Complex geometrical optics of Kerr type nonlinear media
NASA Astrophysics Data System (ADS)
Berczynski, P.; Kravtsov, Yu. A.; Sukhorukov, A. P.
2010-03-01
The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2013-12-01
In this paper complex geometrical optics (CGO) is applied to spatiotemporal evolution of 2D Gaussian wavepackets in nonlinear media of Kerr type. Instead of solving the commonly accepted nonlinear Schrödinger equation (NLS), we propose equations of geometrical optics: a complex eikonal equation and a complex transport equation. The eikonal equation lets us derive immediately the ordinary differential equations for spatial and temporal widths, omitting in this way the complicated variational process used in nonlinear optics. Moreover, the obtained CGO equations for actual spatial and temporal widths happen to be identical to those obtained by the variational method approach. From the transport equation we obtain the first order ordinary differential equation for complex amplitude evolution and the conservation principle for energy flux in the packet cross-section. For the combined effect of diffraction, anomalous dispersion and nonlinear refraction, we observe three types of solution for temporal and spatial widths of the packet propagating in a nonlinear medium of Kerr type: the diffraction/dispersion widening, the stationary solution and the solution under the effect of the spatiotemporal collapse. Moreover, we discuss the evolution of the 2D Gaussian wavepacket in a nonlinear inhomogeneous waveguide and we present conditions for stable propagation without the collapse effect. Under these conditions the wavepacket asymptotically approaches stationary solutions when the parameters of the waveguide change over the propagation distance. The paper also discusses the influence of initial spatial and temporal chirps on Gaussian wavepacket evolution in nonlinear media of Kerr type and in nonlinear inhomogeneous waveguides. Moreover, we notice that the equations for temporal and spatial widths of the 2D wavepacket have the same structure as the equations for the evolution of the elliptical Gaussian beam. Thus, the description of the 2D spatiotemporal wavepacket can be
Gaussian Beam Propagation in a Kerr Type Metamaterial Medium Using ABCD Matrix Method
NASA Astrophysics Data System (ADS)
Keshavarz, A.; Naseri, M.
2016-08-01
In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps. Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.
Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Zhong, Wei-Ping; Belić, Milivoj
2014-12-15
We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number, and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.
Polariton spectrum in nonlinear dielectric medium.
Dzedolik, Igor V; Karakchieva, Olga
2013-05-01
We obtain theoretically the phonon-polariton spectrum in nonlinear dielectric medium with the third-order Kerr-type nonlinearity. We investigate the dependence of number of the polariton spectrum branches on the intensity of electromagnetic field and demonstrate that the appearance of new branches located in the polariton spectrum gap is caused by the influence of dispersion of the third-order dielectric susceptibility at the intensive electromagnetic field in the medium. The modulation instability of new spectrum branch waves leads to the appearance of the cnoidal waves or solitons. These new nonlinear waves one can use for designing optical devices such as the nonlinear optical filter converter. PMID:23669776
NASA Astrophysics Data System (ADS)
Tagwo, H.; Tiofack, C. G. L.; Dafounansou, O.; Mohamadou, A.; Kofane, T. C.
2016-03-01
We investigate analytically and numerically the modulational instability (MI) of plane waves under competing nonlocal cubic-local quintic nonlinearities. The generic properties of the MI gain spectra are then demonstrated for the Gaussian response function, exponential response function, and rectangular response function. Special attention is paid to competing nonlocal cubic-local quintic nonlinearities on the MI. We observe that the focusing local quintic nonlinearity increases the growth rate and bandwidth of instability contrary to the small values of defocusing local quintic nonlinearity which decrease the growth rate and bandwidth of instability. Numerical simulations of the full model equation describing the dynamics of the waves are been carried out and leads to the development of pulse trains, depending upon the sign the quintic nonlinearity.
NASA Astrophysics Data System (ADS)
Hayata, K.; Koshiba, M.
1995-11-01
We show analytically that inclusion of contributions from third-order nonlinearities in a theoretical model for optical parametric interactions derived from second-order nonlinearities makes possible the prediction of various kinds of stationary solitary-wave solution. Specifically these waves consist of hyperbolic (bright and dark types), algebraic (bright and dark types), and kink/antikink types. In the limit of vanishing third-order nonlinearities the first solitary-wave family (hyperbolic type) is reduced to solitary waves already reported. Effects of dissipations including one- and two-photon absorption are discussed as well. Copyright (c) 1995 Optical Society of America
Nonlinear Dynamical Friction in a Gaseous Medium
NASA Astrophysics Data System (ADS)
Kim, Hyosun; Kim, Woong-Tae
2009-10-01
Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber Mp moving at velocity Vp through a uniform gaseous medium of adiabatic sound speed a ∞. We model the perturber as a Plummer potential with softening radius rs , and run various models with differing A=GM_p/(a_∞ ^2r_s) and M=V_p/a_∞ by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibrium. We find that the detached shock distance δ and the nonlinear drag force F depend solely on η = A/M^2-1) such that δ/rs = η and F/F_lin=(η/2)^{-0.45} for 100 > η>2, where F lin is the linear drag force of Ostriker. The reduction of F compared with F lin is caused by front-back symmetry in the nonlinear density wakes. In subsonic cases, the flows without involving a shock do not readily reach a steady state. Nevertheless, the subsonic density wake near a perturber is close to being hydrostatic, resulting in the drag force similar to the linear case. Our results suggest that dynamical friction of a very massive object as in a merger of black holes near a galaxy center will take considerably longer than the linear prediction.
NONLINEAR DYNAMICAL FRICTION IN A GASEOUS MEDIUM
Kim, Hyosun; Kim, Woong-Tae E-mail: wkim@astro.snu.ac.k
2009-10-01
Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber M{sub p} moving at velocity V{sub p} through a uniform gaseous medium of adiabatic sound speed a{sub i}nfinity. We model the perturber as a Plummer potential with softening radius r{sub s} , and run various models with differing A=GM{sub p}/(a{sub i}nfinity{sup 2}r{sub s}) and M=V{sub p}/a{sub i}nfinity by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibrium. We find that the detached shock distance delta and the nonlinear drag force F depend solely on eta=A/(M{sup 2}-1) such that delta/r{sub s} = eta and F/F{sub lin}=(eta/2){sup -0.45} for 100 >eta>2, where F {sub lin} is the linear drag force of Ostriker. The reduction of F compared with F{sub lin} is caused by front-back symmetry in the nonlinear density wakes. In subsonic cases, the flows without involving a shock do not readily reach a steady state. Nevertheless, the subsonic density wake near a perturber is close to being hydrostatic, resulting in the drag force similar to the linear case. Our results suggest that dynamical friction of a very massive object as in a merger of black holes near a galaxy center will take considerably longer than the linear prediction.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
Fock State Generation From the Nonlinear Kerr Medium
NASA Technical Reports Server (NTRS)
Leonski, W.; Tanas, R.
1996-01-01
We discuss a system comprising a nonlinear Kerr medium in a cavity driven by an external coherent field directly or through the parametric process. We assume that the system is initially in the vacuum state, and we show that under appropriate conditions, i.e., properly chosen detuning and intensity of the driving field, the one or two-photon Fock states of the electromagnetic field can be achieved.
Spin Hall effect of light in inhomogeneous nonlinear medium
NASA Astrophysics Data System (ADS)
Li, Hehe; Li, Xinzhong
2016-01-01
In this paper, we investigate the spin Hall effect of a polarized Gaussian beam (GB) in a smoothly inhomogeneous isotropic and nonlinear medium using the method of the eikonal-based complex geometrical optics which describes the phase front and cross-section of a light beam using the quadratic expansion of a complex-valued eikonal. The linear complex-valued eikonal terms are introduced to describe the polarization-dependent transverse shifts of the beam in inhomogeneous nonlinear medium which is called the spin Hall effect of beam. We know that the spin Hall effect of beam is affected by the nonlinearity of medium and include two parts, one originates from the coupling between the spin angular momentum and the extrinsic orbital angular momentum due to the curve trajectory of the center of gravity of the polarized GB and the other from the coupling between the spin angular momentum and the intrinsic orbital angular momentum due to the rotation of the beam with respect to the central ray.
Effective-medium theory for weakly nonlinear composites
NASA Astrophysics Data System (ADS)
Zeng, X. C.; Bergman, D. J.; Hui, P. M.; Stroud, D.
1988-11-01
We propose an approximate general method for calculating the effective dielectric function of a random composite in which there is a weakly nonlinear relation between electric displacement and electric field of the form D=ɛE+χ||E||2E, where ɛ and χ are position dependent. In a two phase-comopsite, to first order in the nonlinear coefficients χ1 and χ2, the effective nonlinear dielectric susceptibility is found to be χe=0, where ɛ(0)e is the effective dielectric constant in the linear limit (χi=0,i=1,2) and ɛi and pi are the dielectric function and volume fraction of the ith component. The approximation is applied to a calculation of χe in the Maxwell-Garnett approximation (MGA) and the effective-medium approximation. For low concentrations of nonlinear inclusions in a linear host medium, our MGA reduces to the results of Stroud and Hui. An exact calculation of χe is carried out for the Hashin-Shtrikman microgeometry and compared to our MG approximation.
Nonlinear site response in medium magnitude earthquakes near Parkfield, California
Rubinstein, Justin L.
2011-01-01
Careful analysis of strong-motion recordings of 13 medium magnitude earthquakes (3.7 ≤ M ≤ 6.5) in the Parkfield, California, area shows that very modest levels of shaking (approximately 3.5% of the acceleration of gravity) can produce observable changes in site response. Specifically, I observe a drop and subsequent recovery of the resonant frequency at sites that are part of the USGS Parkfield dense seismograph array (UPSAR) and Turkey Flat array. While further work is necessary to fully eliminate other models, given that these frequency shifts correlate with the strength of shaking at the Turkey Flat array and only appear for the strongest shaking levels at UPSAR, the most plausible explanation for them is that they are a result of nonlinear site response. Assuming this to be true, the observation of nonlinear site response in small (M M 6.5 San Simeon earthquake and the 2004 M 6 Parkfield earthquake).
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Lysak, T. M.
2016-05-01
We demonstrate a new possibility of a soliton velocity control at its propagation in a nonlinear layered structure (1D photonic crystal) which is placed in a nonlinear ambient medium. Nonlinear response of the ambient medium, as well as the PhC layers, is cubic. At the initial time moment, a soliton is spread over a few layers of PhC. Then, soliton propagates across the layered structure because of the initial wave-vector direction presence for the laser beam. The soliton reaches the PhC faces and reflects from them or passes through the face. As a nonlinear medium surrounds the PhC, the laser beam obtains additional impulse after interaction with this medium and accelerates (or slows down or stops near the PhC face). Nonlinear response of the ambient medium can be additionally created by another laser beam which shines near the PhC faces.
Nonlinear model of a granulated medium containing viscous fluid layers and gas cavities
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Sobisevich, A. L.; Sobisevich, L. E.; Hedberg, C. M.; Shamaev, N. V.
2012-01-01
We analyze nonlinear oscillations and waves in a simple model of a granular medium containing inclusions in the form of fluid layers and gas cavities. We show that in such a medium, the velocity of one of the wave modes is low; therefore, the nonlinearity is high and the effects of interaction are more strongly expressed than usual.
Rigorous calculation of nonlinear parameters in graphene-comprising waveguides
NASA Astrophysics Data System (ADS)
Chatzidimitriou, Dimitrios; Pitilakis, Alexandros; Kriezis, Emmanouil E.
2015-07-01
We describe a rigorous formalism for the calculation of the nonlinear parameter of arbitrary three-dimensional nanophotonic graphene-comprising waveguides. Graphene is naturally implemented as a zero-thickness conductive sheet, modeled solely by complex linear and nonlinear surface conductivity tensors, whose values are extracted from theoretical models. This representation is compared to the more commonly employed equivalent bulk-medium representation and is found superior. We numerically calculate the nonlinear parameters of several optical waveguide archetypes overlaid with infinite graphene monolayers, including silicon-wire and plasmonic metal-slot and metal-stripe configurations. The metal-slot configuration offers the most promising performance for Kerr-type nonlinear applications. Finally, we apply the same formalism to probe the potential of graphene nanoribbon waveguide nonlinearity in the terahertz band.
Fresnel drag of light by a moving nonlinear and nanostructured dielectric medium
Peiponen, Kai-Erik; Gornov, Evgeny
2007-12-15
The Fresnel drag is viewed in the frame of nonlinear and/or nanostructured uniformly moving media. It is shown that in the case of intense light pulse interaction with an optically nonlinear medium the relativistic frequency chirp due to self-phase modulation is smaller than in the rest frame. In the case of light interaction with optically linear or nonlinear nanostructured medium the Fresnel drag depends on the effective refractive index of the medium. While the nanostructures are in a liquid matrix the drag can be controlled by the fill fraction of the inclusions. As an example the Fresnel drag for optically linear Bruggeman liquid is considered.
Propagation of femtosecond pulse with self-similar shape in medium with nonlinear absorption
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Zakharova, Irina G.
2015-05-01
We investigate the propagation of laser pulse with self-similar shape in homogeneous medium with various mechanisms of nonlinear absorption: multi-photon absorption or resonant nonlinearity under detuning the frequency, corresponding to energy transition, from the current frequency of wave packet, or nonlinear absorption with its saturation. Both types of sign for frequency detuning are considered. This results in appearance of a refractive index grating which induced a laser pulse self-action. We analyze also the influence of the laser pulse self-modulation due to cubic nonlinearity on existence of the laser pulse propagation mode with self-similar shape. We develop an analytical solution of the corresponding nonlinear eigenfunction problem for laser pulse propagation in medium with nonlinear absorption. This solution is confirmed by computer simulation of the eigenfunction problem for Schrödinger equation with considered nonlinearity. This mode of laser pulse propagation is very important for powerful TW laser pulse propagating in glass.
Geometric phase in cavity QED containing a nonlinear optical medium and a quantum well
NASA Astrophysics Data System (ADS)
Mohamed, A.-B. A.; Eleuch, H.
2015-11-01
The geometric phase (GP) in cavity QED filled with a nonlinear medium and containing a quantum well is analyzed. We observe collapses and revivals. The optical nonlinearity leads to high frequency oscillations of the GP. The GP is very sensitive not only to the dissipation rates but also to the amplitude of the laser pump.
Self-similar pulse-shape mode for femtosecond pulse propagation in medium with resonant nonlinearity
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Zakharova, Irina G.; Konar, Swapan
2014-05-01
We investigate the mode of laser pulse propagation in homogeneous medium with resonant nonlinearity, at which the shape of pulse is self-similar one along some distance of propagation. We take into account a laser pulse frequency detuning from resonant frequency. Both types of sign for frequency detuning are considered. This results in appearance of a refractive index grating which induced self-action of a laser pulse. I certain cases we develop analytical solution of corresponding nonlinear eigenfunction problem of laser pulse propagation in medium for multi-photon resonance. This solution is confirmed by computer simulation of an eigenfunction problem for Schrödinger equation with considered nonlinearity. Using computer simulation, one shows a validity of existence of such kind of laser pulse propagation in a medium with resonant nonlinear response.
Kildishev, Alexander V; Sivan, Yonatan; Litchinitser, Natalia M; Shalaev, Vladimir M
2009-11-01
An enhanced method is developed for analysis of third-order nonlinearities in optical nanostructures with a scalar magnetic field frequency-domain formulation; it is shown to produce fast and accurate results for 2D problems without a superfluous vector electric field formalism. While a standard TM representation using cubic nonlinear susceptibility results in an intractable implicit equation, our technique alleviates this problem. In addition to a universal approach, simpler, more efficient solutions are proposed for media having solely either a real (lossless Kerr-type medium) or an imaginary (nonlinear absorbing medium) nonlinearity. Combining these solutions with a finite-element method, we show simulation examples validated with alternative approaches. PMID:19881595
Phase conjugate mirror system consisting of a rod amplifier and a nonlinear medium
NASA Astrophysics Data System (ADS)
Lee, Hak K.; Lee, Sang-Soo
1990-07-01
The phase conjugate (PC) mirror system consisting of a rod amplifier and a nonlinear medium is presented and the theoretical analysis of the enhanced PC wave in the system is derived by taking into account of the overlap of the probe and counterpropagating PC wave in the amplifier. In order to examine experimentally the enhanced PC reflectivity in degenerate four wave mixing (DFWM) an amplifier is placed in the probe beam path. Experimental result of maximal R/R 90. 25 is obtained where R and R are PC reflectivities in the absence and presence of the amplifier respectively. The experimental results agree within 5 with the theoretical values. 1. THEORETICAL ANALYSIS Schematic digram of the PC mirror system consisting of an amplifier and a nonlinear medium is shown in Fig. 1. The phase distortion 4 is due to several effects such as inhomogemous pumping stress gain saturation thermal leasing and self-focusing/defocusing in the amplifier. 1 The amplifier is palced near the nonlinear medium so that the changes in phase (4) and gain (g) are negligible during the round trip time. Considering phase conjugation at the nonlinear medium the output signal SA8 over the input probe bA. is expressed as 8A ge+/ (ge14''A) J where R is PC reflectivity of nonlinear medium. There is no phase distortion term in output signal. Thus we obtain the following expression for the signal 6M photons/ 2
Nonlinear hydro-magnetic convection at a permeable cylinder in a porous medium
NASA Astrophysics Data System (ADS)
van Gorder, Robert A.; Vajravelu, K.
2011-10-01
We consider the longitudinal steady nonlinear hydromagnetic convection flow over a permeable vertical cylinder in a porous medium. We assume that both the mainstream velocity at the outer edge of the boundary layer and the surface temperature of the cylinder vary linearly with axial distance from the leading edge, and extend the existing literature by including the nonlinear density temperature variation, magnetic field, and heat source/sink.
Mechanical signaling via nonlinear wavefront propagation in a mechanically excitable medium.
Idema, Timon; Liu, Andrea J
2014-06-01
Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain synchronization of developmental processes. In this paper we suggest a kind of signaling based not on diffusion of a chemical species but on the propagation of mechanical stress. We construct a theoretical approach to describe mechanical signaling as a nonlinear wavefront propagation problem and study its dependence on key variables such as the effective elasticity and damping of the medium. PMID:25019816
Mechanical signaling via nonlinear wavefront propagation in a mechanically excitable medium
NASA Astrophysics Data System (ADS)
Idema, Timon; Liu, Andrea J.
2014-06-01
Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain synchronization of developmental processes. In this paper we suggest a kind of signaling based not on diffusion of a chemical species but on the propagation of mechanical stress. We construct a theoretical approach to describe mechanical signaling as a nonlinear wavefront propagation problem and study its dependence on key variables such as the effective elasticity and damping of the medium.
NASA Astrophysics Data System (ADS)
Berczyński, Paweł; Kravtsov, Yury A.; Żeglinski, Grzegorz
2008-09-01
The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.
Optical-soliton and chaotic motions in a nonlocal nonlinear medium
NASA Astrophysics Data System (ADS)
Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Liu, Lei
2016-05-01
The coupled equations for the incoherent optical spatial solitons in a nonlocal nonlinear medium is studied analytically. With the soliton solutions hereby obtained via the symbolic computation, the optical-soliton motion in the nonlocal nonlinear medium is studied: ? is inversely related to ?, ?, and ?, while ? is positively related to ? and ?, but ? is independent of ?, with ? as the slowly varying amplitude of the beam, ? as the refractive index change, ? as the beam intensity distribution, ? as the frequency of the propagating beam, and ? as the unperturbed refractive index. Head-on and overtaking interactions are observed, and head-on interaction is transformed into an overtaking one with ? increasing. Bound-state interaction is displayed, and with ? increasing, the period of ? decreases, while that of ? increases. Considering the external forces in the nonlocal nonlinear medium, we explore the chaotic motions in the nonlinear nonlocal medium, including effects of the external forces on such motions. It is seen that when ? and ?, the two-dimensional attractors with stretching-and-folding structures are exhibited, and the developed chaos occurs, where ? and ? are the amplitudes of external forces, c is the speed of light in vacuum. Such chaotic motions are weakened with ?, ?, ?, and ? increasing, or with ? decreasing, where ? and ? represent the frequencies of external forces.
Localized states and their stability in an anharmonic medium with a nonlinear defect
NASA Astrophysics Data System (ADS)
Gerasimchuk, I. V.
2015-10-01
A comprehensive analysis of soliton states localized near a plane defect (a defect layer) possessing nonlinear properties is carried out within a quasiclassical approach for different signs of nonlinearity of the medium and different characters of interaction of elementary excitations of the medium with the defect. A quantum interpretation is given to these nonlinear localized modes as a bound state of a large number of elementary excitations. The domains of existence of such states are determined, and their properties are analyzed as a function of the character of interaction of elementary excitations between each other and with the defect. A full analysis of the stability of all the localized states with respect to small perturbations of amplitude and phase is carried out analytically, and the frequency of small oscillations of the state localized on the defect is determined.
Localized states and their stability in an anharmonic medium with a nonlinear defect
Gerasimchuk, I. V.
2015-10-15
A comprehensive analysis of soliton states localized near a plane defect (a defect layer) possessing nonlinear properties is carried out within a quasiclassical approach for different signs of nonlinearity of the medium and different characters of interaction of elementary excitations of the medium with the defect. A quantum interpretation is given to these nonlinear localized modes as a bound state of a large number of elementary excitations. The domains of existence of such states are determined, and their properties are analyzed as a function of the character of interaction of elementary excitations between each other and with the defect. A full analysis of the stability of all the localized states with respect to small perturbations of amplitude and phase is carried out analytically, and the frequency of small oscillations of the state localized on the defect is determined.
Electromagnetic Nonlinearity in the Dielectric Medium of Experimental EM Impulse-Momentum Systems
NASA Astrophysics Data System (ADS)
Robertson, Glen A.
2006-01-01
In this paper, an empirical correlation among electromagnetic (EM) impulse-momentum experiments performed by Brito (1999, 2003, 2004, and 2005), Woodward (2004a, 2004b, 2005, and 2006) and March (2006) is developed. This empirical correlation assumes that the dielectric medium exhibits non-linear magnetoelectric effects arising from the interplay of piezo-magnetism and piezo-electricity (Rado, 1975). The modification to the generally accepted electromagnetic field (volume) momentum equation (Jackson, 1999) is derived from Fiegel's (2004) thesis that inside a magnetoelectric, the momenta of counter-propagating vacuum modes do not eliminate each other, in contrast to the other materials. Whereby, a time independent vacuum mode component can be subtracted from the impulse-momentum to give a constant force. This vacuum mode component is interpreted as the nonlinearity of the dielectric medium with respect to the applied frequency of the input power.
Wigner distribution function in nonlinear optics.
Dragoman, D
1996-07-20
Transformation laws for the Wigner distribution function, the radiant intensity, the radiant emittance, and the first- and second-order moments of the Wigner distribution function through an inhomogeneous, Kerr-type medium have been derived as well as for the beam quality factor and the kurtosis parameter. It is shown that the inhomogeneous Kerr-type medium can be approximated from the Wigner-distribution-function transformation-law point of view with a symplectic ABCD matrix with elements depending on the field distribution. PMID:21102821
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
NASA Astrophysics Data System (ADS)
Chirkunov, Yu. A.
2015-10-01
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
Chirkunov, Yu. A.
2015-10-15
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
NASA Astrophysics Data System (ADS)
Gallot, T.; Fehler, M. C.; Brown, S. R.; Buns, D.; Szabo, T.; Malcolm, A. E.
2013-12-01
The nonlinear mechanical behavior of rocks is a well known phenomenon at a laboratory scale and has been observed during earthquakes, slow slip events, volcanic activity, reservoir fracturing, etc. he present work explores the possibility of measuring nonlinear parameters in a semi-infinite medium. Contrary to existing methods that rely on vibrating a sample at a fixed resonant frequency, a pulsed wave is used to create a high amplitude perturbation (the pump) responsible for the nonlinear response. At the same time, a low amplitude wave probes the material to measure changes in elastic properties. Laboratory experiments have been performed in rocks (berea sandstones) to explore the possibility of using such a method for Earth imaging. The strain created by the pump (a shear wave in the tens of kHz), is on the order of a microstrain and is measured by laser vibrometry and extrapolated to the whole sample by a finite difference simulation. A compressional pulse (in the hundreds of kHz range) probes the 15-cm size sample. The variation in time of flight is related to a change in elasticity as described as a function of the strain through quadratic and cubic nonlinearities. Those nonlinear coefficients are shown to be sensitive to several environmental parameters such as temperature, humidity, and also physical properties such as the amplitude of the strain and the relative orientation of the pump and the probing wave. Experimental set-up: a P-wave transducer generates an ultrasonic pulse at 500 kHz recorded by an identical transducer after propagation through the sample. The medium is then perturbed with a S-wave transducer on the top of the sample at 50 kHz .
NASA Astrophysics Data System (ADS)
Chew, J. V. L.; Sulaiman, J.
2016-06-01
This paper considers Newton-MSOR iterative method for solving 1D nonlinear porous medium equation (PME). The basic concept of proposed iterative method is derived from a combination of one step nonlinear iterative method which known as Newton method with Modified Successive Over Relaxation (MSOR) method. The reliability of Newton-MSOR to obtain approximate solution for several PME problems is compared with Newton-Gauss-Seidel (Newton-GS) and Newton-Successive Over Relaxation (Newton-SOR). In this paper, the formulation and implementation of these three iterative methods have also been presented. From four examples of PME problems, numerical results showed that Newton-MSOR method requires lesser number of iterations and computational time as compared with Newton-GS and Newton-SOR methods.
Vector–vortex solitons in nonlinear photonic crystal fibers
NASA Astrophysics Data System (ADS)
Salgueiro, José R.
2016-07-01
In this article, I study a system of two incoherently coupled components in a nonlinear Kerr-type photonic crystal fiber presenting angular momentum in one or both components. I classify the different families of solutions and study their bifurcations in the power dispersion diagram. Finally, I analyze the stability of the different nonlinear modes by means of numerical simulations.
Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium
Moatimid, Galal M.; Alali, Elham M. M. Ali, Hoda S. M.
2014-09-15
Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg–Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted for
Li Liang; Huang Guoxiang
2010-08-15
We present a systematic theoretical study to deal with linear and nonlinear light propagations in a Doppler-broadened three-level {Lambda} system via electromagnetically induced transparency (EIT), with incoherent population exchange between two lower energy levels taken into account. Through a careful analysis of base state and linear excitation, we show that the EIT condition of the system is given by |{Omega}{sub c}|{sup 2{gamma}}{sub 31}>>2{gamma}{sub 21{Delta}{omega}D}{sup 2}, where {Omega}{sub c} is half the Rabi frequency of the control field, {Delta}{omega}{sub D} is the Doppler width, and {gamma}{sub jl} is the decay rate of the coherence between states |j> and |l>. Under this condition, the effect of incoherent population exchange is insignificant, while dephasing dominates the decoherence of the system. This condition also ensures the validity of the weak nonlinear perturbation theory used in this work for solving the Maxwell-Bloch equations with inhomogeneous broadening. We then investigate the nonlinear propagation of the probe field and show that it is possible to form temporal optical solitons in the Doppler-broadened medium. Such solitons have ultraslow propagating velocity and can be generated in very low light power. The possibility of realizing (1+1)-dimensional and (2+1)-dimensional spatial optical solitons in the adiabatic regime of the system is also discussed.
Dynamic behavior of the incoherent optical spatial solitons in a nonlocal nonlinear medium
NASA Astrophysics Data System (ADS)
Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Sun, Ya
2015-06-01
Dynamic behavior of the propagation of incoherent optical spatial solitons in a nonlocal nonlinear medium is investigated. By means of the Hirota method, we obtain the soliton solutions, based on which we find that ? is positively related to ?, but inversely related to ? and ?, whereas ? is independent of them, with ? as the slowly varying amplitude of the beam, ? as the refractive index change, ?, ?, and ? as the unperturbed refractive index, frequency of the propagating beam, and beam intensity distribution, respectively. Head-on and bound-state soliton interactions are both given, and one interaction period decreases with ? and ? increasing in the bound state one. With the external perturbations taken into consideration, the associated chaotic motions of the perturbed model are studied, and the corresponding power spectra and phase projections are obtained. Both the weak and developed chaotic states are investigated, and the difference between them roots in the relative magnitude of nonlinearities and perturbations. Such chaotic motions can be weakened via increasing ? and ? or decreasing ?. Periodic motion is obtained with the nonlinearities and perturbations balanced.
Synergetic events in geological medium and nonlinear features of wave propagation.
NASA Astrophysics Data System (ADS)
Hachay, O. A.
2009-04-01
Geological medium is an open dynamical system, which is artificially and naturally influenced on different scale levels, which change it's state and which lead to a complicated many ranked hierarchic evolution. That is a topic of the synergetic theory (or science of self organization). The idea of physical meso mechanics which was elaborated by Russian academician Panin V.E., which includes the synergetic approach, is a constructive method for research of the state of heterogenic materials. That result had been obtained for specimens of different materials. In our investigations of time-dependent geological medium in the frame of natural experiments in real rock massive, which are hard man-caused influenced it had been showed, that the dynamics of the state can be revealed by using synergetic approach for hierarchic media. The important role for research of dynamic geological systems play the use of active and passive geophysical monitoring, which can be achieved with use of electromagnetic and seismic fields. As it had been showed by our experience the change of the system on the researched space bases and times can be revealed by parameters, linked with peculiarities of the medium of the second and higher rank. Thus the research of the state dynamics and the events of self organization we can provide with geophysical methods, oriented on the many ranked hierarchic time-dependent model of the medium. For fields of plastic deformation and stresses it had been considered a system of differential equations. The developing theory of modelling and interpretation of geophysical monitoring data must be active guided by the mathematical methods of nonlinear dynamics and control. The developing of that direction can allow us to forecast and prevent catastrophic man-made events (rock bursts). We had elaborated a new approach of forecasting such events using the method of constructing phase portraits using the data of electromagnetic monitoring and detailed seismological
Higher order nonlinear chirp scaling algorithm for medium Earth orbit synthetic aperture radar
NASA Astrophysics Data System (ADS)
Wang, Pengbo; Liu, Wei; Chen, Jie; Yang, Wei; Han, Yu
2015-01-01
Due to the larger orbital arc and longer synthetic aperture time in medium Earth orbit (MEO) synthetic aperture radar (SAR), it is difficult for conventional SAR imaging algorithms to achieve a good imaging result. An improved higher order nonlinear chirp scaling (NLCS) algorithm is presented for MEO SAR imaging. First, the point target spectrum of the modified equivalent squint range model-based signal is derived, where a concise expression is obtained by the method of series reversion. Second, the well-known NLCS algorithm is modified according to the new spectrum and an improved algorithm is developed. The range dependence of the two-dimensional point target reference spectrum is removed by improved CS processing, and accurate focusing is realized through range-matched filter and range-dependent azimuth-matched filter. Simulations are performed to validate the presented algorithm.
Squeezed Light in Laguerre-Gaussian Modes through Non-linear Medium
NASA Astrophysics Data System (ADS)
Xiao, Zhihao; Lanning, R. Nicholas; Zhang, Mi; Novikova, Irina; Mikhailov, Eugeniy E.; Dowling, Jonathan P.
2016-05-01
We examine the propagation of squeezed light, in Laguerre-Gaussian spatial modes, through a non-linear medium such as Rb vapor. We examine the quantum states in varies spatial modes. We simulate the injection into a Rb vapor cell a linearly polarized laser beam to create squeezed vacuum state of light linearly polarized in the perpendicular direction. We fully quantize the optical field's propagation which is based on previous semi-classical calculation. The Rb atomic structure is simplified to a three-level system. We reveal the mechanism that how squeezed state of light is generated in this process and compare the theory with our experiment. Further, we simulate and compare the different squeezing that can be achieved due to the change of parameters or altering experimental setups, such as multiple passing of the beam through the Rb vapor cell.
Convection and reaction in a diffusive boundary layer in a porous medium: Nonlinear dynamics
NASA Astrophysics Data System (ADS)
Andres, Jeanne Therese H.; Cardoso, Silvana S. S.
2012-09-01
We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.
NASA Astrophysics Data System (ADS)
Pikichyan, H. V.
2016-06-01
It is shown that for the nonlinear boundary value problem of determining the radiation field inside a one-dimensional anisotropic medium illuminated from outside at its boundaries on both sides, the formulas for adding layers in semilinear systems of differential equations for radiative transfer, invariant embedding, and total Ambartsumyan invariance can be used to reduce the equations for the problem to separable equations with initial conditions. The fields travelling to the left and right are thereby found independently of one another. In addition, when one of them has been determined, the other can be found directly using an explicit expression. A general equivalence property of operators with respect to a certain mathematical form, expression, or functional is formulated mathematically. New equations, referred to as kinetic equations of equivalency, are derived from the mutual equivalence of the differential operators of the Boltzmann kinetic equation (the equations of radiative transfer) and the functional equation of the Ambartsumian's complete invariance. Besides separability, these new equations also have the property of linearity. Formulas are also introduced for special problems of single sided illumination of a medium that in this case serve as supplementary information in the initial conditions for formulating Cauchy problems.
NASA Astrophysics Data System (ADS)
Amooshahi, M.
2016-08-01
Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.
Kitsak, M A; Kitsak, A I
2008-04-30
The cross modulation method of transformation of the spatial coherence of low-power pulsed laser radiation in a nonlinear medium is proposed. The method is realised experimentally in a multimode optical fibre. The estimates of the degree of spatial coherence of radiation subjected to the phase cross modulation demonstrated the high efficiency of this radiation decorrelation mechanism. (control of laser radiation parameters)
Position-momentum-entangled photon pairs in nonlinear waveguides and transmission lines
NASA Astrophysics Data System (ADS)
Sherkunov, Y.; Whittaker, David M.; Fal'ko, Vladimir
2016-04-01
We analyze the correlation properties of light in nonlinear waveguides and transmission lines, predict the position-momentum realization of the Einstein-Podolsky-Rosen paradox for photon pairs in Kerr-type nonlinear photonic circuits, and we show how two-photon entangled states can be generated and detected.
NONLINEAR DYNAMICAL FRICTION OF A CIRCULAR-ORBIT PERTURBER IN A GASEOUS MEDIUM
Kim, Woong-Tae
2010-12-10
We use three-dimensional hydrodynamic simulations to investigate the nonlinear gravitational responses of gas to, and the resulting drag forces on, very massive perturbers moving in circular orbits. This work extends our previous studies that explored the cases of low-mass perturbers in circular orbits and massive perturbers on straight-line trajectories. The background medium is assumed to be non-rotating, adiabatic with index 5/3, and uniform with density {rho}{sub 0} and sound speed a{sub 0}. We model the gravitating perturber using a Plummer sphere with mass M{sub p} and softening radius r{sub s} in a uniform circular motion at speed V{sub p} and orbital radius R{sub p} , and run various models with differing R{identical_to}r{sub s}/R{sub p}, M{identical_to}V{sub p}/a{sub 0}, and B{identical_to}GM{sub p}/(a{sub 0}{sup 2}R{sub p}). A quasi-steady density wake of a supersonic model consists of a hydrostatic envelope surrounding the perturber, an upstream bow shock, and a trailing low-density region. The continuous change in the direction of the perturber motion reduces the detached shock distance compared to the linear-trajectory cases, while the orbit-averaged gravity of the perturber gathers the gas toward the center of the orbit, modifying the background preshock density to {rho}{sub 1}{approx}(1+0.46B{sup 1.1}){rho}{sub 0} depending weakly on M. For sufficiently massive perturbers, the presence of a hydrostatic envelope makes the drag force smaller than the prediction of the linear perturbation theory, resulting in F=4{pi}{rho}{sub 1}(GM{sub p})?2/V{sub p}?2 x (0.7{eta}{sub B}?-?1) for {eta}{sub B{identical_to}}B/(M?2-1)>0.1; the drag force for low-mass perturbers with {eta}{sub B}<0.1 agrees well with the linear prediction. The nonlinear drag force becomes independent of R as long as R<{eta}{sub B}/2, which places an upper limit on the perturber size for accurate evaluation of the drag force in numerical simulations.
NASA Astrophysics Data System (ADS)
Sharma, Rajesh; Bhargava, Rama
2015-07-01
In this article, the two-dimensional boundary layer problem of Hiemenz flow (two-dimensional flow of a fluid near a stagnation point) of an incompressible micropolar fluid towards a nonlinear stretching surface placed in a porous medium in the presence of transverse magnetic field is examined. The resulting nonlinear differential equations governing the problem have been transformed by a similarity transformation into a system of nonlinear ordinary differential equations which are solved numerically by the Element Free Galerkin method. The influence of various parameters on the velocity, microrotation, temperature, and concentration is shown. Some of the results are compared with the Finite Element Method. Finally, validation of the numerical results is demonstrated for local skin friction ? for hydrodynamic micropolar fluid flow on a linearly stretching surface.
NASA Astrophysics Data System (ADS)
Ahmad, Harith; Hassan, Nor Ahya; Aidit, Siti Nabila; Tiu, Zian Cheak
2016-07-01
The applications of graphene thin film as a nonlinear medium and stabilizer to generate a stable multi-wavelength is proposed and demonstrated. A 50 m long highly nonlinear photonic crystal fiber (PCF) is incorporated into the cavity to achieve unstable multi-wavelength based on nonlinear polarization rotation (NPR) effect. By introducing the graphene thin film into the cavity, a stable multi-wavelength oscillation is obtained. The laser generates more than 7 lasings with constant spacing of 0.47 nm. The output is highly stable with power fluctuation of less than 3 dB within a period of 30 min. The multi-wavelength EDFL exhibits a tunability from the center wavelength of 1550 nm to 1560 nm.
NASA Astrophysics Data System (ADS)
Zhu, Chengjie; Deng, L.; Hagley, E. W.
2013-08-01
We investigate linear and nonlinear Faraday effects in a room-temperature, coherently driven four-level active-Raman-gain (ARG) medium. By using the multiple-scale method, we derive two nonlinear coupled envelope equations governing the dynamics of left- and right-polarized components of a linearly polarized probe field. Under the weak probe field approximation, we demonstrate a factor of four increase of the Faraday rotation angle by the linear and nonlinear response of the ARG scheme without probe field loss. We further compare this ARG system with an M-type five-state electromagnetically induced transparency (EIT) scheme and demonstrate the superiority of the ARG scheme over the conventional EIT scheme.
NASA Technical Reports Server (NTRS)
Lobashov, A. A.; Mostepanenko, V. M.
1993-01-01
The theory of quantum effects in nonlinear dielectric media is developed. The nonlinear dielectric media is influenced by an external pumping field. The diagonalization of the Hamiltonian of a quantized field is obtained by the canonical Bogoliubov transformations. The transformations allow us to obtain the general expressions for the number of created photons and for the degree of squeezing. In the case of a plane pumping wave, for example, the results are calculated by using the zero order of the secular perturbation theory, with small parameters characterizing the medium nonlinearity. The Heisenberg equations of motion are obtained for non-stationary case and a commonly used Hamiltonian is derived from the first principles of quantum electrodynamics.
NASA Astrophysics Data System (ADS)
Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan
2012-12-01
Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.
Nonlinear k⊥-factorization: a New Paradigm for Hard Processes in a Nuclear Medium
NASA Astrophysics Data System (ADS)
Nikolaev, N. N.; Schäfer, W.; Zakharov, B. G.; Zoller, V. R.
2006-04-01
We review the origin, and salient features, of the breaking of the conventional linear k⊥-factorization for hard processes in a nuclear environment. A realization of the nonlinear k ⊥-factorization which emerges instead is shown to depend on color properties of the underlying pQCD subprocesses. We discuss the emerging universality classes and extend nonlinear k ⊥-factorization to AGK unitarity rules for the excitation of the target nucleus.
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
Abdel-Gawad, Hamdy I.; Osman, Mohamed
2014-01-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE’s. PMID:26199750
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.
Abdel-Gawad, Hamdy I; Osman, Mohamed
2015-07-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE's. PMID:26199750
Propagation of Weakly Guided Waves in a Kerr Nonlinear Medium using a Perturbation Approach
Dacles-Mariani, J; Rodrigue, G
2004-10-06
The equations are represented in a simplified format with only a few leading terms needed in the expansion. The set of equations are then solved numerically using vector finite element method. To validate the algorithm, they analyzed a two-dimensional rectangular waveguide consisting of a linear core and nonlinear identical cladding. The exact nonlinear solutions for three different modes of propagations, TE0, TE1, and TE2 modes are generated and compared with the computed solutions. Next, they investigate the effect of a more intense monochromatic field on the propagation of a 'weak' optical field in a fully three-dimensional cylindrical waveguide.
Nonlinear shear wave in a non Newtonian visco-elastic medium
Banerjee, D.; Janaki, M. S.; Chakrabarti, N.
2012-06-15
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.
Medium-Range Ordering in Liquids Appearing in Nonlinear Dielectric Effect Studies
NASA Astrophysics Data System (ADS)
Zioło, Jerzy; Rzoska, Sylwester J.; Drozd-Rzoska, Aleksandra
Results of nonlinear dielectric effect (NDE) studies in supercooling epoxy resin EPON 5, nitrobenzene and menthol are presented. In each case on cooling a non-exponential decay of the NDE response after switching-off the strong electric field was found. The obtained "nonlinear" relaxation time is more than 106 times longer than the structural relaxation time (alpha relaxation) detected from "linear" broad band dielectric spectroscopy. For EPON 5 it is shown that for the whole tested range of temperatures the NDE relaxation time can be well parameterized by the Vogel-Fulcher-Tamman relation. For higher temperatures the NDE decay time can also be portrayed by the critical-like dependence, with the power exponent y=1.
Tensor of the nonlinear polarizability of anisotropic medium and ``local'' field method
NASA Astrophysics Data System (ADS)
Lavric, V. V.; Ovander, L. N.; Shunyakov, V. T.
1983-08-01
The nonlinear polarizability tensor (NPT) for a molecular crystal of arbitrary symmetry has been obtained within the framework of polariton theory. Use of the Göppert-Mayer unitary transformation for the Hamiltonian of the crystal plus quantized electromagnetic field system made it possible to represent finally the result for the NPT in a compact form and to compare with results of semiphenomenological calculation of the NPT and to go out of the framework of the Gaitler-London approximation.
Light steering of Air-Gaussian beam in Nonlocal Nonlinear Medium
NASA Astrophysics Data System (ADS)
Chen, Ran; Zhang, Xiaping
2016-07-01
With a nonlocal model, we investigate the propagation dynamics of a single Airy-Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results show that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Espesically, by tuning the phase difference between the two beams, we can steer the centre of the bound AiG beams in nonlocal nonlinear media.
Polarization-dependent colored conical emission in a quadratically nonlinear medium
NASA Astrophysics Data System (ADS)
Bi, Jie; Zhou, Lina; Zheng, Anshou; Lv, Tao; Xiang, Dong
2012-07-01
Both supercontinuum conical emission (SCCE) and blue-green conical emission (CE) by means of second harmonic generation (SHG) were observed alternately in a β-barium borate (BBO) crystal induced by femtosecond laser pulses with vertical polarization state. Three theoretical models were analyzed to interpret the angular beam of SCCE. The experimental conical angles with different wavelengths in BBO crystal and BK-7 glass can be explained well by nonlinear X-wave model and Cerenkov type phase matching model other than four-wave mixing (FWM) model.
Bound states of breathing Airy-Gaussian beams in nonlocal nonlinear medium
NASA Astrophysics Data System (ADS)
Zhang, Xiaping
2016-05-01
With a nonlocal model, we investigate the propagation dynamics of a single Airy-Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results shows that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Especially, by tuning the phase difference between the two beams, we can steer the center of the bound AiG beams in nonlocal nonlinear media.
NASA Astrophysics Data System (ADS)
Xie, Xi-Yang; Tian, Bo; Jiang, Yan; Sun, Wen-Rong; Sun, Ya; Gao, Yi-Tian
2016-07-01
Under investigation in this paper is an inhomogeneous nonlinear system, which describes the marginally-unstable baroclinic wave packets in a geophysical fluid or ultra-short pulses in nonlinear optics with certain inhomogeneous medium existing. By virtue of a kind of the Darboux transformation, under the Painlevé integrable condition, the first- and second-order bright and dark rogue-wave solutions are derived. Properties of the first- and second-order bright and dark rogue waves with α(t), which measures the state of the basic flow, and β(t), representing the interaction of the wave packet and mean flow, are graphically presented and analyzed: α(t) and β(t) have no influence on the wave packet, but affect the correction of the basic flow. When we choose α(t) as a constant and linear function, respectively, the shapes of the first- and second-order dark rogue waves change, and the peak heights and widths of them alter with the value of β(t) changing.
NASA Astrophysics Data System (ADS)
Nandeppanavar, M. M.; Siddalingappa, M. N.
2013-06-01
In this present paper, we have discussed the effects of viscous dissipation and thermal radiation on heat transfer over a non-linear stretching sheet through a porous medium. Usual similarity transformations are considered to convert the non-linear partial differential equation of motion and heat transfer into ODE's. Solutions of motion and heat transfer are obtained by the Runge-Kutta integration scheme with most efficient shooting technique. The graphical results are presented to interpret various physical parameters of interest. It is found that the velocity profile decreases with an increase of the porous parameter asymptotically. The temperature field decreases with an increase in the parametric values of the Prandtl number and thermal radiation while with an increase in parameters of the Eckert number and porous parameter, the temperature field increases in both PST (power law surface temperature) and PHF (power law heat flux) cases. The numerical values of the non-dimensional wall temperature gradient and wall temperature are tabulated and discussed.
Nonlinear Stress/Strain Behavior of a Synthetic Porous Medium at Seismic Frequencies
NASA Astrophysics Data System (ADS)
Roberts, P. M.; Ibrahim, R. H.
2008-12-01
Laboratory experiments on porous core samples have shown that seismic-band (100 Hz or less) mechanical, axial stress/strain cycling of the porous matrix can influence the transport behavior of fluids and suspended particles during steady-state fluid flow through the cores. In conjunction with these stimulated transport experiments, measurements of the applied dynamic axial stress/strain were made to investigate the nonlinear mechanical response of porous media for a poorly explored range of frequencies from 1 to 40 Hz. A unique core-holder apparatus that applies low-frequency mechanical stress/strain to 2.54-cm-diameter porous samples during constant-rate fluid flow was used for these experiments. Applied stress was measured with a load cell in series with the source and porous sample, and the resulting strain was measured with an LVDT attached to the core face. A synthetic porous system consisting of packed 1-mm-diameter glass beads was used to investigate both stress/strain and stimulated mass-transport behavior under idealized conditions. The bead pack was placed in a rubber sleeve and static confining stresses of 2.4 MPa radial and 1.7 MPa axial were applied to the sample. Sinusoidal stress oscillations were applied to the sample at 1 to 40 Hz over a range of RMS stress amplitude from 37 to 275 kPa. Dynamic stress/strain was measured before and after the core was saturated with deionized water. The slope of the linear portion of each stress/strain hysteresis loop was used to estimate Young's modulus as a function of frequency and amplitude for both the dry and wet sample. The modulus was observed to increase after the dry sample was saturated. For both dry and wet cases, the modulus decreased with increasing dynamic RMS stress amplitude at a constant frequency of 23 Hz. At constant RMS stress amplitude, the modulus increased with increasing frequency for the wet sample but remained constant for the dry sample. The observed nonlinear behavior of Young's modulus
Three-photon interactions and spin exchange in a quantum nonlinear medium
NASA Astrophysics Data System (ADS)
Cantu, Sergio; Liang, Qi-Yu; Thompson, Jeff; Nicholson, Travis; Venkatramani, Aditya; Gullans, Michael; Gorshkov, Alexey; Choi, Soonwon; Lukin, Mikhail; Vuletic, Vladan
2016-05-01
Robust quantum gates for photonic qubits are a longstanding goal of quantum information science. One promising approach to achieve this goal requires strong nonlinear interactions between single photons, which is impossible with conventional optical media. We realize these interactions with electromagnetically induced transparency (EIT), and strongly interacting Rydberg states to mediate strong interactions between photons. Operating in the dispersive regime of EIT, we have recently shown that two photons propagating in our system can bind into a photonic molecule. Extending these two-photon experiments to many-body physics would lead to exotic phenomena like photon crystallization. To that end, we have scaled up our two-photon measurements to three-photon experiments. We are now able to discern signatures of three-photon molecules from a variety of two- and three-photon interactions. Three-photon bound states manifest as an increase in photon bunching in g (3) correlation measurements. We also present a recent observation of coherent spin exchange interactions in Rydberg EIT.
Zhang, Jitao; He, Wei; Zhang, Ming; Zhao, Hongmei; Yang, Qian; Guo, Shuting; Wang, Xiaolei; Zheng, Xiaowan; Cao, Lingzhi
2015-09-01
A broadband current-sensing device with frequency-conversion mechanism consisting of Terfenol-D/Pb(Zr.Ti)O3 (PZT)/Terfenol-D magnetoelectric laminate and Fe73.5Cu1Nb3Si13.5B9 nanocrystalline flux concentrator is fabricated and characterized. For the purpose of acquiring resonance-enhanced sensitivity within broad bandwidth, a frequency-modulation mechanism is introduced into the presented device through the nonlinearity of field-dependence giant magnetostrictive materials. The presented configuration provides a solution to monitor the weak currents and achieves resonance-enhanced sensitivity of 178.4 mV/A at power-line frequency, which exhibits ∼3.86 times higher than that of direct output at power-line frequency of 50 Hz. Experimental results demonstrate that a weak step-change input current of 1 mA can be clearly distinguished by the output amplitude or phase. This miniature current-sensing device provides a promising application in power-line weak current measurement. PMID:26429473
NASA Astrophysics Data System (ADS)
Krishna Sarkar, Ram; Medhekar, S.
2007-12-01
In this paper, we have investigated the propagation behavior of a Gaussian beam in cubic quintic nonlinear medium with and without absorption or gain. A governing differential equation for the evolution of beam width with the distance of propagation has been derived using the standard parabolic equation approach. By solving the governing equation numerically for different sets of parameters, we have shown that spatial solitons of fixed width and desired intensity and of fixed intensity and desired width are possible. Such liberty does not exist in other saturable media. We have also investigated self-tapering and self-uptapering of spatial solitons in the presence of absorption or gain and showed that the rate of self-tapering/uptapering is not only controlled by the magnitude of absorption or gain but also by the values of cubic and quintic terms. It is revealed that by self-tapering, the smallest achievable soliton width decreases/increases by increasing the magnitude of the cubic/quintic term. It is also revealed that the smallest achievable soliton width by self-tapering, is smaller for a larger initial width.
Fedotov, Il'ya V; Fedotov, Andrei B; Zheltikov, Aleksei M
2006-09-01
Coherent anti-Stokes Raman scattering (CARS) is used to measure relations between the resonant (Raman) and nonresonant (Kerr-type) optical nonlinearities of air-guided modes in a hollow-core photonic-crystal fiber (PCF). We demonstrate that, due to its interference nature, CARS provides a convenient tool for measuring the contribution of the fiber cladding to the total nonlinearity sensed by air-guided modes in hollow PCFs. On a Raman resonance with molecular vibrations in the gas that fills the fiber core, a two-color laser field is shown to induce optical nonlinearities that are several orders of magnitude higher than the nonresonant Kerr-type nonlinearities typical of air-guided PCF modes. PMID:16902633
Eliminating material constraints for nonlinearity with plasmonic metamaterials
Neira, Andres D.; Olivier, Nicolas; Nasir, Mazhar E.; Dickson, Wayne; Wurtz, Gregory A.; Zayats, Anatoly V.
2015-01-01
Nonlinear optical materials comprise the foundation of modern photonics, offering functionalities ranging from ultrafast lasers to optical switching, harmonic and soliton generation. Optical nonlinearities are typically strong near the electronic resonances of a material and thus provide limited tuneability for practical use. Here we show that in plasmonic nanorod metamaterials, the Kerr-type nonlinearity is not limited by the nonlinear properties of the constituents. Compared with gold's nonlinearity, the measured nonlinear absorption and refraction demonstrate more than two orders of magnitude enhancement over a broad spectral range that can be engineered via geometrical parameters. Depending on the metamaterial's effective plasma frequency, either a focusing or defocusing nonlinearity is observed. The ability to obtain strong and fast optical nonlinearities in a given spectral range makes these metamaterials a flexible platform for the development of low-intensity nonlinear applications. PMID:26195182
NASA Astrophysics Data System (ADS)
Blackstock, David T.
1993-08-01
Research on nonlinear acoustics has been performed during the 12-month period ending 30 September 1993. The following projects were completed: (1) propagation in a periodic waveguide, (2) finite-amplitude propagation in a medium having a distribution of relaxation processes, and (3) production of an isolated negative pulse in water. Public communication of the research was accomplished through three theses, four oral papers, one journal article published, four journal articles submitted, and one paper in a symposium proceedings.
NASA Astrophysics Data System (ADS)
RamReddy, Chetteti; Pradeepa, Teegala
2016-05-01
Based on the nonlinear variation of density with temperature (NDT) in the buoyancy term, the mixed convection flow along a vertical plate of a micropolar fluid saturated porous medium is considered. In addition, the effect of homogeneous-heterogeneous reaction and convective boundary condition has been taken into account. Using lie scaling group transformations, the similarity representation is attained for the system of partial differential equations, prior to being solved by a spectral quasilinearization method. The results show that in the presence of aiding and opposing flow situations, both the species concentration and mass transfer rate decreases when the strength of homogeneous and heterogeneous reaction parameters are enhanced.
Vu, Cung Khac; Nihei, Kurt; Johnson, Paul A.; Guyer, Robert; Ten Cate, James A.; Le Bas, Pierre-Yves; Larmat, Carene S.
2015-12-29
A method and system includes generating a first coded acoustic signal including pulses each having a modulated signal at a central frequency; and a second coded acoustic signal each pulse of which includes a modulated signal a central frequency of which is a fraction d of the central frequency of the modulated signal for the corresponding pulse in the first plurality of pulses. A receiver detects a third signal generated by a non-linear mixing process in the mixing zone and the signal is processed to extract the third signal to obtain an emulated micro-seismic event signal occurring at the mixing zone; and to characterize properties of the medium or creating a 3D image of the properties of the medium, or both, based on the emulated micro-seismic event signal.
Volkova, E. A.; Popov, A. M. Tikhonova, O. V.
2013-03-15
The nonlinear polarization response of a quantum system modeling a silver atom in the field of high-intensity radiation in the IR and UV spectral ranges has been studied by direct numerical integration of a nonstationary Schroedinger equation. The domains of applicability of perturbation theory and polarization expansion in powers of the field intensity are determined. The contribution of excited atoms and electrons in a continuum to the atomic polarization response at the field frequency, which arises due to the radiation-induced excitation and photoionization processes, is analyzed. Features of the nonlinear response to an external field under conditions of atom stabilization are considered.
Optical nonlinearities in plasmonic metamaterials (Conference Presentation)
NASA Astrophysics Data System (ADS)
Zayats, Anatoly V.
2016-04-01
Metals exhibit strong and fast nonlinearities making metallic, plasmonic, structures very promising for ultrafast all-optical applications at low light intensities. Combining metallic nanostructures in metamaterials provides additional functionalities via prospect of precise engineering of spectral response and dispersion. From this point of view, hyperbolic metamaterials, in particular those based on plasmonic nanorod arrays, provide wealth of exciting possibilities in nonlinear optics offering designed linear and nonlinear properties, polarization control, spontaneous emission control and many others. Experiments and modeling have already demonstrated very strong Kerr-nonlinear response and its ultrafast recovery due to the nonlocal nature of the plasmonic mode of the metamaterial, so that small changes in the permittivity of the metallic component under the excitation modify the nonlocal response that in turn leads to strong changes of the metamaterial transmission. In this talk, we will discuss experimental studies and numerical modeling of second- and third-order nonlinear optical processes in hyperbolic metamaterials based on metallic nanorods and other plasmonic systems where coupling between the resonances plays important role in defining nonlinear response. Second-harmonic generation and ultrafast Kerr-type nonlinearity originating from metallic component of the metamaterial will be considered, including nonlinear magneto-optical effects. Nonlinear optical response of stand-alone as well as integrated metamaterial components will be presented. Some of the examples to be discussed include nonlinear polarization control, nonlinear metamaterial integrated in silicon photonic circuitry and second-harmonic generation, including magneto-optical effects.
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Lysak, Tatiana M.
2016-02-01
We investigate a femtosecond pulse propagation in a medium, containing nanorods, with taking into account the dependence of multi-photon absorption from the aspect ratio of nanorods. Nanorods melting due to the laser energy absorption leads to the non-stationary interaction of laser pulse with the medium and time-dependent nanorod aspect ratio changing. Under certain conditions, we found out the soliton-like mode of a laser pulse propagation and the superluminality effect: acceleration of light (fast light) in comparison with light propagation in a linear medium. We discuss a physical mechanism of superluminality effect for considering laser pulse propagation. Using spatio-temporal analogy, one can see the similarity between the pulse centre evolution along longitudinal coordinate and the beam centre evolution under the infrared optical radiation propagation in a cloud, or fog, which moves across the beam, with taking into account its thermal blooming.
NASA Astrophysics Data System (ADS)
Almaev, R. Kh; Suvorov, A. A.
1993-09-01
We investigate the statistical characteristics of the phase of a wave propagating along a ranging path that includes a phase-conjugate mirror through a medium whose complex permittivity ɛ varies randomly. We obtain expressions for the mean change and variance of fluctuations in the phase of a plane wave. We show that phase fluctuations caused by the random changes of the imaginary part of ɛ are not canceled by the phase-conjugate mirror. We obtain conditions for the appearance of enhanced backward scattering in comparison with the mean phase and variance of phase fluctuations for the reflected wave in this absorbing, randomly inhomogeneous medium.
Higher-order nonlinear effects in a Josephson parametric amplifier
NASA Astrophysics Data System (ADS)
Kochetov, Bogdan A.; Fedorov, Arkady
2015-12-01
Nonlinearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA) as well as for a Josephson traveling-wave parametric amplifier, the only devices in which the quantum limit for added noise has so far been approached at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) nonlinearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type nonlinearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction nonlinearity in the linear response regime. We then analyze gain saturation effect for stronger signals within a semiclassical approach. Our results reveal nonlinear effects of higher orders and their implications for operation of a JPA.
Nonlinear quantum optical properties of graphene
NASA Astrophysics Data System (ADS)
Semnani, Behrooz; Hamed Majedi, Amir; Safavi-Naeini, Safieddin
2016-03-01
We present a semiclassical theory of the linear and nonlinear optical response of graphene. The emphasis is placed on the nonlinear optical response of graphene from the standpoint of the underlying chiral symmetry. The Bloch quasiparticles in the low-energy limit around the degeneracy points are dominantly chiral. It is shown that this chiral behavior in conjunction with scale invariance in graphene around the Dirac points results in the strong nonlinear optical response. Explicit expressions for the linear and nonlinear conductivity tensors are derived based on semiconductor Bloch equations (SBEs). The linear terms agree with the result of Kubo formulation. The three main additive mechanisms contribute in the nonlinear optical response of graphene: pure intraband, pure interband and the interplay between them. For each contribution, an explicit response function is derived. The Kerr-type nonlinearity of graphene is then numerically studied and it is demonstrated that the nonlinear refractive index of graphene can be tuned and enhanced by applying a gate voltage. It is also discussed that a strong Kerr nonlinearity can be achieved in a gated graphene monolayer. However, this nonlinearity is accompanied with a significant amount of absorption loss.
NASA Astrophysics Data System (ADS)
Sznitko, Lech; Mysliwiec, Jaroslaw; Karpinski, Pawel; Palewska, Krystyna; Parafiniuk, Kacper; Bartkiewicz, Stanislaw; Rau, Ileana; Kajzar, Francois; Miniewicz, Andrzej
2011-07-01
In this paper, we present results of detailed studies on amplified spontaneous emission (ASE) and lasing achieved in a double-layer system consisted of a biopolymer based matrix loaded with 3-(1,1-dicyanoethenyl1)-1phenyl-4,5dihydro-1H-pyrazole organic nonlinear optical dye and photochromic polymer. The laser action was achieved via distributed feedback configuration with third order of Bragg scattering on surface relief grating generated in photochromic polymer. To excite the luminescence, we have used 6 ns pulses of Nd:YAG laser at 532 nm. The ASE and lasing thresholds were estimated to be 17 mJ/cm2 and 11 mJ/cm2, respectively.
Nonlinear interaction of two trapped-mode resonances in a bilayer fish-scale metamaterial
NASA Astrophysics Data System (ADS)
Tuz, Vladimir R.; Novitsky, Denis V.; Mladyonov, Pavel L.; Prosvirnin, Sergey L.; Novitsky, Andrey V.
2014-09-01
We report on a bistable light transmission through a bilayer "fish-scale" (meander-line) metamaterial. It is demonstrated that an all-optical switching may be achieved nearly the frequency of the high-quality-factor Fano-shaped trapped-mode resonance excitation. The nonlinear interaction of two closely spaced trapped-mode resonances in the bilayer structure composed with a Kerr-type nonlinear dielectric slab is analyzed in both frequency and time domains. It is demonstrated that these two resonances react differently on the applied intense light which leads to destination of a multistable transmission.
NASA Astrophysics Data System (ADS)
Walasik, Wiktor; Renversez, Gilles; Kartashov, Yaroslav V.
2014-02-01
We present three complementary methods to study stationary nonlinear solutions in one-dimensional nonlinear metal-dielectric structures. Two of them use an approximate treatment of the Kerr-type nonlinear term taking into account only the leading electric-field component, while the third one allows for an exact treatment of the nonlinearity. A direct comparison of the results obtained with all three models is presented and the excellent agreement between them justifies the assumptions that have been used to construct the models. A systematic study of the configurations made of two, three, or four layers that contain a semi-infinite Kerr-type nonlinear dielectric, a metal film, and linear dielectrics is presented. A detailed analysis of properties, type, and number of solutions in these three types of structures is performed. The parameter ranges where plasmon-soliton waves exist are found. Structures with realistic optogeometric parameters where plasmon solitons exist at power levels already used in spatial soliton studies are proposed and studied.
Complex geometrical optics of nonlinear inhomogeneous fibres
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2011-03-01
This paper analyses the Gaussian beam (GB) evolution in nonlinear fibres with special attention given to the influence of the initial curvature of the wavefront and to the fibres' permittivity profile. The analysis is performed in the framework of paraxial complex geometrical optics (PCGO). This method reduces the problem of GB evolution in nonlinear and inhomogeneous media to the solution of ordinary differential equations, which can be easily solved either analytically or numerically. It is shown that the PCGO approach radically simplifies modelling of nonlinear phenomena in fibres as compared with standard methods of nonlinear optics such as the variational method approach and the method of moments. It is shown that the PCGO method readily supplies the solution of the nonlinear Schrödinger equation (NLS) for a self-focusing fibre with a focusing permittivity profile and provides a number of new results. The discussion on the interplay between the nonlinear (self-focusing and self-defocusing) and linear (focusing and defocusing) components of the total permittivity demonstrates the new possibilities to limit the collapse phenomenon in nonlinear fibres of Kerr type taking into account the effect of initial beam divergence.
Improved nonlinear slot waveguides using dielectric buffer layers: properties of TM waves.
Elsawy, Mahmoud M R; Renversez, Gilles
2016-04-01
We propose an improved version of the symmetric metal slot waveguides with a Kerr-type nonlinear dielectric core adding linear dielectric buffer layers between the metal regions and the core. Using a finite element method to compute the stationary nonlinear modes, we provide the full phase diagrams of its main transverse magnetic modes as a function of the total power, buffer layer, and core thicknesses that are more complex than the ones of the simple nonlinear metal slot. We show that these modes can exhibit spatial transitions toward specific modes of the new structure as a function of power. We also demonstrate that, for the main modes, the losses are reduced compared to the previous structures, and that they can now decrease with power. Finally, we describe the stability properties of the main stationary solutions using nonlinear FDTD simulations. PMID:27192282
Interplay of diffraction and nonlinear effects in the propagation of ultrashort pulses
NASA Astrophysics Data System (ADS)
Korpa, C. L.; Tóth, Gy; Hebling, J.
2016-02-01
We investigate the interplay of diffraction and nonlinear effects during the propagation of very short light pulses. Adapting the factorization approach to the problem at hand by keeping the transverse-derivative terms apart from the residual nonlinear contributions we derive an unidirectional propagation equation which is valid for weak dispersion and reduces to the slowly-evolving-wave-approximation in the case of paraxial rays. A comparison of the numerical simulation results for the two equations shows pronounced differences when self-focusing plays an important role. We devote special attention to modelling the propagation of ultrashort terahertz pulses taking into account diffraction as well as Kerr-type and second-order nonlinearities. Comparing the measured and simulated wave forms we deduce the value of the nonlinear refractive index of lithium niobate in the terahertz region to be three orders of magnitude larger than in the visible part of the spectrum.
Galushkin, M G; Mitin, Konstantin V; Ionin, Andrei A; Kotkov, A A
1998-10-31
Numerical simulation is used as the basis of an analysis of nonlinear optical properties of the active medium in intracavity four-wave mixing of the radiation of a pulsed electron-beam-controlled discharge CO{sub 2} laser on saturated-gain and refractive-index diffraction gratings. The reflection coefficient of the phase-conjugated signal is determined for various cavity Q-factors, specific input energies, and pressures of the laser-active mixture. A comparison is made of the theoretical and experimental results. It is found that the rate of formation of amplitude gratings is governed primarily by the initial population inversion and by the intensities of the interacting waves. It is shown that transient phase gratings make the dominant contribution to the phase-conjugate reflection coefficient at high pressures of the mixture. (nonlinear optical phenomena)
NASA Astrophysics Data System (ADS)
Hristov, Jordan
2016-03-01
Closed form approximate solutions to nonlinear heat (mass) diffusion equation with power-law nonlinearity of the thermal (mass) diffusivity have been developed by the integral-balance method avoiding the commonly used linearization by the Kirchhoff transformation. The main improvement of the solution is based on the double-integration technique and a new approach to the space derivative. Solutions to Dirichlet and Neumann boundary condition problems have been developed and benchmarked against exact numerical and approximate analytical solutions available in the literature.
NASA Astrophysics Data System (ADS)
McGurn, Arthur R.
2013-10-01
The barrier transmission characteristics of a one-dimensional chain of optically linear split-ring resonators (SRRs) containing a barrier composed of optically nonlinear split-ring resonators are studied. (This is an analogy to the quantum mechanical problem of the resonant transmission of a particle through a finite barrier potential.) The SRRs are idealized as inductor-resistor-capacitor-equivalent resonator circuits where the capacitance is either from a linear dielectric medium (optically linear SRRs) or from a Kerr-type nonlinear dielectric medium (optically nonlinear SRRs). The SRRs are arrayed in a one-dimensional chain and interact with one another through weak nearest-neighbor mutually inductive couplings. The transmission maxima of the SRR barrier problem are studied as they are located in a two-dimensional parameter space characterizing the linear mutually inductive coupling and the nonlinear Kerr dielectric of the SRRs of the barrier. The result is a two-dimensional map giving the conditions for the existence of the resonant-barrier modes that are excited in the transmission process. The various lines of transmission maxima in the two-dimensional plot are associated with different types of resonant excitations in the barrier. The map is similar to one recently made in McGurn [Phys. Rev. BPRBMDO0163-182910.1103/PhysRevB.77.115105 77, 115105 (2008)] for the resonant-transmission modes of a nonlinear barrier in a photonic crystal waveguide. The SRR problem, however, is quite different from the photonic crystal problem as the nonlinear difference equations of the two systems are different in the nature of their nonlinear interactions. Consequently, the results for the two systems are briefly compared. The transmission maxima of the SRR system occur along lines in the two-dimensional plot, which are associated with modes resonantly excited in the barrier. These lines of resonant modes either originate as a simple evolution from the resonant modes of the
Galushkin, M G; Mitin, Konstantin V; Ionin, Andrei A; Kotkov, A A; Seleznev, L V
1998-08-31
An experimental investigation was made of phase conjugation in the course of intracavity degenerate four-wave mixing of radiation in the active medium of a pulsed electron-beam-controlled discharge CO{sub 2} laser generating long pulses. An analysis was carried out of the dependences of the energy and temporal characteristics of a phase-conjugated signal on the specific input energy deposited in the electron-beam-controlled discharge, on the Q-factor of the laser cavity, on the composition and pressure of the laser-active mixture, on the angle of interaction and optical delay between the probe and reference waves, on the ratio of the intensities of these two waves, and on the polarisation and spectral composition of laser radiation. The energy reflection coefficient of the phase-conjugated signal increased with increase in the input energy and with reduction in the probe wave intensity. An increase in the proportion of nitrogen and a reduction in the proportion of helium in the laser-active mixture increased the reflection coefficient and gave rise to a specific profile of the phase-conjugated signal with two maxima, attributed to amplitude and phase nonlinearities of the active medium. An increase in the specific input energy and of the cavity Q-factor reduced the response time of the phase-conjugate signal. (nonlinear optical phenomena and devices)
NASA Astrophysics Data System (ADS)
Derbov, V. L.; Mel'Nikov, L. A.; Novikov, A. D.
1989-08-01
A modification of the generalized method of moments is applied to off-axis Gaussian beams in nonlinear inhomogeneous media. Numerical estimates of the induced astigmatism, spot distortion, and beam curvature are obtained for the conventional saturation spectroscopy scheme with a probing counterpropagating beam slightly deflected from the axis of the saturating beam. It is shown that this deflection causes asymmetry in the radial dependence of the saturation resonance frequency shift.
Slow light in nonlinear photonic crystal coupled-cavity waveguides
NASA Astrophysics Data System (ADS)
Zhu, Na; Wang, Yige; Ren, Qingqing; Zhu, Li; Yuan, Minmin; An, Guimin
2014-04-01
Nonlinear photonic crystals can be formed by inserting Kerr-type nonlinear dielectric rods into perfect photonic crystals. Based on nonlinear photonic crystal, nonlinear photonic crystal coupled-cavity waveguide is constructed and its slow light properties are studied by using the Plane Wave expansion Method (PWM). Both single-defect coupled cavity and two-defect coupled cavity are proposed to optimize slow light properties. The result shows that using single-defect coupled cavity in waveguide is beneficial to obtain larger Normalized Delay-Bandwidth Product (NDBP) but it contributes little to decrease the group velocity of light and enlarging Q factor and delay time; While using two-defect cavity in waveguide can efficiently reduce the group velocity of light and enlarge Q factor and delay time. Compared to normal structures, our new designed nonlinear photonic crystal coupled cavity waveguide owns group velocity that is three magnitudes smaller than the vacuum speed of light. Delay time is of magnitude order of 10 ns and Q factor is of magnitude order of 1000, it means less loss and higher ability of storing energy.
Quantum Effects in the Nonlinear Response of Graphene Plasmons.
Cox, Joel D; Silveiro, Iván; García de Abajo, F Javier
2016-02-23
The ability of graphene to support long-lived, electrically tunable plasmons that interact strongly with light, combined with its highly nonlinear optical response, has generated great expectations for application of the atomically thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Here we show that finite-size effects produce large contributions that increase the nonlinear response of nanostructured graphene to significantly higher levels than those predicted by classical theories. We base our analysis on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation. While classical and quantum descriptions agree well for the linear response when either the plasmon energy is below the Fermi energy or the size of the structure exceeds a few tens of nanometers, this is not always the case for the nonlinear response, and in particular, third-order Kerr-type nonlinearities are generally underestimated by the classical theory. Our results reveal the complex quantum nature of the optical response in nanostructured graphene, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices. PMID:26718484
NASA Technical Reports Server (NTRS)
Dede, Christopher J.
1990-01-01
Claims and rebuttals that hypermedia (the associative, nonlinear interconnection of multimedia materials) is a fundamentally innovative means of thinking and communicating are described. This representational architecture has many advantages that make it a major advance over other media; however, it also has several intrinsic problems that severly limits its effectiveness as a medium. These advantages and limits in applications are discussed.
NASA Astrophysics Data System (ADS)
Bakirova, M. I.; Dorodnitsyn, V. A.; Kurdiumov, S. P.; Samarskii, A. A.; Dimova, S. N.
The directed propagation of heat and combustion in an anisotropic medium is analyzed numerically. It is shown that at the asymptotic stage this process is described by an invariant (self-similar) solution obtained by Dorodnitsyn et al. (1983). In the isotropic case, an invariant solution is indicated which can describe circular and spiral combustion waves. The invariant solutions are obtained on the basis of the group properties of the heat-conduction equation.
Ding, Yujie J
2010-01-15
Owing to strong coupling between transverse-optical phonons and high-frequency terahertz waves in zinc-blende semiconductors, second-order nonlinear coefficients can be dramatically enhanced within the forbidden band of the polariton resonance. However, linear absorption in this regime is also dramatically increased. We show that transverse-pumping geometry can be exploited for achieving an efficient terahertz generation at the polariton resonance. Our estimates illustrate that pump powers as low as 100 mW are sufficient for causing the significant depletion of the pump beams. PMID:20081988
NASA Astrophysics Data System (ADS)
Zarei, A.; Z. R. R. Rosdin, R.; M. Ali, N.; H., Ahmad; W. Harun, S.
2014-05-01
A single-wavelength Brillouin laser is demonstrated by using a 3-m-long erbium doped fiber (EDF) in a ring cavity. The EDF is used to provide both nonlinear and linear gains to generate a stimulated Brillouin scattering (SBS) and to amplify the generated SBS, respectively. The Brillouin erbium fiber laser (BEFL) operates at 1561.5 nm, where the operating wavelength is up-shifted by 0.08nm from the Brillouin pump. The operation wavelength is also tunable within 1560.6-1562.6 nm. The BEFL also shows a self-pulsing characteristic with repetition of 66.7 kHz when the BP is set around the threshold pump power of 13mW. Compared to the conventional Brillouin fiber laser with a long cavity length, the proposed BEFL exhibits a significantly lower amplitude of pulse. This laser has many potential applications, such as in optical communication and sensors.
NASA Astrophysics Data System (ADS)
Sadhu, Arunangshu; Sarkar, Somenath
2016-05-01
We report a simple and straightforward approximate analysis to investigate the effect of Kerr type nonlinear optical processes in sub-wavelength diameter step index optical fibers based on Marcuse method in single mode region. Optimum core diameters of such fibers, predicted by us, together with relevant core nonlinearity coefficient and effective area are seen to be compatible with the analytical values indicating the validity of this novel application of the elegant approximate method. However, the corresponding values, obtained by earlier variational method, show larger discrepancy with analytical findings in comparison with ours. Also, maximum enhancement of nonlinear processes within single mode region, confirming almost the analytical method, assures less diffraction. Formulations, coupled with simplicity and novelty of the present analysis, should find wide use by system users and experimentalists in this emerging area.
Nonlinear heat conduction with combustion
Galaktionov, V.A.; Kurclyumov, S.P.; Samarskiv, A.A. )
1991-01-01
This paper deals with a study of the properties of high-intensity combustion of a solid nonlinear heat conducting medium which is described by the quasilinear parabolic-type equation for nonlinear heat conduction with a source. The paper summarizes a significant range of investigations dealing with the study of high-intensity thermal processes in solid nonlinear media carried out by the authors in the past decade.
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics. PMID:25401574
NASA Astrophysics Data System (ADS)
Berczynski, P.
2013-09-01
The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear Kerr type and saturable fibres. CGO reduces the problem of Gaussian beam evolution in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to other methods of nonlinear optics such as variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of Gaussian beam propagation in saturable fibres with either focusing and defocusing refractive profiles. Besides, the influence of initial curvature of the wave front, phenomenon of weak absorption and effect of either transverse and longitudinal inhomogeneity on GB propagation in nonlinear fibres is discussed in this paper.
Improved nonlinear plasmonic slot waveguide: a full study
NASA Astrophysics Data System (ADS)
Elsawy, Mahmoud M. R.; Nazabal, Virginie; Chauvet, Mathieu; Renversez, Gilles
2016-04-01
We present a full study of an improved nonlinear plasmonic slot waveguides (NPSWs) in which buffer linear dielectric layers are added between the Kerr type nonlinear dielectric core and the two semi-infinite metal regions. Our approach computes the stationary solutions using the fixed power algorithm, in which for a given structure the wave power is an input parameter and the outputs are the propagation constant and the corresponding field components. For TM polarized waves, the inclusion of these supplementary layers have two consequences. First, they reduced the overall losses. Secondly, they modify the types of solutions that propagate in the NPSWs adding new profiles enlarging the possibilities offered by these nonlinear waveguides. In addition to the symmetric linear plasmonic profile obtained in the simple plasmonic structure with linear core such that its effective index is above the linear core refractive index, we obtained a new field profile which is more localized in the core with an effective index below the core linear refractive index. In the nonlinear case, if the effective index of the symmetric linear mode is above the core linear refractive index, the mode field profiles now exhibit a spatial transition from a plasmonic type profile to a solitonic type one. Our structure also provides longer propagation length due to the decrease of the losses compared to the simple nonlinear slot waveguide and exhibits, for well-chosen refractive index or thickness of the buffer layer, a spatial transition of its main modes that can be controlled by the power. We provide a full phase diagram of the TM wave operating regimes of these improved NPSWs. The stability of the main TM modes is then demonstrated numerically using the FDTD. We also demonstrate the existence of TE waves for both linear and nonlinear cases (for some configurations) in which the maximum intensity is located in the middle of the waveguide. We indicate the bifurcation of the nonlinear
Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions
Fibich, G. . E-mail: fibich@math.tau.ac.il; Tsynkov, S. . E-mail: tsynkov@math.ncsu.edu
2005-11-20
In [J. Comput. Phys. 171 (2001) 632-677] we developed a fourth-order numerical method for solving the nonlinear Helmholtz equation which governs the propagation of time-harmonic laser beams in media with a Kerr-type nonlinearity. A key element of the algorithm was a new nonlocal two-way artificial boundary condition (ABC), set in the direction of beam propagation. This two-way ABC provided for reflectionless propagation of the outgoing waves while also fully transmitting the given incoming beam at the boundaries of the computational domain. Altogether, the algorithm of [J. Comput. Phys. 171 (2001) 632-677] has allowed for a direct simulation of nonlinear self-focusing without neglecting nonparaxial effects and backscattering. To the best of our knowledge, this capacity has never been achieved previously in nonlinear optics. In the current paper, we propose an improved version of the algorithm. The principal innovation is that instead of using the Dirichlet boundary conditions in the direction orthogonal to that of the laser beam propagation, we now introduce Sommerfeld-type local radiation boundary conditions, which are constructed directly in the discrete framework. Numerically, implementation of the Sommerfeld conditions requires evaluation of eigenvalues and eigenvectors for a non-Hermitian matrix. Subsequently, the separation of variables, which is a key building block of the aforementioned nonlocal ABC, is implemented through an expansion with respect to the nonorthogonal basis of the eigenvectors. Numerical simulations show that the new algorithm offers a considerable improvement in its numerical performance, as well as in the range of physical phenomena that it is capable of simulating.
``Once Nonlinear, Always Nonlinear''
NASA Astrophysics Data System (ADS)
Blackstock, David T.
2006-05-01
The phrase "Once nonlinear, always nonlinear" is attributed to David F. Pernet. In the 1970s he noticed that nonlinearly generated higher harmonic components (both tones and noise) don't decay as small signals, no matter how far the wave propagates. Despite being out of step with the then widespread notion that small-signal behavior is restored in "old age," Pernet's view is supported by the Burgers-equation solutions of the early 1960s. For a plane wave from a sinusoidally vibrating source in a thermoviscous fluid, the old-age decay of the nth harmonic is e-nαx, not e-n2αx (small-signal expectation), where α is the absorption coefficient at the fundamental frequency f and x is propagation distance. Moreover, for spherical waves (r the distance) the harmonic diminishes as e-nαx/rn, not e-n2αx/r. While not new, these results have special application to aircraft noise propagation, since the large propagation distances of interest imply old age. The virtual source model may be used to explain the "anomalous" decay rates. In old age most of the nth harmonic sound comes from virtual sources close to the receiver. Their strength is proportional to the nth power of the local fundamental amplitude, and that sets the decay law for the nth harmonic.
Photon correlations in a two-site nonlinear cavity system under coherent drive and dissipation
Ferretti, Sara; Andreani, Lucio Claudio; Tuereci, Hakan E.; Gerace, Dario
2010-07-15
We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: The master equation for the model, which takes into account both a coherent continuous drive and radiative as well as nonradiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between 0 and 1, and divides the diagram identified by the two energy scales of the system - the tunneling and the nonlinear Kerr interaction - into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities, and the emitted light is coherent. In the opposite limit, photon blockade sets in, and the system shows an insulatorlike state with photons locked on each cavity, identified by antibunching of emitted light.
Transparency in nonlinear frequency conversion
NASA Astrophysics Data System (ADS)
Longhi, Stefano
2016-04-01
Suppression of wave scattering and the realization of transparency effects in engineered optical media and surfaces have attracted great attention in the past recent years. In this work the problem of transparency is considered for optical wave propagation in a nonlinear dielectric medium with second-order χ(2 ) susceptibility. Because of nonlinear interaction, a reference signal wave at carrier frequency ω1 can exchange power, thus being amplified or attenuated, when phase-matching conditions are satisfied and frequency conversion takes place. Therefore, rather generally the medium is not transparent to the signal wave because of "scattering" in the frequency domain. Here we show that broadband transparency, corresponding to the full absence of frequency conversion in spite of phase matching, can be observed for the signal wave in the process of sum frequency generation whenever the effective susceptibility χ(2 ) along the nonlinear medium is tailored following a suitable spatial apodization profile and the power level of the pump wave is properly tuned. While broadband transparency is observed under such conditions, the nonlinear medium is not invisible owing to an additional effective dispersion for the signal wave introduced by the nonlinear interaction.
Modulation instability of optical nonlinear media: a route to chaos
NASA Astrophysics Data System (ADS)
Sharif, Morteza A.
2011-12-01
Modulation Instability is known as intrinsic property of a nonlinear medium like Kerr medium or photorefractive medium; through the such media, the system behavior is possible to transit form stationary regime to chaotic regime; this paper deals with Modulation Instability (MI) in a nonlinear medium and investigates the analogy of MI of optical nonlinear medium and the consequent chaotic regime based on extracting Lyapunov exponent through the power spectrum and equivalently intensity-time diagram of MI; the experimental observation truly confirms the results of MI as the route to the chaotic regime.
NASA Astrophysics Data System (ADS)
H, R. Baghshahi; M, K. Tavassoly; A, Behjat
2014-07-01
The interaction between a two-level atom and a single-mode field in the k-photon Jaynes—Cummings model (JCM) in the presence of the Stark shift and a Kerr medium is studied. All terms in the Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be f-deformed. In particular, the effect of the initial state of the radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states (coherent, squeezed and thermal states).
Guided waves in a multi-layered optical structure
NASA Astrophysics Data System (ADS)
Torres, Pedro J.
2006-09-01
Motivated by the study of the propagation of electromagnetic waves through a multi-layered optical medium, we prove the existence of two different kinds of homoclinic solutions to the origin in a Schrödinger equation with a nonlinear term. We use a Krasnoselskii fixed point theorem together with a compactness criterion due to Zima. The main results are illustrated with concrete examples of practical interest such as self-focusing nonlinearities of Kerr and non-Kerr type.
Golubkov, A A; Makarov, Vladimir A
2011-06-30
We have proved for the first time and proposed an algorithm of unique spatial profile reconstruction of the components {chi}-circumflex {sup (3)}{sub yyyy} of complex tensors {chi}-circumflex {sup (3)}(z, {omega}', {omega}', -{omega}, {omega}) and {chi}-circumflex {sup (3)}(z, 2{omega}{+-}{omega}', {+-}{omega}', {omega}, {omega}), describing four-photon interaction of light waves in a one-dimensionally inhomogeneous plate, whose medium has a symmetry plane m{sub y} that is perpendicular to its surface. For the media with an additional symmetry axis 2{sub z}, 4{sub z}, 6{sub z} or {infinity}{sub z} that is perpendicular to the plate surface, the proposed method can be used to reconstruct about one-fifth of all independent components of the above tensors. (nonlinear optical phenomena)
Wave propagation in ordered, disordered, and nonlinear photonic band gap materials
Lidorikis, Elefterios
1999-12-10
Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model in which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.
Nonlinear Stokes-Mueller polarimetry
NASA Astrophysics Data System (ADS)
Samim, Masood; Krouglov, Serguei; Barzda, Virginijus
2016-01-01
The Stokes-Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations with Kleinman symmetry. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional 4 ×1 Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, the relations between components of nonlinear susceptibility tensor and Mueller matrix are explicitly provided. The approach of combining linear and nonlinear optical elements is discussed within the context of polarimetry.
Forward model nonlinearity versus inverse model nonlinearity
Mehl, S.
2007-01-01
The issue of concern is the impact of forward model nonlinearity on the nonlinearity of the inverse model. The question posed is, "Does increased nonlinearity in the head solution (forward model) always result in increased nonlinearity in the inverse solution (estimation of hydraulic conductivity)?" It is shown that the two nonlinearities are separate, and it is not universally true that increased forward model nonlinearity increases inverse model nonlinearity. ?? 2007 National Ground Water Association.
NASA Astrophysics Data System (ADS)
SjöBerg, Daniel
2003-04-01
We investigate the propagation of electromagnetic waves in a cylindrical waveguide with an arbitrary cross section filled with a nonlinear material. The electromagnetic field is expanded in the usual eigenmodes of the waveguide, and the coupling between the modes is quantified. We derive the wave equations governing each mode with special emphasis on the situation with a dominant TE mode. The result is a strictly hyperbolic system of nonlinear partial differential equations for the dominating mode, whereas the minor modes satisfy hyperbolic systems of linear, nonstationary, and partial differential equations. A growth estimate is given for the minor modes.
Some aspects of the comparison between optics and nonlinear acoustics
NASA Technical Reports Server (NTRS)
Perrin, B.
1980-01-01
Some results concerning nonlinear acoustics deduced from a comparison of nonlinear processes in optics and acoustics are discussed. An aspect of nonlinearity in acoustics connected with the dimensionality of the medium of propagation is emphasized and illustrated by the proof of static instability of an ideal linear solid. In addition a phenomenon, which can be called acoustical rectification by analogy with nonlinear optics, is propounded to measure the third order elastic constants. Its experimental consequences are predicted in a particular case.
Nonlinear combining of laser beams.
Lushnikov, Pavel M; Vladimirova, Natalia
2014-06-15
We propose to combine multiple laser beams into a single diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. Beams with total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with Kerr nonlinearity. Random fluctuations during propagation eventually trigger a strong self-focusing event and produce a diffraction-limited beam carrying the critical power. PMID:24978503
NASA Astrophysics Data System (ADS)
Ranjbar, Monireh; Bahari, Ali
2016-09-01
Four-wave mixing in propagation of cylindrical waves in a homogeneous nonlinear optical media has been investigated theoretically. An explicit analytical expression which contains all the main nonlinear optical effects, including third harmonic generation, sum and difference frequency generation has been obtained. A comparison between sum frequency efficiency for exact and approximation expression in a homogeneous nonlinear medium has been done. The effect of increasing the nonlinear optical coefficient (χeff(3)) and increasing the frequency difference between two adjacent waves (Δ ω) , on the efficiency of sum frequency generation in homogeneous media has been investigated.
Solute transport through a deforming porous medium
NASA Astrophysics Data System (ADS)
Peters, Glen P.; Smith, David W.
2002-06-01
Solute transport through a porous medium is typically modelled assuming the porous medium is rigid. However, many applications exist where the porous medium is deforming, including, municipal landfill liners, mine tailings dams, and land subsidence. In this paper, mass balance laws are used to derive the flow and transport equations for a deforming porous medium. The equations are derived in both spatial and material co-ordinate systems. Solute transport through an engineered landfill liner is used as an illustrative example to show the differences between the theory for a rigid porous medium, and small and large deformation analysis of a deforming porous medium. It is found that the large deformation model produces shorter solute breakthrough times, followed by the small deformation model, and then the rigid porous medium model. It is also found that it is important to include spatial and temporal void ratio variations in the large deformation analysis. It is shown that a non-linear large deformation model may greatly reduce the solute breakthrough time, compared to a standard transport analysis typically employed by environmental engineers.
Spectral Hole Burning via Kerr Nonlinearity
NASA Astrophysics Data System (ADS)
Khan, Anwar Ali; Abdul Jabar, M. S.; Jalaluddin, M.; Bacha, Bakht Amin; Iftikhar, Ahmad
2015-10-01
Spectral hole burning is investigated in an optical medium in the presence of Doppler broadening and Kerr nonlinearity. The Kerr nonlinearity generates coherent hole burning in the absorption spectrum. The higher order Kerr nonlinearity enhances the typical lamb dip of the hole. Normal dispersion in the hole burning region while Steep anomalous dispersion between the two hole burning regions also enhances with higher order Kerr effect. A large phase shift creates large delay or advancement in the pulse propagation while no distortion is observed in the pulse. These results provide significant steps to improve optical memory, telecom devices, preservation of information and image quality. Supported by Higher Education Commission (HEC) of Pakistan
Large nonlocal nonlinear optical response of castor oil
NASA Astrophysics Data System (ADS)
Souza, Rogério F.; Alencar, Márcio A. R. C.; Meneghetti, Mario R.; Hickmann, Jandir M.
2009-09-01
The nonlocal nonlinearity of castor oil was investigated using the Z-scan technique in the CW regime at 514 nm and in femtosecond regime at 810 nm. Large negative nonlinear refractive indexes of thermal origin, thermo-optical coefficients and degree of nonlocality were obtained for both laser excitation wavelengths. The results indicate that the electronic part of the nonlinear refractive index and nonlinear absorption were negligible. Our results suggest that castor oil is promising candidate as a nonlinear medium for several nonlocal optical applications, such as in spatial soliton propagation, as well as a dispersant agent in the measurement of absorptive properties of nanoparticles.
Nonlinear common-path interferometer: an image processor.
Treviño-Palacios, Carlos Gerardo; Iturbe-Castillo, Marcelo David; Sánchez-de-la-Llave, David; Ramos-García, Ruben; Olivos-Pérez, Luis Ignacio
2003-09-01
A single-lens optical setup with a nonlinear medium placed in its geometrical focal plane is used to contrast a phase disturbance. This setup blends the robustness of phase-contrast methods with an optical nonlinear intensity-dependent medium and the usefulness of traditional interferometric techniques. We show that the ratio of the total illumination area to the phase-object area determines an adequate phase-disturbance contrast. PMID:12962385
Modulational instability and solitons in nonlocal media with competing nonlinearities
Esbensen, B. K.; Bache, M.; Bang, O.; Wlotzka, A.; Krolikowski, W.
2011-11-15
We investigate analytically and numerically propagation and spatial localization of light in nonlocal media with competing nonlinearities. In particular, we discuss conditions for the modulational instability of plane waves and formation of spatial solitons. We show that the competing focusing and defocusing nonlinearities enable coexistence of dark or bright spatial solitons in the same medium by varying the intensity of the beam.
Light steering in a strongly nonlocal nonlinear medium
Ouyang Shigen; Hu Wei; Guo Qi
2007-11-15
With a strongly nonlocal model, we present an analytical solution of the coherent interaction of two Gaussian beams with an arbitrary phase difference and arbitrary incident angles. Numerical simulations show that the analytical solution can describe the interaction of two Gaussian beams very well in the strongly nonlocal case. It is theoretically shown that one can steer lights in strongly nonlocal media by tuning the incident conditions of coherently interacting beams like the phase difference between beams and their relative amplitude.
ERIC Educational Resources Information Center
Higginbotham-Wheat, Nancy L.
This paper addresses one area of conflict in decisionmaking in computer-based instruction (CBI) research: the relationship between the researcher's definition of CBI either as a medium or as an integrated system and the design of meaningful research questions. (A medium is defined here as a device for the delivery of instruction, while an…
Nonlocal nonlinear refraction in Hibiscus sabdariffa with large phase shifts.
Ramírez-Martínez, D; Alvarado-Méndez, E; Trejo-Durán, M; Vázquez-Guevara, M A
2014-10-20
In this work we present a study of nonlinear optical properties in organic materials (hibiscus sabdariffa). Our results demonstrate that the medium exhibits a highly nonlocal nonlinear response. We show preliminary numerical results of the transmittance as nonlocal response by considering, simultaneously, the nonlinear absorption and refraction in media. Numerical results are accord to measurement obtained by Z- scan technique where we observe large phase shifts. We also analyze the far field diffraction ring patterns of the sample. PMID:25401548
Multistable laser through a nonlinear mirror
Dlodlo, T.S.
1983-03-01
In this paper we show that a multistable laser is realizable by the use of a nonlinear p medium as one of the resonant cavity mirrors. Using the semiclassical laser theory we derive a gain function with many maxima. The resulting gain equation has many real solutions. We discuss the possible application in switching by use of a suitable external perturbation.
Stokowski, Stanley E.
1989-01-01
A laser medium is particularly useful in high average power solid state lasers. The laser medium includes a chormium dopant and preferably neodymium ions as codopant, and is primarily a gadolinium scandium gallium garnet, or an analog thereof. Divalent cations inhibit spiral morphology as large boules from which the laser medium is derived are grown, and a source of ions convertible between a trivalent state and a tetravalent state at a low ionization energy are in the laser medium to reduce an absorption coefficient at about one micron wavelength otherwise caused by the divalent cations. These divalent cations and convertible ions are dispersed in the laser medium. Preferred convertible ions are provided from titanium or cerium sources.
Stokowski, S.E.
1987-10-20
A laser medium is particularly useful in high average power solid state lasers. The laser medium includes a chromium dopant and preferably neodymium ions as codopant, and is primarily a gadolinium scandium gallium garnet, or an analog thereof. Divalent cations inhibit spiral morphology as large boules from which the laser medium is derived are grown, and a source of ions convertible between a trivalent state and a tetravalent state at a low ionization energy are in the laser medium to reduce an absorption coefficient at about one micron wavelength otherwise caused by the divalent cations. These divalent cations and convertible ions are dispersed in the laser medium. Preferred convertible ions are provided from titanium or cerium sources.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
NEW NONLINEAR ACOUSTIC TECHNIQUES FOR NDE
J. A. TENCATE
2000-09-01
Acoustic nonlinearity in a medium may occur as a result of a variety of mechanisms. Some of the more common nonlinear effects may come from: (1) one or several cracks, volumetrically distributed due to age or fatigue or single disbonds or delamination; (2) imperfect grain-to-grain contacts, e.g., materials like concretes that are cemented together and have less than perfect bonds; (3) hard parts in a soft matrix, e.g., extreme duty materials like tungsten/copper alloys; or (4) atomic-scale nonlinearities. Nonlinear effects that arise from the first two mechanisms are considerably larger than the last two; thus, we have focused considerable attention on these. The most pervasive nonlinear measure of damage today is a second harmonic measurement. We show that for many cases of interest to NDE, a second harmonic measurement may not be the best choice. We examine the manifestations of nonlinearity in (nonlinear) materials with cracks and/or imperfect bonds and illustrate their applicability to NDE. For example, nonlinear resonance frequency shifts measured at increasing drive levels correlate strongly with the amount of ASR (alkali-silica reaction) damage of concrete cores. Memory effects (slow dynamics) also seem to correlate with the amount of damage.
[Nonlinear magnetohydrodynamics
Not Available
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday`s law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm`s law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile.
"Wandering" soliton in a nonlinear photonic crystal
NASA Astrophysics Data System (ADS)
Lysak, T. M.; Trofimov, V. A.
2015-12-01
On the basis of computer simulation, we demonstrate the possibility of a new type of "wandering" solitons implementation in nonlinear periodic layered structures. "Wandering" soliton moves across the layers, repeatedly changing its direction of motion due to the reflection from the photonic crystal (PC) boundaries with the ambient medium. The initial soliton is located inside a PC and occupies several of its layers. Its profile can be found as the solution of the corresponding nonlinear eigenvalue problem. "Wandering" solitons are formed as a result of a large perturbation of the wave vector, which leads to the soliton motion across photonic crystal layers. In the process of reflection from the boundary with the ambient medium, the soliton partly penetrates into the ambient medium at a depth equal to the width of several PC layers. A slow return of light energy, which previously left the PC, can take place at this moment.
Nonlinear Talbot effect of rogue waves
NASA Astrophysics Data System (ADS)
Zhang, Yiqi; Belić, Milivoj R.; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-03-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Coda wave interferometry for estimating nonlinear behavior in seismic velocity.
Snieder, Roel; Grêt, Alexandre; Douma, Huub; Scales, John
2002-03-22
In coda wave interferometry, one records multiply scattered waves at a limited number of receivers to infer changes in the medium over time. With this technique, we have determined the nonlinear dependence of the seismic velocity in granite on temperature and the associated acoustic emissions. This technique can be used in warning mode, to detect the presence of temporal changes in the medium, or in diagnostic mode, where the temporal change in the medium is quantified. PMID:11910107
Nonlinear Cosmic Ray Diffusion Theories
NASA Astrophysics Data System (ADS)
Shalchi, Andreas
Within cosmic ray transport theory, we investigate the interaction between energetic charged particles like electrons, protons, or heavy ions and astrophysical plasmas such as the solar wind or the interstellar medium. These particles interact with a background magnetic field B 0 and with turbulent electric and magnetic fields ýE and ýB, and they therefore experience scattering parallel and perpendicular to B 0. In this introductory chapter, general properties of cosmic rays are discussed, as well as the unperturbed motion of the particles. Furthermore, the physics of parallel and perpendicular scattering is investigated. At the end of this chapter, we consider observed mean free paths of cosmic rays in the heliosphere and in the interstel- lar medium. One aim of this book is to demonstrate that a nonlinear description of particle transport is necessary to reproduce these measurements.
Gaussian beam diffraction in inhomogeneous and logarithmically saturable nonlinear media
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2012-08-01
The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, PCGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous and nonlinear media as compared to the numerical and analytical methods of nonlinear optics. The power of PCGO method is presented on the example of Gaussian beam evolution in logarithmically saturable medium with either focusing and defocusing refractive profile. Besides, the influence of initial curvature of the wave front on GB evolution in nonlinear saturable medium is discussed in this paper.
Nonlinear propagation and control of acoustic waves in phononic superlattices
NASA Astrophysics Data System (ADS)
Jiménez, Noé; Mehrem, Ahmed; Picó, Rubén; García-Raffi, Lluís M.; Sánchez-Morcillo, Víctor J.
2016-05-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime. xml:lang="fr"
Matter-wave soliton interferometer based on a nonlinear splitter
NASA Astrophysics Data System (ADS)
Sakaguchi, Hidetsugu; Malomed, Boris A.
2016-02-01
We elaborate a model of the interferometer which, unlike previously studied ones, uses a local (δ-functional) nonlinear repulsive potential, embedded into a harmonic-oscillator trapping potential, as the splitter for the incident soliton. An estimate demonstrates that this setting may be implemented by means of the localized Feshbach resonance controlled by a focused laser beam. The same system may be realized as a nonlinear waveguide in optics. Subsequent analysis produces an exact solution for scattering of a plane wave in the linear medium on the δ -functional nonlinear repulsive potential, and an approximate solution for splitting of the incident soliton when the ambient medium is nonlinear. The most essential result, obtained by means of systematic simulations, is that the use of the nonlinear splitter provides the sensitivity of the soliton-based interferometer to the target, inserted into one of its arms, which is much higher than the sensitivity provided by the usual linear splitter.
Direct detection of optical phase conjugation in a colloidal medium.
López-Mariscal, Carlos; Gutiérrez-Vega, Julio C; McGloin, David; Dholakia, Kishan
2007-05-14
Degenerate four-wave mixing is demonstrated using an artificial Kerr medium and is evidenced by directly observing the phase conjugation of a vortex signal beam. The nonlinear susceptibility is produced by a refractive index grating created in a suspension of dielectric microscopic particles optically confined in the intensity grating distribution of two interfering laser beams. PMID:19546937
Instability of evaporation fronts in the interstellar medium
Kim, Jeong-Gyu; Kim, Woong-Tae E-mail: wkim@astro.snu.ac.kr
2013-12-10
The neutral component of the interstellar medium is segregated into the cold neutral medium (CNM) and warm neutral medium (WNM) as a result of thermal instability. It was found that a plane-parallel CNM-WNM evaporation interface, across which the CNM undergoes thermal expansion, is linearly unstable to corrugational disturbances, in complete analogy with the Darrieus-Landau instability (DLI) of terrestrial flames. We perform a full linear stability analysis as well as nonlinear hydrodynamic simulations of the DLI of such evaporation fronts in the presence of thermal conduction. We find that the DLI is suppressed at short length scales by conduction. The length and time scales of the fastest growing mode are inversely proportional to the evaporation flow speed of the CNM and its square, respectively. In the nonlinear stage, the DLI saturates to a steady state where the front deforms to a finger-like shape protruding toward the WNM, without generating turbulence. The evaporation rate at nonlinear saturation is larger than the initial plane-parallel value by a factor of ∼2.4 when the equilibrium thermal pressure is 1800 k {sub B} cm{sup –3} K. The degrees of front deformation and evaporation-rate enhancement at nonlinear saturation are determined primarily by the density ratio between the CNM and WNM. We demonstrate that the Field length in the thermally unstable medium should be resolved by at least four grid points to obtain reliable numerical outcomes involving thermal instability.
Spatiotemporal coupling in dispersive nonlinear planar waveguides
NASA Astrophysics Data System (ADS)
Ryan, Andrew T.; Agrawal, Govind P.
1995-12-01
The multidimensional nonlinear Schrodinger equation governs the spatial and temporal evolution of an optical field inside a nonlinear dispersive medium. Although spatial (diffractive) and temporal (dispersive) effects can be studied independently in a linear medium, they become mutually coupled in a nonlinear medium. We present the results of numerical simulations showing this spatiotemporal coupling for ultrashort pulses propagating in dispersive Kerr media. We investigate how spatiotemporal coupling affects the behavior of the optical field in each of the four regimes defined by the type of group-velocity dispersion (normal or anomalous) and the type of nonlinearity (focusing or defocusing). We show that dispersion, through spatiotemporal coupling, can either enhance or suppress self-focusing and self-defocusing. Similarly, we demonstrate that diffraction can either enhance or suppress pulse compression or broadening. We also discuss how these effects can be controlled with optical phase modulation, such as that provided by a lens (spatial phase modulation) or frequency chirping (temporal phase modulation). Copyright (c) 1995 Optical Society of America
Composite structures for the enhancement of nonlinear optical materials.
Neeves, A E; Birnboim, M H
1988-12-01
Calculations of the nonlinear optical behavior are developed for model composites consisting of nanospheres with a metallic core and a nonlinear shell suspended in a nonlinear medium. The concept for the enhancement of optical phase conjugation from all these nonlinear regions is that the optical field can be concentrated both inside and in the neighborhood of the metallic core, aided by surface-mediated plasmon resonance. Calculations for gold cores and aluminum cores indicate that phase-conjugate reflectivity enhancements of 10(8) may be possible. PMID:19746133
Theory and design of nonlinear metamaterials
NASA Astrophysics Data System (ADS)
Rose, Alec Daniel
and oscillators. By applying this set of tools and knowledge to microwave metamaterials, I experimentally confirm several novel nonlinear phenomena. Most notably, I construct a backward wave nonlinear medium from varactor-loaded split ring resonators loaded in a rectangular waveguide, capable of generating second-harmonic opposite to conventional nonlinear materials with a conversion efficiency as high as 1.5%. In addition, I confirm nonlinear magnetoelectric coupling in two dual gap varactor-loaded split ring resonator metamaterials through measurement of the amplitude and phase of the second-harmonic generated in the forward and backward directions from a thin slab. I then use the presence of simultaneous nonlinearities in such metamaterials to observe nonlinear interference, manifest as unidirectional difference frequency generation with contrasts of 6 and 12 dB in the forward and backward directions, respectively. Finally, I apply these principles and intuition to several plasmonic platforms with the goal of achieving similar enhancements and configurations at optical frequencies. Using the example of fluorescence enhancement in optical patch antennas, I develop a semi-classical numerical model for the calculation of field-induced enhancements to both excitation and spontaneous emission rates of an embedded fluorophore, showing qualitative agreement with experimental results, with enhancement factors of more than 30,000. Throughout these series of works, I emphasize the indispensability of effective design and retrieval tools in understanding and optimizing both metamaterials and plasmonic systems. Ultimately, when weighed against the disadvantages in fabrication and optical losses, the results presented here provide a context for the application of nonlinear metamaterials within three distinct areas where a competitive advantage over conventional materials might be obtained: fundamental science demonstrations, linear and nonlinear anisotropy engineering, and
Coherent perfect absorption in nonlinear optics
NASA Astrophysics Data System (ADS)
Zheng, Yuanlin; Wan, Wenjie; Chen, Xianfeng
2013-02-01
Recently, a concept of time reversed lasing or coherent perfect absorber (CPA) has been proposed by A. D. Stone and co-workers, and was shortly experimentally demonstrated by them. The CPA system is illuminated coherently and monochromatically by the time reverse of the output of a lasing mode and the incident radiation is perfectly absorbed. Shortly afterwards, Stefano Longhi extended the idea to realize a CPA for colored incident light, and have theoretically shown that the time reversal of optical parametric oscillation (OPO) in a nonlinear medium could also realize a colored CPA for incident signal and idler fields which can be seemed as a kind of nonlinear CPA. Here we present the realization of such time-reversed processes in nonlinear optics regime, including time-reversed second harmonic generation (SHG) for coherent absorption at harmonic frequency of the pump and time-reversed optical parametric amplification (OPA) for coherent attenuation of colored travelling optical fields. Time reversed SHG is carried out at both phase matching and mismatching conditions, which shows parametric near perfect absorption at the harmonic frequency of the pump. The time reversal of OPA is demonstrated experimentally in a nonlinear medium to form a coherent absorber for perpendicularly polarized signal and idler travelling waves, realizing in the condition of OPA by a type II phase matching scheme. The absorption of signal/idler pair occurs at some specific phase difference. This is the first experimental demonstration of coherent absorption processes in nonlinear optics regime.
NASA Astrophysics Data System (ADS)
Lauterborn, Werner; Kurz, Thomas; Akhatov, Iskander
At high sound intensities or long propagation distances at
The violent interstellar medium
NASA Technical Reports Server (NTRS)
Mccray, R.; Snow, T. P., Jr.
1979-01-01
Observational evidence for high-velocity and high-temperature interstellar gas is reviewed. The physical processes that characterize this gas are described, including the ionization and emissivity of coronal gas, the behavior and appearance of high-velocity shocks, and interfaces between coronal gas and cooler interstellar gas. Hydrodynamical models for the action of supernova explosions and stellar winds on the interstellar medium are examined, and recent attempts to synthesize all the processes considered into a global model for the interstellar medium are discussed.
Alignment and nonlinear elasticity in biopolymer gels
NASA Astrophysics Data System (ADS)
Feng, Jingchen; Levine, Herbert; Mao, Xiaoming; Sander, Leonard M.
2015-04-01
We present a Landau-type theory for the nonlinear elasticity of biopolymer gels with a part of the order parameter describing induced nematic order of fibers in the gel. We attribute the nonlinear elastic behavior of these materials to fiber alignment induced by strain. We suggest an application to contact guidance of cell motility in tissue. We compare our theory to simulation of a disordered lattice model for biopolymers. We treat homogeneous deformations such as simple shear, hydrostatic expansion, and simple extension, and obtain good agreement between theory and simulation. We also consider a localized perturbation which is a simple model for a contracting cell in a medium.
Nonlinear holography for acoustic wave detection
NASA Astrophysics Data System (ADS)
Bortolozzo, U.; Dolfi, D.; Huignard, J. P.; Molin, S.; Peigné, A.; Residori, S.
2015-03-01
A liquid crystal medium is used to perform nonlinear dynamic holography and is coupled with multimode optical fibers for optical sensing applications. Thanks to the adaptive character of the nonlinear holography, and to the sensitivity of the multimode fibers, we demonstrate that the system is able to perform efficient acoustic wave detection even with noisy signals. The detection limit is estimated and multimode versus monomode optical fiber are compared. Finally, a wavelength multiplexing protocol is implemented for the spatial localization of the acoustic disturbances.
Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion
NASA Astrophysics Data System (ADS)
Zhou, Qin; Zhu, Qiuping
2015-03-01
In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.
NASA Technical Reports Server (NTRS)
Gange, Robert Allen (Inventor)
1977-01-01
A holographic recording medium comprising a conductive substrate, a photoconductive layer and an electrically alterable layer of a linear, low molecular weight hydrocarbon polymer has improved fatigue resistance. An acrylic barrier layer can be interposed between the photoconductive and electrically alterable layers.
Nonlinear Hysteretic Torsional Waves.
Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V
2015-07-31
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters. PMID:26274421
Nonlinear Hysteretic Torsional Waves
NASA Astrophysics Data System (ADS)
Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.
2015-07-01
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
The function of nonlinear phenomena in meerkat alarm calls.
Townsend, Simon W; Manser, Marta B
2011-02-23
Nonlinear vocal phenomena are a ubiquitous feature of human and non-human animal vocalizations. Although we understand how these complex acoustic intrusions are generated, it is not clear whether they function adaptively for the animals producing them. One explanation is that nonlinearities make calls more unpredictable, increasing behavioural responses and ultimately reducing the chances of habituation to these call types. Meerkats (Suricata suricatta) exhibit nonlinear subharmonics in their predator alarm calls. We specifically tested the 'unpredictability hypothesis' by playing back naturally occurring nonlinear and linear medium-urgency alarm call bouts. Results indicate that subjects responded more strongly and foraged less after hearing nonlinear alarm calls. We argue that these findings support the unpredictability hypothesis and suggest this is the first study in animals or humans to show that nonlinear vocal phenomena function adaptively. PMID:20659926
On the nonlinear theory of Fabry–Perot semiconductor lasers
NASA Astrophysics Data System (ADS)
Noppe, Michael G.
2016-05-01
Fundamentals of the nonlinear theory of Fabry–Perot semiconductor lasers have been developed, an integral part of which is natural linewidth theory. The formula for gain depending on the energy flux specifies the basic nonlinear effect in a laser. Necessary conditions for stimulated emission of the first and second kind are presented. Maxwell’s equations in the gain medium are applied to obtain equations for energy flux and for the description of non-linear phase effect. Based on the nonlinear theory, a number of experiments have been simulated; it indicates that the nonlinear theory is a new paradigm in laser theory. The nonlinear theory has provided recommendations for the development of lasers with improved properties, such as lasers with increased power and lasers with reduced natural linewidth.
Towards the nonlinear acousto-magneto-plasmonics
NASA Astrophysics Data System (ADS)
Temnov, Vasily V.; Razdolski, Ilya; Pezeril, Thomas; Makarov, Denys; Seletskiy, Denis; Melnikov, Alexey; Nelson, Keith A.
2016-09-01
We review the recent progress in experimental and theoretical research of interactions between the acoustic, magnetic and plasmonic transients in hybrid metal-ferromagnet multilayer structures excited by ultrashort laser pulses. The main focus is on understanding the nonlinear aspects of the acoustic dynamics in materials as well as the peculiarities in the nonlinear optical and magneto-optical response. For example, the nonlinear optical detection is illustrated in detail by probing the static magneto-optical second harmonic generation in gold–cobalt–silver trilayer structures in Kretschmann geometry. Furthermore, we show experimentally how the nonlinear reshaping of giant ultrashort acoustic pulses propagating in gold can be quantified by time-resolved plasmonic interferometry and how these ultrashort optical pulses dynamically modulate the optical nonlinearities. An effective medium approximation for the optical properties of hybrid multilayers enables the understanding of novel optical detection techniques. In the discussion we also highlight recent works on the nonlinear magneto-elastic interactions, and strain-induced effects in semiconductor quantum dots.
Liquid chromatographic extraction medium
Horwitz, E.P.; Dietz, M.L.
1994-09-13
A method and apparatus are disclosed for extracting strontium and technetium values from biological, industrial and environmental sample solutions using a chromatographic column. An extractant medium for the column is prepared by generating a solution of a diluent containing a Crown ether and dispersing the solution on a resin substrate material. The sample solution is highly acidic and is introduced directed to the chromatographic column and strontium or technetium is eluted using deionized water. 1 fig.
Liquid chromatographic extraction medium
Horwitz, E. Philip; Dietz, Mark L.
1994-01-01
A method and apparatus for extracting strontium and technetium values from biological, industrial and environmental sample solutions using a chromatographic column is described. An extractant medium for the column is prepared by generating a solution of a diluent containing a Crown ether and dispersing the solution on a resin substrate material. The sample solution is highly acidic and is introduced directed to the chromatographic column and strontium or technetium is eluted using deionized water.
Culture Medium for Enterobacteria
Neidhardt, Frederick C.; Bloch, Philip L.; Smith, David F.
1974-01-01
A new minimal medium for enterobacteria has been developed. It supports growth of Escherichia coli and Salmonella typhimurium at rates comparable to those of any of the traditional media that have high phosphate concentrations, but each of the macronutrients (phosphate, sulfate, and nitrogen) is present at a sufficiently low level to permit isotopic labeling. Buffering capacity is provided by an organic dipolar ion, morpholinopropane sulfonate, which has a desirable pK (7.2) and no apparent inhibitory effect on growth. The medium has been developed with the objectives of (i) providing reproducibility of chemical composition, (ii) meeting the experimentally determined nutritional needs of the cell, (iii) avoiding an unnecessary excess of the major ionic species, (iv) facilitating the adjustment of the levels of individual ionic species, both for isotopic labeling and for nutritional studies, (v) supplying a complete array of micronutrients, (vi) setting a particular ion as the crop-limiting factor when the carbon and energy source is in excess, and (vii) providing maximal convenience in the manufacture and storage of the medium. PMID:4604283
NASA Astrophysics Data System (ADS)
Kamaya, H.
1998-03-01
Many hydrodynamical researches have been developed. Especially, analysis of the compressible flow is significantly improved by interstellar physicists. To obtain sufficient appreciation, we should not analyze only the effect of self-gravity of the system but also consider the property of inhomogeneity of the interstellar medium. I stress that another hydrodynamical approach is appreciated. That is the multi-phase-flow method. In the astrophysical context, there are few preliminary works of it. I intend to develop it in more suitable method for the interstellar physics. This dissertation is only the first step for me. But, fundamental properties of the multi-phase-flow are presented, considering the effect of compressibility, self-(and/or mutual) gravity, and friction between two phases. All of these properties are generally important to examine the origin, destruction and the global distribution of interstellar medium. My motivation is trying to delve into the global properties of the interstellar medium. The method of multi-phase-flow has great advantage for my aim, and its usefulness has been shown in this thesis.
Nonlinear quantum optics mediated by Rydberg interactions
NASA Astrophysics Data System (ADS)
Firstenberg, O.; Adams, C. S.; Hofferberth, S.
2016-08-01
By mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a medium which exhibits a strong optical nonlinearity at the level of individual photons. We review the theoretical concepts and the experimental state-of-the-art of this exciting new field, and discuss first applications in the field of all-optical quantum information processing.
Abe, H.; Okuda, H.
1993-08-01
In this Letter, we first present a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. The model was then used for studying linear and nonlinear wave propagation in the dielectric medium such as an optical fiber. It is shown that the model may be useful for studying nonlinear wave propagation and harmonics generation in the nonlinear dielectric media.
Nonlinear oscillator metamaterial model: numerical and experimental verification.
Poutrina, E; Huang, D; Urzhumov, Y; Smith, D R
2011-04-25
We verify numerically and experimentally the accuracy of an analytical model used to derive the effective nonlinear susceptibilities of a varactor-loaded split ring resonator (VLSRR) magnetic medium. For the numerical validation, a nonlinear oscillator model for the effective magnetization of the metamaterial is applied in conjunction with Maxwell equations and the two sets of equations solved numerically in the time-domain. The computed second harmonic generation (SHG) from a slab of a nonlinear material is then compared with the analytical model. The computed SHG is in excellent agreement with that predicted by the analytical model, both in terms of magnitude and spectral characteristics. Moreover, experimental measurements of the power transmitted through a fabricated VLSRR metamaterial at several power levels are also in agreement with the model, illustrating that the effective medium techniques associated with metamaterials can accurately be transitioned to nonlinear systems. PMID:21643082
Nonlinear noise waves in soft biological tissues
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Gurbatov, S. N.; Demin, I. Yu.
2013-09-01
The study of intense waves in soft biological tissues is necessary both for diagnostics and therapeutic aims. Tissue represents an inherited medium with frequency-dependent dissipative properties, in which waves are described by nonlinear integro-differential equations. The equations for such waves are well known. Their group analysis has been performed, and a number of exact solutions have been found. However, statistical problems for nonlinear waves in tissues have hardly been studied. As well, for medical applications, both intense noise waves and waves with fluctuating parameters can be used. In addition, statistical solutions are simpler in structure than regular solutions; they are useful for understanding the physics of processes. Below a general approach is described for solving nonlinear statistical problems applied to the considered mathematical models of biological tissues. We have calculated the dependences of the intensities of the narrowband noise harmonics on distance. For wideband noise, we have calculated the dependence of the spectral integral intensity on distance. In all cases, wave attenuation is determined both by the specific dissipative properties of the tissue and the nonlinearity of the medium.
On the Doppler effect for light from orbiting sources in Kerr-type metrics
NASA Astrophysics Data System (ADS)
Cisneros, S.; Goedecke, G.; Beetle, C.; Engelhardt, M.
2015-04-01
A formula is derived for the combined motional and gravitational Doppler effect in general stationary axisymmetric metrics for a photon emitted parallel or antiparallel to the assumed circular orbital motion of its source. The same formula is derived by both the eikonal approximation and Killing vector approaches to elucidate connections between observational astronomy and modern relativity. The formula yields expected results in the limits of a moving or stationary source in the exterior Kerr and Schwarzschild metrics and is useful for broad range astrophysical analyses.
DENSE MEDIUM CYCLONE OPTIMIZATON
Gerald H. Luttrell; Chris J. Barbee; Peter J. Bethell; Chris J. Wood
2005-06-30
Dense medium cyclones (DMCs) are known to be efficient, high-tonnage devices suitable for upgrading particles in the 50 to 0.5 mm size range. This versatile separator, which uses centrifugal forces to enhance the separation of fine particles that cannot be upgraded in static dense medium separators, can be found in most modern coal plants and in a variety of mineral plants treating iron ore, dolomite, diamonds, potash and lead-zinc ores. Due to the high tonnage, a small increase in DMC efficiency can have a large impact on plant profitability. Unfortunately, the knowledge base required to properly design and operate DMCs has been seriously eroded during the past several decades. In an attempt to correct this problem, a set of engineering tools have been developed to allow producers to improve the efficiency of their DMC circuits. These tools include (1) low-cost density tracers that can be used by plant operators to rapidly assess DMC performance, (2) mathematical process models that can be used to predict the influence of changes in operating and design variables on DMC performance, and (3) an expert advisor system that provides plant operators with a user-friendly interface for evaluating, optimizing and trouble-shooting DMC circuits. The field data required to develop these tools was collected by conducting detailed sampling and evaluation programs at several industrial plant sites. These data were used to demonstrate the technical, economic and environmental benefits that can be realized through the application of these engineering tools.
NASA Technical Reports Server (NTRS)
Tielens, Alexander G. G. M.
1995-01-01
The Interstellar Medium (ISM) forms an integral part of the lifecycle of stars and the galaxy. Stars are formed by gravitational contraction of interstellar clouds. Over their life, stars return much of their mass to the ISM through winds and supernova explosions, resulting in a slow enrichment in heavy elements. Understanding the origin and evolution of the ISM is a key problem within astrophysics. The KAO has made many important contributions to studies of the interstellar medium both on the macro and on the micro scale. In this overview, I will concentrate on two breakthroughs in the last decade in which KAO observations have played a major role: (1) the importance of large Polycyclic Aromatic Hydrocarbon (PAH) molecules for the ISM (section 3) and (2) the study of Photodissociation Regions (PDRs) as an analog for the diffuse ISM at large (section 4). Appropriately, the micro and macro problem are intricately interwoven in these problems. Finally, section 5 reviews the origin of the (CII) emission observed by COBE.
NASA Astrophysics Data System (ADS)
Redfield, S.
2006-09-01
The Local Interstellar Medium (LISM) is a unique environment that presents an opportunity to study general interstellar phenomena in great detail and in three dimensions. In particular, high resolution optical and ultraviolet spectroscopy have proven to be powerful tools for addressing fundamental questions concerning the physical conditions and three-dimensional (3D) morphology of this local material. After reviewing our current understanding of the structure of gas in the solar neighborhood, I will discuss the influence that the LISM can have on stellar and planetary systems, including LISM dust deposition onto planetary atmospheres and the modulation of galactic cosmic rays through the astrosphere --- the balancing interface between the outward pressure of the magnetized stellar wind and the inward pressure of the surrounding interstellar medium. On Earth, galactic cosmic rays may play a role as contributors to ozone layer chemistry, planetary electrical discharge frequency, biological mutation rates, and climate. Since the LISM shares the same volume as practically all known extrasolar planets, the prototypical debris disks systems, and nearby low-mass star-formation sites, it will be important to understand the structures of the LISM and how they may influence planetary atmospheres.
Radio Is an Educational Medium.
ERIC Educational Resources Information Center
Duby, Aliza
This report summarizes information found in a survey of the literature on radio as an educational medium which covered the published literature from many areas of the world. Comments on the literature reviewed are provided throughout the text, which is organized under seven major headings: (1) Radio, Mass Medium; (2) Radio, the Medium (broadening…
Nonlinear rotordynamics analysis
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.
Soliton transmission in optical fibers with loss and saturable nonlinearity
NASA Astrophysics Data System (ADS)
Aicklen, Gregory H.; Tamil, Lakshman S.
1996-09-01
Optical solitons propagating in media exhibiting saturable nonlinearity offer advantages over Kerr-medium solitons for transmission over large distances through optical fibers with loss. Soliton pulses in saturable media offer greater energy for a given peak power, and upper-branch solitons decrease in width with distance traveled. These properties result in pulses that remain distinct and detectable for greater distances than Kerr-medium solitons do with the same peak power. .
Stationary nonlinear Airy beams
Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.
2011-08-15
We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.
Optical phase conjugation in third-order nonlinear photonic crystals
Xie Ping; Zhang Zhaoqing
2004-05-01
We predict that the efficiency of the optical phase conjugation generation can be enhanced by more than four orders of magnitude in a {chi}{sup (3)} nonlinear superlattice, as compared with that in a homogeneous nonlinear medium of the same sample thickness and {chi}{sup (3)} nonlinearity. Such an effective enhancement utilizes the localized properties of the fields inside the sample at the band-edge state, gap-soliton state, or defect state. Due to the presence of feedback mechanism at each interface of a superlattice, we also predict that the phase conjugation can still be effectively generated when only one pump wave is used.
Organic nonlinear optical materials
NASA Technical Reports Server (NTRS)
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinear optics at interfaces
Chen, C.K.
1980-12-01
Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory.
Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas
NASA Astrophysics Data System (ADS)
Abb, Martina; Wang, Yudong; de Groot, C. H.; Muskens, Otto L.
2014-09-01
Plasmonic devices have a unique ability to concentrate and convert optical energy into a small volume. There is a tremendous interest in achieving active control of plasmon resonances, which would enable switchable hotspots for applications such as surface-enhanced spectroscopy and single molecule emission. The small footprint and strong-field confinement of plasmonic nanoantennas also holds great potential for achieving transistor-type devices for nanoscale-integrated circuits. To achieve such a functionality, new methods for nonlinear modulation are required, which are able to precisely tune the nonlinear interactions between resonant antenna elements. Here we demonstrate that resonant pumping of a nonlinear medium in a plasmonic hotspot produces an efficient transfer of optical Kerr nonlinearity between different elements of a multifrequency antenna. By spatially and spectrally separating excitation and readout, isolation of the hotspot-mediated ultrafast Kerr nonlinearity from slower, thermal effects is achieved.
Nonlinear normal modes in electrodynamic systems: A nonperturbative approach
NASA Astrophysics Data System (ADS)
Kudrin, A. V.; Kudrina, O. A.; Petrov, E. Yu.
2016-06-01
We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.
Necklace beam generation in nonlinear colloidal engineered media.
Silahli, Salih Z; Walasik, Wiktor; Litchinitser, Natalia M
2015-12-15
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, rogue waves, and ring (or necklace) beam formation. To date, a majority of studies of these phenomena have focused on light-matter interactions in self-focusing Kerr media existing in nature. However, a large and tunable nonlinear response of a colloidal suspension can be tailored at will by judiciously engineering the optical polarizability. Here, we analytically and numerically show the possibility of necklace beam generation originating from spatial modulational instability of vortex beams in engineered soft-matter nonlinear media with different types of exponential nonlinearity. PMID:26670494
Nonlinear refraction of silver hydrosols during their aggregation
Karpov, S V; Kodirov, M K; Ryasnyansky, A I; Slabko, V V
2001-10-31
The relation between the degree of aggregation of silver hydrosols and their nonlinear refractive index n{sub 2} is studied experimentally. It is found that the sign of n{sub 2} at a wavelength of 1.064 {mu}m changes with increasing the aggregation degree, which corresponds to the replacing of self-focusing by self-defocusing. The observed effects are explained based on the analysis of a change in nonlinear dispersion of the medium, taking into account the interaction between phases and the photochromic effects, which are typical for colloidal structures with fractal geometry. It is shown that the change in the sign of the nonlinear refractive index of hydrosols upon irradiation by laser pulses of duration of less than 10{sup -7} s is caused by the perturbation of resonances of silver and water and by the competition between Kerr nonlinear polarisations involving these resonances. (nonlinear optical phenomena and devices)
Nonlinear scattering of acoustic waves by vibrating obstacles
NASA Astrophysics Data System (ADS)
Piquette, J. C.
1983-06-01
The problem of the generation of sum- and difference-frequency waves produced via the scattering of an acoustic wave by an obstacle whose surface vibrates harmonically was studied both theoretically and experimentally. The theoretical approach involved solving the nonlinear wave equation, subject to appropriate boundary conditions, by the use of a perturbation expansion of the fields and a Green's function method. In addition to ordinary rigid-body scattering, Censor predicted nongrowing waves at frequencies equal to the sum and to the difference of the frequencies of the primary waves. The solution to the nonlinear wave equation also yields scattered waves at the sum and difference frequencies. However, the nonlinearity of the medium causes these waves to grow with increasing distance from the scatter's surface and, after a very small distance, dominate those predicted by Censor. The simple-source formulation of the second-order nonlinear wave equation for a lossless fluid medium has been derived for arbitrary primary wave fields. This equation was used to solve the problem of nonlinear scattering of acoustic waves by a vibrating obstacle for three geometries: (1) a plane-wave scattering by a vibrating plane, (2) cylindrical-wave scattering by a vibrating cylinder, and (3) plane-wave scattering by a vibrating cylinder. Successful experimental validation of the theory was inhibited by previously unexpected levels of nonlinearity in the hydrophones used. Such high levels of hydrophone nonlinearity appeared in hydrophones that, by their geometry of construction, were expected to be fairly linear.
Wave train generation of solitons in systems with higher-order nonlinearities.
Mohamadou, Alidou; LatchioTiofack, C G; Kofané, Timoléon C
2010-07-01
Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity. PMID:20866749
Nonlinear Coherent Structures, Microbursts and Turbulence
NASA Astrophysics Data System (ADS)
Lakhina, G. S.
2015-12-01
Nonlinear waves are found everywhere, in fluids, atmosphere, laboratory, space and astrophysical plasmas. The interplay of nonlinear effects, dispersion and dissipation in the medium can lead to a variety of nonlinear waves and turbulence. Two cases of coherent nonlinear waves: chorus and electrostatic solitary waves (ESWs) and their impact on modifying the plasma medium are discussed. Chorus is a right-hand, circularly-polarized electromagnetic plane wave. Dayside chorus is a bursty emission composed of rising frequency "elements" with duration of ~0.1 to 1.0 s. Each element is composed of coherent subelements with durations of ~1 to 100 ms or more. The cyclotron resonant interaction between energetic electrons and the coherent chorus waves is studied. An expression for the pitch angle transport due to this interaction is derived considering a Gaussian distribution for the time duration of the chorus elements. The rapid pitch scattering can provide an explanation for the ionospheric microbursts of ~0.1 to 0.5 s in bremsstrahlung x-rays formed by ~10-100 keV precipitating electrons. On the other hand, the ESWs are observed in the electric field component parallel to the background magnetic field, and are usually bipolar or tripolar. Generation of coherent ESWs has been explained in terms of nonlinear fluid models of ion- and electron-acoustic solitons and double layers (DLs) based on Sagdeev pseudopotential technique. Fast Fourier transform of electron- and ion-acoustic solitons/DLs produces broadband wave spectra which can explain the properties of the electrostatic turbulence observed in the magnetosheath and plasma sheet boundary layer, and in the solar wind, respectively.
Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model
NASA Astrophysics Data System (ADS)
Singh, Sudha; Gilhare, Karuna
2016-08-01
We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.
Friction and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
2016-07-01
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
Friction and nonlinear dynamics.
Manini, N; Braun, O M; Tosatti, E; Guerra, R; Vanossi, A
2016-07-27
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction. PMID:27249652
Nonlinear Optics and Applications
NASA Technical Reports Server (NTRS)
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
NASA Astrophysics Data System (ADS)
Solookinejad, G.
2016-09-01
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
Blackbody Emission from Light Interacting with an Effective Moving Dispersive Medium
NASA Astrophysics Data System (ADS)
Petev, M.; Westerberg, N.; Moss, D.; Rubino, E.; Rimoldi, C.; Cacciatori, S. L.; Belgiorno, F.; Faccio, D.
2013-07-01
Intense laser pulses excite a nonlinear polarization response that may create an effective flowing medium and, under appropriate conditions, a blocking horizon for light. Here, we analyze in detail the interaction of light with such laser-induced flowing media, fully accounting for the medium dispersion properties. An analytical model based on a first Born approximation is found to be in excellent agreement with numerical simulations based on Maxwell’s equations and shows that when a blocking horizon is formed, the stimulated medium scatters light with a blackbody emission spectrum. Based on these results, diamond is proposed as a promising candidate medium for future studies of Hawking emission from artificial, dispersive horizons.
Polychromatic solitons in a quadratic medium.
Towers, I N; Malomed, B A
2002-10-01
We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with (slightly) different carrier frequencies [which is a direct analog of wavelength-division multiplexed models, well known in media with cubic nonlinearity]. The model takes a closed form with three different second-harmonic components, and it is formulated in the spatial domain. We demonstrate that the model supports both polychromatic solitons (PCSs), with all the components present in them, and two types of mutually orthogonal simple solitons, both types being stable in a broad parametric region. An essential peculiarity of PCS is that its power is much smaller than that of a simple (usual) soliton (taken at the same values of control parameters), which may be an advantage for experimental generation of PCSs. Collisions between the orthogonal simple solitons are simulated in detail, leading to the conclusion that the collisions are strongly inelastic, converting the simple solitons into polychromatic ones, and generating one or two additional PCSs. A collision velocity at which the inelastic effects are strongest is identified, and it is demonstrated that the collision may be used as a basis to design a simple all-optical XOR logic gate. PMID:12443362
Compensating for dispersion and the nonlinear Kerr effect without phase conjugation.
Paré, C; Villeneuve, A; Bélanger, P A; Doran, N J
1996-04-01
We propose the use of a dispersive medium with a negative nonlinear refractive-index coefficient as a way to compensate for the dispersion and the nonlinear effects resulting from pulse propagation in an optical fiber. The undoing of pulse interaction might allow for increased bit rates. PMID:19865438
NASA Astrophysics Data System (ADS)
Amat-Roldan, Ivan; Cormack, Iain G.; Artigas, David; Loza-Alvarez, Pablo
2004-09-01
In this paper we report the use of a starch as a non-linear medium for characterising ultrashort pulses. The starch suspension in water is sandwiched between a slide holder and a cover-slip and placed within the sample plane of the nonlinear microscope. This simple arrangement enables direct measurement of the pulse where they interact with the sample.
Model of optical nonlinearity of air in the mid-IR wavelength range
Geints, Yu E; Zemlyanov, A A
2014-09-30
A model of optical nonlinearity of air (atmospheric nitrogen and oxygen) is developed. This model can be used to calculate numerically the propagation of radiation with a wavelength close to 10 μm. It takes into account the electronic Kerr effect, higher order nonlinearities, ionisation of a gas medium by electron impact, and pulse group-velocity dispersion. The applicability limits of the Drude approximation for calculating the impact-ionisation rate are also considered. (nonlinear optical phenomena)
Abe, H.; Okuda, H.
1994-06-01
We study linear and nonlinear properties of a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. It is shown that the model may be useful for studying linear and nonlinear wave propagation in the dielectric media.
On the Inverse Problems of Nonlinear Acoustics and Acoustic Turbulence
NASA Astrophysics Data System (ADS)
Gurbatov, S. N.; Rudenko, O. V.
2015-12-01
We consider the problem of retrieval of the radiated acoustic signal parameters from the measured wave field in some cross section of the nonlinear medium. The possibilities of solving regular and statistical inverse problems are discussed on the basis of the solution of the Burgers equation for zero and infinitesimal viscosities.
OPCPA modeling using YCOB as the non-linear crystal
NASA Astrophysics Data System (ADS)
Pires, Hugo; Cardoso, Luis; Wemans, João; João, Celso; Figueira, Gonçalo
2010-04-01
In this work, we evaluate numerically the performance of the nonlinear crystal yttrium calcium oxyborate (YCOB) as the gain medium in a noncollinear, angularly dispersed beam OPCPA configuration, and compare it to other well-studied crystals. In particular, we study its use in the context of an ultrahigh peak and average power amplifier setup. Possible bandwidths are assessed.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis. PMID:27250151
Photonic quantum transport in a nonlinear optical fiber
NASA Astrophysics Data System (ADS)
Hafezi, M.; Chang, D. E.; Gritsev, V.; Demler, E. A.; Lukin, M. D.
2011-06-01
We theoretically study the transmission of few-photon quantum fields through a strongly nonlinear optical medium. We develop a general approach to investigate nonequilibrium quantum transport of bosonic fields through a finite-size nonlinear medium and apply it to a recently demonstrated experimental system where cold atoms are loaded in a hollow-core optical fiber. We show that when the interaction between photons is effectively repulsive, the system acts as a single-photon switch. In the case of attractive interaction, the system can exhibit either antibunching or bunching, associated with the resonant excitation of bound states of photons by the input field. These effects can be observed by probing statistics of photons transmitted through the nonlinear fiber.
Modulational instability in nonlinearity-managed optical media
Centurion, Martin; Porter, Mason A.; Pu Ye; Psaltis, Demetri; Kevrekidis, P. G.; Frantzeskakis, D. J.
2007-06-15
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schroedinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.
Modulational instability in nonlinearity-managed optical media
NASA Astrophysics Data System (ADS)
Centurion, Martin; Porter, Mason A.; Pu, Ye; Kevrekidis, P. G.; Frantzeskakis, D. J.; Psaltis, Demetri
2007-06-01
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schrödinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.
New approaches to nonlinear diffractive field propagation.
Christopher, P T; Parker, K J
1991-07-01
In many domains of acoustic field propagation, such as medical ultrasound imaging, lithotripsy shock treatment, and underwater sonar, a realistic calculation of beam patterns requires treatment of the effects of diffraction from finite sources. Also, the mechanisms of loss and nonlinear effects within the medium are typically nonnegligible. The combination of diffraction, attenuation, and nonlinear effects has been treated by a number of formulations and numerical techniques. A novel model that incrementally propagates the field of baffled planar sources with substeps that account for the physics of diffraction, attenuation, and nonlinearity is presented. The model accounts for the effect of refraction and reflection (but not multiple reflections) in the case of propagation through multiple, parallel layers of fluid medium. An implementation of the model for axis symmetric sources has been developed. In one substep of the implementation, a new discrete Hankel transform is used with spatial transform techniques to propagate the field over a short distance with diffraction and attenuation. In the other substep, the temporal frequency domain solution to Burgers' equation is implemented to account for the nonlinear accretion and depletion of harmonics. This approach yields a computationally efficient procedure for calculating beam patterns from a baffled planar, axially symmetric source under conditions ranging from quasilinear through shock. The model is not restricted by the usual parabolic wave approximation and the field's directionality is explicitly accounted for at each point. Useage of a harmonic-limiting scheme allows the model to propagate some previously intractable high-intensity nonlinear fields. Results of the model are shown to be in excellent agreement with measurements performed on the nonlinear field of an unfocused 2.25-MHz piston source, even in the near field where the established parabolic wave approximation model fails. Next, the model is used to
Non-linear interaction of elastic waves in rocks
NASA Astrophysics Data System (ADS)
Kuvshinov, B. N.; Smit, T. J. H.; Campman, X. H.
2013-09-01
We study theoretically the interaction of elastic waves caused by non-linearities of rock elastic moduli, and assess the possibility to use this phenomenon in hydrocarbon exploration and in the analysis of rock samples. In our calculations we use the five-constant model by Gol'dberg. It is shown that the interaction of plane waves in isotropic solids is completely described by five coupling coefficients, which have the same order of magnitude. By considering scattering of compressional waves generated by controlled sources at the Earth surface from a non-linear layer at the subsurface, we conclude that non-linear signals from deep formations are unlikely to be measured with the current level of technology. Our analysis of field tests where non-linear signals were measured, suggests that these signals are generated either in the shallow subsurface or in the vicinity of sources. Non-linear wave interaction might be observable in lab tests with focused ultrasonic beams. In this case, the non-linear response is generated in the secondary parametric array formed by linear beams scattered from inclusions. Although the strength of this response is controlled by non-linearity of the surrounding medium rather than by non-linearity of inclusions, its measurement can help to obtain better images of rock samples.
Metamaterials with conformational nonlinearity
NASA Astrophysics Data System (ADS)
Lapine, Mikhail; Shadrivov, Ilya V.; Powell, David A.; Kivshar, Yuri S.
2011-11-01
Within a decade of fruitful development, metamaterials became a prominent area of research, bridging theoretical and applied electrodynamics, electrical engineering and material science. Being man-made structures, metamaterials offer a particularly useful playground to develop interdisciplinary concepts. Here we demonstrate a novel principle in metamaterial assembly which integrates electromagnetic, mechanical, and thermal responses within their elements. Through these mechanisms, the conformation of the meta-molecules changes, providing a dual mechanism for nonlinearity and offering nonlinear chirality. Our proposal opens a wide road towards further developments of nonlinear metamaterials and photonic structures, adding extra flexibility to their design and control.
Nonlinear ordinary difference equations
NASA Technical Reports Server (NTRS)
Caughey, T. K.
1979-01-01
Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.
Evolutionary quantitative genetics of nonlinear developmental systems.
Morrissey, Michael B
2015-08-01
In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances. PMID:26174586
Photon Number-Phase Uncertainty Relation in the Evolution of the Field in a Kerr-Like Medium
NASA Technical Reports Server (NTRS)
Fan, An-Fu; Sun, Nian-Chun
1996-01-01
A model of a single-mode field, initially prepared in a coherent state, coupled to a two-level atom surrounded by a nonlinear Kerr-like medium contained inside a very good quality cavity is considered. We derive the photon number-phase uncertainty relation in the evolution of the field for a weak and strong nonlinear coupling respectively, within the Hermitian phase operator formalism of Pegg and Barnett, and discuss the effects of nonlinear coupling of the Kerr-like medium on photon number-phase uncertainty relation of the field.
The f-deformed Jaynes-Cummings model and its nonlinear coherent states
NASA Astrophysics Data System (ADS)
de los Santos-Sánchez, O.; Récamier, J.
2012-01-01
Based on the f-oscillator formalism, we introduce a nonlinear Jaynes-Cummings model (NJCM) which is constructed from the standard JCM by deforming the single-mode field operators. Such a generalization of the JCM describes the interaction of a two-level atom with a single mode of the electromagnetic field in the presence of a nonlinear Kerr-like medium. Since the medium is modelled as an f-oscillator, it is possible to consider the field f-coherent states (nonlinear coherent states) and their evolution.
New medium licensed for campylobacter
Technology Transfer Automated Retrieval System (TEKTRAN)
A medium, “Campy-Cefex”, has been licensed by the ARS Office of Technology Transfer with Becton Dickinson (No. 1412-002) and Neogen (No. 1412-001) based on patent No. 5,891,709, “Campy-Cefex Selective and Differential Medium for Campylobacter” by Dr. Norman Stern of the Poultry Microbiological Safet...
NASA Astrophysics Data System (ADS)
Frank, T. D.
2008-06-01
Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones.
Mesch, Martin; Metzger, Bernd; Hentschel, Mario; Giessen, Harald
2016-05-11
We introduce the concept of nonlinear plasmonic sensing, relying on third harmonic generation from simple plasmonic nanoantennas. Because of the nonlinear conversion process we observe a larger sensitivity to a local change in the refractive index as compared to the commonly used linear localized surface plasmon resonance sensing. Refractive index changes as small as 10(-3) can be detected. In order to determine the spectral position of highest sensitivity, we perform linear and third harmonic spectroscopy on plasmonic nanoantenna arrays, which are the fundamental building blocks of our sensor. Furthermore, simultaneous detection of linear and nonlinear signals allows quantitative comparison of both methods, providing further insight into the working principle of our sensor. While the signal-to-noise ratio is comparable, nonlinear sensing gives about seven times higher relative signal changes. PMID:27050296
NASA Technical Reports Server (NTRS)
1984-01-01
Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.
Nonlinear Dynamics in Cardiology
Krogh-Madsen, Trine; Christini, David J.
2013-01-01
The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counter-intuitively, result from a gradual change in a system parameter –this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work have suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity. PMID:22524390
Library for Nonlinear Optimization
Energy Science and Technology Software Center (ESTSC)
2001-10-09
OPT++ is a C++ object-oriented library for nonlinear optimization. This incorporates an improved implementation of an existing capability and two new algorithmic capabilities based on existing journal articles and freely available software.
Numerical studies of the nonlinear properties of composites
NASA Astrophysics Data System (ADS)
Zhang, X.; Stroud, D.
1994-01-01
Using both numerical and analytical techniques, we investigate various ways to enhance the cubic nonlinear susceptibility χe of a composite material. We start from the exact relation χe =tsumipiχi<(E.E)2>i,lin/ E40, where χi and pi are the cubic nonlinear susceptibility and volume fraction of the ith component, E0 is the applied electric field, and
Nonlinear Refractive Properties
NASA Technical Reports Server (NTRS)
Vikram, Chandra S.; Witherow, William K.
2001-01-01
Using nonlinear refractive properties of a salt-water solution at two wavelengths, numerical analysis has been performed to extract temperature and concentration from interferometric fringe data. The theoretical study, using a commercially available equation solving software, starts with critical fringe counting needs and the role of nonlinear refractive properties in such measurements. Finally, methodology of the analysis, codes, fringe counting accuracy needs, etc. is described in detail.
NASA Astrophysics Data System (ADS)
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear systems in medicine.
Higgins, John P.
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107
Superfluid light in bulk nonlinear media.
Carusotto, Iacopo
2014-09-01
We review how the paraxial approximation naturally leads to a hydrodynamic description of light propagation in a bulk Kerr nonlinear medium in terms of a wave equation analogous to the Gross-Pitaevskii equation for the order parameter of a superfluid. The main features of the many-body collective dynamics of the fluid of light in this propagating geometry are discussed: generation and observation of Bogoliubov sound waves in the fluid of light is first described. Experimentally accessible manifestations of superfluidity are then highlighted. Perspectives in view of realizing analogue models of gravity are finally given. PMID:25197252
Superfluid light in bulk nonlinear media
Carusotto, Iacopo
2014-01-01
We review how the paraxial approximation naturally leads to a hydrodynamic description of light propagation in a bulk Kerr nonlinear medium in terms of a wave equation analogous to the Gross–Pitaevskii equation for the order parameter of a superfluid. The main features of the many-body collective dynamics of the fluid of light in this propagating geometry are discussed: generation and observation of Bogoliubov sound waves in the fluid of light is first described. Experimentally accessible manifestations of superfluidity are then highlighted. Perspectives in view of realizing analogue models of gravity are finally given. PMID:25197252
Nonlinear optical studies of organic monolayers
Shen, Y.R.
1988-02-01
Second-order nonlinear optical effects are forbidden in a medium with inversion symmetry, but are necessarily allowed at a surface where the inversion summary is broken. They are often sufficiently strong so that a submonolayer perturbation of the surface can be readily detected. They can therefore be used as effective tools to study monolayers adsorbed at various interfaces. We discuss here a number of recent experiments in which optical second harmonic generation (SHG) and sum-frequency generation (SFG) are employed to probe and characterize organic monolayers. 15 refs., 5 figs.
Modulational-instability-induced supercontinuum generation with saturable nonlinear response
Raja, R. Vasantha Jayakantha; Porsezian, K.; Nithyanandan, K.
2010-07-15
We theoretically investigate the supercontinuum generation (SCG) on the basis of modulational instability (MI) in liquid-core photonic crystal fibers (LCPCF) with CS{sub 2}-filled central core. The effect of saturable nonlinearity of LCPCF on SCG in the femtosecond regime is studied using an appropriately modified nonlinear Schroedinger equation. We also compare the MI induced spectral broadening with SCG obtained by soliton fission. To analyze the quality of the pulse broadening, we study the coherence of the SC pulse numerically. It is evident from the numerical simulation that the response of the saturable nonlinearity suppresses the broadening of the pulse. We also observe that the MI induced SCG in the presence of saturable nonlinearity degrades the coherence of the SCG pulse when compared to unsaturated medium.
Nonlinear wave propagation in strongly coupled dusty plasmas.
Veeresha, B M; Tiwari, S K; Sen, A; Kaw, P K; Das, A
2010-03-01
The nonlinear propagation of low-frequency waves in a strongly coupled dusty plasma medium is studied theoretically in the framework of the phenomenological generalized hydrodynamic (GH) model. A set of simplified model nonlinear equations are derived from the original nonlinear integrodifferential form of the GH model by employing an appropriate physical ansatz. Using standard perturbation techniques characteristic evolution equations for finite small amplitude waves are then obtained in various propagation regimes. The influence of viscoelastic properties arising from dust correlation contributions on the nature of nonlinear solutions is discussed. The modulational stability of dust acoustic waves to parallel perturbation is also examined and it is shown that dust compressibility contributions influenced by the Coulomb coupling effects introduce significant modification in the threshold and range of the instability domain. PMID:20365882
Nonlinear wave propagation in strongly coupled dusty plasmas
Veeresha, B. M.; Tiwari, S. K.; Sen, A.; Kaw, P. K.; Das, A.
2010-03-15
The nonlinear propagation of low-frequency waves in a strongly coupled dusty plasma medium is studied theoretically in the framework of the phenomenological generalized hydrodynamic (GH) model. A set of simplified model nonlinear equations are derived from the original nonlinear integrodifferential form of the GH model by employing an appropriate physical ansatz. Using standard perturbation techniques characteristic evolution equations for finite small amplitude waves are then obtained in various propagation regimes. The influence of viscoelastic properties arising from dust correlation contributions on the nature of nonlinear solutions is discussed. The modulational stability of dust acoustic waves to parallel perturbation is also examined and it is shown that dust compressibility contributions influenced by the Coulomb coupling effects introduce significant modification in the threshold and range of the instability domain.
Stable spatial and spatiotemporal optical soliton in the core of an optical vortex.
Adhikari, S K
2015-10-01
We demonstrate a robust, stable, mobile, two-dimensional (2D) spatial and three-dimensional (3D) spatiotemporal optical soliton in the core of an optical vortex, while all nonlinearities are of the cubic (Kerr) type. The 3D soliton can propagate with a constant velocity along the vortex core without any deformation. Stability of the soliton under a small perturbation is established numerically. Two such solitons moving along the vortex core can undergo a quasielastic collision at medium velocities. Possibilities of forming such a 2D spatial soliton in the core of a vortical beam are discussed. PMID:26565323
Pu, Mingbo; Yao, Na; Hu, Chenggang; Xin, Xuecheng; Zhao, Zeyu; Wang, Changtao; Luo, Xiangang
2010-09-27
Directional coupler (DC) and nonlinear Mach-Zehnder interferometer (MZI) based on metal-insulator-metal (MIM) plasmonic waveguide are investigated numerically. We show that the coupling length increases almost linearly with the wavelength and this property is utilized in the design of wavelength division multiplexer (WDM). A nonlinear MZI, with one branch filled with Kerr nonlinear medium, is built to ensure controlling light with light. Employing nonlinear processes including self-phase modulation (SPM) and cross-phase modulation (XPM), intensity-based router and all-optical switch are realized. PMID:20940998
Neutron Properties in the Medium
NASA Astrophysics Data System (ADS)
Cloët, I. C.; Miller, Gerald A.; Piasetzky, E.; Ron, G.
2009-08-01
We demonstrate that for small values of momentum transfer Q2 the in-medium change of the GE/GM form factor ratio for a bound neutron is dominated by the change in the electric charge radius and predict within stated assumptions that the in-medium ratio will increase relative to the free result. This effect will act to increase the predicted cross section for the neutron recoil polarization transfer process He4(e→,e'n→)He3. This is in contrast with medium modification effects on the proton GE/GM form factor ratio, which act to decrease the predicted cross section for the He4(e→,e'p→)H3 reaction. Experiments to measure the in-medium neutron form factors are currently feasible in the range 0.1
An improved holographic recording medium
NASA Technical Reports Server (NTRS)
Gange, R. A.
1973-01-01
Solid, linear chain hydrocarbons with molecular weight ranging from about 300 to 2000 can serve as long-lived recording medium in optical memory system. Suitable recording hydrocarbons include microcrystalline waxes and low molecular weight polymers or ethylene.
Monheit, G D
2001-07-01
The combination medium-depth chemical peel (Jessner's solution +35% TCA) has been accepted as a safe, reliable, and effective method for the treatment of moderate photoaging skin. This article discusses the procedure in detail, including postoperative considerations. PMID:11599398
Nonlinear optical Galton board
Navarrete-Benlloch, C.; Perez, A.; Roldan, Eugenio
2007-06-15
We generalize the concept of optical Galton board (OGB), first proposed by Bouwmeester et al. [Phys. Rev. A 61, 013410 (2000)], by introducing the possibility of nonlinear self-phase modulation on the wave function during the walker evolution. If the original Galton board illustrates classical diffusion, the OGB, which can be understood as a grid of Landau-Zener crossings, illustrates the influence of interference on diffusion, and is closely connected with the quantum walk. Our nonlinear generalization of the OGB shows new phenomena, the most striking of which is the formation of nondispersive pulses in the field distribution (solitonlike structures). These exhibit a variety of dynamical behaviors, including ballistic motion, dynamical localization, nonelastic collisions, and chaotic behavior, in the sense that the dynamics is very sensitive to the nonlinearity strength.
Nonlinear optomechanics with graphene
NASA Astrophysics Data System (ADS)
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Nonlinear Ehrenfest's urn model.
Casas, G A; Nobre, F D; Curado, E M F
2015-04-01
Ehrenfest's urn model is modified by introducing nonlinear terms in the associated transition probabilities. It is shown that these modifications lead, in the continuous limit, to a Fokker-Planck equation characterized by two competing diffusion terms, namely, the usual linear one and a nonlinear diffusion term typical of anomalous diffusion. By considering a generalized H theorem, the associated entropy is calculated, resulting in a sum of Boltzmann-Gibbs and Tsallis entropic forms. It is shown that the stationary state of the associated Fokker-Planck equation satisfies precisely the same equation obtained by extremization of the entropy. Moreover, the effects of the nonlinear contributions on the entropy production phenomenon are also analyzed. PMID:25974470
Nonlinear optical interactions in semiconductors
NASA Astrophysics Data System (ADS)
Salour, M. M.
1985-12-01
The optical pumping technique in GaAs has led to the development of a novel and highly sensitive optical temperature sensor. Completed is the experiment on two photon optical pumping in ZnO. An external cavity semiconductor laser involving ZnO as a gain medium was demonstrated under two-photon excitation. This laser should have a major impact on the development of tunable blue-green radiation for submarine communication. Completed is a paper on heat buildup in semiconductor platelets. New lasers are used to explore elementary excitation in optical thin film layers of semiconductors. This has led to the first demonstration of the feasibility of room temperature operation of a tunable coherent source involving multiple quantum well material. Completed is the construction of a simple remote (non-contact) temperature sensor to directly measure heat buildup in semiconductor materials as a result of high power optical laser excitation. Finally, an experiment involving optical frequency mixing to probe electrodynamics in the GaAlAs multiple quantumwell and superlattice structures, utilizing two recently constructed tunabel laser systems,has been successful. Attempts were focused on observing a number of new optical effects including nonlinear absorption and transmission phenomena, enhanced spontaneous and stimulated light scattering processes, etc. The construction of an external cavity semiconductor HgCdTe has been successful.
Maimistov, Andrei I
2010-11-13
The classic examples of optical phenomena resulting in the appearance of solitons are self-focusing, self-induced transparency, and parametric three-wave interaction. To date, the list of the fields of nonlinear optics and models where solitons play an important role has significantly expanded. Now long-lived or stable solitary waves are called solitons, including, for example, dissipative, gap, parametric, and topological solitons. This review considers nonlinear optics models giving rise to the appearance of solitons in a narrow sense: solitary waves corresponding to the solutions of completely integrable systems of equations basic for the models being discussed. (review)
Nonlinear magnetohydrodynamic stability
NASA Technical Reports Server (NTRS)
Bauer, F.; Betancourt, O.; Garabedian, P.
1981-01-01
The computer code developed by Bauer et al. (1978) for the study of the magnetohydrodynamic equilibrium and stability of a plasma in toroidal geometry is extended so that the growth rates of instabilities may be estimated more accurately. The original code, which is based on the variational principle of ideal magnetohydrodynamics, is upgraded by the introduction of a nonlinear formula for the growth rate of an unstable mode which acts as a quantitative measure of instability that is important in estimating numerical errors. The revised code has been applied to the determination of the nonlinear saturation, ballooning modes and beta limits for tokamaks, stellarators and torsatrons.
Slow and fast light propagation in nonlinear Kerr media.
NASA Astrophysics Data System (ADS)
Yang, Qiguang; Ma, Seongmin; Wang, Huitian; Jung, S. S.
2005-04-01
Sub- and superluminal propagation of light pulse in Kerr materials has been investigated. Group velocities as slow as much less than 1 millimeter per second to as fast as negative several hundreds meters per second can be easily obtained in Kerr medium, which possesses large nonlinear refractive index and long relaxation time, such as Cr doped Alexandrite, Ruby, and GdAlO3. The physical mechanism is the strong highly dispersive coupling between different frequency components of the pulse. The new mechanism of slowing down pulses as well as producing superluminal pulses enlarges the very specific materials to all kinds of nonlinear optical materials.
Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy.
Wise, Frank W
2012-01-01
Recent progress in the development of femtosecond-pulse fiber lasers with parameters appropriate for nonlinear microscopy is reviewed. Pulse-shaping in lasers with only normal-dispersion components is briefly described, and the performance of the resulting lasers is summarized. Fiber lasers based on the formation of dissipative solitons now offer performance competitive with that of solid-state lasers, but with the benefits of the fiber medium. Lasers based on self-similar pulse evolution in the gain section of a laser also offer a combination of short pulse duration and high pulse energy that will be attractive for applications in nonlinear bioimaging. PMID:23869163
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time. PMID:26986334
Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy
Wise, Frank W.
2012-01-01
Recent progress in the development of femtosecond-pulse fiber lasers with parameters appropriate for nonlinear microscopy is reviewed. Pulse-shaping in lasers with only normal-dispersion components is briefly described, and the performance of the resulting lasers is summarized. Fiber lasers based on the formation of dissipative solitons now offer performance competitive with that of solid-state lasers, but with the benefits of the fiber medium. Lasers based on self-similar pulse evolution in the gain section of a laser also offer a combination of short pulse duration and high pulse energy that will be attractive for applications in nonlinear bioimaging. PMID:23869163
Westdickenberg, Michael; Wilkening, Jon
2008-12-10
We introduce variational particle schemes for the porous medium equation and the system of isentropic Euler equations in one space dimension. The methods are motivated by the interpretation of each of these partial differential equations as a 'steepest descent' on a suitable abstract manifold. We show that our methods capture very well the nonlinear features of the flows.
Universal nonlinear entanglement witnesses
Kotowski, Marcin; Kotowski, Michal
2010-06-15
We give a universal recipe for constructing nonlinear entanglement witnesses able to detect nonclassical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The constructed witnesses are expressed in terms of expectation values of observables. As such, they are, at least in principle, measurable in experiments.
Intramolecular and nonlinear dynamics
Davis, M.J.
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Nonlinear growing neutrino cosmology
NASA Astrophysics Data System (ADS)
Ayaita, Youness; Baldi, Marco; Führer, Florian; Puchwein, Ewald; Wetterich, Christof
2016-03-01
The energy scale of dark energy, ˜2 ×10-3 eV , is a long way off compared to all known fundamental scales—except for the neutrino masses. If dark energy is dynamical and couples to neutrinos, this is no longer a coincidence. The time at which dark energy starts to behave as an effective cosmological constant can be linked to the time at which the cosmic neutrinos become nonrelativistic. This naturally places the onset of the Universe's accelerated expansion in recent cosmic history, addressing the why-now problem of dark energy. We show that these mechanisms indeed work in the growing neutrino quintessence model—even if the fully nonlinear structure formation and backreaction are taken into account, which were previously suspected of spoiling the cosmological evolution. The attractive force between neutrinos arising from their coupling to dark energy grows as large as 106 times the gravitational strength. This induces very rapid dynamics of neutrino fluctuations which are nonlinear at redshift z ≈2 . Nevertheless, a nonlinear stabilization phenomenon ensures only mildly nonlinear oscillating neutrino overdensities with a large-scale gravitational potential substantially smaller than that of cold dark matter perturbations. Depending on model parameters, the signals of large-scale neutrino lumps may render the cosmic neutrino background observable.
Nonlinear phased array imaging
NASA Astrophysics Data System (ADS)
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Nonlinear Theory and Breakdown
NASA Technical Reports Server (NTRS)
Smith, Frank
2007-01-01
The main points of recent theoretical and computational studies on boundary-layer transition and turbulence are to be highlighted. The work is based on high Reynolds numbers and attention is drawn to nonlinear interactions, breakdowns and scales. The research focuses in particular on truly nonlinear theories, i.e. those for which the mean-flow profile is completely altered from its original state. There appear to be three such theories dealing with unsteady nonlinear pressure-displacement interactions (I), with vortex/wave interactions (II), and with Euler-scale flows (III). Specific recent findings noted for these three, and in quantitative agreement with experiments, are the following. Nonlinear finite-time break-ups occur in I, leading to sublayer eruption and vortex formation; here the theory agrees with experiments (Nishioka) regarding the first spike. II gives rise to finite-distance blowup of displacement thickness, then interaction and break-up as above; this theory agrees with experiments (Klebanoff, Nishioka) on the formation of three-dimensional streets. III leads to the prediction of turbulent boundary-layer micro-scale, displacement-and stress-sublayer-thicknesses.
Nonlinear plasmonic nanorulers.
Butet, Jérémy; Martin, Olivier J F
2014-05-27
The evaluation of distances as small as few nanometers using optical waves is a very challenging task that can pave the way for the development of new applications in biotechnology and nanotechnology. In this article, we propose a new measurement method based on the control of the nonlinear optical response of plasmonic nanostructures by means of Fano resonances. It is shown that Fano resonances resulting from the coupling between a bright mode and a dark mode at the fundamental wavelength enable unprecedented and direct manipulation of the nonlinear electromagnetic sources at the nanoscale. In the case of second harmonic generation from gold nanodolmens, the different nonlinear sources distributions induced by the different coupling regimes are clearly revealed in the far-field distribution. Hence, the configuration of the nanostructure can be accurately determined in 3-dimensions by recording the wave scattered at the second harmonic wavelength. Indeed, the conformation of the different elements building the system is encoded in the nonlinear far-field distribution, making second harmonic generation a promising tool for reading 3-dimension plasmonic nanorulers. Furthemore, it is shown that 3-dimension plasmonic nanorulers can be implemented with simpler geometries than in the linear regime while providing complete information on the structure conformation, including the top nanobar position and orientation. PMID:24697565
Callen, J. D.
2002-11-04
The primary efforts this year have focused on exploring the nonlinear evolution of localized interchange instabilities, some extensions of neoclassical tearing mode theory, and developing a model for the dynamic electrical conductivity in a bumpy cylinder magnetic field. In addition, we have vigorously participated in the computationally-focused NIMROD and CEMM projects.
Oscillatory motion of a viscous fluid in a porous medium
Siraev, R. R.
2015-08-15
An oscillatory flow of an incompressible fluid in a saturated porous medium in the presence of a solid inclusion has been theoretically studied. Unsteady filtration has been described by the Brinkman–Forchheimer equation, where inertial effects and terms with acceleration characteristic of high filtration rates and the presence of pulsations are taken into account. The convective part of the acceleration is responsible for nonlinear effects near macroinhomogeneities. These effects can play a noticeable role in unsteady flows in the porous medium, as is shown for the problem of a solid ball streamed by an oscillatory flow having a given velocity at infinity. The results indicate that a secondary averaged flow appears in the case of high frequencies and cannot be described by Darcy’s or Forchheimer’s filtration laws.
On fluid flow in a heterogeneous medium under nonisothermal conditions
D.W., Vasco
2010-11-01
An asymptotic technique, valid in the presence of smoothly-varying heterogeneity, provides explicit expressions for the velocity of a propagating pressure and temperature disturbance. The governing equations contain nonlinear terms due to the presence of temperature-dependent coefficients and due to the advection of fluids with differing temperatures. Two cases give well-defined expressions in terms of the parameters of the porous medium: the uncoupled propagation of a pressure disturbance and the propagation of a fully coupled temperature and pressure disturbance. The velocity of the coupled disturbance or front, depends upon the medium parameters and upon the change in temperature and pressure across the front. For uncoupled flow, the semi-analytic expression for the front velocity reduces to that associated with a linear diffusion equation. A comparison of the asymptotic travel time estimates with calculations from a numerical simulator indicates reasonably good agreement for both uncoupled and coupled disturbances.
Effective medium approximations for anisotropic composites with arbitrary component orientation
NASA Astrophysics Data System (ADS)
Levy, Ohad; Cherkaev, Elena
2013-10-01
A Maxwell Garnett approximation (MGA) and a symmetric effective medium approximation (SEMA) are derived for anisotropic composites of host-inclusion and symmetric-grains morphologies, respectively, with ellipsoidal grains of arbitrary intrinsic, shape and orientation anisotropies. The effect of anisotropy on the effective dielectric tensor is illustrated in both cases. The MGA shows negative and non-monotonic off-diagonal elements for geometries where the host and inclusions are not mutually aligned. The SEMA leads to an anisotropy-dependent nonlinear behaviour of the conductivity as a function of volume fraction above a percolation threshold of conductor-insulator composites, in contrast to the well-known linear behaviour of the isotropic effective medium model. The percolation threshold obtained for composites of aligned ellipsoids is isotropic and independent of the ellipsoids aspect ratio. Thus, the common identification of the percolation threshold with the depolarization factors of the grains is unjustified and a description of anisotropic percolation requires explicit anisotropic geometric characteristics.
A fractal approach to low velocity non-Darcy flow in a low permeability porous medium
NASA Astrophysics Data System (ADS)
Cai, Jian-Chao
2014-04-01
In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient (TPG) is also obtained. It is notable that the TPG (J) and permeability (K) of the porous medium analytically exhibit the scaling behavior J ~ K-DT/(1=DT), where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.
Schwartz, Sylvain; Feugnet, Gilles; Pocholle, Jean-Paul; Gutty, Francois; Bouyer, Philippe
2008-05-09
We report fine-tuning of nonlinear interactions in a solid-state ring laser gyroscope by vibrating the gain medium along the cavity axis. We demonstrate both experimentally and theoretically that nonlinear interactions vanish for some values of the vibration parameters, leading to quasi-ideal rotation sensing. We eventually point out that our conclusions can be mapped onto other subfields of physics such as ring-shaped superfluid configurations, where nonlinear interactions could be tuned by using Feshbach resonance.