplasticity analyses. This method automotically reproduces certain aspects of real material behavior important in the analysis of Aircraft Gas Turbine Engine (AGTE) components. These include the Bauschinger effect, cross-hardening, and memory. This constitutive equation was implemented in a finite element computer program called CYANIDE. Subsequently, classical time dependent plasticity (creep) was added to the program. Since its inception, this program was assessed against laboratory and component testing and engine experience. The ability of this program to simulate AGTE material response characteristics was verified by this experience and its utility in providing data for life analyses was demonstrated. In this area of life analysis, the multiaxial thermoplasticity capabilities of the method have proved a match for the actual AGTE life experience.

Theoretical Study of Large-Angle Bending Transport of Microparticles by 2D Acoustic Half-Bessel Beams.

PubMed

Li, Yixiang; Qiu, Chunyin; Xu, Shengjun; Ke, Manzhu; Liu, Zhengyou

2015-08-17

Conventional microparticle transports by light or sound are realized along a straight line. Recently, this limit has been overcome in optics as the growing up of the self-accelerating Airy beams, which are featured by many peculiar properties, e.g., bending propagation, diffraction-free and self-healing. However, the bending angles of Airy beams are rather small since they are only paraxial solutions of the two-dimensional (2D) Helmholtz equation. Here we propose a novel micromanipulation by using acoustic Half-Bessel beams, which are strict solutions of the 2D Helmholtz equation. Compared with that achieved by Airy beams, the bending angle of the particle trajectory attained here is much steeper (exceeding 90(o)). The large-angle bending transport of microparticles, which is robust to complex scattering environment, enables a wide range of applications from the colloidal to biological sciences.

General Theory of Aerodynamic Instability and the Mechanism of Flutter

NASA Technical Reports Server (NTRS)

Theodorsen, Theodore

1979-01-01

The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom were determined. The problem resolves itself into the solution of certain definite integrals, which were identified as Bessel functions of the first and second kind, and of zero and first order. The theory, based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability was analyzed. An exact solution, involving potential flow and the adoption of the Kutta condition, was derived. The solution is of a simple form and is expressed by means of an auxiliary parameter k. The flutter velocity, treated as the unknown quantity, was determined as a function of a certain ratio of the frequencies in the separate degrees of freedom for any magnitudes and combinations of the airfoil-aileron parameters.

Analysis of ripple formation in single crystal spot welds

NASA Technical Reports Server (NTRS)

Rappaz, M.; Corrigan, D.; Boatner, L. A.

1997-01-01

Stationary spot welds have been made at the (001) surface of Fe-l5%Ni-15%Cr single crystals using a Gas Tungsten Arc (GTA). On the top surface of the spot welds, very regular and concentric ripples were observed after solidification by differential interference color microscopy. Their height (typically 1--5 micrometers and spacing, typically approximately 60 micrometers) decreased with the radius of the pool. These ripples were successfully accounted for in terms of capillary-wave theory using the fundamental mode frequency f(sub 0) given by the first zero of the zero-order Bessel function. The spacing d between the ripples was then equated to v(sub s)/f(sub 0), where v(sub s) is the solidification rate. From the measured ripple spacing, the velocity of the pool was deduced as a function of the radius, and this velocity was in good agreement with the results of a heat-flow simulation.

Spherical 3D isotropic wavelets

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2012-04-01

Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html

Analysis of forward scattering of an acoustical zeroth-order Bessel beam from rigid complicated (aspherical) structures

NASA Astrophysics Data System (ADS)

Li, Wei; Chai, Yingbin; Gong, Zhixiong; Marston, Philip L.

2017-10-01

The forward scattering from rigid spheroids and endcapped cylinders with finite length (even with a large aspect ratio) immersed in a non-viscous fluid under the illumination of an idealized zeroth-order acoustical Bessel beam (ABB) with arbitrary angles of incidence is calculated and analyzed in the implementation of the T-matrix method (TTM). Based on the present method, the incident coefficients of expansion for the incident ABB are derived and simplifying methods are proposed for the numerical accuracy and computational efficiency according to the geometrical symmetries. A home-made MATLAB software package is constructed accordingly, and then verified and validated for the ABB scattering from rigid aspherical obstacles. Several numerical examples are computed for the forward scattering from both rigid spheroids and finite cylinder, with particular emphasis on the aspect ratios, the half-cone angles of ABBs, the incident angles and the dimensionless frequencies. The rectangular patterns of target strength in the (β, θs) domain (where β is the half-cone angle of the ABB and θs is the scattered polar angle) and local/total forward scattering versus dimensionless frequency are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by rigid spheroids and finite cylinders. The ray diagrams in geometrical models for the scattering in the forward half-space and the optical cross-section theorem help to interpret the scattering mechanisms of ABBs. This research work may provide an alternative for the partial wave series solution under certain circumstances interacting with ABBs for complicated obstacles and benefit some related works in optics and electromagnetics.

[Research of dual-photoelastic-modulator-based beat frequency modulation and Fourier-Bessel transform imaging spectrometer].

PubMed

Wang, Zhi-Bin; Zhang, Rui; Wang, Yao-Li; Huang, Yan-Fei; Chen, You-Hua; Wang, Li-Fu; Yang, Qiang

2014-02-01

As the existing photoelastic-modulator(PEM) modulating frequency in the tens of kHz to hundreds of kHz between, leading to frequency of modulated interference signal is higher, so ordinary array detector cannot effectively caprure interference signal..A new beat frequency modulation method based on dual-photoelastic-modulator (Dual-PEM) and Fourier-Bessel transform is proposed as an key component of dual-photoelastic-modulator-based imaging spectrometer (Dual-PEM-IS) combined with charge coupled device (CCD). The dual-PEM are operated as an electro-optic circular retardance modulator, Operating the PEMs at slightly different resonant frequencies w1 and w2 respectively, generates a differential signal at a much lower heterodyne frequency that modulates the incident light. This method not only retains the advantages of the existing PEM, but also the frequency of modulated photocurrent decreased by 2-3 orders of magnitude (10-500 Hz) and can be detected by common array detector, and the incident light spectra can be obtained by Fourier-Bessel transform of low frequency component in the modulated signal. The method makes the PEM has the dual capability of imaging and spectral measurement. The basic principle is introduced, the basic equations is derived, and the feasibility is verified through the corresponding numerical simulation and experiment. This method has' potential applications in imaging spectrometer technology, and analysis of the effect of deviation of the optical path difference. This work provides the necessary theoretical basis for remote sensing of new Dual-PEM-IS and for engineering implementation of spectra inversion.

Feedback instability of the ionospheric resonant cavity

NASA Technical Reports Server (NTRS)

Lysak, Robert L.

1991-01-01

A model is developed that provides a theoretical basis for previous numerical results showing a feedback instability with frequencies characteristic of Alfven travel times within the region of the large increase of Alfven speed above the ionosphere. These results have been extended to arbitrary ionospheric conductivity by developing a numerical solution of the cavity dispersion relation that involves Bessel functions of complex order and argument. It is concluded that the large contrast between the magnetospheric and ionospheric Alfven speed leads to the formation of resonant cavity modes with frequencies ranging from 0.1 to 1 Hz. The presence of the cavity leads to a modification of the reflection characteristics of Alfven waves with frequencies that compare to the cavity's normal modes.

Stimulated neutrino transformation through turbulence

DOE PAGES

Patton, Kelly M.; Kneller, James P.; McLaughlin, Gail C.

2014-04-30

We derive an analytical solution for the flavor evolution of a neutrino through a turbulent density profile which is found to accurately predict the amplitude and transition wavelength of numerical solutions on a case-by-case basis. The evolution is seen to strongly depend upon those Fourier modes in the turbulence which are approximately the same as the splitting between neutrino eigenvalues. Transitions are strongly enhanced by those Fourier modes in the turbulence which are approximately the same as the splitting between neutrino eigenvalues. Lastly, we also find a suppression of transitions due to the long wavelength modes when the ratio ofmore » their amplitude and the wavenumber is of order, or greater than, the first root of the Bessel function J 0.« less

The Pearson walk with shrinking steps in two dimensions

NASA Astrophysics Data System (ADS)

Serino, C. A.; Redner, S.

2010-01-01

We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth step is random and its length equals λN-1, with λ<1. As λ increases past a critical value λc, the endpoint distribution in two dimensions, P(r), changes from having a global maximum away from the origin to being peaked at the origin. The probability distribution for a single coordinate, P(x), undergoes a similar transition, but exhibits multiple maxima on a fine length scale for λ close to λc. We numerically determine P(r) and P(x) by applying a known algorithm that accurately inverts the exact Bessel function product form of the Fourier transform for the probability distributions.

Bessel smoothing filter for spectral-element mesh

NASA Astrophysics Data System (ADS)

Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.

2017-06-01

Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the efficiency and flexibility of the approach proposed.

Instantaneous axial force of a high-order Bessel vortex beam of acoustic waves incident upon a rigid movable sphere.

PubMed

Mitri, F G; Fellah, Z E A

2011-08-01

The present investigation examines the instantaneous force resulting from the interaction of an acoustical high-order Bessel vortex beam (HOBVB) with a rigid sphere. The rigid sphere case is important in fluid dynamics applications because it perfectly simulates the interaction of instantaneous sound waves in a reduced gravity environment with a levitated spherical liquid soft drop in air. Here, a closed-form solution for the instantaneous force involving the total pressure field as well as the Bessel beam parameters is obtained for the case of progressive, stationary and quasi-stationary waves. Instantaneous force examples for progressive waves are computed for both a fixed and a movable rigid sphere. The results show how the instantaneous force per unit cross-sectional surface and unit pressure varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere's radius), the half-cone angle β and the order m of the HOBVB. It is demonstrated here that the instantaneous force is determined only for (m,n) = (0,1) (where n is the partial-wave number), and vanishes for m>0 because of symmetry. In addition, the instantaneous force and normalized amplitude velocity results are computed and compared with those of a rigid immovable (fixed) sphere. It is shown that they differ significantly for ka values below 5. The proposed analysis may be of interest in the analysis of instantaneous forces on spherical particles for particle manipulation, filtering, trapping and drug delivery. The presented solutions may also serve as a method for comparison to other solutions obtained by strictly numerical or asymptotic approaches. Copyright © 2011 Elsevier B.V. All rights reserved.

Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm

NASA Astrophysics Data System (ADS)

Yang, Minglin; Wu, Yueqian; Sheng, Xinqing; Ren, Kuan Fang

2017-12-01

Computation of scattering of shaped beams by large nonspherical particles is a challenge in both optics and electromagnetics domains since it concerns many research fields. In this paper, we report our new progress in the numerical computation of the scattering diagrams. Our algorithm permits to calculate the scattering of a particle of size as large as 110 wavelengths or 700 in size parameter. The particle can be transparent or absorbing of arbitrary shape, smooth or with a sharp surface, such as the Chebyshev particles or ice crystals. To illustrate the capacity of the algorithm, a zero order Bessel beam is taken as the incident beam, and the scattering of ellipsoidal particles and Chebyshev particles are taken as examples. Some special phenomena have been revealed and examined. The scattering problem is formulated with the combined tangential formulation and solved iteratively with the aid of the multilevel fast multipole algorithm, which is well parallelized with the message passing interface on the distributed memory computer platform using the hybrid partitioning strategy. The numerical predictions are compared with the results of the rigorous method for a spherical particle to validate the accuracy of the approach. The scattering diagrams of large ellipsoidal particles with various parameters are examined. The effect of aspect ratios, as well as half-cone angle of the incident zero-order Bessel beam and the off-axis distance on scattered intensity, is studied. Scattering by asymmetry Chebyshev particle with size parameter larger than 700 is also given to show the capability of the method for computing scattering by arbitrary shaped particles.

Theory of biaxial graded-index optical fiber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Kawalko, Stephen F.

1990-01-01

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

High-performance axicon lenses based on high-contrast, multilayer gratings

NASA Astrophysics Data System (ADS)

Doshay, Sage; Sell, David; Yang, Jianji; Yang, Rui; Fan, Jonathan A.

2018-01-01

Axicon lenses are versatile optical elements that can convert Gaussian beams to Bessel-like beams. In this letter, we demonstrate that axicons operating with high efficiencies and at large angles can be produced using high-contrast, multilayer gratings made from silicon. Efficient beam deflection of incident monochromatic light is enabled by higher-order optical modes in the silicon structure. Compared to diffractive devices made from low-contrast materials such as silicon dioxide, our multilayer devices have a relatively low spatial profile, reducing shadowing effects and enabling high efficiencies at large deflection angles. In addition, the feature sizes of these structures are relatively large, making the fabrication of near-infrared devices accessible with conventional optical lithography. Experimental lenses with deflection angles as large as 40° display field profiles that agree well with theory. Our concept can be used to design optical elements that produce higher-order Bessel-like beams, and the combination of high-contrast materials with multilayer architectures will more generally enable new classes of diffractive photonic structures.

Optical beams with embedded vortices: building blocks for atom optics and quantum information

NASA Astrophysics Data System (ADS)

Chattrapiban, N.; Arakelyan, I.; Mitra, S.; Hill, W. T., III

2006-05-01

Laser beams with embedded vortices, Bessel or Laguerre-Gaussian modes, provide a unique opportunity for creating elements for atom optics, entangling photons and, potentially, mediating novel quantum interconnects between photons and matter. High-order Bessel modes, for example, contain intensity voids and propagate nearly diffraction-free for tens of meters. These vortices can be exploited to produce dark channels oriented longitudinally (hollow beams) or transversely to the laser propagation direction. Such channels are ideal for generating networks or circuits to guide and manipulate cold neutral atoms, an essential requirement for realizing future applications associated with atom interferometry, atom lithography and even some neutral atom-based quantum computing architectures. Recently, we divided a thermal cloud of neutral atoms moving within a blue-detuned beam into two clouds with two different momenta by crossing two hollow beams. In this presentation, we will describe these results and discuss the prospects for extending the process to coherent ensembles of matter.

Channel capacity of OAM based FSO communication systems with partially coherent Bessel-Gaussian beams in anisotropic turbulence

NASA Astrophysics Data System (ADS)

Peng, Juan; Zhang, Li; Zhang, Kecheng; Ma, Junxian

2018-07-01

Based on the Rytov approximation theory, the transmission model of an orbital angular momentum (OAM)-carrying partially coherent Bessel-Gaussian (BG) beams propagating in weak anisotropic turbulence is established. The corresponding analytical expression of channel capacity is presented. Influences of anisotropic turbulence parameters and beam parameters on channel capacity of OAM-based free-space optical (FSO) communication systems are discussed in detail. The results indicate channel capacity increases with increasing of almost all of the parameters except for transmission distance. Raising the values of some parameters such as wavelength, propagation altitude and non-Kolmogorov power spectrum index, would markedly improve the channel capacity. In addition, we evaluate the channel capacity of Laguerre-Gaussian (LG) beams and partially coherent BG beams in anisotropic turbulence. It indicates that partially coherent BG beams are better light sources candidates for mitigating the influences of anisotropic turbulence on channel capacity of OAM-based FSO communication systems.

Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media.

PubMed

Fahrbach, Florian O; Rohrbach, Alexander

2012-01-17

Laser beams that can self-reconstruct their initial beam profile even in the presence of massive phase perturbations are able to propagate deeper into inhomogeneous media. This ability has crucial advantages for light sheet-based microscopy in thick media, such as cell clusters, embryos, skin or brain tissue or plants, as well as scattering synthetic materials. A ring system around the central intensity maximum of a Bessel beam enables its self-reconstruction, but at the same time illuminates out-of-focus regions and deteriorates image contrast. Here we present a detection method that minimizes the negative effect of the ring system. The beam's propagation stability along one straight line enables the use of a confocal line principle, resulting in a significant increase in image contrast. The axial resolution could be improved by nearly 100% relative to the standard light-sheet techniques using scanned Gaussian beams, while demonstrating self-reconstruction also for high propagation depths.

Separation of ballistic and diffusive fluorescence photons in confocal Light-Sheet Microscopy of Arabidopsis roots.

PubMed

Meinert, Tobias; Tietz, Olaf; Palme, Klaus J; Rohrbach, Alexander

2016-08-24

Image quality in light-sheet fluorescence microscopy is strongly affected by the shape of the illuminating laser beam inside embryos, plants or tissue. While the phase of Gaussian or Bessel beams propagating through thousands of cells can be partly controlled holographically, the propagation of fluorescence light to the detector is difficult to control. With each scatter process a fluorescence photon loses information necessary for the image generation. Using Arabidopsis root tips we demonstrate that ballistic and diffusive fluorescence photons can be separated by analyzing the image spectra in each plane without a priori knowledge. We introduce a theoretical model allowing to extract typical scattering parameters of the biological material. This allows to attenuate image contributions from diffusive photons and to amplify the relevant image contributions from ballistic photons through a depth dependent deconvolution. In consequence, image contrast and resolution are significantly increased and scattering artefacts are minimized especially for Bessel beams with confocal line detection.

Separation of ballistic and diffusive fluorescence photons in confocal Light-Sheet Microscopy of Arabidopsis roots

PubMed Central

Meinert, Tobias; Tietz, Olaf; Palme, Klaus J.; Rohrbach, Alexander

2016-01-01

Image quality in light-sheet fluorescence microscopy is strongly affected by the shape of the illuminating laser beam inside embryos, plants or tissue. While the phase of Gaussian or Bessel beams propagating through thousands of cells can be partly controlled holographically, the propagation of fluorescence light to the detector is difficult to control. With each scatter process a fluorescence photon loses information necessary for the image generation. Using Arabidopsis root tips we demonstrate that ballistic and diffusive fluorescence photons can be separated by analyzing the image spectra in each plane without a priori knowledge. We introduce a theoretical model allowing to extract typical scattering parameters of the biological material. This allows to attenuate image contributions from diffusive photons and to amplify the relevant image contributions from ballistic photons through a depth dependent deconvolution. In consequence, image contrast and resolution are significantly increased and scattering artefacts are minimized especially for Bessel beams with confocal line detection. PMID:27553506

Fourier-Bessel Particle-In-Cell (FBPIC) v0.1.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehe, Remi; Kirchen, Manuel; Jalas, Soeren

The Fourier-Bessel Particle-In-Cell code is a scientific simulation software for relativistic plasma physics. It is a Particle-In-Cell code whose distinctive feature is to use a spectral decomposition in cylindrical geometry. This decomposition allows to combine the advantages of spectral 3D Cartesian PIC codes (high accuracy and stability) and those of finite-difference cylindrical PIC codes with azimuthal decomposition (orders-of-magnitude speedup when compared to 3D simulations). The code is built on Python and can run both on CPU and GPU (the GPU runs being typically 1 or 2 orders of magnitude faster than the corresponding CPU runs.) The code has the exactmore » same output format as the open-source PIC codes Warp and PIConGPU (openPMD format: openpmd.org) and has a very similar input format as Warp (Python script with many similarities). There is therefore tight interoperability between Warp and FBPIC, and this interoperability will increase even more in the future.« less

Anisotropic resonator analysis using the Fourier-Bessel mode solver

NASA Astrophysics Data System (ADS)

Gauthier, Robert C.

2018-03-01

A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.

Overset grid implementation of the complex Kohn variational method for electron-polyatomic molecule scattering

NASA Astrophysics Data System (ADS)

McCurdy, C. William; Lucchese, Robert L.; Greenman, Loren

2017-04-01

The complex Kohn variational method, which represents the continuum wave function in each channel using a combination of Gaussians and Bessel or Coulomb functions, has been successful in numerous applications to electron-polyatomic molecule scattering and molecular photoionization. The hybrid basis representation limits it to relatively low energies (< 50 eV) , requires an approximation to exchange matrix elements involving continuum functions, and hampers its coupling to modern electronic structure codes for the description of correlated target states. We describe a successful implementation of the method using completely adaptive overset grids to describe continuum functions, in which spherical subgrids are placed on every atomic center to complement a spherical master grid that describes the behavior at large distances. An accurate method for applying the free-particle Green's function on the grid eliminates the need to operate explicitly with the kinetic energy, enabling a rapidly convergent Arnoldi algorithm for solving linear equations on the grid, and no approximations to exchange operators are made. Results for electron scattering from several polyatomic molecules will be presented. Army Research Office, MURI, WN911NF-14-1-0383 and U. S. DOE DE-SC0012198 (at Texas A&M).

Analytic properties for the honeycomb lattice Green function at the origin

NASA Astrophysics Data System (ADS)

Joyce, G. S.

2018-05-01

The analytic properties of the honeycomb lattice Green function are investigated, where is a complex variable which lies in a plane. This double integral defines a single-valued analytic function provided that a cut is made along the real axis from w  =  ‑3 to . In order to analyse the behaviour of along the edges of the cut it is convenient to define the limit function where . It is shown that and can be evaluated exactly for all in terms of various hypergeometric functions, where the argument function is always real-valued and rational. The second-order linear Fuchsian differential equation satisfied by is also used to derive series expansions for and which are valid in the neighbourhood of the regular singular points and . Integral representations are established for and , where with . In particular, it is proved that where J 0(z) and Y 0(z) denote Bessel functions of the first and second kind, respectively. The results derived in the paper are utilized to evaluate the associated logarithmic integral where w lies in the cut plane. A new set of orthogonal polynomials which are connected with the honeycomb lattice Green function are also briefly discussed. Finally, a link between and the theory of Pearson random walks in a plane is established.

Photoionization of Ne8+

NASA Astrophysics Data System (ADS)

Pindzola, M. S.; Abdel-Naby, Sh. A.; Robicheaux, F.; Colgan, J.

2014-05-01

Single and double photoionization cross sections for Ne8+ are calculated using a non-perturbative fully relativistic time-dependent close-coupling method. A Bessel function expansion is used to include both dipole and quadrupole effects in the radiation field interaction and the repulsive interaction between electrons includes both the Coulomb and Gaunt interactions. The fully correlated ground state of Ne8+ is obtained by solving a time-independent inhomogeneous set of close-coupled equations. Propagation of the time-dependent close-coupled equations yields single and double photoionization cross sections for Ne8+ at energies easily accessible at advanced free electron laser facilities. This work was supported in part by grants from NSF and US DoE. Computational work was carried out at NERSC in Oakland, California, NICS in Knoxville, Tennessee, and OLCF in Oak Ridge, Tennessee.

Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

PubMed

Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

2012-05-01

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

Propagation of mechanical waves through a stochastic medium with spherical symmetry

NASA Astrophysics Data System (ADS)

Avendaño, Carlos G.; Reyes, J. Adrián

2018-01-01

We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.

Insertion device calculations with mathematica

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carr, R.; Lidia, S.

1995-02-01

The design of accelerator insertion devices such as wigglers and undulators has usually been aided by numerical modeling on digital computers, using code in high level languages like Fortran. In the present era, there are higher level programming environments like IDL{reg_sign}, MatLab{reg_sign}, and Mathematica{reg_sign} in which these calculations may be performed by writing much less code, and in which standard mathematical techniques are very easily used. The authors present a suite of standard insertion device modeling routines in Mathematica to illustrate the new techniques. These routines include a simple way to generate magnetic fields using blocks of CSEM materials, trajectorymore » solutions from the Lorentz force equations for given magnetic fields, Bessel function calculations of radiation for wigglers and undulators and general radiation calculations for undulators.« less

Femtosecond laser processing of optical fibres for novel sensor development

NASA Astrophysics Data System (ADS)

Kalli, Kyriacos; Theodosiou, Antreas; Ioannou, Andreas; Lacraz, Amedee

2017-04-01

We present results of recent research where we have utilized a femtosecond laser to micro-structure silica and polymer optical fibres in order to realize versatile optical components such as diffractive optical elements on the fibre end face, the inscription of integrated waveguide circuits in the fibre cladding and novel optical fibre sensors designs based on Bragg gratings in the core. A major hurdle in tailoring or modifying the properties of optical fibres is the development of an inscription method that can prove to be a flexible and reliable process that is generally applicable to all optical fibre types; this requires careful matching of the laser parameters and optics in order to examine the spatial limits of direct laser writing, whether the application is structuring at the surface of the optical fibre or inscription in the core and cladding of the fibre. We demonstrate a variety of optical components such as two-dimensional grating structures, Bessel, Airy and vortex beam generators; moreover, optical bridging waveguides inscribed in the cladding of single-mode fibre as a means to selectively couple light from single-core to multi-core optical fibres, and demonstrate a grating based sensor; finally, we have developed a novel femtosecond laser inscription method for the precise inscription of tailored Bragg grating sensors in silica and polymer optical fibres. We also show that this novel fibre Bragg grating inscription technique can be used to modify and add versatility to an existing, encapsulated optical fibre pressure sensor.

Thermal noise due to surface-charge effects within the Debye layer of endogenous structures in dendrites.

PubMed

Poznanski, Roman R

2010-02-01

An assumption commonly used in cable theory is revised by taking into account electrical amplification due to intracellular capacitive effects in passive dendritic cables. A generalized cable equation for a cylindrical volume representation of a dendritic segment is derived from Maxwell's equations under assumptions: (i) the electric-field polarization is restricted longitudinally along the cable length; (ii) extracellular isopotentiality; (iii) quasielectrostatic conditions; and (iv) homogeneous medium with constant conductivity and permittivity. The generalized cable equation is identical to Barenblatt's equation arising in the theory of infiltration in fissured strata with a known analytical solution expressed in terms of a definite integral involving a modified Bessel function and the solution to a linear one-dimensional classical cable equation. Its solution is used to determine the impact of thermal noise on voltage attenuation with distance at any particular time. A regular perturbation expansion for the membrane potential about the linear one-dimensional classical cable equation solution is derived in terms of a Green's function in order to describe the dynamics of free charge within the Debye layer of endogenous structures in passive dendritic cables. The asymptotic value of the first perturbative term is explicitly evaluated for small values of time to predict how the slowly fluctuating (in submillisecond range) electric field attributed to intracellular capacitive effects alters the amplitude of the membrane potential. It was found that capacitive effects are almost negligible for cables with electrotonic lengths L>0.5 , contributes up to 10% of the signal for cables with electrotonic lengths in the range between 0.25

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

NASA Astrophysics Data System (ADS)

Mingari Scarpello, Giovanni; Ritelli, Daniele

2018-06-01

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

Dispersal of spores following a persistent random walk.

PubMed

Bicout, D J; Sache, I

2003-03-01

A model of a persistent random walk is used to describe the transport and deposition of the spore dispersal process. In this model, the spore particle flies along straight line trajectories, with constant speed v, which are interrupted by scattering, originating from interaction of spores with the field and wind variations, which randomly change its direction. To characterize the spore dispersal gradients, we have derived analytical expressions of the deposition probability epsilon (r|v) of airborne spores as a function of the distance r from the spore source in an infinite free space and in a disk of radius R with an absorbing edge that mimics an agricultural field surrounded with fields of nonhost plants and bare land. It is found in the free space that epsilon (r|v) approximately e(-alphar/l), with alpha a function of l(d)/l, where l and l(d) are the scattering and deposition mean free paths, respectively. In the disk, however, epsilon (r|v) is an infinite series of Bessel functions and, exhibits three regimes: absorbing (Rl(d)).

Implementation of Soft X-ray Tomography on NSTX

NASA Astrophysics Data System (ADS)

Tritz, K.; Stutman, D.; Finkenthal, M.; Granetz, R.; Menard, J.; Park, W.

2003-10-01

A set of poloidal ultrasoft X-ray arrays is operated by the Johns Hopkins group on NSTX. To enable MHD mode analysis independent of the magnetic reconstruction, the McCormick-Granetz tomography code developed at MIT is being adapted to the NSTX geometry. Tests of the code using synthetic data show that that present X-ray system is adequate for m=1 tomography. In addition, we have found that spline basis functions may be better suited than Bessel functions for the reconstruction of radially localized phenomena in NSTX. The tomography code was also used to determine the necessary array expansion and optimal array placement for the characterization of higher m modes (m=2,3) in the future. Initial reconstruction of experimental soft X-ray data has been performed for m=1 internal modes, which are often encountered in high beta NSTX discharges. The reconstruction of these modes will be compared to predictions from the M3D code and magnetic measurements.

Analysis of ripple formation in single crystal spot welds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rappaz, M.; Corrigan, D.; Boatner, L.A.

1997-10-01

Stationary spot welds have been made at the (001) surface of Fe-l5%Ni-15%Cr single crystals using a Gas Tungsten Arc (GTA). On the top surface of the spot welds, very regular and concentric ripples were observed after solidification by differential interference color microscopy. Their height (typically 1--5 {micro}m) and spacing (typically {approximately} 60 {micro}m) decreased with the radius of the pool. These ripples were successfully accounted for in terms of capillary-wave theory using the fundamental mode frequency f{sub 0} given by the first zero of the zero-order Bessel function. The spacing d between the ripples was then equated to v{sub s}/f{submore » 0}, where v{sub s} is the solidification rate. From the measured ripple spacing, the velocity of the pool was deduced as a function of the radius, and this velocity was in good agreement with the results of a heat-flow simulation.« less

Towards automated human gait disease classification using phase space representation of intrinsic mode functions

NASA Astrophysics Data System (ADS)

Pratiher, Sawon; Patra, Sayantani; Pratiher, Souvik

2017-06-01

A novel analytical methodology for segregating healthy and neurological disorders from gait patterns is proposed by employing a set of oscillating components called intrinsic mode functions (IMF's). These IMF's are generated by the Empirical Mode Decomposition of the gait time series and the Hilbert transformed analytic signal representation forms the complex plane trace of the elliptical shaped analytic IMFs. The area measure and the relative change in the centroid position of the polygon formed by the Convex Hull of these analytic IMF's are taken as the discriminative features. Classification accuracy of 79.31% with Ensemble learning based Adaboost classifier validates the adequacy of the proposed methodology for a computer aided diagnostic (CAD) system for gait pattern identification. Also, the efficacy of several potential biomarkers like Bandwidth of Amplitude Modulation and Frequency Modulation IMF's and it's Mean Frequency from the Fourier-Bessel expansion from each of these analytic IMF's has been discussed for its potency in diagnosis of gait pattern identification and classification.

Electron transport in the stochastic fields of the reversed-field pinch

NASA Astrophysics Data System (ADS)

Kim, Myung-Hee; Punjabi, Alkesh

1996-08-01

We employ the Monte Carlo method for the calculation of anomalous transport developed by Punjabi and Boozer to calculate the particle diffusion coefficient for electrons in the stochastic magnetic fields of the reversed-field pinch (RFP). in the Monte Carlo calculations represented here, the transport mechanism is the loss of magnetic surfaces due to resistive perturbations. The equilibrium magnetic fields are represented by the Bessel function model for the RFP. The diffusion coefficient D is calculated as a function of a, the amplitude of the perturbation. We see three regimes as the amplitude of the tearing modes is increased: the Rechester—Rosenbluth regime where D scales as a2 the anomalous regime where D scales more rapidly than a2 and the Mynick—Krornmes regime where D scales more slowly than a2. Inclusion of the effects of loop voltage on the particle drift orbits in the RFP does not affect the intervals in the amplitude a where these regimes operate.

Fracture Mechanics Analysis of an Annular Crack in a Three-concentric-cylinder Composite Model

NASA Technical Reports Server (NTRS)

Kuguoglu, Latife H.; Binienda, Wieslaw K.; Roberts, Gary D.

2004-01-01

A boundary-value problem governing a three-phase concentric-cylinder model was analytically modeled to analyze annular interfacial crack problems with Love s strain functions in order to find the stress intensity factors (SIFs) and strain energy release rates (SERRs) at the tips of an interface crack in a nonhomogeneous medium. The complex form of a singular integral equation (SIE) of the second kind was formulated using Bessel s functions in the Fourier domain, and the SIF and total SERR were calculated using Jacoby polynomials. For the validity of the SIF equations to be established, the SIE of the three-concentric-cylinder model was reduced to the SIE for a two-concentric-cylinder model, and the results were compared with the previous results of Erdogan. A preliminary set of parametric studies was carried out to show the effect of interphase properties on the SERR. The method presented here provides insight about the effect of interphase properties on the crack driving force.

Beyond the plane-parallel approximation for redshift surveys

NASA Astrophysics Data System (ADS)

Castorina, Emanuele; White, Martin

2018-06-01

Redshift -space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modelling of clustering observables, leading to what are frequently called `wide-angle effects'. We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide-angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify in an analytical way the biases that enter and clarify the relation between what we measure and the underlying theoretical modelling. The presence of an angular window function is also discussed. Motivated by this analysis, we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients. We show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.

The continuous spin representations of the Poincare and super-Poincare groups and their construction by the Inonu-Wigner group contraction

NASA Astrophysics Data System (ADS)

Khan, Abu M. A. S.

We study the continuous spin representation (CSR) of the Poincare group in arbitrary dimensions. In d dimensions, the CSRs are characterized by the length of the light-cone vector and the Dynkin labels of the SO(d-3) short little group which leaves the light-cone vector invariant. In addition to these, a solid angle Od-3 which specifies the direction of the light-cone vector is also required to label the states. We also find supersymmetric generalizations of the CSRs. In four dimensions, the supermultiplet contains one bosonic and one fermionic CSRs which transform into each other under the action of the supercharges. In a five dimensional case, the supermultiplet contains two bosonic and two fermionic CSRs which is like N = 2 supersymmetry in four dimensions. When constructed using Grassmann parameters, the light-cone vector becomes nilpotent. This makes the representation finite dimensional, but at the expense of introducing central charges even though the representation is massless. This leads to zero or negative norm states. The nilpotent constructions are valid only for even dimensions. We also show how the CSRs in four dimensions can be obtained from five dimensions by the combinations of Kaluza-Klein (KK) dimensional reduction and the Inonu-Wigner group contraction. The group contraction is a singular transformation. We show that the group contraction is equivalent to imposing periodic boundary condition along one direction and taking a double singular limit. In this form the contraction parameter is interpreted as the inverse KK radius. We apply this technique to both five dimensional regular massless and massive representations. For the regular massless case, we find that the contraction gives the CSR in four dimensions under a double singular limit and the representation wavefunction is the Bessel function. For the massive case, we use Majorana's infinite component theory as a model for the SO(4) little group. In this case, a triple singular limit is required to yield any CSR in four dimensions. The representation wavefunction is the Bessel function, as expected, but the scale factor is not the length of the light-cone vector. The amplitude and the scale factor are implicit functions of the parameter y which is a ratio of the internal and external coordinates. We also state under what conditions our solutions become identical to Wigner's solution.

Contributions of Reaction Time Measures to Studying and Understanding the Reading Process.

DTIC Science & Technology

1982-01-01

transmission of nerve impulses to be practically instantaneous (Boring, 1929). Subsequent investigations of the personal equation by astrono - mers suggested...tively slow as Bessel had hypothesized. However, this fact did not intrigue most physiologists at the time, and they, as did the astrono - mers, lost

Acoustics of finite asymmetric exotic beams: Examples of Airy and fractional Bessel beams

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-12-01

The purpose of this investigation is to examine the properties of finite asymmetric exotic scalar (acoustic) beams with unusual properties using the angular spectrum decomposition in plane waves. Such beams possess intrinsic uncommon characteristics that make them attractive from the standpoint of particle manipulation, handling and rotation, and possibly other applications in particle clearing and separation. Assuming a specific apodization function at the acoustic source, the angular spectrum function is calculated and used to synthesize the radiated pressure field (i.e., excluding evanescent waves that decay away from the source) in the forward direction of wave motion (i.e., away from the source). Moreover, a generalized hybrid method combining the angular spectrum approach with the multipole expansion formalism in spherical coordinates is developed, which is applicable to any finite beam of arbitrary wavefront. The improved approach allows adequate computation of the resonance scattering, radiation force, and spin torque components on an object of arbitrary shape, located on or off the axis of the incident beam in space. Considering the illustrative example of a viscous fluid sphere submerged in a non-viscous liquid and illuminated by finite asymmetric beams such as the Airy and the Bessel vortex beam with fractional order, numerical computations for the scattering, radiation force, and torque components are performed with an emphasis on the distance from the source, the arbitrary location of the particle ,and the asymmetric nature of the incident field. Moreover, beamforming calculations are presented with supplementary animations for the pressure field distribution in space, with an emphasis on the intrinsic properties of the selected beams. The numerical predictions illustrate the scattering, radiation force, and spin torque properties depending on the beam parameters and the distance separating the sphere from the source. This study provides a generalized hybrid method to analyze quantitatively the scattering, radiation force, and spin torque by any finite asymmetric (or symmetric) acoustic beam with potential applications in various fields of applied physics (such as beam-forming, imaging, and mechanical effects of asymmetric sound beams).

Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem

NASA Astrophysics Data System (ADS)

Ahn, Chi Young; Jeon, Kiwan; Park, Won-Kwang

2015-06-01

This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic-TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.

A class of exact solutions for biomacromolecule diffusion-reaction in live cells.

PubMed

Sadegh Zadeh, Kouroush; Montas, Hubert J

2010-06-07

A class of novel explicit analytic solutions for a system of n+1 coupled partial differential equations governing biomolecular mass transfer and reaction in living organisms are proposed, evaluated, and analyzed. The solution process uses Laplace and Hankel transforms and results in a recursive convolution of an exponentially scaled Gaussian with modified Bessel functions. The solution is developed for wide range of biomolecular binding kinetics from pure diffusion to multiple binding reactions. The proposed approach provides solutions for both Dirac and Gaussian laser beam (or fluorescence-labeled biomacromolecule) profiles during the course of a Fluorescence Recovery After Photobleaching (FRAP) experiment. We demonstrate that previous models are simplified forms of our theory for special cases. Model analysis indicates that at the early stages of the transport process, biomolecular dynamics is governed by pure diffusion. At large times, the dominant mass transfer process is effective diffusion. Analysis of the sensitivity equations, derived analytically and verified by finite difference differentiation, indicates that experimental biologists should use full space-time profile (instead of the averaged time series) obtained at the early stages of the fluorescence microscopy experiments to extract meaningful physiological information from the protocol. Such a small time frame requires improved bioinstrumentation relative to that in use today. Our mathematical analysis highlights several limitations of the FRAP protocol and provides strategies to improve it. The proposed model can be used to study biomolecular dynamics in molecular biology, targeted drug delivery in normal and cancerous tissues, motor-driven axonal transport in normal and abnormal nervous systems, kinetics of diffusion-controlled reactions between enzyme and substrate, and to validate numerical simulators of biological mass transport processes in vivo. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

An Accurate and Computationally Efficient Model for Membrane-Type Circular-Symmetric Micro-Hotplates

PubMed Central

Khan, Usman; Falconi, Christian

2014-01-01

Ideally, the design of high-performance micro-hotplates would require a large number of simulations because of the existence of many important design parameters as well as the possibly crucial effects of both spread and drift. However, the computational cost of FEM simulations, which are the only available tool for accurately predicting the temperature in micro-hotplates, is very high. As a result, micro-hotplate designers generally have no effective simulation-tools for the optimization. In order to circumvent these issues, here, we propose a model for practical circular-symmetric micro-hot-plates which takes advantage of modified Bessel functions, computationally efficient matrix-approach for considering the relevant boundary conditions, Taylor linearization for modeling the Joule heating and radiation losses, and external-region-segmentation strategy in order to accurately take into account radiation losses in the entire micro-hotplate. The proposed model is almost as accurate as FEM simulations and two to three orders of magnitude more computationally efficient (e.g., 45 s versus more than 8 h). The residual errors, which are mainly associated to the undesired heating in the electrical contacts, are small (e.g., few degrees Celsius for an 800 °C operating temperature) and, for important analyses, almost constant. Therefore, we also introduce a computationally-easy single-FEM-compensation strategy in order to reduce the residual errors to about 1 °C. As illustrative examples of the power of our approach, we report the systematic investigation of a spread in the membrane thermal conductivity and of combined variations of both ambient and bulk temperatures. Our model enables a much faster characterization of micro-hotplates and, thus, a much more effective optimization prior to fabrication. PMID:24763214

Mathematical models for the reflection coefficients of dielectric half-spaces

NASA Technical Reports Server (NTRS)

Evans, D. D.

1973-01-01

The reflection coefficients at normal incidence are found for a large class of one-dimensionally inhomogeneous or stratified half-spaces, which contain a homogeneous half-space. The formulation of the problem involves a combination of the classical boundary value technique, and the nonclassical principle of invariant imbedding. Solutions are in closed form and expressible in terms of Bessel functions. All results are given in terms of the ratio of the distance between free space and the homogeneous half-space to the wavelength in vacuo. One special case is that of an arbitrary number of layers lying on a homogeneous half-space where the dielectric constant of each layer has a constant gradient. A number of other special cases, limiting cases, and generalizations are developed including one in which the thickness of the top layer obeys a probability distribution.

A theoretical study of a laminar diffusion flame

NASA Technical Reports Server (NTRS)

Frair, K. L.

1978-01-01

Theoretical models of an axisymmetric laminar diffusion flame are discussed, with an emphasis on the behavior of such flames at increasing pressures. The flame-sheet or Burke-Schumann model (in terms of Bessel functions) and various boundary layer numerical solutions are presented and their results compared with experimental data. The most promising theoretical model combines the numerical flow field solution of the Patankar-Spalding computer code with the Pratt-Wormeck chemical reaction subroutine. The flame shapes for pressures of 1, 5, 10, 20, and 50 atmospheres were computed and agree remarkably well with experimental data. There is a noticeable shape change with pressure, believed to be a result of buoyancy effects. The chemical concentration profiles do not exhibit much dependence on pressure, a reflection of the fact that only one chemical mechanism was utilized at all pressures.

Unsteady flow of fractional Oldroyd-B fluids through rotating annulus

NASA Astrophysics Data System (ADS)

Tahir, Madeeha; Naeem, Muhammad Nawaz; Javaid, Maria; Younas, Muhammad; Imran, Muhammad; Sadiq, Naeem; Safdar, Rabia

2018-04-01

In this paper exact solutions corresponding to the rotational flow of a fractional Oldroyd-B fluid, in an annulus, are determined by applying integral transforms. The fluid starts moving after t = 0+ when pipes start rotating about their axis. The final solutions are presented in the form of usual Bessel and hypergeometric functions, true for initial and boundary conditions. The limiting cases for the solutions for ordinary Oldroyd-B, fractional Maxwell and Maxwell and Newtonian fluids are obtained. Moreover, the solution is obtained for the fluid when one pipe is rotating and the other one is at rest. At the end of this paper some characteristics of fluid motion, the effect of the physical parameters on the flow and a correlation between different fluid models are discussed. Finally, graphical representations confirm the above affirmation.

Theoretical Modeling of Ultrashot Laser Pulse Interaction With Dielectric and Semiconductor Materials

DTIC Science & Technology

2010-05-24

of linearly polarized electromagnetic radiation re- sults in an anisotropic electronic transition rate characterized by field dependence via a Bessel...where Ω ( ~k, ~r ) is the renormalized Rabi frequency defined by: ~Ω ( ~k, ~r ) = µ ( ~k ) ~E (~r, t) + ∑ ~k′ p ( ~k′, ~r ) V s~k−~k′ . (12) The second

Fundamental and dressed annular solitons in saturable nonlinearity with parity–time symmetric Bessel potential

NASA Astrophysics Data System (ADS)

Wang, Hong-Cheng; Wei, Ya-Dong; Huang, Xiao-Yuan; Chen, Gui-Hua; Ye, Hai

2018-04-01

Not Available Project supported by the National Natural Science Foundation of China (Grant No. 61308019), the Guangdong Provincial Natural Science Foundation, China (Grant Nos. 2015A030313650 and 2014A030310262), and the Guangdong Provincial Science and Technology Planning Program, China (Grant No. 2017A010102019).

Ultrahigh resolution optical coherence elastography using a Bessel beam for extended depth of field

NASA Astrophysics Data System (ADS)

Curatolo, Andrea; Villiger, Martin; Lorenser, Dirk; Wijesinghe, Philip; Fritz, Alexander; Kennedy, Brendan F.; Sampson, David D.

2016-03-01

Visualizing stiffness within the local tissue environment at the cellular and sub-cellular level promises to provide insight into the genesis and progression of disease. In this paper, we propose ultrahigh-resolution optical coherence elastography, and demonstrate three-dimensional imaging of local axial strain of tissues undergoing compressive loading. The technique employs a dual-arm extended focus optical coherence microscope to measure tissue displacement under compression. The system uses a broad bandwidth supercontinuum source for ultrahigh axial resolution, Bessel beam illumination and Gaussian beam detection, maintaining sub-2 μm transverse resolution over nearly 100 μm depth of field, and spectral-domain detection allowing high displacement sensitivity. The system produces strain elastograms with a record resolution (x,y,z) of 2×2×15 μm. We benchmark the advances in terms of resolution and strain sensitivity by imaging a suitable inclusion phantom. We also demonstrate this performance on freshly excised mouse aorta and reveal the mechanical heterogeneity of vascular smooth muscle cells and elastin sheets, otherwise unresolved in a typical, lower resolution optical coherence elastography system.

VizieR Online Data Catalog: Photometry of multiple stars at NAOR&ASV in 2015 (Cvetkovic+, 2017)

NASA Astrophysics Data System (ADS)

Cvetkovic, Z.; Pavlovic, R.; Boeva, S.

2018-05-01

This is the ninth series of CCD observations of double and multiple stars, obtained at the Bulgarian National Astronomical Observatory at Rozhen (NAOR) over five nights. As previously, the CCD camera VersArray 1300B was used, which was attached to the 2 m telescope. For each double or multiple star, five CCD frames in the Johnson B filter and five frames in the Johnson V filter were taken, which enabled us to determine the magnitude difference for these filters. In 2015 at the Astronomical Station at Vidojevica (ASV), over a total of 23 nights, observations were carried out by using the 60 cm telescope with a Cassegrain optical system. This is the fourth observational series at ASV since the work started there in 2011. In the observations we used the Apogee Alta U42 CCD camera whose characteristics can be found in the paper by Cvetkovic et al. (2016, J/AJ/151/58). Every pair was observed five times in the Cousins/Bessel B filter and five times in the Cousins/Bessel V one. (3 data files).

Radiation force on drops and bubbles in acoustic Bessel beams modeled using finite elements

NASA Astrophysics Data System (ADS)

Marston, Philip L.; Thiessen, David B.; Zhang, Likun

2009-11-01

Analysis of the scattering of sound by spheres centered on ordinary and helicoidal (higher-order) Bessel beams makes it possible to evaluate the acoustic radiation force on idealized drops and bubbles centered on the beam [1]. For potential applications it would be necessary to know if a small transverse displacement of the sphere from the beam's axis causes a radiation force that pushes the sphere toward (or away from) the axis of the beam. We applied 3D-finite elements to that problem. To trust FEM calculations of the radiation force with helicoidal beams it was first necessary to verify that analytical values for the axial force are recovered in the on-axis helicoidal case since only the zero-order beam had been previously studied with FEM. Cases have been identified where the force pushes a slightly off-set drop or bubble toward the axis. For some cases the effective potential method of Gorkov may be used to predict the transverse stability of small spheres.[4pt] [1] P. L. Marston, J. Acoust. Soc. Am. 125, 3539-3545 (2009).

Deviations from plane-wave Mie scattering and precise retrieval of refractive index for a single spherical particle in an optical cavity.

PubMed

Mason, Bernard J; Walker, Jim S; Reid, Jonathan P; Orr-Ewing, Andrew J

2014-03-20

The extinction cross-sections of individual, optically confined aerosol particles with radii of a micrometer or less can, in principle, be measured using cavity ring-down spectroscopy (CRDS). However, when the particle radius is comparable in magnitude to the wavelength of light stored in a high-finesse cavity, the phenomenological cross-section retrieved from a CRDS experiment depends on the location of the particle in the intracavity standing wave and differs from the Mie scattering cross-section for plane-wave irradiation. Using an evaporating 1,2,6-hexanetriol particle of initial radius ∼1.75 μm confined within the 4.5 μm diameter core of a Bessel beam, we demonstrate that the scatter in the retrieved extinction efficiency of a single particle is determined by its lateral motion, which spans a few wavelengths of the intracavity standing wave used for CRDS measurements. Fits of experimental measurements to Mie calculations, modified to account for the intracavity standing wave, allow precise retrieval of the refractive index of 1,2,6-hexanetriol particles (with relative humidity, RH < 10%) of 1.47824 ± 0.00072.

VizieR Online Data Catalog: Bessel (1825) calculation for geodesic measurements (Karney+, 2010)

NASA Astrophysics Data System (ADS)

Karney, C. F. F.; Deakin, R. E.

2010-06-01

The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table, -4.4, should be parsed as "-4" (the characteristic) and ".4" (the mantissa); the anti-log for this entry is 10(-4+0.4)=2.5e-4. The "Delta" columns give the first difference of the preceding column, i.e., the difference of the preceding column in the next row and the preceding column in the current row. In the printed tables these are expressed as "units in the last place" and the differences are of the rounded representations in the preceding columns (to minimize interpolation errors). In table1.dat these are given scaled to a match the format used for the preceding column, as indicated by the units given for these columns. The unit log(") (in the description within square brackets [arcsec]) means the logarithm of a quantity expressed in arcseconds. (3 data files).

The Sentinel-3 Surface Topography Mission (S-3 STM): Level 2 SAR Ocean Retracker

NASA Astrophysics Data System (ADS)

Dinardo, S.; Lucas, B.; Benveniste, J.

2015-12-01

The SRAL Radar Altimeter, on board of the ESA Mission Sentinel-3 (S-3), has the capacity to operate either in the Pulse-Limited Mode (also known as LRM) or in the novel Synthetic Aperture Radar (SAR) mode. Thanks to the initial results from SAR Altimetry obtained exploiting CryoSat-2 data, lately the interest by the scientific community in this new technology has significantly increased and consequently the definition of accurate processing methodologies (along with validation strategies) has now assumed a capital importance. In this paper, we present the algorithm proposed to retrieve from S-3 STM SAR return waveforms the standard ocean geophysical parameters (ocean topography, wave height and sigma nought) and the validation results that have been so far achieved exploiting the CryoSat-2 data as well as the simulated data. The inversion method (retracking) to extract from the return waveform the geophysical information is a curve best-fitting scheme based on the bounded Levenberg-Marquardt Least-Squares Estimation Method (LEVMAR-LSE). The S-3 STM SAR Ocean retracking algorithm adopts, as return waveform’s model, the “SAMOSA” model [Ray et al, 2014], named after the R&D project SAMOSA (led by Satoc and funded by ESA), in which it has been initially developed. The SAMOSA model is a physically-based model that offers a complete description of a SAR Altimeter return waveform from ocean surface, expressed in the form of maps of reflected power in Delay-Doppler space (also known as stack) or expressed as multilooked echoes. SAMOSA is able to account for an elliptical antenna pattern, mispointing errors in roll and yaw, surface scattering pattern, non-linear ocean wave statistics and spherical Earth surface effects. In spite of its truly comprehensive character, the SAMOSA model comes with a compact analytical formulation expressed in term of Modified Bessel functions. The specifications of the retracking algorithm have been gathered in a technical document (DPM) and delivered as baseline for industrial implementation. For operational needs, thanks to the fine tuning of the fitting library parameters and the usage of look-up table for Bessel functions computation, the CPU execution time was accelerated over 100 times and made the execution in par with real time. In the course of the ESA-funded project CryoSat+ for Ocean (CP4O), new technical evolutions for the algorithm have been proposed (as usage of PTR width look up table and application of a stack masking). One of the main outcomes of the CP4O project was that, with these latest evolutions, the SAMOSA SAR retracking was giving equivalent results to CNES CPP retracking prototype, which was built with a totally different approach, which enforces the validation results. Work actually is underway to align the industrial implementation with the last new evolutions. Further, in order to test the algorithm with a dataset as realistic as possible, a set of simulated Test Data Set (generated by S-3 STM End-to-End Simulator) has been created by CLS following the specifications as described in a test data set requirements document drafted by ESA. In this work, we will show the baseline algorithm details, the evolutions, the impact of the evolutions and the results obtained processing the CryoSat-2 data and the simulated test data set.

Shapes of cometary isophotes with Maxwellian distribution of initial velocities for neutral molecules

NASA Astrophysics Data System (ADS)

Žáček, P.; Wolf, M.

2017-10-01

This paper contains necessary modification of Bessel's equations for the axial cometary syndyne. This correction provides the accurate values of molecular acceleration in a cometary tail and precise values of decay constants for radiating molecules and their lifetimes. In consequence the hypothesis of the predissociation of molecules seems to be useless.

Lp-estimates on diffusion processes

NASA Astrophysics Data System (ADS)

Yan, Litan; Zhu, Bei

2005-03-01

Let be a diffusion process on given by where B=(Bt)t[greater-or-equal, slanted]0 is a standard Brownian motion starting at zero and [mu],[sigma] are two continuous functions on , and [sigma](x)>0 if x[not equal to]0. For a nonnegative continuous function [phi] we define the functional by , t[greater-or-equal, slanted]0. Then under suitable conditions we establish the relationship between Lp-norm of sup0[less-than-or-equals, slant]t[less-than-or-equals, slant][tau]Xt and Lp-norm of J[tau] for all stopping times [tau]. In particular, for a Bessel process Z of dimension [delta]>0 starting at zero, we show that the inequalities hold for all 00, where Cp and cp are some positive constants depending only on p, and H[mu],h[mu] are the inverses of x|->(e2[mu]x-2[mu]x-1)/2[mu]2 and x|->(e-2[mu]x+2[mu]x-1)/2[mu]2 on (0,[infinity]), respectively.

Expressions Module for the Satellite Orbit Analysis Program

NASA Technical Reports Server (NTRS)

Edmonds, Karina

2008-01-01

The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.

Dynamics of optically levitated microparticles in vacuum placed in 2D and 3D optical potentials possessing orbital angular momentum

NASA Astrophysics Data System (ADS)

Arita, Yoshihiko; Mazilu, Michael; Chen, Mingzhou; Vettenburg, Tom; Auñón, Juan M.; Wright, Ewan M.; Dholakia, Kishan

2017-04-01

We demonstrate the transfer of orbital angular momentum to optically levitated microparticles in vacuum [1]. We prepare two-dimensional and three-dimensional optical potentials. In the former case the microparticle is placed within a Laguerre-Gaussian beam and orbits the annular beam profile with increasing angular velocity as the air drag coefficient is reduced. We explore the particle dynamics as a function of the topological charge of the levitating beam. Our results reveal that there is a fundamental limit to the orbital angular momentum that may be transferred to a trapped particle, dependent upon the beam parameters and inertial forces present. This effect was predicted theoretically [2] and can be understood considering the underlying dynamics arising from the link between the magnitude of the azimuthal index and the beam radius [3]. Whilst a Laguerre-Gaussian beam scales in size with azimuthal index `, recently we have created a "perfect" vortex beam whose radial intensity profile and radius are both independent of topological charge [4, 5]. As the Fourier transform of a perfect vortex yields a Bessel beam. Imaging a perfect vortex, with its subsequent propagation thus realises a complex three dimensional optical field. In this scenario we load individual silica microparticles into this field and observe their trajectories. The optical gradient and scattering forces interplay with the inertial and gravitational forces acting on the trapped particle, including the rotational degrees of freedom. As a result the trapped microparticle exhibits a complex three dimensional motion that includes a periodic orbital motion between the Bessel and the perfect vortex beam. We are able to determine the three dimensional optical potential in situ by tracking the particle. This first demonstration of trapping microparticles within a complex three dimensional optical potential in vacuum opens up new possibilities for fundamental studies of many-body dynamics, mesoscopic entanglement [6, 7], and optical binding [8, 9].

Windowing technique in FM radar realized by FPGA for better target resolution

NASA Astrophysics Data System (ADS)

Ponomaryov, Volodymyr I.; Escamilla-Hernandez, Enrique; Kravchenko, Victor F.

2006-09-01

Remote sensing systems, such as SAR usually apply FM signals to resolve nearly placed targets (objects) and improve SNR. Main drawbacks in the pulse compression of FM radar signal that it can add the range side-lobes in reflectivity measurements. Using weighting window processing in time domain it is possible to decrease significantly the side-lobe level (SLL) of output radar signal that permits to resolve small or low power targets those are masked by powerful ones. There are usually used classical windows such as Hamming, Hanning, Blackman-Harris, Kaiser-Bessel, Dolph-Chebyshev, Gauss, etc. in window processing. Additionally to classical ones in here we also use a novel class of windows based on atomic functions (AF) theory. For comparison of simulation and experimental results we applied the standard parameters, such as coefficient of amplification, maximum level of side-lobe, width of main lobe, etc. In this paper we also proposed to implement the compression-windowing model on a hardware level employing Field Programmable Gate Array (FPGA) that offers some benefits like instantaneous implementation, dynamic reconfiguration, design, and field programmability. It has been investigated the pulse compression design on FPGA applying classical and novel window technique to reduce the SLL in absence and presence of noise. The paper presents simulated and experimental examples of detection of small or nearly placed targets in the imaging radar. Paper also presents the experimental hardware results of windowing in FM radar demonstrating resolution of the several targets for classical rectangular, Hamming, Kaiser-Bessel, and some novel ones: Up(x), fup 4(x)•D 3(x), fup 6(x)•G 3(x), etc. It is possible to conclude that windows created on base of the AFs offer better decreasing of the SLL in cases of presence or absence of noise and when we move away of the main lobe in comparison with classical windows.

Structure of Kinetic Alfvén Waves of Small Transverse Scale

NASA Astrophysics Data System (ADS)

Morales, G. J.; Maggs, J. E.

1996-11-01

This analytical study illustrates the spatial pattern of kinetic Alfvén waves excited by a current-modulating disk whose dimension R transverse to the confining magnetic field is comparable to cs / Ω_i. The radial structure of the wave azimuthal magnetic field consists of 3 regions: a Bessel function behavior for r < R, a near null at r ~ R, and a driven Airy pattern for r >> R. The pattern spreads at an angle given by tan θ = (ω/Ω_i)(c_s/V_A)/(2 \\cdot 6), where ω is the modulation frequency and VA the Alfvén speed. This arises because there is a maximum value at finite k_⊥ for the ratio of the perpendicular to parallel group velocity, which differs from the cone spreading(G.J. Morales, R.S. Loritsch, and J.E. Maggs, Phys. Plasmas) 1, 3765 (1994) associated with inertial Alfvén waves. Sponsored by ONR

Imaging of the stroke-related changes in the vascular system of the mouse brain with the use of extended focus optical coherence microscopy

NASA Astrophysics Data System (ADS)

Tamborski, Szymon; Lyu, Hong Chou; Bukowska, Danuta; Dolezyczek, Hubert; Wilczynski, Grzegorz; Szlag, Daniel; Lasser, Theo; Wojtkowski, Maciej; Szkulmowski, Maciej

2016-03-01

We used Optical Coherence Microscopy (OCM) to monitor structural and functional changes due to ischemic stroke in small animals brains in vivo. To obtain lateral resolution of 2.2 μm over the range of 600 μm we used extended focus configuration of OCM instrument involving Bessel beam. It provided access to detailed 3D information about the changes in brain vascular system up to the level of capillaries across I and II/III layers of neocortex. We used photothrombotic stroke model involving photoactive application of rose bengal to assure minimal invasiveness of the procedure and precise localization of the clot distribution center. We present the comparative analysis involving structural and angiographic maps of the stroke-affected brain enabling in-depth insight to the process of development of the disorder.

The observational constraint on constant-roll inflation

NASA Astrophysics Data System (ADS)

Gao, Qing

2018-07-01

We discuss the constant-roll inflation with constant ɛ2 and constant \\bar η . By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of ɛ1. The model with constant ɛ2 is ruled out by the observations at the 3σ confidence level, and the model with constant \\bar η is consistent with the observations at the 1σ confidence level. The potential for the model with constant \\bar η is also obtained from the Hamilton-Jacobi equation. Although the observations constrain the constant-roll inflation to be the slow-roll inflation, the n s- r results from the constant-roll inflation are not the same as those from the slow-roll inflation even when \\bar η 0.01.

Quantum communication through an unmodulated spin chain.

PubMed

Bose, Sougato

2003-11-14

We propose a scheme for using an unmodulated and unmeasured spin chain as a channel for short distance quantum communications. The state to be transmitted is placed on one spin of the chain and received later on a distant spin with some fidelity. We first obtain simple expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using our scheme. We then apply this to the realizable case of an open ended chain with nearest neighbor interactions. The fidelity of quantum state transfer is obtained as an inverse discrete cosine transform and as a Bessel function series. We find that in a reasonable time, a qubit can be directly transmitted with better than classical fidelity across the full length of chains of up to 80 spins. Moreover, our channel allows distillable entanglement to be shared over arbitrary distances.

Experimental and numerical investigations of microwave return loss of aircraft inlets with low-pressure plasma

NASA Astrophysics Data System (ADS)

Zhang, Yachun; He, Xiang; Chen, Jianping; Chen, Hongqing; Chen, Li; Zhang, Hongchao; Ni, Xiaowu; Lu, Jian; Shen, Zhonghua

2018-03-01

The relationships between return losses of the cylindrical inlet and plasma discharge parameters are investigated experimentally and numerically. The return losses are measured using a high dynamic range measurement system and simulated by COMSOL Multiphysics when the frequency band of the microwaves is in the range 1-4 GHz. The profiles of the plasma density are estimated using Epstein and Bessel functions. Results show that the incident microwaves can be absorbed by plasma efficaciously. The maximal return loss can reach -13.84 dB when the microwave frequency is 2.3 GHz. The increase of applied power implies augmentation of the return loss, which behaves conversely for gas pressure. The experimental and numerical results display reasonable agreement on return loss, suggesting that the use of plasma is effective in the radar cross section reduction of aircraft inlets.

S-Wave Normal Mode Propagation in Aluminum Cylinders

USGS Publications Warehouse

Lee, Myung W.; Waite, William F.

2010-01-01

Large amplitude waveform features have been identified in pulse-transmission shear-wave measurements through cylinders that are long relative to the acoustic wavelength. The arrival times and amplitudes of these features do not follow the predicted behavior of well-known bar waves, but instead they appear to propagate with group velocities that increase as the waveform feature's dominant frequency increases. To identify these anomalous features, the wave equation is solved in a cylindrical coordinate system using an infinitely long cylinder with a free surface boundary condition. The solution indicates that large amplitude normal-mode propagations exist. Using the high-frequency approximation of the Bessel function, an approximate dispersion relation is derived. The predicted amplitude and group velocities using the approximate dispersion relation qualitatively agree with measured values at high frequencies, but the exact dispersion relation should be used to analyze normal modes for full ranges of frequency of interest, particularly at lower frequencies.

On the validity of the use of a localized approximation for helical beams. I. Formal aspects

NASA Astrophysics Data System (ADS)

Gouesbet, Gérard; André Ambrosio, Leonardo

2018-03-01

The description of an electromagnetic beam for use in light scattering theories may be carried out by using an expansion over vector spherical wave functions with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to evaluate these BSCs has been the use of localized approximations (with several existing variants). We recently established that the use of any existing localized approximation is of limited validity in the case of Bessel and Mathieu beams. In the present paper, we address a warning against the use of any existing localized approximation in the case of helical beams. More specifically, we demonstrate that a procedure used to validate any existing localized approximation fails in the case of helical beams. Numerical computations in a companion paper will confirm that existing localized approximations are of limited validity in the case of helical beams.

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

NASA Astrophysics Data System (ADS)

Romero, G.; Alvarez, L.; Alanís, E.; Nallim, L.; Grossi, R.

2003-07-01

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh-Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram-Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.

Video-rate volumetric functional imaging of the brain at synaptic resolution.

PubMed

Lu, Rongwen; Sun, Wenzhi; Liang, Yajie; Kerlin, Aaron; Bierfeld, Jens; Seelig, Johannes D; Wilson, Daniel E; Scholl, Benjamin; Mohar, Boaz; Tanimoto, Masashi; Koyama, Minoru; Fitzpatrick, David; Orger, Michael B; Ji, Na

2017-04-01

Neurons and neural networks often extend hundreds of micrometers in three dimensions. Capturing the calcium transients associated with their activity requires volume imaging methods with subsecond temporal resolution. Such speed is a challenge for conventional two-photon laser-scanning microscopy, because it depends on serial focal scanning in 3D and indicators with limited brightness. Here we present an optical module that is easily integrated into standard two-photon laser-scanning microscopes to generate an axially elongated Bessel focus, which when scanned in 2D turns frame rate into volume rate. We demonstrated the power of this approach in enabling discoveries for neurobiology by imaging the calcium dynamics of volumes of neurons and synapses in fruit flies, zebrafish larvae, mice and ferrets in vivo. Calcium signals in objects as small as dendritic spines could be resolved at video rates, provided that the samples were sparsely labeled to limit overlap in their axially projected images.

A lumped-circuit model for the radiation impedance of a circular piston in a rigid baffle.

PubMed

Bozkurt, Ayhan

2008-09-01

The radiation impedance of a piston transducer mounted in a rigid baffle has been widely addressed in the literature. The real and imaginary parts of the impedance are described by the first order Bessel and Struve functions, respectively. Although there are power series expansions for both functions, the analytic formulation of a lumped circuit is not trivial. In this paper, we present an empirical approach to the derivation of a lumped-circuit model for the radiation impedance expression, based on observations on the near-field behavior of stored kinetic and elastic energy. The field analysis is carried out using a finite element method model of the piston and surrounding fluid medium. We show that fluctuations in the real and imaginary components of the impedance can be modeled by series and shunt tank circuits, each of which shape a certain section of the impedance curve. Because the model is composed of lumped-circuit elements, it can be used in circuit simulators. Consequently, the proposed model is useful for the analysis of transducer front-end circuits.

Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response

NASA Astrophysics Data System (ADS)

Floerchinger, Stefan; Wiedemann, Urs Achim

2014-08-01

An interesting opportunity to determine thermodynamic and transport properties in more detail is to identify generic statistical properties of initial density perturbations. Here we study event-by-event fluctuations in terms of correlation functions for two models that can be solved analytically. The first assumes Gaussian fluctuations around a distribution that is fixed by the collision geometry but leads to non-Gaussian features after averaging over the reaction plane orientation at non-zero impact parameter. In this context, we derive a three-parameter extension of the commonly used Bessel-Gaussian event-by-event distribution of harmonic flow coefficients. Secondly, we study a model of N independent point sources for which connected n-point correlation functions of initial perturbations scale like 1 /N n-1. This scaling is violated for non-central collisions in a way that can be characterized by its impact parameter dependence. We discuss to what extent these are generic properties that can be expected to hold for any model of initial conditions, and how this can improve the fluid dynamical analysis of heavy ion collisions.

Computation of solar perturbations with Poisson series

NASA Technical Reports Server (NTRS)

Broucke, R.

1974-01-01

Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.

Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

PubMed

Kiselev, Aleksei P; Plachenov, Alexandr B

2016-04-01

The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

Bessel Fourier orientation reconstruction: an analytical EAP reconstruction using multiple shell acquisitions in diffusion MRI.

PubMed

Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L

2011-01-01

The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.

Small-Angle Scatter Measurement.

NASA Astrophysics Data System (ADS)

Wein, Steven Jay

The design, analysis, and performance of a small -angle scatterometer are presented. The effects of the diffraction background, geometrical aberrations and system scatter at the small-angles are separated. Graphs are provided that quantify their contribution. The far-field irradiance distributions of weakly truncated and untruncated Gaussian beams are compared. The envelope of diffraction ringing is shown to decrease proportionately with the level of truncation in the pupil. Spherical aberration and defocus are shown to have little effect on the higher-order diffraction rings of Gaussian apertures and as such will have a negligible effect on most scatter measurements. A method is presented for determining the scattered irradiance level for a given BRDF in relation to the peak irradiance of the point spread function. A method of Gaussian apodization is presented and tested that allows the level of diffraction ringing to become a design parameter. Upon sufficient reduction of the diffraction background, the scattered light from the scatterometers' primary mirror is seen to be the limiting component of the small-angle instrument profile. The scatterometer described was able to make a meaningful measurement close enough to the specular direction at 0.6328mum in order to observe the characteristic height and width of the scatter function. This allowed the rms roughness and autocorrelation length of the surface to be determined from the scatter data at this wavelength. The inferred rms roughness agreed well with an independent optical profilometer measurement of the surface. The BRDF of the samples were also measured at 10.6mum. The rms roughness inferred from this scatter data did not agree with the other measurements. The BRDF did not scale in accordance with the scaler diffraction theory of microrough surfaces. The scattering in the visible was dominated by the effects of surface roughness whereas the scattering in the far-infrared was apparently dominated by the effects of contaminants and surface defects. The model for the surface statistics is investigated. A K_0 (modified Bessel function) autocorrelation function is shown to predict the scattered light distribution of these samples much better than the conventional negative -exponential function. Additionally, a sampling theory is developed that addresses the negative-exponentially correlated output of lock-in amplifiers, detectors, and electronic circuits in general. It is shown that the optimum sampling rate is approximately one sample per time constant and at this rate the improvement in SNR is sqrt {N/2} where N is the number of measurements.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, Trilateral Euregio Cluster, P.O. Box 1207, 3430 BE Nieuwegein

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possiblemore » to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain.« less

A constrained regularization method for inverting data represented by linear algebraic or integral equations

NASA Astrophysics Data System (ADS)

Provencher, Stephen W.

1982-09-01

CONTIN is a portable Fortran IV package for inverting noisy linear operator equations. These problems occur in the analysis of data from a wide variety experiments. They are generally ill-posed problems, which means that errors in an unregularized inversion are unbounded. Instead, CONTIN seeks the optimal solution by incorporating parsimony and any statistical prior knowledge into the regularizor and absolute prior knowledge into equallity and inequality constraints. This can be greatly increase the resolution and accuracyh of the solution. CONTIN is very flexible, consisting of a core of about 50 subprograms plus 13 small "USER" subprograms, which the user can easily modify to specify special-purpose constraints, regularizors, operator equations, simulations, statistical weighting, etc. Specjial collections of USER subprograms are available for photon correlation spectroscopy, multicomponent spectra, and Fourier-Bessel, Fourier and Laplace transforms. Numerically stable algorithms are used throughout CONTIN. A fairly precise definition of information content in terms of degrees of freedom is given. The regularization parameter can be automatically chosen on the basis of an F-test and confidence region. The interpretation of the latter and of error estimates based on the covariance matrix of the constrained regularized solution are discussed. The strategies, methods and options in CONTIN are outlined. The program itself is described in the following paper.

Dynamics of Longitudinal Impact in the Variable Cross-Section Rods

NASA Astrophysics Data System (ADS)

Stepanov, R.; Romenskyi, D.; Tsarenko, S.

2018-03-01

Dynamics of longitudinal impact in rods of variable cross-section is considered. Rods of various configurations are used as elements of power pulse systems. There is no single method to the construction of a mathematical model of longitudinal impact on rods. The creation of a general method for constructing a mathematical model of longitudinal impact for rods of variable cross-section is the goal of the article. An elastic rod is considered with a cross-sectional area varying in powers of law from the longitudinal coordinate. The solution of the wave equation is obtained using the Fourier method. Special functions are introduced on the basis of recurrence relations for Bessel functions for solving boundary value problems. The expression for the square of the norm is obtained taking into account the orthogonality property of the eigen functions with weight. For example, the impact of an inelastic mass along the wide end of a conical rod is considered. The expressions for the displacements, forces and stresses of the rod sections are obtained for the cases of sudden velocity communication and the application of force. The proposed mathematical model makes it possible to carry out investigations of the stress-strain state in rods of variable and constant cross-section for various conditions of dynamic effects.

A wavelet-based statistical analysis of FMRI data: I. motivation and data distribution modeling.

PubMed

Dinov, Ivo D; Boscardin, John W; Mega, Michael S; Sowell, Elizabeth L; Toga, Arthur W

2005-01-01

We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural magnetic resonance imaging (MRI) and fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and spatial locations. An anatomical subvolume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of which is processed separately. A frequency-adaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals on all the regions are computed in a compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that the Cauchy, Bessel K Forms, and Pareto distributions provide the most accurate asymptotic models for the distribution of the wavelet coefficients of the data. Finally, we propose a new model for statistical analysis of functional MRI data using this atlas-based wavelet space representation. In the second part of our investigation, we will apply this technique to analyze a large fMRI dataset involving repeated presentation of sensory-motor response stimuli in young, elderly, and demented subjects.

Acoustic metasurface for refracted wave manipulation

NASA Astrophysics Data System (ADS)

Han, Li-Xiang; Yao, Yuan-Wei; Zhang, Xin; Wu, Fu-Gen; Dong, Hua-Feng; Mu, Zhong-Fei; Li, Jing-bo

2018-02-01

Here we present a design of a transmitted acoustic metasurface based on a single row of Helmholtz resonators with varying geometric parameters. The proposed metasurface can not only steer an acoustic beam as expected from the generalized Snell's law of refraction, but also exhibits various interesting properties and potential applications such as insulation of two quasi-intersecting transmitted sound waves, ultrasonic Bessel beam generator, frequency broadening effect of anomalous refraction and focusing.

Generation of light-sheet at the end of multimode fibre (Conference Presentation)

NASA Astrophysics Data System (ADS)

Plöschner, Martin; Kollárová, Véra; Dostál, Zbyněk.; Nylk, Jonathan; Barton-Owen, Thomas; Ferrier, David E. K.; Chmelik, Radim; Dholakia, Kishan; Cizmár, TomáÅ.¡

2017-02-01

Light-sheet fluorescence microscopy is quickly becoming one of the cornerstone imaging techniques in biology as it provides rapid, three-dimensional sectioning of specimens at minimal levels of phototoxicity. It is very appealing to bring this unique combination of imaging properties into an endoscopic setting and be able to perform optical sectioning deep in tissues. Current endoscopic approaches for delivery of light-sheet illumination are based on single-mode optical fibre terminated by cylindrical gradient index lens. Such configuration generates a light-sheet plane that is axially fixed and a mechanical movement of either the sample or the endoscope is required to acquire three-dimensional information about the sample. Furthermore, the axial resolution of this technique is limited to 5um. The delivery of the light-sheet through the multimode fibre provides better axial resolution limited only by its numerical aperture, the light-sheet is scanned holographically without any mechanical movement, and multiple advanced light-sheet imaging modalities, such as Bessel and structured illumination Bessel beam, are intrinsically supported by the system due to the cylindrical symmetry of the fibre. We discuss the holographic techniques for generation of multiple light-sheet types and demonstrate the imaging on a sample of fluorescent beads fixed in agarose gel, as well as on a biological sample of Spirobranchus Lamarcki.

Exploring possibilities of band gap measurement with off-axis EELS in TEM.

PubMed

Korneychuk, Svetlana; Partoens, Bart; Guzzinati, Giulio; Ramaneti, Rajesh; Derluyn, Joff; Haenen, Ken; Verbeeck, Jo

2018-06-01

A technique to measure the band gap of dielectric materials with high refractive index by means of energy electron loss spectroscopy (EELS) is presented. The technique relies on the use of a circular (Bessel) aperture and suppresses Cherenkov losses and surface-guided light modes by enforcing a momentum transfer selection. The technique also strongly suppresses the elastic zero loss peak, making the acquisition, interpretation and signal to noise ratio of low loss spectra considerably better, especially for excitations in the first few eV of the EELS spectrum. Simulations of the low loss inelastic electron scattering probabilities demonstrate the beneficial influence of the Bessel aperture in this setup even for high accelerating voltages. The importance of selecting the optimal experimental convergence and collection angles is highlighted. The effect of the created off-axis acquisition conditions on the selection of the transitions from valence to conduction bands is discussed in detail on a simplified isotropic two band model. This opens the opportunity for deliberately selecting certain transitions by carefully tuning the microscope parameters. The suggested approach is experimentally demonstrated and provides good signal to noise ratio and interpretable band gap signals on reference samples of diamond, GaN and AlN while offering spatial resolution in the nm range. Copyright © 2018 Elsevier B.V. All rights reserved.

Ultrahigh-sensitive multimode interference-based fiber optic liquid-level sensor realized using illuminating zero-order Bessel-Gauss beam

NASA Astrophysics Data System (ADS)

Saha, Ardhendu; Datta, Arijit; Kaman, Surjit

2018-03-01

A proposal toward the enhancement in the sensitivity of a multimode interference-based fiber optic liquid-level sensor is explored analytically using a zero-order Bessel-Gauss (BG) beam as the input source. The sensor head consists of a suitable length of no-core fiber (NCF) sandwiched between two specialty high-order mode fibers. The coupling efficiency of various order modes inside the sensor structure is assessed using guided-mode propagation analysis and the performance of the proposed sensor has been benchmarked against the conventional sensor using a Gaussian beam. Furthermore, the study has been corroborated using a finite-difference beam propagation method in Lumerical's Mode Solutions software to investigate the propagation of the zero-order BG beam inside the sensor structure. Based on the simulation outcomes, the proposed scheme yields a maximum absolute sensitivity of up to 3.551 dB / mm and a sensing resolution of 2.816 × 10 - 3 mm through the choice of an appropriate length of NCF at an operating wavelength of 1.55 μm. Owing to this superior sensing performance, the reported sensing technology expedites an avenue to devise a high-performance fiber optic-level sensor that finds profound implication in different physical, biological, and chemical sensing purposes.

Transmission characteristics of Bessel-Gaussian vortex beams propagating along both longitudinal and transverse directions in a subway tunnel

NASA Astrophysics Data System (ADS)

Wang, Xiaohui; Song, Yingxiong

2018-02-01

By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel-Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.

High-Frequency Normal Mode Propagation in Aluminum Cylinders

USGS Publications Warehouse

Lee, Myung W.; Waite, William F.

2009-01-01

Acoustic measurements made using compressional-wave (P-wave) and shear-wave (S-wave) transducers in aluminum cylinders reveal waveform features with high amplitudes and with velocities that depend on the feature's dominant frequency. In a given waveform, high-frequency features generally arrive earlier than low-frequency features, typical for normal mode propagation. To analyze these waveforms, the elastic equation is solved in a cylindrical coordinate system for the high-frequency case in which the acoustic wavelength is small compared to the cylinder geometry, and the surrounding medium is air. Dispersive P- and S-wave normal mode propagations are predicted to exist, but owing to complex interference patterns inside a cylinder, the phase and group velocities are not smooth functions of frequency. To assess the normal mode group velocities and relative amplitudes, approximate dispersion relations are derived using Bessel functions. The utility of the normal mode theory and approximations from a theoretical and experimental standpoint are demonstrated by showing how the sequence of P- and S-wave normal mode arrivals can vary between samples of different size, and how fundamental normal modes can be mistaken for the faster, but significantly smaller amplitude, P- and S-body waves from which P- and S-wave speeds are calculated.

Relationship of scattering phase shifts to special radiation force conditions for spheres in axisymmetric wave-fields.

PubMed

Marston, Philip L; Zhang, Likun

2017-05-01

When investigating the radiation forces on spheres in complicated wave-fields, the interpretation of analytical results can be simplified by retaining the s-function notation and associated phase shifts imported into acoustics from quantum scattering theory. For situations in which dissipation is negligible, as taken to be the case in the present investigation, there is an additional simplification in that partial-wave phase shifts become real numbers that vanish when the partial-wave index becomes large and when the wave-number-sphere-radius product vanishes. By restricting attention to monopole and dipole phase shifts, transitions in the axial radiation force for axisymmetric wave-fields are found to be related to wave-field parameters for traveling and standing Bessel wave-fields by considering the ratio of the phase shifts. For traveling waves, the special force conditions concern negative forces while for standing waves, the special force conditions concern vanishing radiation forces. An intermediate step involves considering the functional dependence on phase shifts. An appendix gives an approximation for zero-force plane standing wave conditions. Connections with early investigations of acoustic levitation are mentioned and some complications associated with viscosity are briefly noted.

On a new coordinate system with astrophysical application: Spiral coordinates

NASA Astrophysics Data System (ADS)

Campos, L. M. B. C.; Gil, P. J. S.

In this presentation are introduced spiral coordinates, which are a particular case of conformal coordinates, i.e. orthogonal curvelinear coordinates with equal factors along all coordinate axis. The spiral coordinates in the plane have as coordinate curves two families of logarithmic spirals, making a constant angle, respectively phi and pi / 2-phi, with all radial lines, where phi is a parameter. They can be obtained from a complex function, representing a spiral potential flow, due to the superposition of a source/sink with a vortex; the parameter phi in this case specifies the ratio of the ass flux of source/sink to the circulation of the vortex. Regardless of hydrodynamical or other interpretations, spiral coordinates are particulary convenient in situation where physical quantities vary only along a logarithmicspiral. The example chosen is the propagation of Alfven waves along a logarithmic spiral, as an approximation to Parker's spiral. The equation of dissipative MHD are written in spiral coordinates, and eliminated to specify the Alfven wave equation in spiral coordinates; the latter is solved exactly in terms of Bessel functions, and the results analyzed for values of the parameters corresponding to the solar wind.

Magnetic Flux Distribution of Linear Machines with Novel Three-Dimensional Hybrid Magnet Arrays

PubMed Central

Yao, Nan; Yan, Liang; Wang, Tianyi; Wang, Shaoping

2017-01-01

The objective of this paper is to propose a novel tubular linear machine with hybrid permanent magnet arrays and multiple movers, which could be employed for either actuation or sensing technology. The hybrid magnet array produces flux distribution on both sides of windings, and thus helps to increase the signal strength in the windings. The multiple movers are important for airspace technology, because they can improve the system’s redundancy and reliability. The proposed design concept is presented, and the governing equations are obtained based on source free property and Maxwell equations. The magnetic field distribution in the linear machine is thus analytically formulated by using Bessel functions and harmonic expansion of magnetization vector. Numerical simulation is then conducted to validate the analytical solutions of the magnetic flux field. It is proved that the analytical model agrees with the numerical results well. Therefore, it can be utilized for the formulation of signal or force output subsequently, depending on its particular implementation. PMID:29156577

Means and method for nonuniform poling of piezoelectric transducers

DOEpatents

Hsu, David K.; Margetan, Frank J.; Hasselbusch, Michael D.; Wormley, Samuel J.; Hughes, Michael S.; Thompson, Donald O.

1990-10-09

An apparatus and method for nonuniform poling of piezoelectric transducers includes machining one or more indentation into an end of a piezoelectric rod and cutting the rod to present a thickened disk shape. Highly electrically conductive material is deposited on at least the indentations in the one end and on at least portions of the opposite face of the member. One or more electrodes are configured to matingly fit within the indentations on the one face of the disk, with a like number of electrodes being positionable on the opposite face of the material. Electrical power is then applied to the electrodes in desired amounts, polarity, and duration. The indentations vary the electrical field produced within the piezoelectric material to produce nonuniform poling in the material. The thick disk is then cut to remove the indentations and to present a thin, flat two sided disk for installation in a conventional piezoelectric transducer probe. The indentations are selected to produce poling in accordance with desired transducer response profiles such as Gaussian or Bessel functions.

Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background

DOE PAGES

Floerchinger, Stefan; Martinez, Mauricio

2015-12-11

Baryon number density perturbations offer a possible route to experimentally measure baryon number susceptibilities and heat conductivity of the quark gluon plasma. We study the fluid dynamical evolution of local and event-by-event fluctuations of baryon number density, flow velocity, and energy density on top of a (generalized) Bjorken expansion. To that end we use a background-fluctuation splitting and a Bessel-Fourier decomposition for the fluctuating part of the fluid dynamical fields with respect to the azimuthal angle, the radius in the transverse plane, and rapidity. Here, we examine how the time evolution of linear perturbations depends on the equation of statemore » as well as on shear viscosity, bulk viscosity, and heat conductivity for modes with different azimuthal, radial, and rapidity wave numbers. Finally we discuss how this information is accessible to experiments in terms of the transverse and rapidity dependence of correlation functions for baryonic particles in high energy nuclear collisions.« less

Partially coherent surface plasmon modes

NASA Astrophysics Data System (ADS)

Niconoff, G. M.; Vara, P. M.; Munoz-Lopez, J.; Juárez-Morales, J. C.; Carbajal-Dominguez, A.

2011-04-01

Elementary long-range plasmon modes are described assuming an exponential dependence of the refractive index in the neighbourhood of the interface dielectric-metal thin film. The study is performed using coupling mode theory. The interference between two long-range plasmon modes generated that way allows the synthesis of surface sinusoidal plasmon modes, which can be considered as completely coherent generalized plasmon modes. These sinusoidal plasmon modes are used for the synthesis of new partially coherent surface plasmon modes, which are obtained by means of an incoherent superposition of sinusoidal plasmon modes where the period of each one is considered as a random variable. The kinds of surface modes generated have an easily tuneable profile controlled by means of the probability density function associated to the period. We show that partially coherent plasmon modes have the remarkable property to control the length of propagation which is a notable feature respect to the completely coherent surface plasmon mode. The numerical simulation for sinusoidal, Bessel, Gaussian and Dark Hollow plasmon modes are presented.

To construct a stable and tunable optical trap in the focal region of a high numerical aperture lens

NASA Astrophysics Data System (ADS)

Kandasamy, Gokulakrishnan; Ponnan, Suresh; Sivasubramonia Pillai, T. V.; Balasundaram, Rajesh K.

2014-05-01

Based on the diffraction theory, the focusing properties of a radially polarized quadratic Bessel-Gaussian beam (QBG) with on-axis radial phase variance wavefront are investigated theoretically in the focal region of a high numerical aperture (NA) objective lens. The phase wavefront C and pupil beam parameter μ of QBG are the functions of the radial coordinate. The detailed numerical calculation of the focusing property of a QBG beam is presented. The numerical calculation shows that the beam parameter μ and phase parameter C have greater effect on the total electric field intensity distribution. It is observed that under the condition of different μ, evolution principle of focal pattern differs very remarkably on increasing C. Also, some different focal shapes may appear, including rhombic shape, quadrangular shape, two-spherical crust focus shape, two-peak shape, one dark hollow focus, two dark hollow focuses pattern, and triangle dark hollow focus, which find wide optical applications such as optical trapping and nanopatterning.

A 4D Hyperspherical Interpretation of q-Space

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Bendlin, Barbara B.; Alexander, Andrew L.

2015-01-01

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space. PMID:25624043

A 4D hyperspherical interpretation of q-space.

PubMed

Pasha Hosseinbor, A; Chung, Moo K; Wu, Yu-Chien; Bendlin, Barbara B; Alexander, Andrew L

2015-04-01

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space. Copyright © 2014 Elsevier B.V. All rights reserved.

Study of V-OTDR stability for dynamic strain measurement in piezoelectric vibration

NASA Astrophysics Data System (ADS)

Ren, Meiqi; Lu, Ping; Chen, Liang; Bao, Xiaoyi

2016-09-01

In a phase-sensitive optical-time domain reflectometry (Φ-OTDR) system, the challenge for dynamic strain measurement lies in large intensity fluctuations from trace to trace. The intensity fluctuation caused by stochastic characteristics of Rayleigh backscattering sets detection limit for the minimum strength of vibration measurement and causes the large measurement uncertainty. Thus, a trace-to-trace correlation coefficient is introduced to quantify intensity fluctuation of Φ-OTDR traces and stability of the sensor system theoretically and experimentally. A novel approach of measuring dynamic strain induced by various driving voltages of lead zirconate titanate (PZT) in Φ-OTDR is also demonstrated. Piezoelectric vibration signals are evaluated through analyzing peak values of fast Fourier transform spectra at the fundamental frequency and high-order harmonics based on Bessel functions. High trace-to-trace correlation coefficients varying from 0.824 to 0.967 among 100 measurements are obtained in experimental results, showing the good stability of our sensor system, as well as small uncertainty of measured peak values.

ON THE ROTATION SPEED OF THE MILKY WAY DETERMINED FROM H i EMISSION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reid, M. J.; Dame, T. M.

2016-12-01

The circular rotation speed of the Milky Way at the solar radius, Θ{sub 0}, has been estimated to be 220 km s{sup −1} by fitting the maximum velocity of H i emission as a function of Galactic longitude. This result is in tension with a recent estimate of Θ{sub 0} = 240 km s{sup −1}, based on Very Long Baseline Interferometry (VLBI) parallaxes and proper motions from the BeSSeL and VERA surveys for large numbers of high-mass star-forming regions across the Milky Way. We find that the rotation curve best fitted to the VLBI data is slightly curved, and that this curvaturemore » results in a biased estimate of Θ{sub 0} from the H i data when a flat rotation curve is assumed. This relieves the tension between the methods and favors Θ{sub 0} = 240 km s{sup −1}.« less

Magnetic Flux Distribution of Linear Machines with Novel Three-Dimensional Hybrid Magnet Arrays.

PubMed

Yao, Nan; Yan, Liang; Wang, Tianyi; Wang, Shaoping

2017-11-18

The objective of this paper is to propose a novel tubular linear machine with hybrid permanent magnet arrays and multiple movers, which could be employed for either actuation or sensing technology. The hybrid magnet array produces flux distribution on both sides of windings, and thus helps to increase the signal strength in the windings. The multiple movers are important for airspace technology, because they can improve the system's redundancy and reliability. The proposed design concept is presented, and the governing equations are obtained based on source free property and Maxwell equations. The magnetic field distribution in the linear machine is thus analytically formulated by using Bessel functions and harmonic expansion of magnetization vector. Numerical simulation is then conducted to validate the analytical solutions of the magnetic flux field. It is proved that the analytical model agrees with the numerical results well. Therefore, it can be utilized for the formulation of signal or force output subsequently, depending on its particular implementation.

An Empirical UBV RI JHK Color-Temperature Calibration for Stars

NASA Astrophysics Data System (ADS)

Worthey, Guy; Lee, Hyun-chul

2011-03-01

A collection of Johnson/Cousins photometry for stars with known [Fe/H] is used to generate color-color relations that include the abundance dependence. Literature temperature and bolometric correction (BC) dependences are attached to the color relations. The JHK colors are transformed to the Bessell & Brett homogenized system. The main result of this work is the tabulation of seven colors and the V-band BC as a function of T eff, log g, and [Fe/H] for -1.06 < V - K < 10.2 and an accompanying interpolation program. Improvements to the present calibration would involve filling photometry gaps, obtaining more accurate and on-system photometry, knowing better log g and [Fe/H] values, improving the statistics for data-impoverished groups of stars such as metal-poor K dwarfs, applying small tweaks in the processing pipeline, and obtaining better empirical temperature and BC relations, especially for supergiants and M stars. A way to estimate dust extinction from M dwarf colors is pointed out.

VizieR Online Data Catalog: UBVRIJHK color-temperature calibration (Worthey+, 2011)

NASA Astrophysics Data System (ADS)

Worthey, G.; Lee, H.-C.

2011-04-01

A collection of Johnson/Cousins photometry for stars with known [Fe/H] is used to generate color-color relations that include the abundance dependence. Literature temperature and bolometric correction (BC) dependences are attached to the color relations. The JHK colors are transformed to the Bessell & Brett (1988PASP..100.1134B) homogenized system. The main result of this work is the tabulation of seven colors and the V-band BC as a function of Teff, logg, and [Fe/H] for -1.06

Tailoring femtosecond laser pulse filamentation using plasma photonic lattices

NASA Astrophysics Data System (ADS)

Suntsov, Sergiy; Abdollahpour, Daryoush; Papazoglou, Dimitrios G.; Panagiotopoulos, Paris; Couairon, Arnaud; Tzortzakis, Stelios

2013-07-01

We demonstrate experimentally that by using transient plasma photonic lattices, the attributes of intense femtosecond laser filaments, such as peak intensity and length, can be dynamically controlled. The extended plasma lattice structure is generated using two co-propagating non-diffracting intense Bessel beams in water. The use of such transient lattice structures to control the competition between linear and nonlinear effects involved in filamentation opens the way for extensive control of the filamentation process.

The Physics of Ultrabroadband Frequency Comb Generation and Optimized Combs for Measurements in Fundamental Physics

DTIC Science & Technology

2016-07-02

beams Superresolution machining Threshold effect of ablation means that structure diameter is less than the beam diameter fs pulses at 800 nm yield 200...Approved for public release: distribution unlimited. Applications of Bessel beams Superresolution machining Threshold effect of ablation means that... Superresolution machining Threshold effect of ablation means that structure diameter is less than the beam diameter fs pulses at 800 nm yield 200 nm

Depth perception

NASA Astrophysics Data System (ADS)

Sirola, Christopher

2017-03-01

In most disciplines, finding the distance from one object to the next is, at least in theory, a simple operation. Not so in astronomy. While the size of Earth itself was determined with a fair degree of accuracy in ancient times, the scale of the solar system wasn't fully understood until just a few centuries ago, and the distances to even the closest of stars wasn't reliably determined until Friedrich Bessel measured the distance to 61 Cygni in 1838.

VizieR Online Data Catalog: BVRI light curves of GR Boo (Wang+, 2017)

NASA Astrophysics Data System (ADS)

Wang, D.; Zhang, L.; Han, X. L.; Lu, H.

2017-11-01

We observed the eclipsing binary GR Boo on May 12, 22 and 24 in 2015 using the SARA 90-cm telescope located at Kitt Peak National Observatory, Arizona, USA. This telescope was equipped with an ARC CCD camera with a resolution of 2048x2048pixels but used at 2x2 binning, resulting in 1024x1024pixels. We used the Bessel BVRI filters. (1 data file).

Charge distribution of the neven sulphur isotopes from elastic electron scattering

NASA Astrophysics Data System (ADS)

Rychel, D.; Emrich, H. J.; Miska, H.; Gyufko, R.; Wiedner, C. A.

1983-10-01

Elastic electron scattering experiments on the isotopes 32,34,36S were performed covering a range in momentum transfer q = 0.5-2.6 fm -. The cross sections were analysed with the Fourier-Bessel method yielding model-independent charge distributions and their differences. The extracted rms radii follow approximately the systematics of even-even nuclei; this also holds for the gross features as expressed in dms radii and skin thicknesses.

Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faccio, Daniele; CNISM and Department of Physics and Mathematics, Universita dell'Insubria, Via Valleggio 11, I-22100 Como; Serrat, Carles

2010-01-15

The process of high-order harmonic generation in gases is numerically investigated in the presence of a few-cycle pulsed-Bessel-beam pump, featuring a periodic modulation in the peak intensity due to large carrier-envelope-phase mismatch. A two-decade enhancement in the conversion efficiency is observed and interpreted as the consequence of a mechanism known as a nonlinearly induced modulation in the phase mismatch.

Ground-based transit observations of the super-Earth GJ 1214 b

NASA Astrophysics Data System (ADS)

Cáceres, C.; Kabath, P.; Hoyer, S.; Ivanov, V. D.; Rojo, P.; Girard, J. H.; Miller-Ricci Kempton, E.; Fortney, J. J.; Minniti, D.

2014-05-01

Context. GJ 1214 b is one of the few known transiting super-Earth-sized exoplanets with a measured mass and radius. It orbits an M-dwarf, only 14.55 pc away, making it a favorable candidate for follow-up studies. However, the composition of GJ 1214 b's mysterious atmosphere has yet to be fully unveiled. Aims: Our goal is to distinguish between the various proposed atmospheric models to explain the properties of GJ 1214 b: hydrogen-rich or hydrogen-He mix, or a heavy molecular weight atmosphere with reflecting high clouds, as latest studies have suggested. Methods: Wavelength-dependent planetary radii measurements from the transit depths in the optical/NIR are the best tool to investigate the atmosphere of GJ 1214 b. We present here (i) photometric transit observations with a narrow-band filter centered on 2.14 μm and a broad-band I-Bessel filter centered on 0.8665 μm, and (ii) transmission spectroscopy in the H and K atmospheric windows that cover three transits. The photometric and spectrophotometric time series obtained were analyzed with MCMC simulations to measure the planetary radii as a function of wavelength. We determined radii ratios of 0.1173-0.0024+0.0022 for I-Bessel and 0.11735-0.00076+0.00072 at 2.14 μm. Results: Our measurements indicate a flat transmission spectrum, in agreement with the last atmospheric models that favor featureless spectra with clouds and high molecular weight compositions. Based on observations obtained at the Southern Astrophysical Research (SOAR) Telescope, which is a joint project of the Ministério da Ciência, Tecnologia, e Inovação (MCTI) da República Federativa do Brasil, the US National Optical Astronomy Observatory (NOAO), the University of North Carolina at Chapel Hill (UNC), and Michigan State University (MSU). SofI results are based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 087.C-0509.Tables of the lightcurve data are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/565/A7

Color Transformations for the 2MASS Second Incremental Data Release

NASA Astrophysics Data System (ADS)

Carpenter, John M.

2001-05-01

Transformation equations are presented to convert colors and magnitudes measured in the AAO, ARNICA, CIT, DENIS, ESO, LCO (Persson standards), MSSSO, SAAO, and UKIRT photometric systems to the photometric system inherent in the 2MASS Second Incremental Data Release. The transformations have been derived by comparing 2MASS photometry with published magnitudes and colors for stars observed in these systems. Transformation equations have also been derived indirectly for the Bessell & Brett and Koornneef homogenized photometric systems.

VizieR Online Data Catalog: Transiting planet WASP-6b (Tregloan-Reed+, 2015)

NASA Astrophysics Data System (ADS)

Tregloan-Reed, J.; Southworth, J.; Burgdorf, M.; Calchi Novati, S.; Dominik, M.; Finet, F.; Jorgensen, U. G.; Maier, G.; Mancini, L.; Prof, S.; Ricci, D.; Snodgrass, C.; Bozza, V.; Browne, P.; Dodds, P.; Gerner, T.; Harpsoe, K.; Hinse, T. C.; Hundertmark, M.; Kains, N.; Kerins, E.; Liebig, C.; Penny, M. T.; Rahvar, S.; Sahu, K.; Scarpetta, G.; Schafer, S.; Schonebeck, F.; Skottfelt, J.; Surdej, J.

2018-05-01

Four light curves of transits of the extrasolar planetary system WASP-6 are presented. They were obtained using the Danish 1.54m telescope at ESO La Silla, Chile, in the Bessell R passband. The errorbars for each transit have been scaled so the best-fitting model (obtained using the JKTEBOP code and without accounting for the presence of starspots) has a reduced chi-squared value of 1.0. (1 data file).

Broadband Photometry of the Potentially Hazardous Asteroid 2013 RH74

NASA Astrophysics Data System (ADS)

Hicks, M.; Ebelhar, S.

2013-11-01

The Near-Earth Asteroid (NEA) 2013 RH74 was discovered by the Catalina Sky Survey on September 15 2013 (MPEC 2013-S15) and has been designated as a Potentially Hazardous Asteroid (PHA) by the Minor Planet Center. We obtained six partial nights of broadband Bessel BVRI photometry at the JPL Table Mountain 0.6-m telescope (TMO), as summarized in Table 1. This object was detected by planetary radar soon after discovery (http://echo.jpl.nasa.gov/asteroids/index.html).

Generation of spirally polarized propagation-invariant beam using fiber microaxicon.

PubMed

Philip, Geo M; Viswanathan, Nirmal K

2011-10-01

We present here a fiber microaxicon (MA)based method to generate spirally polarized propagation-invariant optical beam. MA chemically etched in the tip of a two-mode fiber efficiently converts the generic cylindrically polarized vortex fiber mode into a spirally polarized propagation-invariant (Bessel-type) beam via radial dependence of polarization rotation angle. The combined roles of helico-conical phase and nonparaxial propagation in the generation and characteristics of the output beam from the fiber MA are discussed. © 2011 Optical Society of America

Physical characterization of (333358) 2001 WN1: a large, possibly water-rich, low delta-V near-Earth asteroid.

NASA Astrophysics Data System (ADS)

Hicks, M.; Dombroski, D.

2012-12-01

The near-Earth asteroid (333358) 2001 WN1 was discovered on 2001 November 17 by the LINEAR NEO survey (MPEC 2001-W30). We obtained one night of Bessel BVRI on 2012 November 25 at the JPL Table Mountain Observatory (TMO) 0.6-m telescope. The observational circumstances are summarized in Table 1, with heliocentric, geocentric, solar phase angle, lunar elongation, and expected V magnitude as computed by the JPL HORIZONS ephemeris service.

On analytic design of loudspeaker arrays with uniform radiation characteristics

PubMed

Aarts; Janssen

2000-01-01

Some notes on analytical derived loudspeaker arrays with uniform radiation characteristics are presented. The array coefficients are derived via analytical means and compared with so-called maximal flat sequences known from telecommunications and information theory. It appears that the newly derived array, i.e., the quadratic phase array, has a higher efficiency than the Bessel array and a flatter response than the Barker array. The method discussed admits generalization to the design of arrays with desired nonuniform radiating characteristics.

The optimal digital filters of sine and cosine transforms for geophysical transient electromagnetic method

NASA Astrophysics Data System (ADS)

Zhao, Yun-wei; Zhu, Zi-qiang; Lu, Guang-yin; Han, Bo

2018-03-01

The sine and cosine transforms implemented with digital filters have been used in the Transient electromagnetic methods for a few decades. Kong (2007) proposed a method of obtaining filter coefficients, which are computed in the sample domain by Hankel transform pair. However, the curve shape of Hankel transform pair changes with a parameter, which usually is set to be 1 or 3 in the process of obtaining the digital filter coefficients of sine and cosine transforms. First, this study investigates the influence of the parameter on the digital filter algorithm of sine and cosine transforms based on the digital filter algorithm of Hankel transform and the relationship between the sine, cosine function and the ±1/2 order Bessel function of the first kind. The results show that the selection of the parameter highly influences the precision of digital filter algorithm. Second, upon the optimal selection of the parameter, it is found that an optimal sampling interval s also exists to achieve the best precision of digital filter algorithm. Finally, this study proposes four groups of sine and cosine transform digital filter coefficients with different length, which may help to develop the digital filter algorithm of sine and cosine transforms, and promote its application.

Leptospirosis risk around a potential source of infection

NASA Astrophysics Data System (ADS)

Loaiza-Echeverry, Erica; Hincapié-Palacio, Doracelly; Ochoa Acosta, Jesús; Ospina Giraldo, Juan

2015-05-01

Leptospirosis is a bacterial zoonosis with world distribution and multiform clinical spectrum in men and animals. The etiology of this disease is the pathogenic species of Leptospira, which cause diverse manifestations of the disease, from mild to serious, such as the Weil disease and the lung hemorrhagic syndrome with lethal proportions of 10% - 50%. This is an emerging problem of urban health due to the growth of marginal neighborhoods without basic sanitary conditions and an increased number of rodents. The presence of rodents and the probability of having contact with their urine determine the likelihood for humans to get infected. In this paper, we simulate the spatial distribution of risk infection of human leptospirosis according to the proximity to rodent burrows considered as potential source of infection. The Bessel function K0 with an r distance from the potential point source, and the scale parameter α in meters was used. Simulation inputs were published data of leptospirosis incidence rate (range of 5 to 79 x 10 000), and a distance of 100 to 5000 meters from the source of infection. We obtained an adequate adjustment between the function and the simulated data. The risk of infection increases with the proximity of the potential source. This estimation can become a guide to propose effective measures of control and prevention.

Structure of kinetic Alfvén waves with small transverse scale length

NASA Astrophysics Data System (ADS)

Morales, G. J.; Maggs, J. E.

1997-11-01

This analytical study illustrates the spatial pattern of kinetic Alfvén waves excited by a current-modulating disk whose dimension a, transverse to the confining magnetic field, is comparable to the ion sound gyroradius cs/Ωi, where cs is the sound speed and Ωi the ion cyclotron frequency. The radial structure of the wave azimuthal magnetic field is found to consist of four regions: a Bessel function behavior for r

Means and method for nonuniform poling of piezoelectric transducers

DOEpatents

Hsu, D.K.; Margetan, F.J.; Hasselbusch, M.D.; Wormley, S.J.; Hughes, M.S.; Thompson, D.O.

1990-10-09

An apparatus and method are disclosed for nonuniform poling of piezoelectric transducers includes machining one or more indentation into an end of a piezoelectric rod and cutting the rod to present a thickened disk shape. Highly electrically conductive material is deposited on at least the indentations in the one end and on at least portions of the opposite face of the member. One or more electrodes are configured to matingly fit within the indentations on the one face of the disk, with a like number of electrodes being positionable on the opposite face of the material. Electrical power is then applied to the electrodes in desired amounts, polarity, and duration. The indentations vary the electrical field produced within the piezoelectric material to produce nonuniform poling in the material. The thick disk is then cut to remove the indentations and to present a thin, flat two sided disk for installation in a conventional piezoelectric transducer probe. The indentations are selected to produce poling in accordance with desired transducer response profiles such as Gaussian or Bessel functions. 14 figs.

A new probability distribution model of turbulent irradiance based on Born perturbation theory

NASA Astrophysics Data System (ADS)

Wang, Hongxing; Liu, Min; Hu, Hao; Wang, Qian; Liu, Xiguo

2010-10-01

The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled. Theory reliably describes the behavior in the weak turbulence regime, but theoretical description in the strong and whole turbulence regimes are still controversial. Based on Born perturbation theory, the physical manifestations and correlations of three typical PDF models (Rice-Nakagami, exponential-Bessel and negative-exponential distribution) were theoretically analyzed. It is shown that these models can be derived by separately making circular-Gaussian, strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory, which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications. In addition, a common shortcoming of the three models is that they are all approximations. A new model, called the Maclaurin-spread distribution, is proposed without any approximation except for assuming the correlation coefficient to be zero. So, it is considered that the new model can exactly reflect the Born perturbation theory. Simulated results prove the accuracy of this new model.

Transient fields produced by a cylindrical electron beam flowing through a plasma

NASA Astrophysics Data System (ADS)

Firpo, Marie-Christine

2012-10-01

Fast ignition schemes (FIS) for inertial confinement fusion should involve in their final stage the interaction of an ignition beam composed of MeV electrons laser generated at the critical density surface with a dense plasma target. In this study, the out-of-equilibrium situation in which an initially sharp-edged cylindrical electron beam, that could e.g. model electrons flowing within a wire [1], is injected into a plasma is considered. A detailed computation of the subsequently produced magnetic field is presented [2]. The control parameter of the problem is shown to be the ratio of the beam radius to the electron skin depth. Two alternative ways to address analytically the problem are considered: one uses the usual Laplace transform approach, the other one involves Riemann's method in which causality conditions manifest through some integrals of triple products of Bessel functions.[4pt] [1] J.S. Green et al., Surface heating of wire plasmas using laser-irradiated cone geometries, Nature Physics 3, 853--856 (2007).[0pt] [2] M.-C. Firpo, http://hal.archives-ouvertes.fr/hal-00695629, to be published (2012).

Shaping non-diffracting beams with a digital micromirror device

NASA Astrophysics Data System (ADS)

Ren, Yu-Xuan; Fang, Zhao-Xiang; Lu, Rong-De

2016-02-01

The micromechanical digital micromirror device (DMD) performs as a spatial light modulator to shape the light wavefront. Different from the liquid crystal devices, which use the birefringence to modulate the light wave, the DMD regulates the wavefront through an amplitude modulation with the digitally controlled mirrors switched on and off. The advantages of such device are the fast speed, polarization insensitivity, and the broadband modulation ability. The fast switching ability for the DMD not only enables the shaping of static light mode, but also could dynamically compensate for the wavefront distortion due to scattering medium. We have employed such device to create the higher order modes, including the Laguerre-Gaussian, Hermite-Gaussian, as well as Mathieu modes. There exists another kind of beam with shape-preservation against propagation, and self-healing against obstacles. Representative modes are the Bessel modes, Airy modes, and the Pearcey modes. Since the DMD modulates the light intensity, a series of algorithms are developed to calculate proper amplitude hologram for shaping the light. The quasi-continuous gray scale images could imitate the continuous amplitude hologram, while the binary amplitude modulation is another means to create the modulation pattern for a steady light field. We demonstrate the generation of the non-diffracting beams with the binary amplitude modulation via the DMD, and successfully created the non-diffracting Bessel beam, Airy beam, and the Pearcey beam. We have characterized the non-diffracting modes through propagation measurements as well as the self-healing measurements.

Polarization-maintaining performance of large effective area, higher order modes fiber in a coiled configuration

NASA Astrophysics Data System (ADS)

Ahmad, Raja; Nicholson, Jeffrey W.; Abedin, Kazi S.; Westbrook, Paul S.; Headley, Clifford; Wisk, Patrick W.; Monberg, Eric M.; Yan, Man F.; DiGiovanni, David J.

2018-02-01

Scaling the power-level of fiber sources has many practical advantages, while also enabling fundamental studies on the light-matter interaction in amorphous guiding media. In order to scale the power-level of fiber-sources without encountering nonlinear impairments, a strategy is to increase the effective-area of the guided optical-mode. Increasing the effective-area of the fundamental mode in a fiber, however, presents the challenges of increased susceptibility to mode-distortion and effective-area-reduction under the influence of bends. Therefore, higher-order-mode (HOM) fibers, which guide light in large effective-area (Aeff) Bessel-like modes, are a good candidate for scaling the power-level of robust fiber-sources. Many applications of high-power fiber-sources also demand a deterministic control on the polarization-state of light. Furthermore, a polarization-maintaining (PM)-type HOM fiber can afford the added possibility of coherent-beam combination and polarization multiplexing of high-power fiber-lasers. Previously, we reported polarization-maintaining operation in a 1.3 m length of PM-HOM fiber that was held straight. The PM-HOM fiber guided Bessel-like modes with Aeff ranging from 1200-2800 μm2. In this work, we report, for the first time, that the polarization-extinction-ratio (PER) of the HOM exceeds 10 dB in an 8 m long fiber that is coiled down to a diameter of 40 cm. This opens a path towards compact and polarization-controlled high-power fiber-systems.

Conserved Genes Act as Modifiers of Invertebrate SMN Loss of Function Defects

PubMed Central

Chang, Howard C.; Sen, Anindya; Kalloo, Geetika; Harris, Jevede; Barsby, Tom; Walsh, Melissa B.; Satterlee, John S.; Li, Chris; Van Vactor, David; Artavanis-Tsakonas, Spyros; Hart, Anne C.

2010-01-01

Spinal Muscular Atrophy (SMA) is caused by diminished function of the Survival of Motor Neuron (SMN) protein, but the molecular pathways critical for SMA pathology remain elusive. We have used genetic approaches in invertebrate models to identify conserved SMN loss of function modifier genes. Drosophila melanogaster and Caenorhabditis elegans each have a single gene encoding a protein orthologous to human SMN; diminished function of these invertebrate genes causes lethality and neuromuscular defects. To find genes that modulate SMN function defects across species, two approaches were used. First, a genome-wide RNAi screen for C. elegans SMN modifier genes was undertaken, yielding four genes. Second, we tested the conservation of modifier gene function across species; genes identified in one invertebrate model were tested for function in the other invertebrate model. Drosophila orthologs of two genes, which were identified originally in C. elegans, modified Drosophila SMN loss of function defects. C. elegans orthologs of twelve genes, which were originally identified in a previous Drosophila screen, modified C. elegans SMN loss of function defects. Bioinformatic analysis of the conserved, cross-species, modifier genes suggests that conserved cellular pathways, specifically endocytosis and mRNA regulation, act as critical genetic modifiers of SMN loss of function defects across species. PMID:21124729

Audio frequency in vivo optical coherence elastography

NASA Astrophysics Data System (ADS)

Adie, Steven G.; Kennedy, Brendan F.; Armstrong, Julian J.; Alexandrov, Sergey A.; Sampson, David D.

2009-05-01

We present a new approach to optical coherence elastography (OCE), which probes the local elastic properties of tissue by using optical coherence tomography to measure the effect of an applied stimulus in the audio frequency range. We describe the approach, based on analysis of the Bessel frequency spectrum of the interferometric signal detected from scatterers undergoing periodic motion in response to an applied stimulus. We present quantitative results of sub-micron excitation at 820 Hz in a layered phantom and the first such measurements in human skin in vivo.

Follow-up Photometry of the Microlensing Event TCP J05074264+2447555

NASA Astrophysics Data System (ADS)

Konyves-Toth, R.; Pal, A.; Ordasi, A.; Vinko, J.

2017-11-01

We report photometric observations of TCP J05074264+2447555 (R.A. = 05:08:43, Dec=+24:47:56), a proposed microlensing event at peak magnitude of V 11.5, discovered by T.Kojima UT 2017-10-25.688, and later confirmed by ASAS-SN (ATel #10923) Our data were taken with the 60/90 cm Schmidt telescope and the 1-meter RCC Telescope through Bessell B,V,R,I filters at Konkoly Observatory, Piszkesteto, Hungary between UT 2017-11-03.9 and 2017-11-04.9.

Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces.

PubMed

Aieta, Francesco; Genevet, Patrice; Kats, Mikhail A; Yu, Nanfang; Blanchard, Romain; Gaburro, Zeno; Capasso, Federico

2012-09-12

The concept of optical phase discontinuities is applied to the design and demonstration of aberration-free planar lenses and axicons, comprising a phased array of ultrathin subwavelength-spaced optical antennas. The lenses and axicons consist of V-shaped nanoantennas that introduce a radial distribution of phase discontinuities, thereby generating respectively spherical wavefronts and nondiffracting Bessel beams at telecom wavelengths. Simulations are also presented to show that our aberration-free designs are applicable to high-numerical aperture lenses such as flat microscope objectives.

Experimental demonstration of highly localized pulses (X waves) at microwave frequencies

NASA Astrophysics Data System (ADS)

Chiotellis, Nikolaos; Mendez, Victor; Rudolph, Scott M.; Grbic, Anthony

2018-02-01

A device that radiates transverse magnetic Bessel beams in the radiative near field is reported. The cone angle of the emitted radiation remains constant over a wide frequency range (18-30 GHz), allowing highly localized pulses (X waves) to be generated under a broadband excitation. The design process, based on ray optics, is discussed. Both frequency and time domain experimental results for a prototype are presented. The measured fields show close agreement with simulation results, and demonstrate the radiator's ability to emit X waves within its nondiffracting range.

The mathematical model of radon-222 accumulation in underground mines

NASA Astrophysics Data System (ADS)

Klimshin, A.

2012-04-01

Necessity to control underground mine air radon level arises during building and operating mines as well as auto and railway tunnels including those for metros. Calculation of underground mine air radon level can be fulfilled for estimation of potential radon danger of area for underground structure building. In this work the new mathematical model of radon accumulation in underground mines has been suggested. It takes into consideration underground mine dimensions, air exchange factor and soils ability to emanate radon. The following assumptions have been taken for model development. It is assumed that underground mine is a cylinder of length L and of base area S. Due to ventilation atmosphere air of volume activity Catm, is coming in through one cylinder base and is going out of volume activity Cind from underground mine. Diffusion radon flux is coming in through side surfaces of underground mine. The sources of this flux are radium-226 atoms distributed evenly in rock. For simplification of the task it considered possible to disregard radon emanation by loosened rock and underground waters. As a result of solution of the radon diffusion equation the following expression for calculation of radon volume activity in underground space air has been got: 2·r0 ·λv ·Catm-·l·K0(r0/l)-+D-·K1(r0/l)·C0- Cind = 2·(λ+ λv)·r0 ·l·K0 (r0/l)+ D ·K1(r0/l) . The following designations are used in this expression: Kν(r) - the second genus modified Bessel's function, C0 - equilibrium radon volume activity in soil air, l - diffusion radon length in soil, D - radon diffusion factor, r0 - radius of underground tunnel, λv - factor of air exchange. Expression found may be used for calculation of the minimum factor of necessary air exchange for ensuring safe radon levels in underground spaces. With this worked out model expected levels of radon volume activity were calculated for air in the second metro line underground spaces in the city of Yekaterinburg, Russia.

Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves.

PubMed

Mitri, F G

2016-03-01

This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications. Copyright © 2015 Elsevier B.V. All rights reserved.

A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

NASA Astrophysics Data System (ADS)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

NASA Astrophysics Data System (ADS)

Kang, Daekyoung; Lee, Christopher; Vaidya, Varun

2018-04-01

We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons ( γ ∗, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.

A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kang, Daekyoung; Lee, Christopher; Vaidya, Varun

Here, we propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons (γ*, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impactmore » parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.« less

Spatial resolution, contrast sensitivity, and sensitivity to defocus of chicken retinal ganglion cells in vitro.

PubMed

Diedrich, Erich; Schaeffel, Frank

2009-11-01

The chicken has been extensively studied as an animal model for myopia because its eye growth is tightly controlled by visual experience. It has been found that the retina controls the axial eye growth rates depending on the amount and the sign of defocus imposed in the projected image. Glucagonergic amacrine cells were discovered that appear to encode for the sign of imposed defocus. It is not clear whether the downstream neurons, the retinal ganglion cells, still have access to this information-and whether it ultimately reaches the brain. We have analyzed the spike rates of chicken retinal ganglion cells in vitro using a microelectrode array. For this purpose, we initially defined spatial resolution and contrast sensitivity in vitro. Two classes of chicken retinal ganglions were found, depending on the linearity of their responses with increasing contrast. Responses generally declined with increasing defocus of the visual stimulus. These responses were well predicted by the modulation transfer function for a diffraction-limited defocused optical system, the first Bessel function. Thus, the studied retinal ganglion cells did not distinguish between a loss of contrast at a given spatial frequency due to reduced contrast of the stimulus pattern or because the pattern was presented out of focus. Furthermore, there was no indication that the retinal ganglion cells responded differently to defocus of either sign, at least for the cells that were recorded in this study.

A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

DOE PAGES

Kang, Daekyoung; Lee, Christopher; Vaidya, Varun

2018-04-27

Here, we propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons (γ*, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impactmore » parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.« less

Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry.

PubMed

Toto-Arellano, Noel-Ivan; Rodriguez-Zurita, Gustavo; Meneses-Fabian, Cruz; Vazquez-Castillo, Jose F

2008-11-10

Among several techniques, phase shifting interferometry can be implemented with a grating used as a beam divider to attain several interference patterns around each diffraction order. Because each pattern has to show a different phase-shift, a suitable shifting technique must be employed. Phase gratings are attractive to perform the former task due to their higher diffraction efficiencies. But as is very well known, the Fourier coefficients of only-phase gratings are integer order Bessel functions of the first kind. The values of these real-valued functions oscillate around zero, so they can adopt negative values, thereby introducing phase shifts of pi at certain diffraction orders. Because this almost trivial fact seems to have been overlooked in the literature regarding its practical implications, in this communication such phase shifts are stressed in the description of interference patterns obtained with grating interferometers. These patterns are obtained by placing two windows in the object plane of a 4f system with a sinusoidal grating/grid in the Fourier plane. It is shown that the corresponding experimental observations of the fringe modulation, as well as the corresponding phase measurements, are all in agreement with the proposed description. A one-shot phase shifting interferometer is finally proposed taking into account these properties after proper incorporation of modulation of polarization.

Novel windowing technique realized in FPGA for radar system

NASA Astrophysics Data System (ADS)

Escamilla-Hernandez, E.; Kravchenko, V. F.; Ponomaryov, V. I.; Ikuo, Arai

2006-02-01

To improve the weak target detection ability in radar applications a pulse compression is usually used that in the case linear FM modulation can improve the SNR. One drawback in here is that it can add the range side-lobes in reflectivity measurements. Using weighting window processing in time domain it is possible to decrease significantly the side-lobe level (SLL) and resolve small or low power targets those are masked by powerful ones. There are usually used classical windows such as Hamming, Hanning, etc. in window processing. Additionally to classical ones in this paper we also use a novel class of windows based on atomic functions (AF) theory. For comparison of simulation and experimental results we applied the standard parameters, such as coefficient of amplification, maximum level of side-lobe, width of main lobe, etc. To implement the compression-windowing model on hardware level it has been employed FPGA. This work aims at demonstrating a reasonably flexible implementation of FM-linear signal, pulse compression and windowing employing FPGA's. Classical and novel AF window technique has been investigated to reduce the SLL taking into account the noise influence and increasing the detection ability of the small or weak targets in the imaging radar. Paper presents the experimental hardware results of windowing in pulse compression radar resolving several targets for rectangular, Hamming, Kaiser-Bessel, (see manuscript for formula) functions windows. The windows created by use the atomic functions offer sufficiently better decreasing of the SLL in case of noise presence and when we move away of the main lobe in comparison with classical windows.

Mathieu Progressive Waves

NASA Astrophysics Data System (ADS)

Andrei, B. Utkin

2011-10-01

A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal curvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.

A plane-polar approach for far-field construction from near-field measurements. [of large space-craft antennas

NASA Technical Reports Server (NTRS)

Rahmat-Samii, Y.; Galindo-Israel, V.; Mittra, R.

1980-01-01

The planar configuration with a probe scanning a polar geometry is discussed with reference to its usefulness in the determination of a far field from near-field measurements. The accuracy of the method is verified numerically, using the concept of probe compensation as a vector deconvolution. Advantages of the Jacobi-Bessel series over the fast Fourier transforms for the plane-polar geometry are demonstrated. Finally, the far-field pattern of the Viking high gain antenna is constructed from the plane-polar near-field measured data and compared with the previously measured far-field pattern.

Contributions to the History of Astronomy, Vol. 5 (German Title: Beiträge zur Astronomiegeschichte, Band 5)

NASA Astrophysics Data System (ADS)

Dick, Wolfgang R.; Hamel, Jürgen

This book contains articles on 16th century horoscopes, on Athanasius Kircher's ``Organum Mathematicum'', on Gottfried Kirch's idea of an astronomical society, on a stellar photometer dating from 1786, on Bessel's review of Gauss' ``Theoria Motus'', on letters by F.X. von Zach, on the discovery of the minor planet Eros, as well as on the astronomers Christoph Scheiner, Johann Philipp von Wurzelbau, Georg Koch and Felix Linke. Short contributions and book reviews conclude this volume. Most papers are written in German. Main papers have English abstracts.

Generation of multi-millijoule red-shifted pulses for seeding stimulated Raman backscattering amplifiers.

PubMed

Landgraf, Björn; Hoffmann, Andreas; Kartashov, Daniil; Gärtner, Felix; Samsonova, Zhanna; Polynkin, Pavel; Jacoby, Joachim; Kühl, Thomas; Spielmann, Christian

2015-03-23

The efficient generation of redshifted pulses from chirped femtosecond joule level Bessel beam pulses in gases is studied. The redshift spans from a few 100 cm⁻¹ to several 1000 cm⁻¹ corresponding to a shift of 50-500 nm for Nd:glass laser systems. The generated pulses have an almost perfect Gaussian beam profile insensitive of the pump beam profile, and are much shorter than the pump pulses. The highest measured energy is as high as 30 mJ, which is significantly higher than possible with solid state nonlinear frequency shifters.

Polarization holograms allow highly efficient generation of complex light beams.

PubMed

Ruiz, U; Pagliusi, P; Provenzano, C; Volke-Sepúlveda, K; Cipparrone, Gabriella

2013-03-25

We report a viable method to generate complex beams, such as the non-diffracting Bessel and Weber beams, which relies on the encoding of amplitude information, in addition to phase and polarization, using polarization holography. The holograms are recorded in polarization sensitive films by the interference of a reference plane wave with a tailored complex beam, having orthogonal circular polarizations. The high efficiency, the intrinsic achromaticity and the simplicity of use of the polarization holograms make them competitive with respect to existing methods and attractive for several applications. Theoretical analysis, based on the Jones formalism, and experimental results are shown.

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

NASA Astrophysics Data System (ADS)

Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-01-01

The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Effect of beam types on the scintillations: a review

NASA Astrophysics Data System (ADS)

Baykal, Yahya; Eyyuboglu, Halil T.; Cai, Yangjian

2009-02-01

When different incidences are launched in atmospheric turbulence, it is known that the intensity fluctuations exhibit different characteristics. In this paper we review our work done in the evaluations of the scintillation index of general beam types when such optical beams propagate in horizontal atmospheric links in the weak fluctuations regime. Variation of scintillation indices versus the source and medium parameters are examined for flat-topped-Gaussian, cosh- Gaussian, cos-Gaussian, annular, elliptical Gaussian, circular (i.e., stigmatic) and elliptical (i.e., astigmatic) dark hollow, lowest order Bessel-Gaussian and laser array beams. For flat-topped-Gaussian beam, scintillation is larger than the single Gaussian beam scintillation, when the source sizes are much less than the Fresnel zone but becomes smaller for source sizes much larger than the Fresnel zone. Cosh-Gaussian beam has lower on-axis scintillations at smaller source sizes and longer propagation distances as compared to Gaussian beams where focusing imposes more reduction on the cosh- Gaussian beam scintillations than that of the Gaussian beam. Intensity fluctuations of a cos-Gaussian beam show favorable behaviour against a Gaussian beam at lower propagation lengths. At longer propagation lengths, annular beam becomes advantageous. In focused cases, the scintillation index of annular beam is lower than the scintillation index of Gaussian and cos-Gaussian beams starting at earlier propagation distances. Cos-Gaussian beams are advantages at relatively large source sizes while the reverse is valid for annular beams. Scintillations of a stigmatic or astigmatic dark hollow beam can be smaller when compared to stigmatic or astigmatic Gaussian, annular and flat-topped beams under conditions that are closely related to the beam parameters. Intensity fluctuation of an elliptical Gaussian beam can also be smaller than a circular Gaussian beam depending on the propagation length and the ratio of the beam waist size along the long axis to that along the short axis (i.e., astigmatism). Comparing against the fundamental Gaussian beam on equal source size and equal power basis, it is observed that the scintillation index of the lowest order Bessel-Gaussian beam is lower at large source sizes and large width parameters. However, for excessively large width parameters and beyond certain propagation lengths, the advantage of the lowest order Bessel-Gaussian beam seems to be lost. Compared to Gaussian beam, laser array beam exhibits less scintillations at long propagation ranges and at some midrange radial displacement parameters. When compared among themselves, laser array beams tend to have reduced scintillations for larger number of beamlets, longer wavelengths, midrange radial displacement parameters, intermediate Gaussian source sizes, larger inner scales and smaller outer scales of turbulence. The number of beamlets used does not seem to be so effective in this improvement of the scintillations.

Functionalized graphene with polymer toughener as novel interface modifier for property-tailored poly(lactic acid)/graphene nanocomposites

USDA-ARS?s Scientific Manuscript database

In this work, an effective strategy for engineering the interfacial compatibility between graphene and polylactic acid (PLA) was developed by manipulating the functionalization of graphene and introducing an epoxy-containing elastomer modifier. Curing between the functional groups of the modified gr...

Continuous time quantum random walks in free space

NASA Astrophysics Data System (ADS)

Eichelkraut, Toni; Vetter, Christian; Perez-Leija, Armando; Christodoulides, Demetrios; Szameit, Alexander

2014-05-01

We show theoretically and experimentally that two-dimensional continuous time coherent random walks are possible in free space, that is, in the absence of any external potential, by properly tailoring the associated initial wave function. These effects are experimentally demonstrated using classical paraxial light. Evidently, the usage of classical beams to explore the dynamics of point-like quantum particles is possible since both phenomena are mathematically equivalent. This in turn makes our approach suitable for the realization of random walks using different quantum particles, including electrons and photons. To study the spatial evolution of a wavefunction theoretically, we consider the one-dimensional paraxial wave equation (i∂z +1/2 ∂x2) Ψ = 0 . Starting with the initially localized wavefunction Ψ (x , 0) = exp [ -x2 / 2σ2 ] J0 (αx) , one can show that the evolution of such Gaussian-apodized Bessel envelopes within a region of validity resembles the probability pattern of a quantum walker traversing a uniform lattice. In order to generate the desired input-field in our experimental setting we shape the amplitude and phase of a collimated light beam originating from a classical HeNe-Laser (633 nm) utilizing a spatial light modulator.

Dynamically sculpturing plasmonic vortices: from integer to fractional orbital angular momentum

PubMed Central

Wang, Yu; Zhao, Peng; Feng, Xue; Xu, Yuntao; Liu, Fang; Cui, Kaiyu; Zhang, Wei; Huang, Yidong

2016-01-01

As a fundamental tool for light-matter interactions, plasmonic vortex (PV) is extremely useful due to the unique near field property. However, it is a pity that, up to now, the orbital angular momentum (OAM) carried by PVs could not be dynamically and continuously tuned in practice as well as the properties of fractional PVs are still not well investigated. By comparing with two previously reported methods, it is suggested that our proposal of utilizing the propagation induced radial phase gradient of incident Laguerre-Gaussian (LG) beam is a promising candidate to sculpture PVs from integer to fractional OAM dynamically. Consequently, the preset OAM of PVs could have four composing parts: the incident spin and orbital angular momentum, the geometric contribution of chiral plasmonic structure, and the radial phase gradient dependent contribution. Moreover, an analytical expression for the fractional PV is derived as a linear superposition of infinite numbers of integer PVs described by Bessel function of the first kind. It is also shown that the actual mean OAM of a fractional PV would deviate from the preset value, which is similar with previous results for spatial fractional optical vortices. PMID:27811986

Well test mathematical model for fractures network in tight oil reservoirs

NASA Astrophysics Data System (ADS)

Diwu, Pengxiang; Liu, Tongjing; Jiang, Baoyi; Wang, Rui; Yang, Peidie; Yang, Jiping; Wang, Zhaoming

2018-02-01

Well test, especially build-up test, has been applied widely in the development of tight oil reservoirs, since it is the only available low cost way to directly quantify flow ability and formation heterogeneity parameters. However, because of the fractures network near wellbore, generated from artificial fracturing linking up natural factures, traditional infinite and finite conductivity fracture models usually result in significantly deviation in field application. In this work, considering the random distribution of natural fractures, physical model of fractures network is proposed, and it shows a composite model feature in the large scale. Consequently, a nonhomogeneous composite mathematical model is established with threshold pressure gradient. To solve this model semi-analytically, we proposed a solution approach including Laplace transform and virtual argument Bessel function, and this method is verified by comparing with existing analytical solution. The matching data of typical type curves generated from semi-analytical solution indicates that the proposed physical and mathematical model can describe the type curves characteristic in typical tight oil reservoirs, which have up warping in late-term rather than parallel lines with slope 1/2 or 1/4. It means the composite model could be used into pressure interpretation of artificial fracturing wells in tight oil reservoir.

Optical choppers with rotational elements: modeling, design and prototypes

NASA Astrophysics Data System (ADS)

Duma, Virgil-Florin; Cira, Octavian; Demian, Dorin

2017-05-01

We present a brief overview of our contributions regarding the analysis and design of optical choppers. Their applications range numerous domains, from optical sensing in radiometry or telescopes to laser manufacturing and biomedical imaging - for example for the controlled attenuation of light, the elimination of selected spectral domains, or the switching of optical paths. While these aspects are pointed out, the paper describes our analysis, modeling, and manufacturing of prototypes for choppers with: (a) wheels with windows with linear margins; (b) wheels with windows with non-linear margins (semi-circular or elliptical), outward or inward; (c) rotational shafts with different shapes, with slits or with holes. While variant (a) represents classical choppers, variant (b) represents the "eclipse" choppers that we have developed and also patented for the solution with two adjustable wheels that can produce circular windows. Variant (c), of choppers with shafts is also a patent application. Their transmission functions are discussed, for the shape of the laser pulses produced and for the attenuation coefficients obtained. While this discussion has been completed analytically for top-hat laser beams, it has been modeled using simulations for Gaussian and Bessel beams. Design, manufacturing aspects, and prototypes of the different chopper configurations complete the presentation.

Controlling Fringe Sensitivity of Electro-Optic Holography Systems Using Laser Diode Current Modulation

NASA Technical Reports Server (NTRS)

Bybee, Shannon J.

2001-01-01

Electro-Optic Holography (EOH) is a non-intrusive, laser-based, displacement measurement technique capable of static and dynamic displacement measurements. EOH is an optical interference technique in which fringe patterns that represent displacement contour maps are generated. At excessively large displacements the fringe density may be so great that individual fringes are not resolvable using typical EOH techniques. This thesis focuses on the development and implementation of a method for controlling the sensitivity of the EOH system. This method is known as Frequency Translated Electro-Optic Holography (FTEOH). It was determined that by modulating the current source of the laser diode at integer multiples of the object vibration, the fringe pattern is governed by higher order Bessel function of the first kind and the number of fringes that represent a given displacement can be controlled. The reduction of fringes is theoretically unlimited but physically limited by the frequency bandwidth of the signal generator, providing modulation to the laser diode. Although this research technique has been verified theoretically and experimentally in this thesis, due to the current laser diode capabilities it is a tedious and time consuming process to acquire data using the FTEOH technique.

Effects of virtual reality training with modified constraint-induced movement therapy on upper extremity function in acute stage stroke: a preliminary study.

PubMed

Ji, Eun-Kyu; Lee, Sang-Heon

2016-11-01

[Purpose] The purpose of this study was to investigate the effects of virtual reality training combined with modified constraint-induced movement therapy on upper extremity motor function recovery in acute stage stroke patients. [Subjects and Methods] Four acute stage stroke patients participated in the study. A multiple baseline single subject experimental design was utilized. Modified constraint-induced movement therapy was used according to the EXplaining PLastICITy after stroke protocol during baseline sessions. Virtual reality training with modified constraint-induced movement therapy was applied during treatment sessions. The Manual Function Test and the Box and Block Test were used to measure upper extremity function before every session. [Results] The subjects' upper extremity function improved during the intervention period. [Conclusion] Virtual reality training combined with modified constraint-induced movement is effective for upper extremity function recovery in acute stroke patients.

Control of atomic transition rates via laser-light shaping

NASA Astrophysics Data System (ADS)

Jáuregui, R.

2015-04-01

A modular systematic analysis of the feasibility of modifying atomic transition rates by tailoring the electromagnetic field of an external coherent light source is presented. The formalism considers both the center of mass and internal degrees of freedom of the atom, and all properties of the field: frequency, angular spectrum, and polarization. General features of recoil effects for internal forbidden transitions are discussed. A comparative analysis of different structured light sources is explicitly worked out. It includes spherical waves, Gaussian beams, Laguerre-Gaussian beams, and propagation invariant beams with closed analytical expressions. It is shown that increments in the order of magnitude of the transition rates for Gaussian and Laguerre-Gaussian beams, with respect to those obtained in the paraxial limit, require waists of the order of the wavelength, while propagation invariant modes may considerably enhance transition rates under more favorable conditions. For transitions that can be naturally described as modifications of the atomic angular momentum, this enhancement is maximal (within propagation invariant beams) for Bessel modes, Mathieu modes can be used to entangle the internal and center-of-mass involved states, and Weber beams suppress this kind of transition unless they have a significant component of odd modes. However, if a recoil effect of the transition with an adequate symmetry is allowed, the global transition rate (center of mass and internal motion) can also be enhanced using Weber modes. The global analysis presented reinforces the idea that a better control of the transitions between internal atomic states requires both a proper control of the available states of the atomic center of mass, and shaping of the background electromagnetic field.

Correlation between mobility assessed by the Modified Rivermead Mobility Index and physical function in stroke patients

PubMed Central

Park, Gi-Tae; Kim, Mihyun

2016-01-01

[Purpose] The purpose of this study was to investigate the relationship between mobility assessed by the Modified Rivermead Mobility Index and variables associated with physical function in stroke patients. [Subjects and Methods] One hundred stroke patients (35 males and 65 females; age 58.60 ± 13.91 years) participated in this study. Modified Rivermead Mobility Index, muscle strength (manual muscle test), muscle tone (Modified Ashworth Scale), range of motion of lower extremity, sensory function (light touch and proprioception tests), and coordination (heel to shin and lower-extremity motor coordination tests) were assessed. [Results] The Modified Rivermead Mobility Index was correlated with all the physical function variables assessed, except the degree of knee extension. In addition, stepwise linear regression analysis revealed that coordination (heel to shin test) was the explanatory variable closely associated with mobility in stroke patients. [Conclusion] The Modified Rivermead Mobility Index score was significantly correlated with all the physical function variables. Coordination (heel to shin test) was closely related to mobility function. These results may be useful in developing rehabilitation programs for stroke patients. PMID:27630440

Modified Gaussian influence function of deformable mirror actuators.

PubMed

Huang, Linhai; Rao, Changhui; Jiang, Wenhan

2008-01-07

A new deformable mirror influence function based on a Gaussian function is introduced to analyze the fitting capability of a deformable mirror. The modified expressions for both azimuthal and radial directions are presented based on the analysis of the residual error between a measured influence function and a Gaussian influence function. With a simplex search method, we further compare the fitting capability of our proposed influence function to fit the data produced by a Zygo interferometer with that of a Gaussian influence function. The result indicates that the modified Gaussian influence function provides much better performance in data fitting.

The effects of modified constraint-induced movement therapy and mirror therapy on upper extremity function and its influence on activities of daily living.

PubMed

Ju, Yumi; Yoon, In-Jin

2018-01-01

[Purpose] Modified constraint-induced movement therapy and mirror therapy are recognized as stroke rehabilitation methods. The aim of the present study was to determine whether these therapies influence upper extremity function and whether upper extremity function influences the ability to perform activities of daily living in further. [Subjects and Methods] Twenty-eight stroke patients participated in the study. Interventions were administered five times per week for 3 weeks. Activities of daily living or self-exercise were performed after modified constraint-induced movement therapy or mirror therapy, respectively. Analyses were performed on the results of the Manual Function Test and the Korean version of the Modified Barthel Index to determine the factors influencing activities of daily living. [Results] Both groups showed improvement in upper extremity function, but only the modified constraint-induced movement therapy group showed a correlation between upper extremity function and performance in the hygiene, eating, and dressing. The improved hand manipulation function found in the modified constraint-induced movement therapy had statistically significant influences on eating and dressing. [Conclusion] Our results suggest that a patient's attempts to move the affected side result in improved performance in activities of daily living as well as physical function.

The effects of modified constraint-induced movement therapy and mirror therapy on upper extremity function and its influence on activities of daily living

PubMed Central

Ju, Yumi; Yoon, In-Jin

2018-01-01

[Purpose] Modified constraint-induced movement therapy and mirror therapy are recognized as stroke rehabilitation methods. The aim of the present study was to determine whether these therapies influence upper extremity function and whether upper extremity function influences the ability to perform activities of daily living in further. [Subjects and Methods] Twenty-eight stroke patients participated in the study. Interventions were administered five times per week for 3 weeks. Activities of daily living or self-exercise were performed after modified constraint-induced movement therapy or mirror therapy, respectively. Analyses were performed on the results of the Manual Function Test and the Korean version of the Modified Barthel Index to determine the factors influencing activities of daily living. [Results] Both groups showed improvement in upper extremity function, but only the modified constraint-induced movement therapy group showed a correlation between upper extremity function and performance in the hygiene, eating, and dressing. The improved hand manipulation function found in the modified constraint-induced movement therapy had statistically significant influences on eating and dressing. [Conclusion] Our results suggest that a patient’s attempts to move the affected side result in improved performance in activities of daily living as well as physical function. PMID:29410571

Flatness-based model inverse for feed-forward braking control

NASA Astrophysics Data System (ADS)

de Vries, Edwin; Fehn, Achim; Rixen, Daniel

2010-12-01

For modern cars an increasing number of driver assistance systems have been developed. Some of these systems interfere/assist with the braking of a car. Here, a brake actuation algorithm for each individual wheel that can respond to both driver inputs and artificial vehicle deceleration set points is developed. The algorithm consists of a feed-forward control that ensures, within the modelled system plant, the optimal behaviour of the vehicle. For the quarter-car model with LuGre-tyre behavioural model, an inverse model can be derived using v x as the 'flat output', that is, the input for the inverse model. A number of time derivatives of the flat output are required to calculate the model input, brake torque. Polynomial trajectory planning provides the needed time derivatives of the deceleration request. The transition time of the planning can be adjusted to meet actuator constraints. It is shown that the output of the trajectory planning would ripple and introduce a time delay when a gradual continuous increase of deceleration is requested by the driver. Derivative filters are then considered: the Bessel filter provides the best symmetry in its step response. A filter of same order and with negative real-poles is also used, exhibiting no overshoot nor ringing. For these reasons, the 'real-poles' filter would be preferred over the Bessel filter. The half-car model can be used to predict the change in normal load on the front and rear axle due to the pitching of the vehicle. The anticipated dynamic variation of the wheel load can be included in the inverse model, even though it is based on a quarter-car. Brake force distribution proportional to normal load is established. It provides more natural and simpler equations than a fixed force ratio strategy.

Hydroelastic analysis of surface wave interaction with concentric porous and flexible cylinder systems

NASA Astrophysics Data System (ADS)

Mandal, S.; Datta, N.; Sahoo, T.

2013-10-01

The present study deals with the hydroelastic analysis of gravity wave interaction with concentric porous and flexible cylinder systems, in which the inner cylinder is rigid and the outer cylinder is porous and flexible. The problems are analyzed in finite water depth under the assumption of small amplitude water wave theory and structural response. The cylinder configurations in the present study are namely (a) surface-piercing truncated cylinders, (b) bottom-touching truncated cylinders and (c) complete submerged cylinders extended from free surface to bottom. As special cases of the concentric cylinder system, wave diffraction by (i) porous flexible cylinder and (ii) flexible floating cage with rigid bottom are analyzed. The scattering potentials are evaluated using Fourier-Bessel series expansion method and the least square approximation method. The convergence of the double series is tested numerically to determine the number of terms in the Fourier-Bessel series expansion. The effects of porosity and flexibility of the outer cylinder, in attenuating the hydrodynamic forces and dynamic overturning moments, are analyzed for various cylinder configurations and wave characteristics. A parametric study with respect to wave frequency, ratios of inner-to-outer cylinder radii, annular spacing between the two cylinders and porosities is done. In order to understand the flow distribution around the cylinders, contour plots are provided. The findings of the present study are likely to be of immense help in the design of various types of marine structures which can withstand the wave loads of varied nature in the marine environment. The theory can be easily extended to deal with a large class of problems associated with acoustic wave interaction with flexible porous structures.

Effects of modified constraint-induced movement therapy on reach-to-grasp movements and functional performance after chronic stroke: a randomized controlled study.

PubMed

Lin, K-C; Wu, C-Y; Wei, T-H; Lee, C-Y; Liu, J-S

2007-12-01

To evaluate changes in (1) motor control characteristics of the hemiparetic hand during the performance of a functional reach-to-grasp task and (2) functional performance of daily activities in patients with stroke treated with modified constraint-induced movement therapy. Two-group randomized controlled trial with pretreatment and posttreatment measures. Rehabilitation clinics. Thirty-two chronic stroke patients (21 men, 11 women; mean age=57.9 years, range=43-81 years) 13-26 months (mean 16.3 months) after onset of a first-ever cerebrovascular accident. Thirty-two patients were randomized to receive modified constraint-induced movement therapy (restraint of the unaffected limb combined with intensive training of the affected limb) or traditional rehabilitation for three weeks. Kinematic analysis was used to assess motor control characteristics as patients reached to grasp a beverage can. Functional outcomes were evaluated using the Motor Activity Log and Functional Independence Measure. There were moderate and significant effects of modified constraint-induced movement therapy on some aspects of motor control of reach-to-grasp and on functional ability. The modified constraint-induced movement therapy group preplanned reaching and grasping (P=0.018) more efficiently and depended more on the feedforward control of reaching (P=0.046) than did the traditional rehabilitation group. The modified constraint-induced movement therapy group also showed significantly improved functional performance on the Motor Activity Log (P<0.0001) and the Functional Independence Measure (P=0.016). In addition to improving functional use of the affected arm and daily functioning, modified constraint-induced movement therapy improved motor control strategy during goal-directed reaching, a possible mechanism for the improved movement performance of stroke patients undergoing this therapy.

Quantum centipedes with strong global constraint

NASA Astrophysics Data System (ADS)

Grange, Pascal

2017-06-01

A centipede made of N quantum walkers on a one-dimensional lattice is considered. The distance between two consecutive legs is either one or two lattice spacings, and a global constraint is imposed: the maximal distance between the first and last leg is N  +  1. This is the strongest global constraint compatible with walking. For an initial value of the wave function corresponding to a localized configuration at the origin, the probability law of the first leg of the centipede can be expressed in closed form in terms of Bessel functions. The dispersion relation and the group velocities are worked out exactly. Their maximal group velocity goes to zero when N goes to infinity, which is in contrast with the behaviour of group velocities of quantum centipedes without global constraint, which were recently shown by Krapivsky, Luck and Mallick to give rise to ballistic spreading of extremal wave-front at non-zero velocity in the large-N limit. The corresponding Hamiltonians are implemented numerically, based on a block structure of the space of configurations corresponding to compositions of the integer N. The growth of the maximal group velocity when the strong constraint is gradually relaxed is explored, and observed to be linear in the density of gaps allowed in the configurations. Heuristic arguments are presented to infer that the large-N limit of the globally constrained model can yield finite group velocities provided the allowed number of gaps is a finite fraction of N.

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Federal Register 2010, 2011, 2012, 2013, 2014

2010-11-15

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Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

Detecting photons in the dark region of Laguerre-Gauss beams.

PubMed

Klimov, Vasily; Bloch, Daniel; Ducloy, Martial; Rios Leite, Jose R

2009-06-08

We show that a photon detector, sensitive to the magnetic field or to the gradient of electric field, can help to characterize the quantum properties of spatially-dependent optical fields. We discuss the excitation of an atom through magnetic dipole or electric quadrupole transitions with the photons of a Bessel beam or a Laguerre-Gauss (LG) beams. These spiral beams are shown to be not true hollow beams, due to the presence of magnetic fields and gradients of electric fields on beam axis. This approach paves the way to an analysis at the quantum level of the propagating light beams having a complicated spatial structure.

Light-sheet generation in inhomogeneous media using self-reconstructing beams and the STED-principle.

PubMed

Gohn-Kreuz, Cristian; Rohrbach, Alexander

2016-03-21

Self-reconstruction of Bessel beams in inhomogeneous media is beneficial in light-sheet based microscopy. Although the beam's ring system enables propagation stability, the resulting image contrast is reduced. Here, we show that by a combination of two self-reconstructing beams with different orbital angular momenta it is possible to inhibit fluorescence from the ring system by using stimulated emission depletion (STED) even in strongly scattering media. Our theoretical study shows that the remaining fluorescence γ depends non-linearly on the beams' relative radial and orbital angular momenta. For various scattering media we demonstrate that γ remains remarkably stable over long beam propagation distances.

Shaping perfect optical vortex with amplitude modulated using a digital micro-mirror device

NASA Astrophysics Data System (ADS)

Zhang, Chonglei; Min, Changjun; Yuan, X.-C.

2016-12-01

We propose a technique to generate of perfect optical vortex (POV) via Fourier transformation of Bessel-Gauss (BG) beams through encoding of the amplitude of the optical field with binary amplitude digital micro-mirrors device (DMD). Furthermore, we confirm the correct phase patterns of the POV with the method of Mach-Zehnder interferometer. Our approach to generate the POV has the advantages that rapidly switch among the different modes, wide spectral regions and high energy tolerance. Since the POV possess propagation properties that not shape-invariant, we therefore suppose that our proposed approach will find potential applications in optical microscopy, optical fabrication, and optical communication.