Learning polynomial feedforward neural networks by genetic programming and backpropagation.

PubMed

Nikolaev, N Y; Iba, H

2003-01-01

This paper presents an approach to learning polynomial feedforward neural networks (PFNNs). The approach suggests, first, finding the polynomial network structure by means of a population-based search technique relying on the genetic programming paradigm, and second, further adjustment of the best discovered network weights by an especially derived backpropagation algorithm for higher order networks with polynomial activation functions. These two stages of the PFNN learning process enable us to identify networks with good training as well as generalization performance. Empirical results show that this approach finds PFNN which outperform considerably some previous constructive polynomial network algorithms on processing benchmark time series.

Neural coding of image structure and contrast polarity of Cartesian, hyperbolic, and polar gratings in the primary and secondary visual cortex of the tree shrew.

PubMed

Poirot, Jordan; De Luna, Paolo; Rainer, Gregor

2016-04-01

We comprehensively characterize spiking and visual evoked potential (VEP) activity in tree shrew V1 and V2 using Cartesian, hyperbolic, and polar gratings. Neural selectivity to structure of Cartesian gratings was higher than other grating classes in both visual areas. From V1 to V2, structure selectivity of spiking activity increased, whereas corresponding VEP values tended to decrease, suggesting that single-neuron coding of Cartesian grating attributes improved while the cortical columnar organization of these neurons became less precise from V1 to V2. We observed that neurons in V2 generally exhibited similar selectivity for polar and Cartesian gratings, suggesting that structure of polar-like stimuli might be encoded as early as in V2. This hypothesis is supported by the preference shift from V1 to V2 toward polar gratings of higher spatial frequency, consistent with the notion that V2 neurons encode visual scene borders and contours. Neural sensitivity to modulations of polarity of hyperbolic gratings was highest among all grating classes and closely related to the visual receptive field (RF) organization of ON- and OFF-dominated subregions. We show that spatial RF reconstructions depend strongly on grating class, suggesting that intracortical contributions to RF structure are strongest for Cartesian and polar gratings. Hyperbolic gratings tend to recruit least cortical elaboration such that the RF maps are similar to those generated by sparse noise, which most closely approximate feedforward inputs. Our findings complement previous literature in primates, rodents, and carnivores and highlight novel aspects of shape representation and coding occurring in mammalian early visual cortex. Copyright © 2016 the American Physiological Society.

Active cooling of pulse compression diffraction gratings for high energy, high average power ultrafast lasers

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

Alessi, David A.; Rosso, Paul A.; Nguyen, Hoang T.

Laser energy absorption and subsequent heat removal from diffraction gratings in chirped pulse compressors poses a significant challenge in high repetition rate, high peak power laser development. In order to understand the average power limitations, we have modeled the time-resolved thermo-mechanical properties of current and advanced diffraction gratings. We have also developed and demonstrated a technique of actively cooling Petawatt scale, gold compressor gratings to operate at 600W of average power - a 15x increase over the highest average power petawatt laser currently in operation. As a result, combining this technique with low absorption multilayer dielectric gratings developed in ourmore » group would enable pulse compressors for petawatt peak power lasers operating at average powers well above 40kW.« less

Active cooling of pulse compression diffraction gratings for high energy, high average power ultrafast lasers

DOE PAGES

Alessi, David A.; Rosso, Paul A.; Nguyen, Hoang T.; ...

2016-12-26

Laser energy absorption and subsequent heat removal from diffraction gratings in chirped pulse compressors poses a significant challenge in high repetition rate, high peak power laser development. In order to understand the average power limitations, we have modeled the time-resolved thermo-mechanical properties of current and advanced diffraction gratings. We have also developed and demonstrated a technique of actively cooling Petawatt scale, gold compressor gratings to operate at 600W of average power - a 15x increase over the highest average power petawatt laser currently in operation. As a result, combining this technique with low absorption multilayer dielectric gratings developed in ourmore » group would enable pulse compressors for petawatt peak power lasers operating at average powers well above 40kW.« less

Fabrication of three-dimensional polymer quadratic nonlinear grating structures by layer-by-layer direct laser writing technique

NASA Astrophysics Data System (ADS)

Bich Do, Danh; Lin, Jian Hung; Diep Lai, Ngoc; Kan, Hung-Chih; Hsu, Chia Chen

2011-08-01

We demonstrate the fabrication of a three-dimensional (3D) polymer quadratic nonlinear (χ(2)) grating structure. By performing layer-by-layer direct laser writing (DLW) and spin-coating approaches, desired photobleached grating patterns were embedded in the guest--host dispersed-red-1/poly(methylmethacrylate) (DR1/PMMA) active layers of an active-passive alternative multilayer structure through photobleaching of DR1 molecules. Polyvinyl-alcohol and SU8 thin films were deposited between DR1/PMMA layers serving as a passive layer to separate DR1/PMMA active layers. After applying the corona electric field poling to the multilayer structure, nonbleached DR1 molecules in the active layers formed polar distribution, and a 3D χ(2) grating structure was obtained. The χ(2) grating structures at different DR1/PMMA nonlinear layers were mapped by laser scanning second harmonic (SH) microscopy, and no cross talk was observed between SH images obtained from neighboring nonlinear layers. The layer-by-layer DLW technique is favorable to fabricating hierarchical 3D polymer nonlinear structures for optoelectronic applications with flexible structural design.

Fabrication of three-dimensional polymer quadratic nonlinear grating structures by layer-by-layer direct laser writing technique.

PubMed

Do, Danh Bich; Lin, Jian Hung; Lai, Ngoc Diep; Kan, Hung-Chih; Hsu, Chia Chen

2011-08-10

We demonstrate the fabrication of a three-dimensional (3D) polymer quadratic nonlinear (χ(2)) grating structure. By performing layer-by-layer direct laser writing (DLW) and spin-coating approaches, desired photobleached grating patterns were embedded in the guest-host dispersed-red-1/poly(methylmethacrylate) (DR1/PMMA) active layers of an active-passive alternative multilayer structure through photobleaching of DR1 molecules. Polyvinyl-alcohol and SU8 thin films were deposited between DR1/PMMA layers serving as a passive layer to separate DR1/PMMA active layers. After applying the corona electric field poling to the multilayer structure, nonbleached DR1 molecules in the active layers formed polar distribution, and a 3D χ(2) grating structure was obtained. The χ(2) grating structures at different DR1/PMMA nonlinear layers were mapped by laser scanning second harmonic (SH) microscopy, and no cross talk was observed between SH images obtained from neighboring nonlinear layers. The layer-by-layer DLW technique is favorable to fabricating hierarchical 3D polymer nonlinear structures for optoelectronic applications with flexible structural design.

Configuration and calibration of a flat field grating spectrometer in the wavelength range 7-60 Å with a Manson ultrasoft x-ray source

NASA Astrophysics Data System (ADS)

Yang, Y.; Shi, Z.; Fei, Z.; Jin, X.; Xiao, J.; Hutton, R.; Zou, Y.

2011-06-01

An ultrasoft x-ray and extreme ultraviolet spectrometer built and calibrated in the wavelength range of 7-60 Å is reported here. Details of the alignment of this flat field spectrometer with both a laser and a telescope are presented. The light path function rather than a standard calibration function, i.e. a polynomial function, is introduced as the fit function, which gives good agreement with the spectrometer design values and makes the calibration more reliable when extended to the region outside the points used for calibration, compared with a standard calibration function. The calibration results of a Manson ultrasoft x-ray source (model 2) with source targets of Cu, Fe and Ti are presented with all the peaks marked.

Near-infrared light-controlled tunable grating based on graphene/elastomer composites

NASA Astrophysics Data System (ADS)

Wang, Fei; Jia, Shuhai; Wang, Yonglin; Tang, Zhenhua

2018-02-01

A near-infrared (nIR) light actuated tunable transmission optical grating based on graphene nanoplatelet (GNP)/polydimethylsiloxane (PDMS) and PDMS is proposed. A simple fabrication protocol is studied that allows integration of the grating with the actuation mechanism; both components are made from soft elastomers, and this ensure the tunability and the light-driven operation of the grating. The resulting grating structure demonstrates continuous period tunability of 2.7% under an actuation power density of 220 mW cm-2 within a period of 3 s and also demonstrates a time-independent characteristic. The proposed infrared activated grating can be developed for wireless remote light splitting in bio/chemical sensing and optical telecommunications applications.

Performance testing of an off-plane reflection grating and silicon pore optic spectrograph at PANTER

NASA Astrophysics Data System (ADS)

Marlowe, Hannah; McEntaffer, Randall L.; Allured, Ryan; DeRoo, Casey T.; Donovan, Benjamin D.; Miles, Drew M.; Tutt, James H.; Burwitz, Vadim; Menz, Benedikt; Hartner, Gisela D.; Smith, Randall K.; Cheimets, Peter; Hertz, Edward; Bookbinder, Jay A.; Günther, Ramses; Yanson, Alex; Vacanti, Giuseppe; Ackermann, Marcelo

2015-10-01

An x-ray spectrograph consisting of aligned, radially ruled off-plane reflection gratings and silicon pore optics (SPO) was tested at the Max Planck Institute for Extraterrestrial Physics PANTER x-ray test facility. SPO is a test module for the proposed Arcus mission, which will also feature aligned off-plane reflection gratings. This test is the first time two off-plane gratings were actively aligned to each other and with an SPO to produce an overlapped spectrum. We report the performance of the complete spectrograph utilizing the aligned gratings module and plans for future development.

Optical and Acoustic Device Applications of Ferroelastic Crystals

NASA Astrophysics Data System (ADS)

Meeks, Steven Wayne

This dissertation presents the discovery of a means of creating uniformly periodic domain gratings in a ferroelastic crystal of neodymium pentaphosphate (NPP). The uniform and non-uniform domain structures which can be created in NPP have the potential applications as tunable active gratings for lasers, tunable diffraction gratings, tunable Bragg reflection gratings, tunable acoustic filters, optical modulators, and optical domain wall memories. The interaction of optical and acoustic waves with ferroelastic domain walls in NPP is presented in detail. Acoustic amplitude reflection coefficients from a single domain wall in NPP are much larger than other ferroelastic-ferroelectrics such as gadolinium molybdate (GMO). Domain walls of NPP are used to make two demonstration acoustic devices: a tunable comb filter and a tunable delay line. The tuning process is accomplished by moving the position of the reflecting surface (the domain wall). A theory of the reflection of optical waves from NPP domain walls is discussed. The optical reflection is due to a change in the polarization of the wave, and not a change in the index, as the wave crosses the domain wall. Theoretical optical power reflection coefficients show good agreement with the experimentally measured values. The largest optical reflection coefficient of a single domain wall is at a critical angle and is 2.2% per domain wall. Techniques of injecting periodic and aperiodic domain walls into NPP are presented. The nucleation process of the uniformly periodic domain gratings in NPP is described in terms of a newly-discovered domain structure, namely the ferroelastic bubble. A ferroelastic bubble is the elastic analogue to the well-known magnetic bubble. The period of the uniformly periodic domain grating is tunable from 100 to 0.5 microns and the grating period may be tuned relatively rapidly. The Bragg efficiency of these tunable gratings is 77% for an uncoated crystal. Several demonstration devices which use these periodic structures are discussed. These devices are a tunable active grating laser (TAG laser), a tunable active grating (TAG), and a tunable acoustic bulk wave filter.

Performance testing of a novel off-plane reflection grating and silicon pore optic spectrograph at PANTER

NASA Astrophysics Data System (ADS)

Marlowe, Hannah; McEntaffer, Randall L.; Allured, Ryan; DeRoo, Casey; Miles, Drew M.; Donovan, Benjamin D.; Tutt, James H.; Burwitz, Vadim; Menz, Benedikt; Hartner, Gisela D.; Smith, Randall K.; Günther, Ramses; Yanson, Alex; Vacanti, Giuseppe; Ackermann, Marcelo

2015-05-01

An X-ray spectrograph consisting of aligned, radially ruled off-plane reflection gratings and silicon pore optics (SPO) was tested at the Max Planck Institute for extraterrestrial Physics PANTER X-ray test facility. The SPO is a test module for the proposed Arcus mission, which will also feature aligned off-plane reflection gratings. This test is the first time two off-plane gratings were actively aligned to each other and with a SPO to produce an overlapped spectrum. We report the performance of the complete spectrograph utilizing the aligned gratings module and plans for future development.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

VizieR Online Data Catalog: Massive LMC stars AAOmega spectroscopy (Evans+, 2015)

NASA Astrophysics Data System (ADS)

Evans, C. J.; van Loon, J. T.; Hainich, R.; Bailey, M.

2015-08-01

This catalogue comprises ascii versions of the optical spectra of 263 massive stars in the Large Magellanic Cloud, obtained with the AAOmega spectrograph on the Anglo Australian Telescope. Spectra from the first night (2006 Feb 22) were obtained with a 1700B grating at two wavelength settings. The spectra published here were obtained by median combining the two exposures at both settings, and then median combining them in the overlap region (spanning ~4375-4400Å). Spectra from the second night (2006 Feb 23) were obtained with a 1500V grating at one central wavelength setting (4375Å). The spectra The published spectra have been normalised/rectified using an automated script, which uses pre-defined regions (selected to avoid known absorption lines in early-type stars) to create a polynomial fit to the notional continuum in each spectrum. The published spectra have been divided by those fits to rectify them to unity. As such, we caution the user that quantitative analysis of these data would benefit from tailored rectification of the spectra. In particular, at the ends of the spectral range, and across broad emission features (such as that around HeII 4686 in luminous O-type supergiants). Also note that there were a number of 'hot' columns in the AAOmega CCDs, leading to small breaks (at multiple wavelengths) in the large majority of the spectra. (5 data files).

Open-cavity fiber laser with distributed feedback based on externally or self-induced dynamic gratings.

PubMed

Lobach, Ivan A; Drobyshev, Roman V; Fotiadi, Andrei A; Podivilov, Evgeniy V; Kablukov, Sergey I; Babin, Sergey A

2017-10-15

Dynamic population inversion gratings induced in an active medium by counter-propagating optical fields may have a reverse effect on writing laser radiation via feedback they provide. In this Letter we report, to the best of our knowledge, on the first demonstration of an open-cavity fiber laser in which the distributed feedback is provided by a dynamic grating "written" in a Yb-doped active fiber, either by an external source or self-induced via a weak (∼0.1%) reflection from an angle-cleaved fiber end. It has been shown that meters-long dynamic grating is formed with a narrow bandwidth (<50  MHz) and a relatively high-reflection coefficient (>7%) securing single-frequency operation, but the subsequent hole-burning effects accompanied by new grating formation lead to the switching from one longitudinal mode to another. providing a regular pulse-mode dynamics. As a result, periodically generated pulse trains cover a spectrum range of several terahertz delivering millions of cavity modes in sequent pulses.

Using Tutte polynomials to analyze the structure of the benzodiazepines

NASA Astrophysics Data System (ADS)

Cadavid Muñoz, Juan José

2014-05-01

Graph theory in general and Tutte polynomials in particular, are implemented for analyzing the chemical structure of the benzodiazepines. Similarity analysis are used with the Tutte polynomials for finding other molecules that are similar to the benzodiazepines and therefore that might show similar psycho-active actions for medical purpose, in order to evade the drawbacks associated to the benzodiazepines based medicine. For each type of benzodiazepines, Tutte polynomials are computed and some numeric characteristics are obtained, such as the number of spanning trees and the number of spanning forests. Computations are done using the computer algebra Maple's GraphTheory package. The obtained analytical results are of great importance in pharmaceutical engineering. As a future research line, the usage of the chemistry computational program named Spartan, will be used to extent and compare it with the obtained results from the Tutte polynomials of benzodiazepines.

Fabrication update on critical-angle transmission gratings for soft x-ray grating spectrometers

NASA Astrophysics Data System (ADS)

Heilmann, Ralf K.; Bruccoleri, Alex; Mukherjee, Pran; Yam, Jonathan; Schattenburg, Mark L.

2011-09-01

Diffraction grating-based, wavelength dispersive high-resolution soft x-ray spectroscopy of celestial sources promises to reveal crucial data for the study of the Warm-Hot Intergalactic Medium, the Interstellar Medium, warm absorption and outflows in Active Galactic Nuclei, coronal emission from stars, and other areas of interest to the astrophysics community. Our recently developed critical-angle transmission (CAT) gratings combine the advantages of the Chandra high and medium energy transmission gratings (low mass, high tolerance of misalignments and figure errors, polarization insensitivity) with those of blazed reflection gratings (high broad band diffraction efficiency, high resolution through use of higher diffraction orders) such as the ones on XMM-Newton. Extensive instrument and system configuration studies have shown that a CAT grating-based spectrometer is an outstanding instrument capable of delivering resolving power on the order of 5,000 and high effective area, even with a telescope point-spread function on the order of many arc-seconds. We have fabricated freestanding, ultra-high aspect-ratio CAT grating bars from silicon-on-insulator wafers using both wet and dry etch processes. The 200 nm-period grating bars are supported by an integrated Level 1 support mesh, and a coarser external Level 2 support mesh. The resulting grating membrane is mounted to a frame, resulting in a grating facet. Many such facets comprise a grating array that provides light-weight coverage of large-area telescope apertures. Here we present fabrication results on the integration of CAT gratings and the different high-throughput support mesh levels and on membrane-frame bonding. We also summarize recent x-ray data analysis of 3 and 6 micron deep wet-etched CAT grating prototypes.

Differential Classical Conditioning Selectively Heightens Response Gain of Neural Population Activity in Human Visual Cortex

PubMed Central

Song, Inkyung; Keil, Andreas

2015-01-01

Neutral cues, after being reliably paired with noxious events, prompt defensive engagement and amplified sensory responses. To examine the neurophysiology underlying these adaptive changes, we quantified the contrast-response function of visual cortical population activity during differential aversive conditioning. Steady-state visual evoked potentials (ssVEPs) were recorded while participants discriminated the orientation of rapidly flickering grating stimuli. During each trial, luminance contrast of the gratings was slowly increased and then decreased. Right-tilted gratings (CS+) were paired with loud white noise but left-tilted gratings (CS−) were not. The contrast-following waveform envelope of ssVEPs showed selective amplification of the CS+ only during the high-contrast stage of the viewing epoch. Findings support the notion that motivational relevance, learned in a time frame of minutes, affects vision through a response gain mechanism. PMID:24981277

Astigmatism-corrected echelle spectrometer using an off-the-shelf cylindrical lens.

PubMed

Fu, Xiao; Duan, Fajie; Jiang, Jiajia; Huang, Tingting; Ma, Ling; Lv, Changrong

2017-10-01

As a special kind of spectrometer with the Czerny-Turner structure, the echelle spectrometer features two-dimensional dispersion, which leads to a complex astigmatic condition. In this work, we propose an optical design of astigmatism-corrected echelle spectrometer using an off-the-shelf cylindrical lens. The mathematical model considering astigmatism introduced by the off-axis mirrors, the echelle grating, and the prism is established. Our solution features simplified calculation and low-cost construction, which is capable of overall compensation of the astigmatism in a wide spectral range (200-600 nm). An optical simulation utilizing ZEMAX software, astigmatism assessment based on Zernike polynomials, and an instrument experiment is implemented to validate the effect of astigmatism correction. The results demonstrated that astigmatism of the echelle spectrometer was corrected to a large extent, and high spectral resolution better than 0.1 nm was achieved.

Parameter extraction of coupling-of-modes equations including coupling between two surface acoustic waves on SiO2/Cu/LiNbO3 structures

NASA Astrophysics Data System (ADS)

Huang, Yulin; Bao, Jingfu; Li, Xinyi; Zhang, Benfeng; Omori, Tatsuya; Hashimoto, Ken-ya

2018-07-01

This paper describes extraction of parameters of an extended coupling-of-modes (COM) model including coupling between Rayleigh and shear-horizontal (SH) surface acoustic waves (SAW) on the SiO2-overlay/Cu-grating/LiNbO3-substrate structure. First, dispersion characteristics of two SAWs are calculated by the finite element method (FEM), and are fitted with those given by the extended COM. Then variation of COM parameters is expressed in polynomials in terms of the SiO2 and Cu thicknesses and the rotation angle Θ of LiNbO3. Then it is shown how the optimal Θ giving the SH SAW suppression changes with the thicknesses. The result agrees well with that obtained directly by FEM. It is also shown the optimal Θ changes abruptly at certain Cu thickness, and is due to decoupling between two SAW modes.

Single-mode fiber laser based on core-cladding mode conversion.

PubMed

Suzuki, Shigeru; Schülzgen, Axel; Peyghambarian, N

2008-02-15

A single-mode fiber laser based on an intracavity core-cladding mode conversion is demonstrated. The fiber laser consists of an Er-doped active fiber and two fiber Bragg gratings. One Bragg grating is a core-cladding mode converter, and the other Bragg grating is a narrowband high reflector that selects the lasing wavelength. Coupling a single core mode and a single cladding mode by the grating mode converter, the laser operates as a hybrid single-mode laser. This approach for designing a laser cavity provides a much larger mode area than conventional large-mode-area step-index fibers.

Do early neural correlates of visual consciousness show the oblique effect? A binocular rivalry and event-related potential study.

PubMed

Jack, Bradley N; Roeber, Urte; O'Shea, Robert P

2017-01-01

When dissimilar images are presented one to each eye, we do not see both images; rather, we see one at a time, alternating unpredictably. This is called binocular rivalry, and it has recently been used to study brain processes that correlate with visual consciousness, because perception changes without any change in the sensory input. Such studies have used various types of images, but the most popular have been gratings: sets of bright and dark lines of orthogonal orientations presented one to each eye. We studied whether using cardinal rival gratings (vertical, 0°, and horizontal, 90°) versus oblique rival gratings (left-oblique, -45°, and right-oblique, 45°) influences early neural correlates of visual consciousness, because of the oblique effect: the tendency for visual performance to be greater for cardinal gratings than for oblique gratings. Participants viewed rival gratings and pressed keys indicating which of the two gratings they perceived, was dominant. Next, we changed one of the gratings to match the grating shown to the other eye, yielding binocular fusion. Participants perceived the rivalry-to-fusion change to the dominant grating and not to the other, suppressed grating. Using event-related potentials (ERPs), we found neural correlates of visual consciousness at the P1 for both sets of gratings, as well as at the P1-N1 for oblique gratings, and we found a neural correlate of the oblique effect at the N1, but only for perceived changes. These results show that the P1 is the earliest neural activity associated with visual consciousness and that visual consciousness might be necessary to elicit the oblique effect.

Active phase correction of high resolution silicon photonic arrayed waveguide gratings

DOE PAGES

Gehl, M.; Trotter, D.; Starbuck, A.; ...

2017-03-10

Arrayed waveguide gratings provide flexible spectral filtering functionality for integrated photonic applications. Achieving narrow channel spacing requires long optical path lengths which can greatly increase the footprint of devices. High index contrast waveguides, such as those fabricated in silicon-on-insulator wafers, allow tight waveguide bends which can be used to create much more compact designs. Both the long optical path lengths and the high index contrast contribute to significant optical phase error as light propagates through the device. Thus, silicon photonic arrayed waveguide gratings require active or passive phase correction following fabrication. We present the design and fabrication of compact siliconmore » photonic arrayed waveguide gratings with channel spacings of 50, 10 and 1 GHz. The largest device, with 11 channels of 1 GHz spacing, has a footprint of only 1.1 cm 2. Using integrated thermo-optic phase shifters, the phase error is actively corrected. We present two methods of phase error correction and demonstrate state-of-the-art cross-talk performance for high index contrast arrayed waveguide gratings. As a demonstration of possible applications, we perform RF channelization with 1 GHz resolution. In addition, we generate unique spectral filters by applying non-zero phase offsets calculated by the Gerchberg Saxton algorithm.« less

Active phase correction of high resolution silicon photonic arrayed waveguide gratings.

PubMed

Gehl, M; Trotter, D; Starbuck, A; Pomerene, A; Lentine, A L; DeRose, C

2017-03-20

Arrayed waveguide gratings provide flexible spectral filtering functionality for integrated photonic applications. Achieving narrow channel spacing requires long optical path lengths which can greatly increase the footprint of devices. High index contrast waveguides, such as those fabricated in silicon-on-insulator wafers, allow tight waveguide bends which can be used to create much more compact designs. Both the long optical path lengths and the high index contrast contribute to significant optical phase error as light propagates through the device. Therefore, silicon photonic arrayed waveguide gratings require active or passive phase correction following fabrication. Here we present the design and fabrication of compact silicon photonic arrayed waveguide gratings with channel spacings of 50, 10 and 1 GHz. The largest device, with 11 channels of 1 GHz spacing, has a footprint of only 1.1 cm². Using integrated thermo-optic phase shifters, the phase error is actively corrected. We present two methods of phase error correction and demonstrate state-of-the-art cross-talk performance for high index contrast arrayed waveguide gratings. As a demonstration of possible applications, we perform RF channelization with 1 GHz resolution. Additionally, we generate unique spectral filters by applying non-zero phase offsets calculated by the Gerchberg Saxton algorithm.

Mixing of Chromatic and Luminance Retinal Signals in Primate Area V1

PubMed Central

Li, Xiaobing; Chen, Yao; Lashgari, Reza; Bereshpolova, Yulia; Swadlow, Harvey A.; Lee, Barry B.; Alonso, Jose Manuel

2015-01-01

Vision emerges from activation of chromatic and achromatic retinal channels whose interaction in visual cortex is still poorly understood. To investigate this interaction, we recorded neuronal activity from retinal ganglion cells and V1 cortical cells in macaques and measured their visual responses to grating stimuli that had either luminance contrast (luminance grating), chromatic contrast (chromatic grating), or a combination of the two (compound grating). As with parvocellular or koniocellular retinal ganglion cells, some V1 cells responded mostly to the chromatic contrast of the compound grating. As with magnocellular retinal ganglion cells, other V1 cells responded mostly to the luminance contrast and generated a frequency-doubled response to equiluminant chromatic gratings. Unlike magnocellular and parvocellular retinal ganglion cells, V1 cells formed a unimodal distribution for luminance/color preference with a 2- to 4-fold bias toward luminance. V1 cells associated with positive local field potentials in deep layers showed the strongest combined responses to color and luminance and, as a population, V1 cells encoded a diverse combination of luminance/color edges that matched edge distributions of natural scenes. Taken together, these results suggest that the primary visual cortex combines magnocellular and parvocellular retinal inputs to increase cortical receptive field diversity and to optimize visual processing of our natural environment. PMID:24464943

Simulation of two-dimensional gratings for SERS-active substrate

NASA Astrophysics Data System (ADS)

Zou, Wenlong; Wu, Jianhong

2016-11-01

Raman spectroscopy provides intrinsic vibrational and rotational mode of molecules in materials, which is widely used in chemical, medical and environmental domains. As known, the magnitude of surface enhanced Raman scattering can be amplified several orders. Nowadays, common Raman scattering has been gradually replaced by surface enhanced Raman scattering in low concentration detection domain. Generally speaking, the signal of surface enhanced Raman scattering on periodic nanostructures is more reliable and reproducible than on irregular nanostructures. In this paper, two-dimensional gratings coated by noble metal are used as SERS-active substrate. The surface plasmon resonance can be obtained by tuning the period of two-dimensional grating when the excitation laser interacts on the grating. The local electric field distribution is simulated by finite-difference-time-domain (FDTD). The wavelength of 632.8nm and 785nm are usually assembled on commercial Raman spectrometer. The optimization procedure of two-dimensional grating period is simulated by FDTD for above two wavelengths. The relation between the grating period and surface plasmon resonance is obtained in theory. The parameters such as depth of photoresist and thickness of coated metal are systematic discussed. The simulation results will greatly guide our post manufacture, which can be served for the commercial Raman spectrometer in SERS detection.

In situ simultaneous strain and temperature measurement of adaptive composite materials using a fiber Bragg grating based sensor

NASA Astrophysics Data System (ADS)

Yoon, Hyuk-Jin; Costantini, Daniele M.; Michaud, Veronique; Limberger, Hans G.; Manson, Jan-Anders; Salathe, Rene P.; Kim, Chun-Gon; Hong, Chang-Sun

2005-05-01

An optical fiber sensor to simultaneously measure strain and temperature was designed and embedded into an adaptive composite laminate which exhibits a shape change upon thermal activation. The sensor is formed by two fiber Bragg gratings, which are written in optical fibers with different core dopants. The two gratings were spliced close to each other and a sensing element resulted with Bragg gratings of similar strain sensitivity but different response to temperature. This is due to the dependence of the fiber thermo-optic coefficient on core dopants and relative concentrations. The sensor was tested on an adaptive composite laminate made of unidirectional Kevlar-epoxy pre-preg plies. Several 150μm diameter pre-strained NiTiCu shape memory alloy wires were embedded in the composite laminate together with one fiber sensor. Simultaneous monitoring of strain and temperature during the curing process and activation in an oven was demonstrated.

M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori.

PubMed

Kwun, Young Chel; Munir, Mobeen; Nazeer, Waqas; Rafique, Shazia; Min Kang, Shin

2017-08-18

V-Phenylenic nanotubes and nanotori are most comprehensively studied nanostructures due to widespread applications in the production of catalytic, gas-sensing and corrosion-resistant materials. Representing chemical compounds with M-polynomial is a recent idea and it produces nice formulas of degree-based topological indices which correlate chemical properties of the material under investigation. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules like boiling point, stability, strain energy etc. are correlated with their structures. In this paper, we determine general closed formulae for M-polynomials of V-Phylenic nanotubes and nanotori. We recover important topological degree-based indices. We also give different graphs of topological indices and their relations with the parameters of structures.

Combinatorial Reliability and Repair

DTIC Science & Technology

1992-07-01

Press, Oxford, 1987. [2] G. Gordon and L. Traldi, Generalized activities and the Tutte polynomial, Discrete Math . 85 (1990), 167-176. [3] A. B. Huseby, A...Chromatic polynomials and network reliability, Discrete Math . 67 (1987), 57-79. [7] A. Satayanarayana and R. K. Wood, A linear-time algorithm for comput- ing...K-terminal reliability in series-parallel networks, SIAM J. Comput. 14 (1985), 818-832. [8] L. Traldi, Generalized activities and K-terminal reliability, Discrete Math . 96 (1991), 131-149. 4

Soft x-ray transmission grating spectrometer for X-ray Surveyor and smaller missions with high resolving power

NASA Astrophysics Data System (ADS)

Heilmann, Ralf K.; Bruccoleri, Alexander; Schattenburg, Mark; Kolodziejczak, jeffery; Gaskin, Jessica; O'Dell, Stephen L.

2017-01-01

A number of high priority subjects in astrophysics are addressed by a state-of-the-art soft x-ray grating spectrometer, e.g. the role of Active Galactic Nuclei in galaxy and star formation, characterization of the WHIM and the “missing baryon” problem, characterization of halos around the Milky Way and nearby galaxies, and stellar coronae and surrounding winds and disks. An Explorer-scale, large-area (A > 1,000 cm2), high resolving power (R > 3,000) soft x-ray grating spectrometer is highly feasible based on Critical-Angle Transmission (CAT) grating technology, even for telescopes with angular resolution of 5-10 arcsec. Significantly higher performance could be provided by a CAT grating spectrometer on an X-ray-Surveyor-type mission (A > 4,000 cm2, R > 5,000). CAT gratings combine advantages of blazed reflection gratings (high efficiency, use of higher orders) with those of transmission gratings (low mass, relaxed alignment tolerances and temperature requirements, transparent at higher energies) with minimal mission resource requirements. Blazing is achieved through grazing-incidence reflection off the smooth silicon grating bar sidewalls. Silicon is well matched to the soft x-ray band, and 30% absolute diffraction efficiency has been acheived with clear paths for further improvement. CAT gratings with sidewalls made of high-Z elements allow extension of blazing to higher energies and larger dispersion angles, enabling higher resolving power at shorter wavelengths. X-ray data from CAT gratings coated with a thin layer of platinum using atomic layer deposition demonstrate efficient blazing to higher energies and much larger blaze angles than possible with silicon alone. Measurements of the resolving power of a breadboard CAT grating spectrometer consisting of a Wolter-I slumped-glass focusing optic from GSFC and CAT gratings, taken at the MSFC Stray Light Facility, have demonstrated resolving power > 10,000. Thus currently fabricated CAT gratings are compatible with the most advanced grating spectrometer instrument designs for future soft x-ray spectroscopy missions. We will review the most recent CAT grating fabrication and x-ray test results.

Showcasing the InTeGrate STEP Center principles and implementation programs through interactive webinars and websites

NASA Astrophysics Data System (ADS)

Orr, C. H.; McFadden, R.; Manduca, C. A.; Newman, A.

2016-12-01

Teaching sustainability curriculum provides an opportunity for building connections between academic learning and examples, experiences, and issues from beyond academia. Done well, this can increase students interest in a topic that feels relevant to their lives and help them transfer this learning to real life situations in their professional and personal lives. To support this approach to teaching, the NSF STEP Center InTeGrate developed a set of five core principles to guide development of teaching materials and programs that draw content from grand challenges to society and work to improve students' ability to understand the nature of science and think like a scientist. These principles include both effective pedagogical approaches and an interdisciplinary framework and are reflected in example curriculum modules, and implementation programs supported by InTeGrate. In order to promote adoption of teaching aligned with the InTeGrate philosophy and to use the InTeGrate-developed materials as tools, we organized a public webinar series led by materials developers and program leaders in the InTeGrate community. The webinars highlight programs that have addressed bigger-scale challenges such as increasing diversity of our majors and creating pathways to the workforce, as well as the materials used by these programs. They provide detailed examples designed to help other groups implement similar programs including showcase teaching activities and examples of their use in a wide range of settings. The webinars are interactive, with built-in activities and reflections that promote discussion among participants and speakers. Topics include natural hazards and risks, water resources and sustainability, energy and atmosphere, integrating sustainability into your course, and tracing environmental contaminants. These have clear components of geoscience, but promote an interdisciplinary perspective, that provides a deeper and more thorough discussion. Each webinar is archived on the InTeGrate website. We invite people to learn about InTeGrate teaching strategies, activities, and interdisciplinary approaches, and models for implementing the principles highlighted through the STEP Center work.

Wideband plasmonic beam steering in metal gratings.

PubMed

de Ceglia, Domenico; Vincenti, Maria Antonietta; Scalora, Michael

2012-01-15

We demonstrate controllable light deflection in thick metal gratings with periodic subwavelength slits filled with an active material. Under specific illumination conditions, the grating becomes nearly transparent and acts as a uniform optical phased-array antenna where the phase of the radiating elements is controlled by modifying the index of refraction of the material that fills each slit. The beam-steering operational regime occurs in a wide wavelength band, and it is relatively insensitive to the input angle.

Mixing of Chromatic and Luminance Retinal Signals in Primate Area V1.

PubMed

Li, Xiaobing; Chen, Yao; Lashgari, Reza; Bereshpolova, Yulia; Swadlow, Harvey A; Lee, Barry B; Alonso, Jose Manuel

2015-07-01

Vision emerges from activation of chromatic and achromatic retinal channels whose interaction in visual cortex is still poorly understood. To investigate this interaction, we recorded neuronal activity from retinal ganglion cells and V1 cortical cells in macaques and measured their visual responses to grating stimuli that had either luminance contrast (luminance grating), chromatic contrast (chromatic grating), or a combination of the two (compound grating). As with parvocellular or koniocellular retinal ganglion cells, some V1 cells responded mostly to the chromatic contrast of the compound grating. As with magnocellular retinal ganglion cells, other V1 cells responded mostly to the luminance contrast and generated a frequency-doubled response to equiluminant chromatic gratings. Unlike magnocellular and parvocellular retinal ganglion cells, V1 cells formed a unimodal distribution for luminance/color preference with a 2- to 4-fold bias toward luminance. V1 cells associated with positive local field potentials in deep layers showed the strongest combined responses to color and luminance and, as a population, V1 cells encoded a diverse combination of luminance/color edges that matched edge distributions of natural scenes. Taken together, these results suggest that the primary visual cortex combines magnocellular and parvocellular retinal inputs to increase cortical receptive field diversity and to optimize visual processing of our natural environment. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Multisite silicon neural probes with integrated silicon nitride waveguides and gratings for optogenetic applications.

PubMed

Shim, Euijae; Chen, Yu; Masmanidis, Sotiris; Li, Mo

2016-03-04

Optimal optogenetic perturbation of brain circuit activity often requires light delivery in a precise spatial pattern that cannot be achieved with conventional optical fibers. We demonstrate an implantable silicon-based probe with a compact light delivery system, consisting of silicon nitride waveguides and grating couplers for out-of-plane light emission with high spatial resolution. 473 nm light is coupled into and guided in cm-long waveguide and emitted at the output grating coupler. Using the direct cut-back and out-scattering measurement techniques, the propagation optical loss of the waveguide is measured to be below 3 dB/cm. The grating couplers provide collimated light emission with sufficient irradiance for neural stimulation. Finally, a probe with multisite light delivery with three output grating emitters from a single laser input is demonstrated.

Predicting Visual Consciousness Electrophysiologically from Intermittent Binocular Rivalry

PubMed Central

O’Shea, Robert P.; Kornmeier, Jürgen; Roeber, Urte

2013-01-01

Purpose We sought brain activity that predicts visual consciousness. Methods We used electroencephalography (EEG) to measure brain activity to a 1000-ms display of sine-wave gratings, oriented vertically in one eye and horizontally in the other. This display yields binocular rivalry: irregular alternations in visual consciousness between the images viewed by the eyes. We replaced both gratings with 200 ms of darkness, the gap, before showing a second display of the same rival gratings for another 1000 ms. We followed this by a 1000-ms mask then a 2000-ms inter-trial interval (ITI). Eleven participants pressed keys after the second display in numerous trials to say whether the orientation of the visible grating changed from before to after the gap or not. Each participant also responded to numerous non-rivalry trials in which the gratings had identical orientations for the two eyes and for which the orientation of both either changed physically after the gap or did not. Results We found that greater activity from lateral occipital-parietal-temporal areas about 180 ms after initial onset of rival stimuli predicted a change in visual consciousness more than 1000 ms later, on re-presentation of the rival stimuli. We also found that less activity from parietal, central, and frontal electrodes about 400 ms after initial onset of rival stimuli predicted a change in visual consciousness about 800 ms later, on re-presentation of the rival stimuli. There was no such predictive activity when the change in visual consciousness occurred because the stimuli changed physically. Conclusion We found early EEG activity that predicted later visual consciousness. Predictive activity 180 ms after onset of the first display may reflect adaption of the neurons mediating visual consciousness in our displays. Predictive activity 400 ms after onset of the first display may reflect a less-reliable brain state mediating visual consciousness. PMID:24124536

High-Average-Power Diffraction Pulse-Compression Gratings Enabling Next-Generation Ultrafast Laser Systems

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

Alessi, D.

Pulse compressors for ultrafast lasers have been identified as a technology gap in the push towards high peak power systems with high average powers for industrial and scientific applications. Gratings for ultrashort (sub-150fs) pulse compressors are metallic and can absorb a significant percentage of laser energy resulting in up to 40% loss as well as thermal issues which degrade on-target performance. We have developed a next generation gold grating technology which we have scaled to the petawatt-size. This resulted in improvements in efficiency, uniformity and processing as compared to previous substrate etched gratings for high average power. This new designmore » has a deposited dielectric material for the grating ridge rather than etching directly into the glass substrate. It has been observed that average powers as low as 1W in a compressor can cause distortions in the on-target beam. We have developed and tested a method of actively cooling diffraction gratings which, in the case of gold gratings, can support a petawatt peak power laser with up to 600W average power. We demonstrated thermo-mechanical modeling of a grating in its use environment and benchmarked with experimental measurement. Multilayer dielectric (MLD) gratings are not yet used for these high peak power, ultrashort pulse durations due to their design challenges. We have designed and fabricated broad bandwidth, low dispersion MLD gratings suitable for delivering 30 fs pulses at high average power. This new grating design requires the use of a novel Out Of Plane (OOP) compressor, which we have modeled, designed, built and tested. This prototype compressor yielded a transmission of 90% for a pulse with 45 nm bandwidth, and free of spatial and angular chirp. In order to evaluate gratings and compressors built in this project we have commissioned a joule-class ultrafast Ti:Sapphire laser system. Combining the grating cooling and MLD technologies developed here could enable petawatt laser systems to operate at 50kW average power.« less

Dual interface gratings design for absorption enhancement in thin crystalline silicon solar cells

NASA Astrophysics Data System (ADS)

Zhang, Jinqiannan; Yu, Zhongyuan; Liu, Yumin; Chai, Hongyu; Hao, Jing; Ye, Han

2017-09-01

We numerically study and analyze the light absorption enhancement in thin crystalline silicon solar cell with dual interface gratings. The structure combines the front dielectric nanowalls and the sinusoidal plasmonic grating at back reflector. We show that having specific interfaces with well-chosen period, fill factor and height can allow more efficient dielectric and plasmonic modes coupling into active layer and can improve the solar cell performance. For 1 μm active layer case, the optimal result for the proposed structure achieves short-circuit current of 23.6 mA/cm2, which performs over 50% better than flat solar cell structure, the short-circuit current of which is 15.5 mA/cm2. In addition, the active layer thickness and angular analysis show that the proposed structure maintains its advantage over flat structure.

Single-order, subwavelength resonant nanograting as a uniformly hot substrate for surface-enhanced Raman spectroscopy.

PubMed

Deng, Xuegong; Braun, Gary B; Liu, Sheng; Sciortino, Paul F; Koefer, Bob; Tombler, Thomas; Moskovits, Martin

2010-05-12

The surface-enhanced Raman spectroscopy (SERS) activity and the optical reflectance of a subwavelength gold nanograting fabricated entirely using top down technologies on silicon wafers are presented. The grating consists of 120 nm gold cladding on top of parallel silica nanowires constituting the grating's lines, with gaps between nanowires <10 nm wide at their narrowest point. The grating produces inordinately intense SERS and shows very strong polarization dependence. Reflectance measurements for the optimized grating indicate that (when p-polarization is used and at least one of the incident electric field components lies across the grating lines) the reflectance drops to <1% at resonance, indicating that essentially all of the radiant energy falling on the surface is coupled into the grating. The SERS intensity and the reflectance at resonance anticorrelate predicatively, suggesting that reflectance measurements can provide a nondestructive, wafer-level test of SERS efficacy. The SERS performance of the gratings is very uniform and reproducible. Extensive measurements on samples cut from both the same wafer and from different wafers, produce a SERS intensity distribution function that is similar to that obtained for ordinary Raman measurements carried out at multiple locations on a polished (100) silicon wafer.

Spatial summation revealed in the earliest visual evoked component C1 and the effect of attention on its linearity.

PubMed

Chen, Juan; Yu, Qing; Zhu, Ziyun; Peng, Yujia; Fang, Fang

2016-01-01

In natural scenes, multiple objects are usually presented simultaneously. How do specific areas of the brain respond to multiple objects based on their responses to each individual object? Previous functional magnetic resonance imaging (fMRI) studies have shown that the activity induced by a multiobject stimulus in the primary visual cortex (V1) can be predicted by the linear or nonlinear sum of the activities induced by its component objects. However, there has been little evidence from electroencephelogram (EEG) studies so far. Here we explored how V1 responded to multiple objects by comparing the EEG signals evoked by a three-grating stimulus with those evoked by its two components (the central grating and 2 flanking gratings). We focused on the earliest visual component C1 (onset latency of ∼50 ms) because it has been shown to reflect the feedforward responses of neurons in V1. We found that when the stimulus was unattended, the amplitude of the C1 evoked by the three-grating stimulus roughly equaled the sum of the amplitudes of the C1s evoked by its two components, regardless of the distances between these gratings. When the stimulus was attended, this linear spatial summation existed only when the three gratings were far apart from each other. When the three gratings were close to each other, the spatial summation became compressed. These results suggest that the earliest visual responses in V1 follow a linear summation rule when attention is not involved and that attention can affect the earliest interactions between multiple objects. Copyright © 2016 the American Physiological Society.

Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

NASA Astrophysics Data System (ADS)

Miller, W., Jr.; Li, Q.

2015-04-01

The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.

Ligand Shaping in Induced Fit Docking of MraY Inhibitors. Polynomial Discriminant and Laplacian Operator as Biological Activity Descriptors.

PubMed

Lungu, Claudiu N; Diudea, Mircea V; Putz, Mihai V

2017-06-27

Docking-i.e., interaction of a small molecule (ligand) with a proteic structure (receptor)-represents the ground of drug action mechanism of the vast majority of bioactive chemicals. Ligand and receptor accommodate their geometry and energy, within this interaction, in the benefit of receptor-ligand complex. In an induced fit docking, the structure of ligand is most susceptible to changes in topology and energy, comparative to the receptor. These changes can be described by manifold hypersurfaces, in terms of polynomial discriminant and Laplacian operator. Such topological surfaces were represented for each MraY (phospho-MurNAc-pentapeptide translocase) inhibitor, studied before and after docking with MraY. Binding affinities of all ligands were calculated by this procedure. For each ligand, Laplacian and polynomial discriminant were correlated with the ligand minimum inhibitory concentration (MIC) retrieved from literature. It was observed that MIC is correlated with Laplacian and polynomial discriminant.

Laterally coupled distributed feedback lasers emitting at 2 μm with quantum dash active region and high-duty-cycle etched semiconductor gratings

NASA Astrophysics Data System (ADS)

Papatryfonos, Konstantinos; Saladukha, Dzianis; Merghem, Kamel; Joshi, Siddharth; Lelarge, Francois; Bouchoule, Sophie; Kazazis, Dimitrios; Guilet, Stephane; Le Gratiet, Luc; Ochalski, Tomasz J.; Huyet, Guillaume; Martinez, Anthony; Ramdane, Abderrahim

2017-02-01

Single-mode diode lasers on an InP(001) substrate have been developed using InAs/In0.53Ga0.47As quantum dash (Qdash) active regions and etched lateral Bragg gratings. The lasers have been designed to operate at wavelengths near 2 μm and exhibit a threshold current of 65 mA for a 600 μm long cavity, and a room temperature continuous wave output power per facet >5 mW. Using our novel growth approach based on the low ternary In0.53Ga0.47As barriers, we also demonstrate ridge-waveguide lasers emitting up to 2.1 μm and underline the possibilities for further pushing the emission wavelength out towards longer wavelengths with this material system. By introducing experimentally the concept of high-duty-cycle lateral Bragg gratings, a side mode suppression ratio of >37 dB has been achieved, owing to an appreciably increased grating coupling coefficient of κ ˜ 40 cm-1. These laterally coupled distributed feedback (LC-DFB) lasers combine the advantage of high and well-controlled coupling coefficients achieved in conventional DFB lasers, with the regrowth-free fabrication process of lateral gratings, and exhibit substantially lower optical losses compared to the conventional metal-based LC-DFB lasers.

Optical Performance Modeling of FUSE Telescope Mirror

NASA Technical Reports Server (NTRS)

Saha, Timo T.; Ohl, Raymond G.; Friedman, Scott D.; Moos, H. Warren

2000-01-01

We describe the Metrology Data Processor (METDAT), the Optical Surface Analysis Code (OSAC), and their application to the image evaluation of the Far Ultraviolet Spectroscopic Explorer (FUSE) mirrors. The FUSE instrument - designed and developed by the Johns Hopkins University and launched in June 1999 is an astrophysics satellite which provides high resolution spectra (lambda/Delta(lambda) = 20,000 - 25,000) in the wavelength region from 90.5 to 118.7 nm The FUSE instrument is comprised of four co-aligned, normal incidence, off-axis parabolic mirrors, four Rowland circle spectrograph channels with holographic gratings, and delay line microchannel plate detectors. The OSAC code provides a comprehensive analysis of optical system performance, including the effects of optical surface misalignments, low spatial frequency deformations described by discrete polynomial terms, mid- and high-spatial frequency deformations (surface roughness), and diffraction due to the finite size of the aperture. Both normal incidence (traditionally infrared, visible, and near ultraviolet mirror systems) and grazing incidence (x-ray mirror systems) systems can be analyzed. The code also properly accounts for reflectance losses on the mirror surfaces. Low frequency surface errors are described in OSAC by using Zernike polynomials for normal incidence mirrors and Legendre-Fourier polynomials for grazing incidence mirrors. The scatter analysis of the mirror is based on scalar scatter theory. The program accepts simple autocovariance (ACV) function models or power spectral density (PSD) models derived from mirror surface metrology data as input to the scatter calculation. The end product of the program is a user-defined pixel array containing the system Point Spread Function (PSF). The METDAT routine is used in conjunction with the OSAC program. This code reads in laboratory metrology data in a normalized format. The code then fits the data using Zernike polynomials for normal incidence systems or Legendre-Fourier polynomials for grazing incidence systems. It removes low order terms from the metrology data, calculates statistical ACV or PSD functions, and fits these data to OSAC models for the scatter analysis. In this paper we briefly describe the laboratory image testing of FUSE spare mirror performed in the near and vacuum ultraviolet at John Hopkins University and OSAC modeling of the test setup performed at NASA/GSFC. The test setup is a double-pass configuration consisting of a Hg discharge source, the FUSE off-axis parabolic mirror under test, an autocollimating flat mirror, and a tomographic imaging detector. Two additional, small fold flats are used in the optical train to accommodate the light source and the detector. The modeling is based on Zernike fitting and PSD analysis of surface metrology data measured by both the mirror vendor (Tinsley) and JHU. The results of our models agree well with the laboratory imaging data, thus validating our theoretical model. Finally, we predict the imaging performance of FUSE mirrors in their flight configuration at far-ultraviolet wavelengths.

A Sub-Millimetric 3-DOF Force Sensing Instrument with Integrated Fiber Bragg Grating for Retinal Microsurgery

PubMed Central

He, Xingchi; Handa, James; Gehlbach, Peter; Taylor, Russell; Iordachita, Iulian

2013-01-01

Vitreoretinal surgery requires very fine motor control to perform precise manipulation of the delicate tissue in the interior of the eye. Besides physiological hand tremor, fatigue, poor kinesthetic feedback, and patient movement, the absence of force sensing is one of the main technical challenges. Previous two degrees of freedom (DOF) force sensing instruments have demonstrated robust force measuring performance. The main design challenge is to incorporate high sensitivity axial force sensing. This paper reports the development of a sub-millimetric 3-DOF force sensing pick instrument based on fiber Bragg grating (FBG) sensors. The configuration of the four FBG sensors is arranged to maximize the decoupling between axial and transverse force sensing. A super-elastic nitinol flexure is designed to achieve high axial force sensitivity. An automated calibration system was developed for repeatability testing, calibration, and validation. Experimental results demonstrate a FBG sensor repeatability of 1.3 pm. The linear model for calculating the transverse forces provides an accurate global estimate. While the linear model for axial force is only locally accurate within a conical region with a 30° vertex angle, a second-order polynomial model can provide a useful global estimate for axial force. Combining the linear model for transverse forces and nonlinear model for axial force, the 3-DOF force sensing instrument can provide sub-millinewton resolution for axial force and a quarter millinewton for transverse forces. Validation with random samples show the force sensor can provide consistent and accurate measurement of three dimensional forces. PMID:24108455

Computing border bases using mutant strategies

NASA Astrophysics Data System (ADS)

Ullah, E.; Abbas Khan, S.

2014-01-01

Border bases, a generalization of Gröbner bases, have actively been addressed during recent years due to their applicability to industrial problems. In cryptography and coding theory a useful application of border based is to solve zero-dimensional systems of polynomial equations over finite fields, which motivates us for developing optimizations of the algorithms that compute border bases. In 2006, Kehrein and Kreuzer formulated the Border Basis Algorithm (BBA), an algorithm which allows the computation of border bases that relate to a degree compatible term ordering. In 2007, J. Ding et al. introduced mutant strategies bases on finding special lower degree polynomials in the ideal. The mutant strategies aim to distinguish special lower degree polynomials (mutants) from the other polynomials and give them priority in the process of generating new polynomials in the ideal. In this paper we develop hybrid algorithms that use the ideas of J. Ding et al. involving the concept of mutants to optimize the Border Basis Algorithm for solving systems of polynomial equations over finite fields. In particular, we recall a version of the Border Basis Algorithm which is actually called the Improved Border Basis Algorithm and propose two hybrid algorithms, called MBBA and IMBBA. The new mutants variants provide us space efficiency as well as time efficiency. The efficiency of these newly developed hybrid algorithms is discussed using standard cryptographic examples.

Tamm plasmon sub-wavelength structuration for loss reduction and resonance tuning

NASA Astrophysics Data System (ADS)

Gubaydullin, A. R.; Symonds, C.; Benoit, J.-M.; Ferrier, L.; Benyattou, T.; Jamois, C.; Lemaître, A.; Senellart, P.; Kaliteevski, M. A.; Bellessa, J.

2017-12-01

We have demonstrated experimentally and theoretically that losses in Tamm plasmon structures can be reduced by using a subwavelength structuration of the metal layer. The structures consist of a GaAs/Al0.95Ga0.05As Bragg reflector covered with a sub-wavelength silver grating. An active quantum dot layer is inserted to perform photoluminescence experiments. Experimental results show that the quality factor of the Tamm plasmon mode with grating increases substantially, with respect to the same structure without a grating. Moreover, a fine-tuning of the Tamm spectral position is obtained by changing the grating parameters. Finite element method simulations are in good agreement with the experimental values. Our results will promote the realization of lasing with the TP based devices at room temperature.

Femtosecond-pulse inscription of fiber Bragg gratings with single or multiple phase-shifts in the structure

NASA Astrophysics Data System (ADS)

Wolf, Alexey; Dostovalov, Alexandr; Skvortsov, Mikhail; Raspopin, Kirill; Parygin, Alexandr; Babin, Sergey

2018-05-01

In this work, long high-quality fiber Bragg gratings with phase shifts in the structure are inscribed directly in the optical fiber by point-by-point technique using femtosecond laser pulses. Phase shifts are introduced during the inscription process with a piezoelectric actuator, which rapidly shifts the fiber along the direction of its movement in a chosen point of the grating with a chosen shift value. As examples, single and double π phase shifts are introduced in fiber Bragg gratings with a length up to 34 mm in passive fibers, which provide corresponding transmission peaks with bandwidth less than 1 pm. It is shown that 37 mm π -phase-shifted grating inscribed in an active Er-doped fiber forms high-quality DFB laser cavity generating single-frequency radiation at 1550 nm with bandwidth of 20 kHz and signal-to-noise ratio of >70 dB. The inscription technique has a high degree of performance and flexibility and can be easily implemented in fibers of various types.

Piezo activated mode tracking system for widely tunable mode-hop-free external cavity mid-IR semiconductor lasers

NASA Technical Reports Server (NTRS)

Tittel, Frank K. (Inventor); Curl, Robert F. (Inventor); Wysocki, Gerard (Inventor)

2010-01-01

A widely tunable, mode-hop-free semiconductor laser operating in the mid-IR comprises a QCL laser chip having an effective QCL cavity length, a diffraction grating defining a grating angle and an external cavity length with respect to said chip, and means for controlling the QCL cavity length, the external cavity length, and the grating angle. The laser of claim 1 wherein said chip may be tuned over a range of frequencies even in the absence of an anti-reflective coating. The diffraction grating is controllably pivotable and translatable relative to said chip and the effective QCL cavity length can be adjusted by varying the injection current to the chip. The laser can be used for high resolution spectroscopic applications and multi species trace-gas detection. Mode-hopping is avoided by controlling the effective QCL cavity length, the external cavity length, and the grating angle so as to replicate a virtual pivot point.

Binocular rivalry from invisible patterns

PubMed Central

Zou, Jinyou; He, Sheng; Zhang, Peng

2016-01-01

Binocular rivalry arises when incompatible images are presented to the two eyes. If the two eyes’ conflicting features are invisible, leading to identical perceptual interpretations, does rivalry competition still occur? Here we investigated whether binocular rivalry can be induced from conflicting but invisible spatial patterns. A chromatic grating counterphase flickering at 30 Hz appeared uniform, but produced significant tilt aftereffect and orientation-selective adaptation. The invisible pattern also generated significant BOLD activities in the early visual cortex, with minimal response in the parietal and frontal cortical areas. Compared with perceptually matched uniform stimuli, a monocularly presented invisible chromatic grating enhanced the rivalry competition with a low-contrast visible grating presented to the other eye. Furthermore, switching from a uniform field to a perceptually matched invisible chromatic grating produced interocular suppression at approximately 200 ms after onset of the invisible grating. Experiments using briefly presented monocular probes revealed evidence for sustained rivalry competition between two invisible gratings during continuous dichoptic presentations. These findings indicate that even without visible interocular conflict, and with minimal engagement of frontoparietal cortex and consciousness related top-down feedback, perceptually identical patterns with invisible conflict features produce rivalry competition in the early visual cortex. PMID:27354535

Terahertz amplification in RTD-gated HEMTs with a grating-gate wave coupling topology

NASA Astrophysics Data System (ADS)

Condori Quispe, Hugo O.; Encomendero-Risco, Jimy J.; Xing, Huili Grace; Sensale-Rodriguez, Berardi

2016-08-01

We theoretically analyze the operation of a terahertz amplifier consisting of a resonant-tunneling-diode gated high-electron-mobility transistor (RTD-gated HEMT) in a grating-gate topology. In these devices, the key element enabling substantial power gain is the efficient coupling of terahertz waves into and out of plasmons in the RTD-gated HEMT channel, i.e., the gain medium, via the grating-gate itself, part of the active device, rather than by an external antenna structure as discussed in previous works, therefore potentially enabling terahertz amplification with associated power gains >40 dB.

Terahertz amplification in RTD-gated HEMTs with a grating-gate wave coupling topology

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

Condori Quispe, Hugo O.; Sensale-Rodriguez, Berardi; Encomendero-Risco, Jimy J.

2016-08-08

We theoretically analyze the operation of a terahertz amplifier consisting of a resonant-tunneling-diode gated high-electron-mobility transistor (RTD-gated HEMT) in a grating-gate topology. In these devices, the key element enabling substantial power gain is the efficient coupling of terahertz waves into and out of plasmons in the RTD-gated HEMT channel, i.e., the gain medium, via the grating-gate itself, part of the active device, rather than by an external antenna structure as discussed in previous works, therefore potentially enabling terahertz amplification with associated power gains >40 dB.

Electro-Optic Effect in Thin Films of a Dielectric and a Ferroelectric with Subwavelength Aluminum Grating

NASA Astrophysics Data System (ADS)

Blinov, L. M.; Lazarev, V. V.; Yudin, S. G.; Artemov, V. V.; Palto, S. P.; Gorkunov, M. V.

2018-01-01

The electro-optic effect in three nanoscale heterostructures, in each of which a thin layer of dielectric or ferroelectric material is inserted between two planar metal electrodes, has been studied. Each structure has one aluminum layer, containing a subwavelength grating with a period of 400 nm, contacting with either the glass substrate or air. The light transmission spectra of structures with subwavelength grating contain characteristic plasmon dips. Short external-voltage pulses affect the change in the refractive index of the corresponding active layer. Significant values of these changes may be useful for designing optical modulators.

Long-period fiber phase grating devices

NASA Astrophysics Data System (ADS)

Stegall, David Brian

In recent years, the explosive growth of the internet has virtually surpassed the limits of the global communications infrastructure. As a result, the fiber- optic communications industry is spearheading research and development to transmit information at ever increasing rates and over longer distances. The industry faces several obstacles to improving the performance of these systems. One problem is dispersion, which manifests at faster transmission rates when pulse spreading and distortion scramble the signal. Furthermore, high transmission powers needed for longer distances introduce deleterious optical nonlinearity phenomenon. Several waveguide and bulk devices have been implemented to address these issues, but each have shortcomings. Many of these problems and challenges have also impacted other fiber-optic industries, such as sensor systems. Long- period optical fiber gratings pose simple solutions to these problems and offer novel applications previously impractical through any other means. In this dissertation, research is presented in which modeling and fabrication of long-period gratings is improved over existing techniques by incorporating the effects of waveguide dispersion. An arbitrary dispersion also can be introduced into a long-period grating intentionally and a theoretical examination is made relating the chirp of a long-period grating and the resulting dispersion. In addition, several device applications such as a biological sensor and the concept of an actively controlled transmission spectrum of a long-period grating are explored. Finally, multiple in-series Bragg and long- period gratings are investigated for novel device configurations.

Ligand Shaping in Induced Fit Docking of MraY Inhibitors. Polynomial Discriminant and Laplacian Operator as Biological Activity Descriptors

PubMed Central

Diudea, Mircea V.; Putz, Mihai V.

2017-01-01

Docking—i.e., interaction of a small molecule (ligand) with a proteic structure (receptor)—represents the ground of drug action mechanism of the vast majority of bioactive chemicals. Ligand and receptor accommodate their geometry and energy, within this interaction, in the benefit of receptor–ligand complex. In an induced fit docking, the structure of ligand is most susceptible to changes in topology and energy, comparative to the receptor. These changes can be described by manifold hypersurfaces, in terms of polynomial discriminant and Laplacian operator. Such topological surfaces were represented for each MraY (phospho-MurNAc-pentapeptide translocase) inhibitor, studied before and after docking with MraY. Binding affinities of all ligands were calculated by this procedure. For each ligand, Laplacian and polynomial discriminant were correlated with the ligand minimum inhibitory concentration (MIC) retrieved from literature. It was observed that MIC is correlated with Laplacian and polynomial discriminant. PMID:28653980

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Polymer optical fiber grating as water activity sensor

NASA Astrophysics Data System (ADS)

Zhang, Wei; Webb, David J.

2014-05-01

Controlling the water content within a product has long been required in the chemical processing, agriculture, food storage, paper manufacturing, semiconductor, pharmaceutical and fuel industries. The limitations of water content measurement as an indicator of safety and quality are attributed to differences in the strength with which water associates with other components in the product. Water activity indicates how tightly water is "bound," structurally or chemically, in products. Water absorption introduces changes in the volume and refractive index of poly(methyl methacrylate) PMMA. Therefore for a grating made in PMMA based optical fiber, its wavelength is an indicator of water absorption and PMMA thus can be used as a water activity sensor. In this work we have investigated the performance of a PMMA based optical fiber grating as a water activity sensor in sugar solution, saline solution and Jet A-1 aviation fuel. Samples of sugar solution with sugar concentration from 0 to 8%, saline solution with concentration from 0 to 22%, and dried (10ppm), ambient (39ppm) and wet (68ppm) aviation fuels were used in experiments. The corresponding water activities are measured as 1.0 to 0.99 for sugar solution, 1.0 to 0.86 for saline solution, and 0.15, 0.57 and 1.0 for the aviation fuel samples. The water content in the measured samples ranges from 100% (pure water) to 10 ppm (dried aviation fuel). The PMMA based optical fiber grating exhibits good sensitivity and consistent response, and Bragg wavelength shifts as large as 3.4 nm when the sensor is transferred from dry fuel to wet fuel.

Poly-Frobenius-Euler polynomials

NASA Astrophysics Data System (ADS)

Kurt, Burak

2017-07-01

Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

Active exterior cloaking for the 2D Laplace and Helmholtz equations.

PubMed

Vasquez, Fernando Guevara; Milton, Graeme W; Onofrei, Daniel

2009-08-14

A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is close to 1 in a disk and close to 0 in another disk, and such a polynomial is constructed. For the 2D Helmholtz equation it is numerically shown that three exterior cloaking devices placed around the object suffice to hide it.

Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

DTIC Science & Technology

2001-09-11

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

Distributed feedback fiber laser based on a fiber Bragg grating inscribed using the femtosecond point-by-point technique

NASA Astrophysics Data System (ADS)

Skvortsov, M. I.; Wolf, A. A.; Dostovalov, A. V.; Vlasov, A. A.; Akulov, V. A.; Babin, S. A.

2018-03-01

A distributed feedback (DFB) fiber laser based on a 32-mm long pi-phase-shifted fiber Bragg grating inscribed using the femtosecond point-by-point technique in a single-mode erbium-doped optical fiber (CorActive EDF-L 1500) is demonstrated. The lasing power of the DFB laser reaches 0.7 mW at a wavelength of 1550 nm when pumped with a laser diode at a wavelength of 976 nm and power of 525 mW. The width of the lasing spectrum is 17 kHz. It is shown that the pi-phase-shifted fiber Bragg grating fs-inscribed in a non-PM fiber provides the selection of the single polarization mode of the DFB laser. DFB laser formation in a highly doped non-photosensitive optical fiber (CoreActive SCF-ER60-8/125-12) is also demonstrated.

Ethical concerns related to grateful patient philanthropy: the physician's perspective.

PubMed

Wright, Scott M; Wolfe, Leah; Stewart, Rosalyn; Flynn, John A; Paisner, Richard; Rum, Steve; Parson, Gregory; Carrese, Joseph

2013-05-01

Philanthropic contributions to academic medical centers from grateful patients support research, patient care, education, and capital projects. The goal of this study was to identify the ethical concerns associated with philanthropic gifts from grateful patients. A qualitative study design was selected. Investigators conducted in-depth semi-structured interviews with 20 Department of Medicine physicians at Johns Hopkins who were identified by Development Office staff as experienced and successful in this realm-those having relationships with multiple patients who have made philanthropic contributions. Interview transcripts were independently coded by two investigators. Content analysis identified several themes related to ethical concerns. Eighteen informants (90 %) were Associate Professors or Professors; two (10 %) were females. Four thematic domains emerged related to ethical concerns associated with philanthropy from grateful patients: (i) impact of gift on the doctor-patient relationship; (ii) gift acquisition considered beyond the physician's professional role; (iii) justice and fairness; and (iv) vulnerability of patients. Despite acknowledging at least one of the aforementioned concerns, eleven physician informants (55 %) expressed the view that there were no ethical issues involved with grateful patient philanthropy. In this paper, we report that physicians involved in grateful patient philanthropy are aware of, and in some cases troubled by, the ethical concerns related to this activity. Further studies could examine how best to prepare faculty for the challenges that may accompany these gifts so as to help them maintain expected professional and ethical standards when accepting grateful patient philanthropy.

220 microJ Monolithic Single-Frequency Q-switched Fiber Laser at 2 micrometers by Using Highly Tm-doped Germanate Fibers

DTIC Science & Technology

2011-09-15

actively Q-switching all-fiber lasers include mag- netostriction modulation of fiber Bragg gratings ( FBGs ), stretching of FBGs with piezoelectric...report an all- fiber single-frequency actively Q-switched laser operat- ing at ∼1920 nm by using a piezo to press the fiber in the FBG cavity based on...fusion-spliced between two FBGs as shown in Fig. 1. One FBG has a high reflectivity (HR) grating imprinted on a non-PM silica fiber. The other FBG

HotGAS: A Public Archive of Ready-to-Go Chandra High Energy Grating Spectral Products for Active Galactic Nuclei

NASA Astrophysics Data System (ADS)

Yaqoob, T.

2005-12-01

We describe a public WWW archive (HotGAS) containing data products from Chandra observations using the High Energy Grating Spectrometer (HETGS). Spectral products are available from the archive in various formats and are suitable for use by non-experts and experts alike. Lightcurves and cross-dispersion profiles are also available. Easy and user-friendly access for non X-ray astronomers to reprocessed, publishable quality grating data products should help to promote inter-disciplinary and multi-wavelength research on active galactic nuclei (AGN). The archive will also be useful to X-ray astronomers who have not yet had experience with high resolution X-ray spectroscopy, as well as experienced X-ray astronomers who need quick access to clean and ready-to-go data products. Theoreticians may find the archive useful for testing their models without having to deal with the fine details of data processing and reduction. We also anticipate that the archive will be useful for training graduate students in high-resolution X-ray spectroscopy and for providing a resource for projects for high-school and graduate students. We plan to eventually expand the archive to include AGN data from the Chandra Low Energy Grating Spectrometer (LETGS), and the XMM-Newton Reflection-Grating Spectrometer (RGS). Further in the future we plan to extend the archive to include data from other astrophysical sources aside from AGN. The project thus far is funded by an archival Chandra grant.

Spatial attention increases high-frequency gamma synchronisation in human medial visual cortex.

PubMed

Koelewijn, Loes; Rich, Anina N; Muthukumaraswamy, Suresh D; Singh, Krish D

2013-10-01

Visual information processing involves the integration of stimulus and goal-driven information, requiring neuronal communication. Gamma synchronisation is linked to neuronal communication, and is known to be modulated in visual cortex both by stimulus properties and voluntarily-directed attention. Stimulus-driven modulations of gamma activity are particularly associated with early visual areas such as V1, whereas attentional effects are generally localised to higher visual areas such as V4. The absence of a gamma increase in early visual cortex is at odds with robust attentional enhancements found with other measures of neuronal activity in this area. Here we used magnetoencephalography (MEG) to explore the effect of spatial attention on gamma activity in human early visual cortex using a highly effective gamma-inducing stimulus and strong attentional manipulation. In separate blocks, subjects tracked either a parafoveal grating patch that induced gamma activity in contralateral medial visual cortex, or a small line at fixation, effectively attending away from the gamma-inducing grating. Both items were always present, but rotated unpredictably and independently of each other. The rotating grating induced gamma synchronisation in medial visual cortex at 30-70 Hz, and in lateral visual cortex at 60-90 Hz, regardless of whether it was attended. Directing spatial attention to the grating increased gamma synchronisation in medial visual cortex, but only at 60-90 Hz. These results suggest that the generally found increase in gamma activity by spatial attention can be localised to early visual cortex in humans, and that stimulus and goal-driven modulations may be mediated at different frequencies within the gamma range. Copyright © 2013 Elsevier Inc. All rights reserved.

Two-dimensional displacement measurement based on two parallel gratings

NASA Astrophysics Data System (ADS)

Wei, Peipei; Lu, Xi; Qiao, Decheng; Zou, Limin; Huang, Xiangdong; Tan, Jiubin; Lu, Zhengang

2018-06-01

In this paper, a two-dimensional (2-D) planar encoder based on two parallel gratings, which includes a scanning grating and scale grating, is presented. The scanning grating is a combined transmission rectangular grating comprised of a 2-D grating located at the center and two one-dimensional (1-D) gratings located at the sides. The grating lines of the two 1-D gratings are perpendicular to each other and parallel with the 2-D grating lines. The scale grating is a 2-D reflective-type rectangular grating placed in parallel with the scanning grating, and there is an angular difference of 45° between the grating lines of the two 2-D gratings. With the special structural design of the scanning grating, the encoder can measure the 2-D displacement in the grating plane simultaneously, and the measured interference signals in the two directions are uncoupled. Moreover, by utilizing the scanning grating to modulate the phase of the interference signals instead of the prisms, the structure of the encoder is compact. Experiments were implemented, and the results demonstrate the validity of the 2-D planar grating encoder.

High-efficiency, broad-band and wide-angle optical absorption in ultra-thin organic photovoltaic devices.

PubMed

Wang, Wenyan; Hao, Yuying; Cui, Yanxia; Tian, Ximin; Zhang, Ye; Wang, Hua; Shi, Fang; Wei, Bin; Huang, Wei

2014-03-10

Metal nanogratings as one of the promising architectures for effective light trapping in organic photovoltaics (OPVs) have been actively studied over the past decade. Here we designed a novel metal nanowall grating with ultra-small period and ultra-high aspect-ratio as the back electrode of the OPV device. Such grating results in the strong hot spot effect in-between the neighboring nanowalls and the localized surface plasmon effect at the corners of nanowalls. These combined effects make the integrated absorption efficiency of light over the wavelength range from 400 to 650 nm in the active layer for the proposed structure, with respect to the equivalent planar structure, increases by 102% at TM polarization and by 36.5% at the TM/TE hybrid polarization, respectively. Moreover, it is noted that the hot spot effect in the proposed structure is more effective for ultra-thin active layers, which is very favorable for the exciton dissociation and charge collection. Therefore such a nanowall grating is expected to improve the overall performance of OPV devices.

Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

DTIC Science & Technology

2002-07-25

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc., AMS... orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection...1) by generalized polynomial chaos expansion, where the uncertainties can be introduced through κ, f , or g, or some combinations. It is worth

Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils.

PubMed

Mahajan, Virendra N

2012-06-20

In a recent paper, we considered the classical aberrations of an anamorphic optical imaging system with a rectangular pupil, representing the terms of a power series expansion of its aberration function. These aberrations are inherently separable in the Cartesian coordinates (x,y) of a point on the pupil. Accordingly, there is x-defocus and x-coma, y-defocus and y-coma, and so on. We showed that the aberration polynomials orthonormal over the pupil and representing balanced aberrations for such a system are represented by the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point; for example, L(l)(x)L(m)(y), where l and m are positive integers (including zero) and L(l)(x), for example, represents an orthonormal Legendre polynomial of degree l in x. The compound two-dimensional (2D) Legendre polynomials, like the classical aberrations, are thus also inherently separable in the Cartesian coordinates of the pupil point. Moreover, for every orthonormal polynomial L(l)(x)L(m)(y), there is a corresponding orthonormal polynomial L(l)(y)L(m)(x) obtained by interchanging x and y. These polynomials are different from the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil. In this paper, we show that the orthonormal aberration polynomials for an anamorphic system with a circular pupil, obtained by the Gram-Schmidt orthogonalization of the 2D Legendre polynomials, are not separable in the two coordinates. Moreover, for a given polynomial in x and y, there is no corresponding polynomial obtained by interchanging x and y. For example, there are polynomials representing x-defocus, balanced x-coma, and balanced x-spherical aberration, but no corresponding y-aberration polynomials. The missing y-aberration terms are contained in other polynomials. We emphasize that the Zernike circle polynomials, although orthogonal over a circular pupil, are not suitable for an anamorphic system as they do not represent balanced aberrations for such a system.

M-shaped grating by nanoimprinting: a replicable, large-area, highly active plasmonic surface-enhanced Raman scattering substrate with nanogaps.

PubMed

Zhu, Zhendong; Bai, Benfeng; Duan, Huigao; Zhang, Haosu; Zhang, Mingqian; You, Oubo; Li, Qunqing; Tan, Qiaofeng; Wang, Jia; Fan, Shoushan; Jin, Guofan

2014-04-24

Plasmonic nanostructures separated by nanogaps enable strong electromagnetic-field confinement on the nanoscale for enhancing light-matter interactions, which are in great demand in many applications such as surface-enhanced Raman scattering (SERS). A simple M-shaped nanograting with narrow V-shaped grooves is proposed. Both theoretical and experimental studies reveal that the electromagnetic field on the surface of the M grating can be pronouncedly enhanced over that of a grating without such grooves, due to field localization in the nanogaps formed by the narrow V grooves. A technique based on room-temperature nanoimprinting lithography and anisotropic reactive-ion etching is developed to fabricate this device, which is cost-effective, reliable, and suitable for fabricating large-area nanostructures. As a demonstration of the potential application of this device, the M grating is used as a SERS substrate for probing Rhodamine 6G molecules. Experimentally, an average SERS enhancement factor as high as 5×10⁸ has been achieved, which verifies the greatly enhanced light-matter interaction on the surface of the M grating over that of traditional SERS surfaces. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Chirped circular dielectric gratings for near-unity collection efficiency from quantum emitters in bulk diamond

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

Zheng, Jiabao; Liapis, Andreas C.; Chen, Edward H.

Effcient collection of fluorescence from nitrogen vacancy (NV) centers in diamond underlies the spin-dependent optical read-out that is necessary for quantum information processing and enhanced sensing applications. The optical collection effciency from NVs within diamond substrates is limited primarily due to the high refractive index of diamond and the non-directional dipole emission. Here we introduce a light collection strategy based on chirped, circular dielectric gratings that can be fabricated on a bulk diamond substrate to redirect an emitter’s far-field radiation pattern. Using a genetic optimization algorithm, these grating designs achieve 98.9% collection effciency for the NV zero-phonon emission line, collectedmore » from the back surface of the diamond with an objective of aperture 0.9. Across the broadband emission spectrum of the NV (600-800 nm), the chirped grating achieves 82.2% collection e ciency into a numerical aperture of 1.42, corresponding to an oil immersion objective again on the back side of the diamond. Our proposed bulk-dielectric grating structures are applicable to other optically active solid state quantum emitters in high index host materials.« less

Chirped circular dielectric gratings for near-unity collection efficiency from quantum emitters in bulk diamond

DOE PAGES

Zheng, Jiabao; Liapis, Andreas C.; Chen, Edward H.; ...

2017-12-13

Effcient collection of fluorescence from nitrogen vacancy (NV) centers in diamond underlies the spin-dependent optical read-out that is necessary for quantum information processing and enhanced sensing applications. The optical collection effciency from NVs within diamond substrates is limited primarily due to the high refractive index of diamond and the non-directional dipole emission. Here we introduce a light collection strategy based on chirped, circular dielectric gratings that can be fabricated on a bulk diamond substrate to redirect an emitter’s far-field radiation pattern. Using a genetic optimization algorithm, these grating designs achieve 98.9% collection effciency for the NV zero-phonon emission line, collectedmore » from the back surface of the diamond with an objective of aperture 0.9. Across the broadband emission spectrum of the NV (600-800 nm), the chirped grating achieves 82.2% collection e ciency into a numerical aperture of 1.42, corresponding to an oil immersion objective again on the back side of the diamond. Our proposed bulk-dielectric grating structures are applicable to other optically active solid state quantum emitters in high index host materials.« less

The evolution of rural outreach from Package Library to Grateful Med: introduction to the symposium

PubMed Central

Pifalo, Victoria

2000-01-01

Outreach is now a prevailing activity in health sciences libraries. As an introduction to a series of papers on current library outreach to rural communities, this paper traces the evolution of such activities by proponents in health sciences libraries from 1924 to 1992. Definitions of rural and outreach are followed by a consideration of the expanding audience groups. The evolution in approaches covers the package library and enhancements in extension service, library development, circuit librarianship, and self-service arrangements made possible by such programs as the Georgia Interactive Network (GaIN) and Grateful Med. PMID:11055301

Visual pattern recognition based on spatio-temporal patterns of retinal ganglion cells’ activities

PubMed Central

Jing, Wei; Liu, Wen-Zhong; Gong, Xin-Wei; Gong, Hai-Qing

2010-01-01

Neural information is processed based on integrated activities of relevant neurons. Concerted population activity is one of the important ways for retinal ganglion cells to efficiently organize and process visual information. In the present study, the spike activities of bullfrog retinal ganglion cells in response to three different visual patterns (checker-board, vertical gratings and horizontal gratings) were recorded using multi-electrode arrays. A measurement of subsequence distribution discrepancy (MSDD) was applied to identify the spatio-temporal patterns of retinal ganglion cells’ activities in response to different stimulation patterns. The results show that the population activity patterns were different in response to different stimulation patterns, such difference in activity pattern was consistently detectable even when visual adaptation occurred during repeated experimental trials. Therefore, the stimulus pattern can be reliably discriminated according to the spatio-temporal pattern of the neuronal activities calculated using the MSDD algorithm. PMID:21886670

Approximating exponential and logarithmic functions using polynomial interpolation

NASA Astrophysics Data System (ADS)

Gordon, Sheldon P.; Yang, Yajun

2017-04-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.

Multi-parameter optimization of monolithic high-index contrast grating reflectors

NASA Astrophysics Data System (ADS)

Marciniak, Magdalena; Gebski, Marcin; Dems, Maciej; Wasiak, Michał; Czyszanowski, Tomasz

2016-03-01

Conventional High-index Contrast Gratings (HCG) consist of periodically distributed high refractive index stripes surrounded by low index media. Practically, such low/high index stack can be fabricated in several ways however low refractive index layers are electrical insulators of poor thermal conductivities. Monolithic High-index Contrast Gratings (MHCGs) overcome those limitations since they can be implemented in any material with a real refractive index larger than 1.75 without the need of the combination of low and high refractive index materials. The freedom of use of various materials allows to provide more efficient current injection and better heat flow through the mirror, in contrary to the conventional HCGs. MHCGs can simplify the construction of VCSELs, reducing their epitaxial design to monolithic wafer with carrier confinement and active region inside and etched stripes on both surfaces in post processing. We present numerical analysis of MHCGs using a three-dimensional, fully vectorial optical model. We investigate possible designs of MHCGs using multidimensional optimization of grating parameters for different refractive indices.

Interaction of surface plasmon polaritons and acoustic waves inside an acoustic cavity.

PubMed

Khokhlov, Nikolai; Knyazev, Grigoriy; Glavin, Boris; Shtykov, Yakov; Romanov, Oleg; Belotelov, Vladimir

2017-09-15

In this Letter, we introduce an approach for manipulation of active plasmon polaritons via acoustic waves at sub-terahertz frequency range. The acoustic structures considered are designed as phononic Fabry-Perot microresonators where mirrors are presented with an acoustic superlattice and the structure's surface, and a plasmonic grating is placed on top of the acoustic cavity so formed. It provides phonon localization in the vicinity of the plasmonic grating at frequencies within the phononic stop band enhancing phonon-light interaction. We consider phonon excitation by shining a femtosecond laser pulse on the plasmonic grating. Appropriate theoretical model was used to describe the acoustic process caused by the pump laser pulse in the GaAs/AlAs-based acoustic cavity with a gold grating on top. Strongest modulation is achieved upon excitation of propagating surface plasmon polaritons and hybridization of propagating and localized plasmons. The relative changes in the optical reflectivity of the structure are more than an order of magnitude higher than for the structure without the plasmonic film.

X-ray phase imaging-From static observation to dynamic observation-

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

Momose, A.; Yashiro, W.; Olbinado, M. P.

2012-07-31

We are attempting to expand the technology of X-ray grating phase imaging/tomography to enable dynamic observation. X-ray phase imaging has been performed mainly for static cases, and this challenge is significant since properties of materials (and hopefully their functions) would be understood by observing their dynamics in addition to their structure, which is an inherent advantage of X-ray imaging. Our recent activities in combination with white synchrotron radiation for this purpose are described. Taking advantage of the fact that an X-ray grating interferometer functions with X-rays of a broad energy bandwidth (and therefore high flux), movies of differential phase imagesmore » and visibility images are obtained with a time resolution of a millisecond. The time resolution of X-ray phase tomography can therefore be a second. This study is performed as a part of a project to explore X-ray grating interferometry, and our other current activities are also briefly outlined.« less

Qualitative photoluminescence study of defect activation in telecommunication fibers and Bragg gratings in hydrogen-loaded fibers

NASA Astrophysics Data System (ADS)

Bastola, B.; Fischer, B.; Roths, J.; Ruediger, A.

2018-07-01

Despite the relevance of glass fibers and integrated optical circuits for an increasing number of cutting-edge applications ranging from telecommunication to sensing and quantum photonics, the knowledge about their structural and chemical properties is still in its infancy. Optical spectroscopy techniques are challenged due to the intrinsically low cross-sections for inelastic processes. Our approach is to detect these properties along the core, extending the interaction to the fiber length. We report on in-situ temperature-dependent photoluminescence (PL) measurements in transmission geometry of a) pristine optical glass fibers (standard commercial telecom grade and different types of photosensitive fibers) and b) type I fiber Bragg grating (FBG) in hydrogen-loaded fibers of the same type. A laser with 473 nm wavelength and TEM 00 mode is coupled to an optical spectrometer through different fibers. The fibers are thermally cycled between room temperature and 950° Celsius. As a first observation, we detect a clearly visible red emission from the uncoated fibers at the location of the fiber Bragg grating. Fitting the luminescence spectra with a single Gaussian and monitoring the intensity as a function of temperature reveals an irreversible, thermally activated degradation of the luminescence associated to the fiber Bragg gratings. A closer inspection of pristine glass fibers without FBG revealed a faint, yet thermally stable luminescence with similar spectral characteristics. Analyzing qualitative data for two consecutive heating cycles confirmed two distinct activation energies. This may be due to several reasons such as different defects at the basis of this emission or different structural or chemical environments for the same defect. Further experiment will be carried out in the future to investigate the main reason of two distinct activation energies.

Equivalences of the multi-indexed orthogonal polynomials

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

Odake, Satoru

2014-01-15

Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.

Soft X-ray holographic grating beam splitter including a double frequency grating for interferometer pre-alignment.

PubMed

Liu, Ying; Tan, Xin; Liu, Zhengkun; Xu, Xiangdong; Hong, Yilin; Fu, Shaojun

2008-09-15

Grating beam splitters have been fabricated for soft X-ray Mach- Zehnder interferometer using holographic interference lithography. The grating beam splitter consists of two gratings, one works at X-ray laser wavelength of 13.9 nm with the spatial frequency of 1000 lines/mm as the operation grating, the other works at visible wavelength of 632.8 nm for pre-aligning the X-ray interferometer with the spatial frequency of 22 lines/mm as the pre-alignment grating. The two gratings lie vertically on the same substrate. The main feature of the beam splitter is the use of low-spatial- frequency beat grating of a holographic double frequency grating as the pre-alignment grating of the X-ray interferometer. The grating line parallelism between the two gratings can be judged by observing the diffraction patterns of the pre-alignment grating directly.

Microfluidic resonant waveguide grating biosensor system for whole cell sensing

NASA Astrophysics Data System (ADS)

Zaytseva, Natalya; Miller, William; Goral, Vasily; Hepburn, Jerry; Fang, Ye

2011-04-01

We report on a fluidic resonant waveguide grating (RWG) biosensor system that enables medium throughput measurements of cellular responses under microfluidics in a 32-well format. Dynamic mass redistribution assays under microfluidics differentiate the cross-desensitization process between the β2-adrenoceptor agonist epinephrine and the adenylate cyclase activator forskolin mediated signaling. This system opens new possibility to study cellular processes that are otherwise difficult to achieve using conventional RWG configurations.

Near-field analysis of metallic DFB lasers at telecom wavelengths.

PubMed

Greusard, L; Costantini, D; Bousseksou, A; Decobert, J; Lelarge, F; Duan, G-H; De Wilde, Y; Colombelli, R

2013-05-06

We image in near-field the transverse modes of semiconductor distributed feedback (DFB) lasers operating at λ ≈ 1.3 μm and employing metallic gratings. The active region is based on tensile-strained InGaAlAs quantum wells emitting transverse magnetic polarized light and is coupled via an extremely thin cladding to a nano-patterned gold grating integrated on the device surface. Single mode emission is achieved, which tunes with the grating periodicity. The near-field measurements confirm laser operation on the fundamental transverse mode. Furthermore--together with a laser threshold reduction observed in the DFB lasers--it suggests that the patterning of the top metal contact can be a strategy to reduce the high plasmonic losses in this kind of systems.

Smart composites with embedded shape memory alloy actuators and fibre Bragg grating sensors: activation and control

NASA Astrophysics Data System (ADS)

Balta, J. A.; Bosia, F.; Michaud, V.; Dunkel, G.; Botsis, J.; Månson, J.-A.

2005-08-01

This paper describes the production of an adaptive composite by embedding thin pre-strained shape memory alloy actuators into a Kevlar-epoxy host material. In order to combine the activation and sensing capabilities, fibre Bragg grating sensors are also embedded into the specimens, and the strain measured in situ during activation. The effect of manufacturing conditions, and hence of the initial stress state in the composite before activation, on the magnitude of the measured strains is discussed. The results of stress and strain simulations are compared with experimental data, and guidelines are provided for the optimization of the composite. Finally, a pilot experiment is carried out to provide an example of how a strain-stabilizing feedback mechanism can be implemented in the smart structure.

Using InTeGrate materials to develop interdisciplinary thinking for a sustainable future

NASA Astrophysics Data System (ADS)

Awad, A. A.; Gilbert, L.; Iverson, E. A. R.; Manduca, C. A.; Steer, D. N.

2017-12-01

InTeGrate materials focus on societal grand challenges, sustainability, and interdisciplinary problems through developing geoscientific habits of mind, the use of credible data, and systems thinking. The materials are freely available 2-3 week modules and courses that allow instructors to focus on a wide variety of topics from regulating carbon emissions, changing biosphere, and storms and community resilience to environmental justice, ocean sustainability, and humans' dependence on mineral resources, integrating a variety of relevant interdisciplinary activities throughout. Presented with interdisciplinary approaches, students learn with tools to integrate engineering, policy, economics, and social aspects with the science to address the challenges. Students' ability to apply interdisciplinary approaches to address sustainability problems is made visible through the essays they write as a part of the materials assessment. InTeGrate modules have been adopted and implemented by faculty members interested in sustainability themes and innovative pedagogy, and have reached more than 50,000 students in all 50 states, Puerto Rico, India, and Micronesia. Student data were collected from 533 assessment essays in 57 undergraduate classes. The essays required students to describe a global challenge in an interdisciplinary manner through identifying scientific implications, and connecting it to economic, social and policy decisions. Students also completed a second essay assessing their systems thinking ability, a geoscience literacy exam (GLE), and demographic and attitudinal surveys. Scores for students enrolled in classes using InTeGrate materials were compared to scores from students in similar classes that did not use InteGrate materials. The InTeGrate and control groups had equivalent GLE scores and demographic characteristics. Essay scores for students in InTeGrate introductory or majors courses outperformed students in comparable level control courses as measured by the average interdisciplinary essay scores.

Orientation-specific contextual modulation of the fMRI BOLD response to luminance and chromatic gratings in human visual cortex.

PubMed

McDonald, J Scott; Seymour, Kiley J; Schira, Mark M; Spehar, Branka; Clifford, Colin W G

2009-05-01

The responses of orientation-selective neurons in primate visual cortex can be profoundly affected by the presence and orientation of stimuli falling outside the classical receptive field. Our perception of the orientation of a line or grating also depends upon the context in which it is presented. For example, the perceived orientation of a grating embedded in a surround tends to be repelled from the predominant orientation of the surround. Here, we used fMRI to investigate the basis of orientation-specific surround effects in five functionally-defined regions of visual cortex: V1, V2, V3, V3A/LO1 and hV4. Test stimuli were luminance-modulated and isoluminant gratings that produced responses similar in magnitude. Less BOLD activation was evident in response to gratings with parallel versus orthogonal surrounds across all the regions of visual cortex investigated. When an isoluminant test grating was surrounded by a luminance-modulated inducer, the degree of orientation-specific contextual modulation was no larger for extrastriate areas than for V1, suggesting that the observed effects might originate entirely in V1. However, more orientation-specific modulation was evident in extrastriate cortex when both test and inducer were luminance-modulated gratings than when the test was isoluminant; this difference was significant in area V3. We suggest that the pattern of results in extrastriate cortex may reflect a refinement of the orientation-selectivity of surround suppression specific to the colour of the surround or, alternatively, processes underlying the segmentation of test and inducer by spatial phase or orientation when no colour cue is available.

Population gratings in saturable optical fibers with randomly oriented rare-earth ions

NASA Astrophysics Data System (ADS)

Stepanov, S.; Martinez, L. M.; Hernandez, E. H.; Agruzov, P.; Shamray, A.

2015-07-01

Formation of the dynamic population gratings in optical fibers with randomly oriented rare-earth ions is analyzed with a special interest to the grating component for readout with the orthogonal light polarization. It is shown that as compared with a simple model case of the collinearly oriented dipole-like centers their random orientation leads to approximately 2-times growth of the effective saturation power P sat when it is estimated from the incident power dependence of the fiber absorption or from that of the fluorescence intensity. An optimal incident power, for which the maximum of the dynamic population grating amplitude for collinear light polarization is observed, also follows this change in P sat, while formation of the grating for orthogonal polarization needs essentially higher light power. The reduced anisotropy of the active centers, which is in charge of the experimentally observed weakening of the polarization hole burning (PHB) and of the fluorescence polarization, compensates in some way the effect of random ion orientation. The ratio between the maximum conventional (i.e. for the interacting waves collinear polarizations) two-wave mixing (TWM) amplitude and the initial not saturable fiber optical density proves to be, however, nearly the same as in the model case of collinearly oriented dipoles. The ratio between the PHB effect and the amplitude of the anisotropic grating, which is responsible for TWM of the orthogonally polarized waves, is also not influenced significantly by the reduced anisotropy of ions.

Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

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

Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

2011-04-15

Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

Solutions of interval type-2 fuzzy polynomials using a new ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

2015-10-01

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

Coherent orthogonal polynomials

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

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

2013-08-15

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relatemore » these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L{sup 2} functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L{sup 2} and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that defines the corresponding OP family. •Generalized coherent polynomials are obtained from OP.« less

Feasibility evaluation of a neutron grating interferometer with an analyzer grating based on a structured scintillator.

PubMed

Kim, Youngju; Kim, Jongyul; Kim, Daeseung; Hussey, Daniel S; Lee, Seung Wook

2018-03-01

We introduce an analyzer grating based on a structured scintillator fabricated by a gadolinium oxysulfide powder filling method for a symmetric Talbot-Lau neutron grating interferometer. This is an alternative way to analyze the Talbot self-image of a grating interferometer without using an absorption grating to block neutrons. Since the structured scintillator analyzer grating itself generates the signal for neutron detection, we do not need an additional scintillator screen as an absorption analyzer grating. We have developed and tested an analyzer grating based on a structured scintillator in our symmetric Talbot-Lau neutron grating interferometer to produce high fidelity absorption, differential phase, and dark-field contrast images. The acquired images have been compared to results of a grating interferometer utilizing a typical absorption analyzer grating with two commercial scintillation screens. The analyzer grating based on the structured scintillator enhances interference fringe visibility and shows a great potential for economical fabrication, compact system design, and so on. We report the performance of the analyzer grating based on a structured scintillator and evaluate its feasibility for the neutron grating interferometer.

Analysis of grating doublets for achromatic beam-splitting

PubMed Central

Pacheco, Shaun; Milster, Tom; Liang, Rongguang

2015-01-01

Achromatic beam-splitting grating doublets are designed for both continuous phase and binary phase gratings. By analyzing the sensitivity to lateral shifts between the two grating layers, it is shown that continuous-profile grating doublets are extremely difficult to fabricate. Achromatic grating doublets that have profiles with a constant first spatial derivative are significantly more resistant to lateral shifts between grating layers, where one design case showed a 17 times improvement in performance. Therefore, binary phase, multi-level phase, and blazed grating doublets perform significantly better than continuous phase grating doublets in the presence of a lateral shift between two grating layers. By studying the sensitivity to fabrication errors in the height of both grating layers, one grating layer height can be adjusted to maintain excellent performance over a large wavelength range if the other grating layer is fabricated incorrectly. It is shown in one design case that the performance of an achromatic Dammann grating doublet can be improved by a factor of 215 if the heights of the grating layers are chosen to minimize the performance change in the presence of fabrication errors. PMID:26368261

Feasibility evaluation of a neutron grating interferometer with an analyzer grating based on a structured scintillator

NASA Astrophysics Data System (ADS)

Kim, Youngju; Kim, Jongyul; Kim, Daeseung; Hussey, Daniel. S.; Lee, Seung Wook

2018-03-01

We introduce an analyzer grating based on a structured scintillator fabricated by a gadolinium oxysulfide powder filling method for a symmetric Talbot-Lau neutron grating interferometer. This is an alternative way to analyze the Talbot self-image of a grating interferometer without using an absorption grating to block neutrons. Since the structured scintillator analyzer grating itself generates the signal for neutron detection, we do not need an additional scintillator screen as an absorption analyzer grating. We have developed and tested an analyzer grating based on a structured scintillator in our symmetric Talbot-Lau neutron grating interferometer to produce high fidelity absorption, differential phase, and dark-field contrast images. The acquired images have been compared to results of a grating interferometer utilizing a typical absorption analyzer grating with two commercial scintillation screens. The analyzer grating based on the structured scintillator enhances interference fringe visibility and shows a great potential for economical fabrication, compact system design, and so on. We report the performance of the analyzer grating based on a structured scintillator and evaluate its feasibility for the neutron grating interferometer.

Simple Proof of Jury Test for Complex Polynomials

NASA Astrophysics Data System (ADS)

Choo, Younseok; Kim, Dongmin

Recently some attempts have been made in the literature to give simple proofs of Jury test for real polynomials. This letter presents a similar result for complex polynomials. A simple proof of Jury test for complex polynomials is provided based on the Rouché's Theorem and a single-parameter characterization of Schur stability property for complex polynomials.

Demonstration of a Rocket-Borne Fiber-Optic Measurement System: The FOVS Experiment of REXUS 15

NASA Astrophysics Data System (ADS)

Rossner, M. R.; Benes, N.; Grubler, T.; Plamauer, S.; Koch, A. W.

2015-09-01

As an in-flight experiment in the REXUS 15 programme, the “Fiber-Optic Vibration Sensing Experiment (FOVS)” aimed at the application of so-called fiber Bragg grating sensors. Fiber Bragg gratings are optical gratings inscribed into the core of an optical fiber. They allow for entirely optical measurements of temperatures, mechanical strain and of deduced quantities, such as vibration. Due to their properties - mechanical robustness, high dynamic range etc. - fiber Bragg gratings are particularly suited for withstanding the harsh environmental conditions in a rocket vehicle (very high and very low temperatures, intense vibrations, presence of flammable propellants, etc.). Measurement systems based on fiber Bragg gratings have the potential to contribute to emerging technologies in the commercial launcher segment. Particularly, large sets of measurement data can be acquired with minor mass contribution. This can be applied to techniques such as structural health monitoring, active vibration damping, and actuator monitoring, enabling lighter structures without compromising on reliability. The FOVS experiment demonstrated a fiber-optic vibration and temperature measurement system in an actual flight, and evaluated its benefits compared to conventional electrical sensing in the challenging launcher environment. As a side product, measurements regarding the environmental conditions on the REXUS platform have been acquired.

On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2003-05-01

A formula expressing the Laguerre coefficients of a general-order derivative of an infinitely differentiable function in terms of its original coefficients is proved, and a formula expressing explicitly the derivatives of Laguerre polynomials of any degree and for any order as a linear combination of suitable Laguerre polynomials is deduced. A formula for the Laguerre coefficients of the moments of one single Laguerre polynomial of certain degree is given. Formulae for the Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Laguerre coefficients are also obtained. A simple approach in order to build and solve recursively for the connection coefficients between Jacobi-Laguerre and Hermite-Laguerre polynomials is described. An explicit formula for these coefficients between Jacobi and Laguerre polynomials is given, of which the ultra-spherical polynomials of the first and second kinds and Legendre polynomials are important special cases. An analytical formula for the connection coefficients between Hermite and Laguerre polynomials is also obtained.

Birefringence Bragg Binary (3B) grating, quasi-Bragg grating and immersion gratings

NASA Astrophysics Data System (ADS)

Ebizuka, Noboru; Morita, Shin-ya; Yamagata, Yutaka; Sasaki, Minoru; Bianco, Andorea; Tanabe, Ayano; Hashimoto, Nobuyuki; Hirahara, Yasuhiro; Aoki, Wako

2014-07-01

A volume phase holographic (VPH) grating achieves high angular dispersion and very high diffraction efficiency for the first diffraction order and for S or P polarization. However the VPH grating could not achieve high diffraction efficiency for non-polarized light at a large diffraction angle because properties of diffraction efficiencies for S and P polarizations are different. Furthermore diffraction efficiency of the VPH grating extinguishes toward a higher diffraction order. A birefringence binary Bragg (3B) grating is a thick transmission grating with optically anisotropic material such as lithium niobate or liquid crystal. The 3B grating achieves diffraction efficiency up to 100% for non-polarized light by tuning of refractive indices for S and P polarizations, even in higher diffraction orders. We fabricated 3B grating with liquid crystal and evaluated the performance of the liquid crystal grating. A quasi-Bragg (QB) grating, which consists long rectangle mirrors aligned in parallel precisely such as a window shade, also achieves high diffraction efficiency toward higher orders. We fabricated QB grating by laminating of silica glass substrates and glued by pressure fusion of gold films. A quasi-Bragg immersion (QBI) grating has smooth mirror hypotenuse and reflector array inside the hypotenuse, instead of step-like grooves of a conventional immersion grating. An incident beam of the QBI grating reflects obliquely at a reflector, then reflects vertically at the mirror surface and reflects again at the same reflector. We are going to fabricate QBI gratings by laminating of mirror plates as similar to fabrication of the QB grating. We will also fabricate silicon and germanium immersion gratings with conventional step-like grooves by means of the latest diamond machining methods. We introduce characteristics and performance of these gratings.

Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

NASA Astrophysics Data System (ADS)

Chen, Zhixiang; Fu, Bin

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O *(3 n s(n)) upper bound for this problem for any polynomial represented by an arithmetic circuit of size s(n). Later, this upper bound is improved to O *(2 n ) for ΠΣΠ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for ΠΣ polynomials. On the negative side, we prove that, even for ΠΣΠ polynomials with terms of degree ≤ 2, the first problem cannot be approximated at all for any approximation factor ≥ 1, nor "weakly approximated" in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time λ-approximation algorithm for ΠΣΠ polynomials with terms of degrees no more a constant λ ≥ 2. On the inapproximability side, we give a n (1 - ɛ)/2 lower bound, for any ɛ> 0, on the approximation factor for ΠΣΠ polynomials. When the degrees of the terms in these polynomials are constrained as ≤ 2, we prove a 1.0476 lower bound, assuming Pnot=NP; and a higher 1.0604 lower bound, assuming the Unique Games Conjecture.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Electro-Optic Diffraction Grating Tuned Laser.

DTIC Science & Technology

The patent concerns an electro - optic diffraction grating tuned laser comprising a laser medium, output mirror, retro-reflective grating and an electro - optic diffraction grating beam deflector positioned between the laser medium and the reflective diffraction grating. An optional angle multiplier may be used between the electro - optic diffraction grating and the reflective grating.

[Technology Development for X-Ray Reflection for the Constellation-X Reflection Grating Spectrometer (RGS)

NASA Technical Reports Server (NTRS)

Schattenburg, Mark L.

2003-01-01

This Grant covers MIT support for the technology development of x-ray reflection gratings for the Constellation-X Reflection Grating Spectrometer (RGS). Since the start of the Grant MIT has extended its previously-developed patterning and super-smooth, blazed grating fabrication technology to ten-times smaller grating periods and ten-times larger blaze angles to demonstrate feasibility and performance in the off-plane grating geometry. In the past year we successfully developed several nanoimprint grating replication methods that achieved very high fidelity replication of master silicon gratings. Grating geometry on the nano and macro scales were faithfully replicated, demonstrating the viability of the process for manufacturing the thousands of gratings required for the RGS. We also successfully developed an improved metrology truss for holding test grating substrates during metrology. The flatness goal of grating substrates is under 500 nm. In the past, grating holders would cause non-repeatable distortion of >> 500 nm to the substrates due to friction and gravity sag. The new holder has a repeatability of under 50 nm which is adequate for the proposed RGS grating substrates.

Nodal Statistics for the Van Vleck Polynomials

NASA Astrophysics Data System (ADS)

Bourget, Alain

The Van Vleck polynomials naturally arise from the generalized Lamé equation as the polynomials of degree for which Eq. (1) has a polynomial solution of some degree k. In this paper, we compute the limiting distribution, as well as the limiting mean level spacings distribution of the zeros of any Van Vleck polynomial as N --> ∞.

Legendre modified moments for Euler's constant

NASA Astrophysics Data System (ADS)

Prévost, Marc

2008-10-01

Polynomial moments are often used for the computation of Gauss quadrature to stabilize the numerical calculation of the orthogonal polynomials, see [W. Gautschi, Computational aspects of orthogonal polynomials, in: P. Nevai (Ed.), Orthogonal Polynomials-Theory and Practice, NATO ASI Series, Series C: Mathematical and Physical Sciences, vol. 294. Kluwer, Dordrecht, 1990, pp. 181-216 [6]; W. Gautschi, On the sensitivity of orthogonal polynomials to perturbations in the moments, Numer. Math. 48(4) (1986) 369-382 [5]; W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Statist. Comput. 3(3) (1982) 289-317 [4

Intracore and extracore examination of fiber gratings with coherent detection

NASA Astrophysics Data System (ADS)

Froggatt, Mark Earl

2001-06-01

This thesis introduces several new methods of measurement to aid in the production and evaluation of Bragg gratings in optical fiber. Five measurements are described: UV fringe visualization for grating production, weak grating measurement for distributed sensing, strong grating measurement for telecommunication applications, second harmonic grating measurement for grating chirp assessment, and grating visualization using radiation diffraction from strong Bragg gratings. The weak grating measurement for distributed strain sensing is a summary of work published prior to beginning the thesis research, and is provided for background purposes. The UV fringe visualization is accomplished by using a phase mask very close to the plane of the fiber to diffract the incoming beams used to write the Bragg grating into nearly parallel alignment, leading to macroscopic fringes indicative of the phase, frequency, amplitude, and contrast of the microscopic fringes incident on the fiber. The weak grating measurement uses Optical Frequency Domain Reflectometry (OFDR) to measure the spatial distribution of the coupling strength of weak gratings. Included in the description of the OFDR technique are recent advances in the precision monitoring of the emission wavelength of tunable lasers. The precise monitoring of wavelength is critical to the functioning of OFDR. The strong grating measurement is based on a modified form of OFDR and an analysis of the problem in the time and frequency domains to produce accurate measurements of both the reflection and transmission Transfer Functions for Bragg gratings. This measurement technique is also applicable to a wide variety of optical fiber devices, and is shown to be scalable to multiple port devices. The second-harmonic measurement for grating chirp analysis is similar to the weak grating measurement, but it was done at a wavelength resonant with the second- harmonic grating in the fiber-780 nm for 1550 nm reflection gratings. The second-harmonic grating results from nonlinearities in the grating growth process and, due to the great sensitivity of OFDR, is detectable for almost all fiber gratings. The grating visualization also uses half-wavelength (780 nm) illumination of the grating through the core. This technique uses the diffraction of light into the radiation modes to make the grating in the fiber externally visible. By operating near the perpendicular radiation condition, and introducing coherent counter- propagating light, the spatial frequency and the amplitude of the grating as functions of distance along the fiber can be measured. To better understand the radiation from Bragg gratings, a technique known as the Volume Current Method (VCM) was used to derive an expression for the radiation from a Bragg grating for all of the LP fiber modes.

Fish biomarkers for environmental monitoring: An integrated model supporting enzyme activity and histopathological lesions

NASA Astrophysics Data System (ADS)

Neta, Raimunda Nonata Fortes Carvalho; Torres Junior, Audalio Rebelo

2014-10-01

We present a mathematical model describing the association between glutathione-S-transferase activity and brachial lesions in the catfish, Sciades herzbergii (Ariidae) from a polluted port. The catfish were sampled from a port known to be contaminated with heavy metals and organic compounds and from a natural reserve in São Marcos Bay, Brazil. Two biomarkers, hepatic glutathione S-transferase (GST) activity and histopathological lesions, in gills tissue were measured. The values for GST activity were modeled with the occurrence of branchial lesions by fitting a third order polynomial. Results from the mathematical model indicate that GST activity has a strong polynomial relationship with the occurrence of branchial lesions in both the wet and the dry seasons, but only at the polluted port site. The model developed in this study indicates that branchial and hepatic lesions are initiated when GST activity reaches 2.15 μmol min-1 mg protein-1. Beyond this limit, GST activity decreased to very low levels and irreversible histopathological lesions occurred. This mathematical model provides a realistic approach to analyze predictive biomarkers of environmental health status.

An Arrhenius-type viscosity function to model sintering using the Skorohod Olevsky viscous sintering model within a finite element code.

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

Ewsuk, Kevin Gregory; Arguello, Jose Guadalupe, Jr.; Reiterer, Markus W.

2006-02-01

The ease and ability to predict sintering shrinkage and densification with the Skorohod-Olevsky viscous sintering (SOVS) model within a finite-element (FE) code have been improved with the use of an Arrhenius-type viscosity function. The need for a better viscosity function was identified by evaluating SOVS model predictions made using a previously published polynomial viscosity function. Predictions made using the original, polynomial viscosity function do not accurately reflect experimentally observed sintering behavior. To more easily and better predict sintering behavior using FE simulations, a thermally activated viscosity function based on creep theory was used with the SOVS model. In comparison withmore » the polynomial viscosity function, SOVS model predictions made using the Arrhenius-type viscosity function are more representative of experimentally observed viscosity and sintering behavior. Additionally, the effects of changes in heating rate on densification can easily be predicted with the Arrhenius-type viscosity function. Another attribute of the Arrhenius-type viscosity function is that it provides the potential to link different sintering models. For example, the apparent activation energy, Q, for densification used in the construction of the master sintering curve for a low-temperature cofire ceramic dielectric has been used as the apparent activation energy for material flow in the Arrhenius-type viscosity function to predict heating rate-dependent sintering behavior using the SOVS model.« less

On multiple orthogonal polynomials for discrete Meixner measures

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

Sorokin, Vladimir N

2010-12-07

The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves. Bibliography: 9 titles.

Direct calculation of modal parameters from matrix orthogonal polynomials

NASA Astrophysics Data System (ADS)

El-Kafafy, Mahmoud; Guillaume, Patrick

2011-10-01

The object of this paper is to introduce a new technique to derive the global modal parameter (i.e. system poles) directly from estimated matrix orthogonal polynomials. This contribution generalized the results given in Rolain et al. (1994) [5] and Rolain et al. (1995) [6] for scalar orthogonal polynomials to multivariable (matrix) orthogonal polynomials for multiple input multiple output (MIMO) system. Using orthogonal polynomials improves the numerical properties of the estimation process. However, the derivation of the modal parameters from the orthogonal polynomials is in general ill-conditioned if not handled properly. The transformation of the coefficients from orthogonal polynomials basis to power polynomials basis is known to be an ill-conditioned transformation. In this paper a new approach is proposed to compute the system poles directly from the multivariable orthogonal polynomials. High order models can be used without any numerical problems. The proposed method will be compared with existing methods (Van Der Auweraer and Leuridan (1987) [4] Chen and Xu (2003) [7]). For this comparative study, simulated as well as experimental data will be used.

Continuous wavelength tunable laser source with optimum positioning of pivot axis for grating

DOEpatents

Pushkarsky, Michael; Amone, David F.

2010-06-08

A laser source (10) for generating a continuously wavelength tunable light (12) includes a gain media (16), an optical output coupler (36F), a cavity collimator (38A), a diffraction grating (30), a grating beam (54), and a beam attacher (56). The diffraction grating (30) is spaced apart from the cavity collimator (38A) and the grating (30) cooperates with the optical output coupler (36F) to define an external cavity (32). The grating (30) includes a grating face surface (42A) that is in a grating plane (42B). The beam attacher (56) retains the grating beam (54) and allows the grating beam (54) and the grating (30) to effectively pivot about a pivot axis (33) that is located approximately at an intersection of a pivot plane (50) and the grating plane (42B). As provided herein, the diffraction grating (30) can be pivoted about the unique pivot axis (33) to move the diffraction grating (30) relative to the gain media (16) to continuously tune the lasing frequency of the external cavity (32) and the wavelength of the output light (12) so that the output light (12) is mode hop free.

Transmission grating spectroscopy and the Advanced X-ray Astrophysics Facility (AXAF)

NASA Technical Reports Server (NTRS)

Schattenburg, M. L.; Canizares, C. R.; Dewey, D.; Levine, A. M.; Markert, T. H.

1988-01-01

The use of transmission gratings with grazing-incidence telescopes in celestial X-ray astrononmy is reviewed. The basic properties of transmission grating spectrometers and the use of 'phased' gratings to enhance the diffraction efficiency are outlined. The fabrication of the gratings is examined, giving special attention to the AXAF High Energy Transmission Grating. The performance of finite-period thick gratings is briefly discussed, and the performance of the transmission grating spectrometers planned for SPECTROSAT and AXAF are examined.

Deep-etched sinusoidal polarizing beam splitter grating.

PubMed

Feng, Jijun; Zhou, Changhe; Cao, Hongchao; Lv, Peng

2010-04-01

A sinusoidal-shaped fused-silica grating as a highly efficient polarizing beam splitter (PBS) is investigated based on the simplified modal method. The grating structure depends mainly on the ratio of groove depth to grating period and the ratio of incident wavelength to grating period. These ratios can be used as a guideline for the grating design at different wavelengths. A sinusoidal-groove PBS grating is designed at a wavelength of 1310 nm under Littrow mounting, and the transmitted TM and TE polarized waves are mainly diffracted into the zeroth order and the -1st order, respectively. The grating profile is optimized by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient (>95.98%) over the O-band wavelength range (1260-1360 nm) for both TE and TM polarizations. The sinusoidal grating can exhibit higher diffraction efficiency, larger extinction ratio, and less reflection loss than the rectangular-groove PBS grating. By applying wet etching technology on the rectangular grating, which was manufactured by holographic recording and inductively coupled plasma etching technology, the sinusoidal grating can be approximately fabricated. Experimental results are in agreement with theoretical values.

Off-plane x-ray reflection grating fabrication

NASA Astrophysics Data System (ADS)

Peterson, Thomas J.; DeRoo, Casey T.; Marlowe, Hannah; McEntaffer, Randall L.; Miles, Drew M.; Tutt, James H.; Schultz, Ted B.

2015-09-01

Off-plane X-ray diffraction gratings with precision groove profiles at the submicron scale will be used in next generation X-ray spectrometers. Such gratings will be used on a current NASA suborbital rocket mission, the Off-plane Grating Rocket Experiment (OGRE), and have application for future grating missions. The fabrication of these gratings does not come without challenges. High performance off-plane gratings must be fabricated with precise radial grating patterns, optically at surfaces, and specific facet angles. Such gratings can be made using a series of common micro-fabrication techniques. The resulting process is highly customizable, making it useful for a variety of different mission architectures. In this paper, we detail the fabrication method used to produce high performance off-plane gratings and report the results of a preliminary qualification test of a grating fabricated in this manner. The grating was tested in the off-plane `Littrow' configuration, for which the grating is most efficient for a given diffraction order, and found to achieve 42% relative efficiency in the blaze order with respect to all diffracted light.

Overview of diffraction gratings technologies for spaceflight satellites and ground-based telescopes

NASA Astrophysics Data System (ADS)

Cotel, A.; Liard, A.; Desserouer, F.; Pichon, P.

2017-11-01

The diffraction gratings are widely used in Space-flight satellites for spectrograph instruments or in ground-based telescopes in astronomy. The diffraction gratings are one of the key optical components of such systems and have to exhibit very high optical performances. HORIBA Jobin Yvon S.A.S. (part of HORIBA Group) is in the forefront of such gratings development for more than 40 years. During the past decades, HORIBA Jobin Yvon (HJY) has developed a unique expertise in diffraction grating design and manufacturing processes for holographic, ruled or etched gratings. We will present in this paper an overview of diffraction grating technologies especially designed for space and astronomy applications. We will firstly review the heritage of the company in this field with the space qualification of different grating types. Then, we will describe several key grating technologies developed for specific space or astronomy projects: ruled blazed low groove density plane reflection grating, high-groove density holographic toroidal and spherical grating, and finally transmission Fused Silica Etched (FSE) grism-assembled grating. We will not present the Volume Phase Holographic (VPHG) grating type which is used in Astronomy.

Overview of diffraction gratings technologies for space-flight satellites and astronomy

NASA Astrophysics Data System (ADS)

Cotel, Arnaud; Liard, Audrey; Desserouer, Frédéric; Bonnemason, Francis; Pichon, Pierre

2014-09-01

The diffraction gratings are widely used in Space-flight satellites for spectrograph instruments or in ground-based telescopes in astronomy. The diffraction gratings are one of the key optical components of such systems and have to exhibit very high optical performances. HORIBA Jobin Yvon S.A.S. (part of HORIBA Group) is in the forefront of such gratings development for more than 40 years. During the past decades, HORIBA Jobin Yvon (HJY) has developed a unique expertise in diffraction grating design and manufacturing processes for holographic, ruled or etched gratings. We will present in this paper an overview of diffraction grating technologies especially designed for space and astronomy applications. We will firstly review the heritage of the company in this field with the space qualification of different grating types. Then, we will describe several key grating technologies developed for specific space or astronomy projects: ruled blazed low groove density plane reflection grating, holographic blazed replica plane grating, high-groove density holographic toroidal and spherical grating and transmission Fused Silica Etched (FSE) grismassembled grating.

Field lens multiplexing in holographic 3D displays by using Bragg diffraction based volume gratings

NASA Astrophysics Data System (ADS)

Fütterer, G.

2016-11-01

Applications, which can profit from holographic 3D displays, are the visualization of 3D data, computer-integrated manufacturing, 3D teleconferencing and mobile infotainment. However, one problem of holographic 3D displays, which are e.g. based on space bandwidth limited reconstruction of wave segments, is to realize a small form factor. Another problem is to provide a reasonable large volume for the user placement, which means to provide an acceptable freedom of movement. Both problems should be solved without decreasing the image quality of virtual and real object points, which are generated within the 3D display volume. A diffractive optical design using thick hologram gratings, which can be referred to as Bragg diffraction based volume gratings, can provide a small form factor and high definition natural viewing experience of 3D objects. A large collimated wave can be provided by an anamorphic backlight unit. The complex valued spatial light modulator add local curvatures to the wave field he is illuminated with. The modulated wave field is focused onto to the user plane by using a volume grating based field lens. Active type liquid crystal gratings provide 1D fine tracking of approximately +/- 8° deg. Diffractive multiplex has to be implemented for each color and for a set of focus functions providing coarse tracking. Boundary conditions of the diffractive multiplexing are explained. This is done in regards to the display layout and by using the coupled wave theory (CWT). Aspects of diffractive cross talk and its suppression will be discussed including longitudinal apodized volume gratings.

Temperature Dependence of Mineral Solubility in Water. Part 3. Alkaline and Alkaline Earth Sulfates

NASA Astrophysics Data System (ADS)

Krumgalz, B. S.

2018-06-01

The databases of alkaline and alkaline earth sulfate solubilities in water at various temperatures were created using experimental data from the publications over about the last two centuries. Statistical critical evaluation of the created databases was produced since there were enough independent data sources to justify such evaluation. The reliable experimental data were adequately described by polynomial expressions over various temperature ranges. Using the Pitzer approach for ionic activity and osmotic coefficients, the thermodynamic solubility products for the discussed minerals have been calculated at various temperatures and represented by polynomial expressions.

Temperature Dependence of Mineral Solubility in Water. Part 2. Alkaline and Alkaline Earth Bromides

NASA Astrophysics Data System (ADS)

Krumgalz, B. S.

2018-03-01

Databases of alkaline and alkaline earth bromide solubilities in water at various temperatures were created using experimental data from publications over about the last two centuries. Statistical critical evaluation of the created databases was produced since there were enough independent data sources to justify such evaluation. The reliable experimental data were adequately described by polynomial expressions over various temperature ranges. Using the Pitzer approach for ionic activity and osmotic coefficients, the thermodynamic solubility products for the discussed bromide minerals have been calculated at various temperature intervals and also represented by polynomial expressions.

Fabrication of high edge-definition steel-tape gratings for optical encoders.

PubMed

Ye, Guoyong; Liu, Hongzhong; Yan, Jiawei; Ban, Yaowen; Fan, Shanjin; Shi, Yongsheng; Yin, Lei

2017-10-01

High edge definition of a scale grating is the basic prerequisite for high measurement accuracy of optical encoders. This paper presents a novel fabrication method of steel tape gratings using graphene oxide nanoparticles as anti-reflective grating strips. Roll-to-roll nanoimprint lithography is adopted to manufacture the steel tape with hydrophobic and hydrophilic pattern arrays. Self-assembly technology is employed to obtain anti-reflective grating strips by depositing the graphene oxide nanoparticles on hydrophobic regions. A thin SiO 2 coating is deposited on the grating to protect the grating strips. Experimental results confirm that the proposed fabrication process enables a higher edge definition in making steel-tape gratings, and the new steel tape gratings offer better performance than conventional gratings.

Fabrication of high edge-definition steel-tape gratings for optical encoders

NASA Astrophysics Data System (ADS)

Ye, Guoyong; Liu, Hongzhong; Yan, Jiawei; Ban, Yaowen; Fan, Shanjin; Shi, Yongsheng; Yin, Lei

2017-10-01

High edge definition of a scale grating is the basic prerequisite for high measurement accuracy of optical encoders. This paper presents a novel fabrication method of steel tape gratings using graphene oxide nanoparticles as anti-reflective grating strips. Roll-to-roll nanoimprint lithography is adopted to manufacture the steel tape with hydrophobic and hydrophilic pattern arrays. Self-assembly technology is employed to obtain anti-reflective grating strips by depositing the graphene oxide nanoparticles on hydrophobic regions. A thin SiO2 coating is deposited on the grating to protect the grating strips. Experimental results confirm that the proposed fabrication process enables a higher edge definition in making steel-tape gratings, and the new steel tape gratings offer better performance than conventional gratings.

Independence polynomial and matching polynomial of the Koch network

NASA Astrophysics Data System (ADS)

Liao, Yunhua; Xie, Xiaoliang

2015-11-01

The lattice gas model and the monomer-dimer model are two classical models in statistical mechanics. It is well known that the partition functions of these two models are associated with the independence polynomial and the matching polynomial in graph theory, respectively. Both polynomials have been shown to belong to the “#P-complete” class, which indicate the problems are computationally “intractable”. We consider these two polynomials of the Koch networks which are scale-free with small-world effects. Explicit recurrences are derived, and explicit formulae are presented for the number of independent sets of a certain type.

Colorimetric characterization models based on colorimetric characteristics evaluation for active matrix organic light emitting diode panels.

PubMed

Gong, Rui; Xu, Haisong; Tong, Qingfen

2012-10-20

The colorimetric characterization of active matrix organic light emitting diode (AMOLED) panels suffers from their poor channel independence. Based on the colorimetric characteristics evaluation of channel independence and chromaticity constancy, an accurate colorimetric characterization method, namely, the polynomial compensation model (PC model) considering channel interactions was proposed for AMOLED panels. In this model, polynomial expressions are employed to calculate the relationship between the prediction errors of XYZ tristimulus values and the digital inputs to compensate the XYZ prediction errors of the conventional piecewise linear interpolation assuming the variable chromaticity coordinates (PLVC) model. The experimental results indicated that the proposed PC model outperformed other typical characterization models for the two tested AMOLED smart-phone displays and for the professional liquid crystal display monitor as well.

The influence of grating shape formation fluctuation on DFB laser diode threshold condition

NASA Astrophysics Data System (ADS)

Bao, Shiwei; Song, Qinghai; Xie, Chunmei

2018-03-01

Not only the grating material refractive index itself but also the Bragg grating physical shape formation affects the coupling strength greatly. The Bragg grating shape includes three factors, namely grating depth, duty ratio and grating angle. During the lithography and wet etching process, there always will be some fluctuation between the target and real grating shape formation after fabrication process. This grating shape fluctuation will affect the DFB coupling coefficient κ , and then consequently threshold current and corresponding wavelength. This paper studied the grating shape formation fluctuation influence to improve the DFB fabrication yield. A truncated normal random distribution fluctuation is considered in this paper. The simulation results conclude that it is better to choose relative thicker grating depth with lower refractive index to obtain a better fabrication tolerance, while not quite necessary to spend too much effort on improving lithography and wet etching process to get a precisely grating duty ratio and grating angle.

The influence of grating shape formation fluctuation on DFB laser diode threshold condition

NASA Astrophysics Data System (ADS)

Bao, Shiwei; Song, Qinghai; Xie, Chunmei

2018-06-01

Not only the grating material refractive index itself but also the Bragg grating physical shape formation affects the coupling strength greatly. The Bragg grating shape includes three factors, namely grating depth, duty ratio and grating angle. During the lithography and wet etching process, there always will be some fluctuation between the target and real grating shape formation after fabrication process. This grating shape fluctuation will affect the DFB coupling coefficient κ, and then consequently threshold current and corresponding wavelength. This paper studied the grating shape formation fluctuation influence to improve the DFB fabrication yield. A truncated normal random distribution fluctuation is considered in this paper. The simulation results conclude that it is better to choose relative thicker grating depth with lower refractive index to obtain a better fabrication tolerance, while not quite necessary to spend too much effort on improving lithography and wet etching process to get a precisely grating duty ratio and grating angle.

Learning Activity Package, Algebra.

ERIC Educational Resources Information Center

Evans, Diane

A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…

A model to environmental monitoring based on glutathione-S-transferase activity and branchial lesions in catfish

NASA Astrophysics Data System (ADS)

Neta, Raimunda Nonata Fortes Carvalho; Torres, Audalio Rebelo

2017-11-01

In this work, we validate the glutathione-S-transferase and branchial lesions as biomarkers in catfish Sciades herzbergii to obtain a predictive model of the environmental impact effects in a harbor of Brazil. The catfish were sampled from a port known to be contaminated with heavy metals and organic compounds and from a natural reserve in São Marcos Bay, Maranhão. Two biomarkers, hepatic glutathione S-transferase (GST) activity and branchial lesions were analyzed. The values for GST activity were modeled with the occurrence of branchial lesions by fitting a third order polynomial. Results from the mathematical model indicate that GST activity has a strong polynomial relationship with the occurrence of branchial lesions in both the wet and the dry seasons, but only at the polluted port site. Our mathematic model indicates that when the GST ceases to act, serious branchial lesions are observed in the catfish of the contaminated port area.

Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

NASA Astrophysics Data System (ADS)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2008-10-01

We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e-[phi](x), giving a unified treatment for the so-called Freud (i.e., when [phi] has polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.

A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

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

Vignat, C.; Lamberti, P. W.

2009-10-15

Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positivemore » curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.« less

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

NASA Astrophysics Data System (ADS)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Effective grating theory for resonance domain surface-relief diffraction gratings.

PubMed

Golub, Michael A; Friesem, Asher A

2005-06-01

An effective grating model, which generalizes effective-medium theory to the case of resonance domain surface-relief gratings, is presented. In addition to the zero order, it takes into account the first diffraction order, which obeys the Bragg condition. Modeling the surface-relief grating as an effective grating with two diffraction orders provides closed-form analytical relationships between efficiency and grating parameters. The aspect ratio, the grating period, and the required incidence angle that would lead to high diffraction efficiencies are predicted for TE and TM polarization and verified by rigorous numerical calculations.

Hadamard Factorization of Stable Polynomials

NASA Astrophysics Data System (ADS)

Loredo-Villalobos, Carlos Arturo; Aguirre-Hernández, Baltazar

2011-11-01

The stable (Hurwitz) polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p,q ∈ R[x]:p(x) = anxn+an-1xn-1+...+a1x+a0q(x) = bmx m+bm-1xm-1+...+b1x+b0the Hadamard product (p × q) is defined as (p×q)(x) = akbkxk+ak-1bk-1xk-1+...+a1b1x+a0b0where k = min(m,n). Some results (see [16]) shows that if p,q ∈R[x] are stable polynomials then (p×q) is stable, also, i.e. the Hadamard product is closed; however, the reciprocal is not always true, that is, not all stable polynomial has a factorization into two stable polynomials the same degree n, if n> 4 (see [15]).In this work we will give some conditions to Hadamard factorization existence for stable polynomials.

On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2004-01-01

Formulae expressing explicitly the Jacobi coefficients of a general-order derivative (integral) of an infinitely differentiable function in terms of its original expansion coefficients, and formulae for the derivatives (integrals) of Jacobi polynomials in terms of Jacobi polynomials themselves are stated. A formula for the Jacobi coefficients of the moments of one single Jacobi polynomial of certain degree is proved. Another formula for the Jacobi coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its original expanded coefficients is also given. A simple approach in order to construct and solve recursively for the connection coefficients between Jacobi-Jacobi polynomials is described. Explicit formulae for these coefficients between ultraspherical and Jacobi polynomials are deduced, of which the Chebyshev polynomials of the first and second kinds and Legendre polynomials are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Jacobi and Hermite-Jacobi are developed.

Grating scattering BRDF and imaging performances: A test survey performed in the frame of the flex mission

NASA Astrophysics Data System (ADS)

Harnisch, Bernd; Deep, Atul; Vink, Ramon; Coatantiec, Claude

2017-11-01

Key components in optical spectrometers are the gratings. Their influence on the overall infield straylight of the spectrometer depends not only on the technology used for grating fabrication but also on the potential existence of ghost images caused by irregularities of the grating constant. For the straylight analysis of spectrometer no general Bidirectional Reflectance Distribution Function (BRDF) model of gratings exist, as it does for optically smooth surfaces. These models are needed for the determination of spectrometer straylight background and for the calculation of spectrometer out of band rejection performances. Within the frame of the Fluorescence Earth Explorer mission (FLEX), gratings manufactured using different technologies have been investigated in terms of straylight background and imaging performance in the used diffraction order. The gratings which have been investigated cover a lithographically written grating, a volume Bragg grating, two holographic gratings and an off-the-shelf ruled grating. In this paper we present a survey of the measured bidirectional reflectance/transmittance distribution function and the determination of an equivalent surface micro-roughness of the gratings, describing the scattering of the grating around the diffraction order. This is specifically needed for the straylight modeling of the spectrometer.

Monolithic integrated optic fiber Bragg grating sensor interrogator

NASA Astrophysics Data System (ADS)

Mendoza, Edgar A.; Esterkin, Yan; Kempen, Cornelia; Sun, Songjian

2010-04-01

Fiber Bragg gratings (FBGs) are a mature sensing technology that has gained rapid acceptance in civil, aerospace, chemical and petrochemical, medicine, aviation and automotive industries. Fiber Bragg grating sensors can be use for a variety of measurements including strain, stress, vibration, acoustics, acceleration, pressure, temperature, moisture, and corrosion distributed at multiple locations within the structure using a single fiber element. The most prominent advantages of FBGs are: small size and light weight, multiple FBG transducers on a single fiber, and immunity to radio frequency interference. A major disadvantage of FBG technology is that conventional state-of-the-art fiber Bragg grating interrogation systems are typically bulky, heavy, and costly bench top instruments that are assembled from off-the-shelf fiber optic and optical components integrated with a signal electronics board into an instrument console. Based on the need for a compact FBG interrogation system, this paper describes recent progress towards the development of a miniature fiber Bragg grating sensor interrogator (FBG-TransceiverTM) system based on multi-channel monolithic integrated optic sensor microchip technology. The integrated optic microchip technology enables the monolithic integration of all of the functionalities, both passive and active, of conventional bench top FBG sensor interrogators systems, packaged in a miniaturized, low power operation, 2-cm x 5-cm small form factor (SFF) package suitable for the long-term structural health monitoring in applications where size, weight, and power are critical for operation.

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Percolation critical polynomial as a graph invariant

DOE PAGES

Scullard, Christian R.

2012-10-18

Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0; 1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer withmore » increasing subgraph size. In this paper, I show how the critical polynomial can be viewed as a graph invariant like the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p c = 0:52440572:::, which differs from the numerical value, p c = 0:52440503(5), by only 6:9 X 10 -7.« less

On Certain Wronskians of Multiple Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Zhang, Lun; Filipuk, Galina

2014-11-01

We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes classical results for orthogonal polynomials due to Karlin and Szegő. There are two applications of our results. The first application arises from the observation that the m-th moment of the average characteristic polynomials for multiple orthogonal polynomial ensembles can be expressed as a Wronskian of the type II multiple orthogonal polynomials. Hence, it is straightforward to obtain the distinct behavior of the moments for odd and even m in a special multiple orthogonal ensemble - the AT ensemble. As the second application, we derive some Turán type inequalities for m! ultiple Hermite and multiple Laguerre polynomials (of two kinds). Finally, we study numerically the geometric configuration of zeros for the Wronskians of these multiple orthogonal polynomials. We observe that the zeros have regular configurations in the complex plane, which might be of independent interest.

A novel method for inverse fiber Bragg grating structure design

NASA Astrophysics Data System (ADS)

Yin, Yu-zhe; Chen, Xiang-fei; Dai, Yi-tang; Xie, Shi-zhong

2003-12-01

A novel grating inverse design method is proposed in this paper, which is direct in physical meaning and easy to accomplish. The key point of the method is design and implement desired spectra response in grating strength modulation domain, while not in grating period chirp domain. Simulated results are in good coincidence with design target. By transforming grating period chirp to grating strength modulation, a novel grating with opposite dispersion characters is proposed.

Nature-inspired optimization of quasicrystalline arrays and all-dielectric optical filters and metamaterials

NASA Astrophysics Data System (ADS)

Namin, Frank Farhad A.

Quasicrystalline solids were first observed in nature in 1980s. Their lattice geometry is devoid of translational symmetry; however it possesses long-range order as well as certain orders of rotational symmetry forbidden by translational symmetry. Mathematically, such lattices are related to aperiodic tilings. Since their discovery there has been great interest in utilizing aperiodic geometries for a wide variety of electromagnetic (EM) and optical applications. The first thrust of this dissertation addresses applications of quasicrystalline geometries for wideband antenna arrays and plasmonic nano-spherical arrays. The first application considered is the design of suitable antenna arrays for micro-UAV (unmanned aerial vehicle) swarms based on perturbation of certain types of aperiodic tilings. Due to safety reasons and to avoid possible collision between micro-UAVs it is desirable to keep the minimum separation distance between the elements several wavelengths. As a result typical periodic planar arrays are not suitable, since for periodic arrays increasing the minimum element spacing beyond one wavelength will lead to the appearance of grating lobes in the radiation pattern. It will be shown that using this method antenna arrays with very wide bandwidths and low sidelobe levels can be designed. It will also be shown that in conjunction with a phase compensation method these arrays show a large degree of versatility to positional noise. Next aperiodic aggregates of gold nano-spheres are studied. Since traditional unit cell approaches cannot be used for aperiodic geometries, we start be developing new analytical tools for aperiodic arrays. A modified version of generalized Mie theory (GMT) is developed which defines scattering coefficients for aperiodic spherical arrays. Next two specific properties of quasicrystalline gold nano-spherical arrays are considered. The optical response of these arrays can be explained in terms of the grating response of the array (photonic resonance) and the plasmonic response of the spheres (plasmonic resonance). In particular the couplings between the photonic and plasmonic modes are studied. In periodic arrays this coupling leads to the formation of a so called photonic-plasmonic hybrid mode. The formation of hybrid modes is studied in quasicrystalline arrays. Quasicrystalline structures in essence possess several periodicities which in some cases can lead to the formation of multiple hybrid modes with wider bandwidths. It is also demonstrated that the performance of these arrays can be further enhanced by employing a perturbation method. The second property considered is local field enhancements in quasicrystalline arrays of gold nanospheres. It will be shown that despite a considerably smaller filling factor quasicrystalline arrays generate larger local field enhancements which can be even further enhanced by optimally placing perturbing spheres within the prototiles that comprise the aperiodic arrays. The second thrust of research in this dissertation focuses on designing all-dielectric filters and metamaterial coatings for the optical range. In higher frequencies metals tend to have a high loss and thus they are not suitable for many applications. Hence dielectrics are used for applications in optical frequencies. In particular we focus on designing two types of structures. First a near-perfect optical mirror is designed. The design is based on optimizing a subwavelength periodic dielectric grating to obtain appropriate effective parameters that will satisfy the desired perfect mirror condition. Second, a broadband anti-reflective all-dielectric grating with wide field of view is designed. The second design is based on a new computationally efficient genetic algorithm (GA) optimization method which shapes the sidewalls of the grating based on optimizing the roots of polynomial functions.

Multilayer diffraction grating

DOEpatents

Barbee, T.W. Jr.

1990-04-10

This invention is for a reflection diffraction grating that functions at X-ray to VUV wavelengths and at normal angles of incidence. The novel grating is comprised of a laminar grating of period D with flat-topped grating bars. A multiplicity of layered synthetic microstructures, of period d and comprised of alternating flat layers of two different materials, are disposed on the tops of the grating bars of the laminar grating. In another embodiment of the grating, a second multiplicity of layered synthetic microstructures are also disposed on the flat faces, of the base of the grating, between the bars. D is in the approximate range from 3,000 to 50,000 Angstroms, but d is in the approximate range from 10 to 400 Angstroms. The laminar grating and the layered microstructures cooperatively interact to provide many novel and beneficial instrumentational advantages. 2 figs.

Multilayer diffraction grating

DOEpatents

Barbee, Jr., Troy W.

1990-01-01

This invention is for a reflection diffraction grating that functions at X-ray to VUV wavelengths and at normal angles of incidence. The novel grating is comprised of a laminar grating of period D with flat-topped grating bars. A multiplicity of layered synthetic microstructures, of period d and comprised of alternating flat layers of two different materials, are disposed on the tops of the grating bars of the laminar grating. In another embodiment of the grating, a second multiplicity of layered synthetic microstructures are also disposed on the flat faces, of the base of the grating, between the bars. D is in the approximate range from 3,000 to 50,000 Angstroms, but d is in the approximate range from 10 to 400 Angstroms. The laminar grating and the layered microstructures cooperatively interact to provide many novel and beneficial instrumentational advantages.

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

Lottes, Steven A.; Bojanowski, Cezary

Resurfacing of urban roads with concurrent repairs and replacement of sections of curb and sidewalk may require pedestrian ramps that are compliant with the American Disabilities Act (ADA), and when street drains are in close proximity to the walkway, ADA compliant street grates may also be required. The Minnesota Department of Transportation ADA Operations Unit identified a foundry with an available grate that meets ADA requirements. Argonne National Laboratory’s Transportation Research and Analysis Computing Center used full scale three dimensional computational fluid dynamics to determine the performance of the ADA compliant grate and compared it to that of a standardmore » vane grate. Analysis of a parametric set of cases was carried out, including variation in longitudinal, gutter, and cross street slopes and the water spread from the curb. The performance of the grates was characterized by the fraction of the total volume flow approaching the grate from the upstream that was captured by the grate and diverted into the catch basin. The fraction of the total flow entering over the grate from the side and the fraction of flow directly over a grate diverted into the catch basin were also quantities of interest that aid in understanding the differences in performance of the grates. The ADA compliant grate performance lagged that of the vane grate, increasingly so as upstream Reynolds number increased. The major factor leading to the performance difference between the two grates was the fraction of flow directly over the grates that is captured by the grates.« less

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

How calibration and reference spectra affect the accuracy of absolute soft X-ray solar irradiance measured by the SDO/EVE/ESP during high solar activity

NASA Astrophysics Data System (ADS)

Didkovsky, Leonid; Wieman, Seth; Woods, Thomas

2016-10-01

The Extreme ultraviolet Spectrophotometer (ESP), one of the channels of SDO's Extreme ultraviolet Variability Experiment (EVE), measures solar irradiance in several EUV and soft x-ray (SXR) bands isolated using thin-film filters and a transmission diffraction grating, and includes a quad-diode detector positioned at the grating zeroth-order to observe in a wavelength band from about 0.1 to 7.0 nm. The quad diode signal also includes some contribution from shorter wavelength in the grating's first-order and the ratio of zeroth-order to first-order signal depends on both source geometry, and spectral distribution. For example, radiometric calibration of the ESP zeroth-order at the NIST SURF BL-2 with a near-parallel beam provides a different zeroth-to-first-order ratio than modeled for solar observations. The relative influence of "uncalibrated" first-order irradiance during solar observations is a function of the solar spectral irradiance and the locations of large Active Regions or solar flares. We discuss how the "uncalibrated" first-order "solar" component and the use of variable solar reference spectra affect determination of absolute SXR irradiance which currently may be significantly overestimated during high solar activity.

Electrically-programmable diffraction grating

DOEpatents

Ricco, Antonio J.; Butler, Michael A.; Sinclair, Michael B.; Senturia, Stephen D.

1998-01-01

An electrically-programmable diffraction grating. The programmable grating includes a substrate having a plurality of electrodes formed thereon and a moveable grating element above each of the electrodes. The grating elements are electrostatically programmable to form a diffraction grating for diffracting an incident beam of light as it is reflected from the upper surfaces of the grating elements. The programmable diffraction grating, formed by a micromachining process, has applications for optical information processing (e.g. optical correlators and computers), for multiplexing and demultiplexing a plurality of light beams of different wavelengths (e.g. for optical fiber communications), and for forming spectrometers (e.g. correlation and scanning spectrometers).

Explicit error bounds for the α-quasi-periodic Helmholtz problem.

PubMed

Lord, Natacha H; Mulholland, Anthony J

2013-10-01

This paper considers a finite element approach to modeling electromagnetic waves in a periodic diffraction grating. In particular, an a priori error estimate associated with the α-quasi-periodic transformation is derived. This involves the solution of the associated Helmholtz problem being written as a product of e(iαx) and an unknown function called the α-quasi-periodic solution. To begin with, the well-posedness of the continuous problem is examined using a variational formulation. The problem is then discretized, and a rigorous a priori error estimate, which guarantees the uniqueness of this approximate solution, is derived. In previous studies, the continuity of the Dirichlet-to-Neumann map has simply been assumed and the dependency of the regularity constant on the system parameters, such as the wavenumber, has not been shown. To address this deficiency, in this paper an explicit dependence on the wavenumber and the degree of the polynomial basis in the a priori error estimate is obtained. Since the finite element method is well known for dealing with any geometries, comparison of numerical results obtained using the α-quasi-periodic transformation with a lattice sum technique is then presented.

Proof of Monogamy of non-local correlations in three and four qubit states

NASA Astrophysics Data System (ADS)

Sharma, Santosh Shelly; Sharma, Naresh Kumar

2015-03-01

Recently, we used the process of selective construction of invariants to obtain physically meaningful polynomial invariants for three and four qubit pure states. In this article, we report the exact relations between the concurrence of a two qubit reduced state and corresponding three or four qubit pure state invariants. Firstly, we obtain an analytical expression for concurrence of a given mixed state of two qubits in terms of determinants of negativity fonts in the three or four qubit pure state. For three qubits, a comparison with three tangle and squared negativity expressed in terms of determinants of negativity fonts leads to three relations. These three conditions satisfied by the two-way and three-way correlations sum together and lead to well known CKW inequality. When a qubit pair is part of a four qubit pure state, it may be entangled to the rest of the system through two-way, three-way and four-way correlations. Monogamy equalities, satisfied by two-way, three-way and four-way non-local quantum correlatios are presented for states belonging to classes of four qubit pure states with distinct entanglement types. We gratefully acknowledge financial support from CNPq and Capes Brazil.

Exploiting structure: Introduction and motivation

NASA Technical Reports Server (NTRS)

Xu, Zhong Ling

1993-01-01

Research activities performed during the period of 29 June 1993 through 31 Aug. 1993 are summarized. The Robust Stability of Systems where transfer function or characteristic polynomial are multilinear affine functions of parameters of interest in two directions, Algorithmic and Theoretical, was developed. In the algorithmic direction, a new approach that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty is found. This technique is called 'Stability by linear process.' In fact, the 'Stability by linear process' described gives an algorithm. In analysis, we obtained a robustness criterion for the family of polynomials with coefficients of multilinear affine function in the coefficient space and obtained the result for the robust stability of diamond families of polynomials with complex coefficients also. We obtained the limited results for SPR design and we provide a framework for solving ACS. Finally, copies of the outline of our results are provided in the appendix. Also, there is an administration issue in the appendix.

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

NASA Astrophysics Data System (ADS)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

The Gibbs Phenomenon for Series of Orthogonal Polynomials

ERIC Educational Resources Information Center

Fay, T. H.; Kloppers, P. Hendrik

2006-01-01

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

Determinants with orthogonal polynomial entries

NASA Astrophysics Data System (ADS)

Ismail, Mourad E. H.

2005-06-01

We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determinants formed by the orthogonal polynomials. We also study the Hankel determinants which start with pn on the top left-hand corner. As examples we evaluate the Hankel determinants whose entries are q-ultraspherical or Al-Salam-Chihara polynomials.

Sensitivity analysis and optimization method for the fabrication of one-dimensional beam-splitting phase gratings

PubMed Central

Pacheco, Shaun; Brand, Jonathan F.; Zaverton, Melissa; Milster, Tom; Liang, Rongguang

2015-01-01

A method to design one-dimensional beam-spitting phase gratings with low sensitivity to fabrication errors is described. The method optimizes the phase function of a grating by minimizing the integrated variance of the energy of each output beam over a range of fabrication errors. Numerical results for three 1x9 beam splitting phase gratings are given. Two optimized gratings with low sensitivity to fabrication errors were compared with a grating designed for optimal efficiency. These three gratings were fabricated using gray-scale photolithography. The standard deviation of the 9 outgoing beam energies in the optimized gratings were 2.3 and 3.4 times lower than the optimal efficiency grating. PMID:25969268

Novel diffraction gratings for next generation spectrographs with high spectral dispersion

NASA Astrophysics Data System (ADS)

Ebizuka, N.; Okamoto, T.; Hosobata, T.; Yamagata, Y.; Sasaki, M.; Uomoto, M.; Shimatsu, T.; Sato, S.; Hashimoto, N.; Tanaka, I.; Hattori, T.; Ozaki, S.; Aoki, W.

2016-07-01

As a transmission grating, a surface-relief (SR) grating with sawtooth shaped ridges and volume phase holographic (VPH) grating are widely used for instruments of astronomical observations. However the SR grating is difficult to achieve high diffraction efficiency at high angular dispersion, and the VPH grating has low diffraction efficiency in high diffraction orders. We propose novel gratings that solve these problems. We introduce the hybrid grism which combines a high refractive index prism with a replicated transmission grating, which has sawtooth shaped ridges of an acute apex angle. The birefringence VPH (B-VPH) grating which contains an anisotropic medium, such as a liquid crystal, achieves diffraction efficiency up to 100% at the first diffraction order for natural polarization and for circular polarization. The quasi-Bragg (QB) grating which consists of long rectangular mirrors aligned in parallel precisely, like a window blind, achieves diffraction efficiency of 60% or more in higher than the 4th diffraction order. The volume binary (VB) grating with narrow grooves also achieves diffraction efficiency of 60% or more in higher than the 6th diffraction order. The reflector facet transmission (RFT) grating which is a SR grating with sawtooth shaped ridges of an acute apex angle achieves diffraction efficiency up to 80% in higher than the 4th diffraction order.

From sequences to polynomials and back, via operator orderings

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

Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu

2013-12-15

Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

Demonstration of coherent addition of multiple gratings for high-energy chirped-pulse-amplified lasers.

PubMed

Kessler, Terrance J; Bunkenburg, Joachim; Huang, Hu; Kozlov, Alexei; Meyerhofer, David D

2004-03-15

Petawatt solid-state lasers require meter-sized gratings to reach multiple-kilojoule energy levels without laser-induced damage. As an alternative to large single gratings, we demonstrate that smaller, coherently added (tiled) gratings can be used for subpicosecond-pulse compression. A Fourier-transform-limited, 650-fs chirped-pulse-amplified laser pulse is maintained by replacing a single compression grating with a tiled-grating assembly. Grating tiling provides a means to scale the energy and irradiance of short-pulse lasers.

The characteristics of grating structure in magnetic field measurements based on polarization properties of fiber gratings

NASA Astrophysics Data System (ADS)

Su, Yang; Peng, Hui; Feng, Kui; Li, Yu-quan

2009-11-01

In this paper the characteristics of grating structure in magnetic field measurements based on differential group delay of fiber gratings are analyzed. Theoretical simulations are realized using the coupled-mode theory and transfer matrix method. The effects of grating parameters of uniform Bragg grating on measurement range and sensitivity are analyzed. The impacts of chirped, phase-shifted and apodized gratings on DGD peak values are also monitored. FBG transmitted spectrums and DGD spectrums are recorded by means of an optical vector analyzer (OVA). Both the simulations and experiments demonstrate that the phase-shifted gratings can obviously improve the sensitivity.

Geometrical optics modeling of the grating-slit test.

PubMed

Liang, Chao-Wen; Sasian, Jose

2007-02-19

A novel optical testing method termed the grating-slit test is discussed. This test uses a grating and a slit, as in the Ronchi test, but the grating-slit test is different in that the grating is used as the incoherent illuminating object instead of the spatial filter. The slit is located at the plane of the image of a sinusoidal intensity grating. An insightful geometrical-optics model for the grating-slit test is presented and the fringe contrast ratio with respect to the slit width and object-grating period is obtained. The concept of spatial bucket integration is used to obtain the fringe contrast ratio.

Electrically-programmable diffraction grating

DOEpatents

Ricco, A.J.; Butler, M.A.; Sinclair, M.B.; Senturia, S.D.

1998-05-26

An electrically-programmable diffraction grating is disclosed. The programmable grating includes a substrate having a plurality of electrodes formed thereon and a moveable grating element above each of the electrodes. The grating elements are electrostatically programmable to form a diffraction grating for diffracting an incident beam of light as it is reflected from the upper surfaces of the grating elements. The programmable diffraction grating, formed by a micromachining process, has applications for optical information processing (e.g. optical correlators and computers), for multiplexing and demultiplexing a plurality of light beams of different wavelengths (e.g. for optical fiber communications), and for forming spectrometers (e.g. correlation and scanning spectrometers). 14 figs.

Surface normal coupling to multiple-slot and cover-slotted silicon nanocrystalline waveguides and ring resonators

NASA Astrophysics Data System (ADS)

Covey, John; Chen, Ray T.

2014-03-01

Grating couplers are ideal for coupling into the tightly confined propagation modes of semiconductor waveguides. In addition, nonlinear optics has benefited from the sub-diffraction limit confinement of horizontal slot waveguides. By combining these two advancements, slot-based nonlinear optics with mode areas less than 0.02 μm2 can become as routine as twisting fiber connectors together. Surface normal fiber alignment to a chip is also highly desirable from time, cost, and manufacturing considerations. To meet these considerable design challenges, a custom genetic algorithm is created which, starting from purely random designs, creates a unique four stage grating coupler for two novel horizontal slot waveguide platforms. For horizontal multiple-slot waveguides filled with silicon nanocrystal, a theoretical fiber-towaveguide coupling efficiency of 68% is obtained. For thin silicon waveguides clad with optically active silicon nanocrystal, known as cover-slot waveguides, a theoretical fiber-to-waveguide coupling efficiency of 47% is obtained, and 1 dB and 3 dB theoretical bandwidths of 70 nm and 150 nm are obtained, respectively. Both waveguide platforms are fabricated from scratch, and their respective on-chip grating couplers are experimentally measured from a standard single mode fiber array that is mounted surface normally. The horizontal multiple-slot grating coupler achieved an experimental 60% coupling efficiency, and the horizontal cover-slot grating coupler achieved an experimental 38.7% coupling efficiency, with an extrapolated 1 dB bandwidth of 66 nm. This report demonstrates the promise of genetic algorithm-based design by reducing to practice the first large bandwidth vertical grating coupler to a novel silicon nanocrystal horizontal cover-slot waveguide.

Extending Romanovski polynomials in quantum mechanics

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

Quesne, C.

2013-12-15

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties ofmore » second-order differential equations of Schrödinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.« less

Polynomial solutions of the Monge-Ampère equation

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

Aminov, Yu A

2014-11-30

The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction ofmore » such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.« less

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

Multiple zeros of polynomials

NASA Technical Reports Server (NTRS)

Wood, C. A.

1974-01-01

For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.

Spherical grating based x-ray Talbot interferometry.

PubMed

Cong, Wenxiang; Xi, Yan; Wang, Ge

2015-11-01

Grating interferometry is a state-of-the-art x-ray imaging approach, which can acquire information on x-ray attenuation, phase shift, and small-angle scattering simultaneously. Phase-contrast imaging and dark-field imaging are very sensitive to microstructural variation and offers superior contrast resolution for biological soft tissues. However, a common x-ray tube is a point-like source. As a result, the popular planar grating imaging configuration seriously restricts the flux of photons and decreases the visibility of signals, yielding a limited field of view. The purpose of this study is to extend the planar x-ray grating imaging theory and methods to a spherical grating scheme for a wider range of preclinical and clinical applications. A spherical grating matches the wave front of a point x-ray source very well, allowing the perpendicular incidence of x-rays on the grating to achieve a higher visibility over a larger field of view than the planer grating counterpart. A theoretical analysis of the Talbot effect for spherical grating imaging is proposed to establish a basic foundation for x-ray spherical gratings interferometry. An efficient method of spherical grating imaging is also presented to extract attenuation, differential phase, and dark-field images in the x-ray spherical grating interferometer. Talbot self-imaging with spherical gratings is analyzed based on the Rayleigh-Sommerfeld diffraction formula, featuring a periodic angular distribution in a polar coordinate system. The Talbot distance is derived to reveal the Talbot self-imaging pattern. Numerical simulation results show the self-imaging phenomenon of a spherical grating interferometer, which is in agreement with the theoretical prediction. X-ray Talbot interferometry with spherical gratings has a significant practical promise. Relative to planar grating imaging, spherical grating based x-ray Talbot interferometry has a larger field of view and improves both signal visibility and dose utilization for pre-clinical and clinical applications.

Spherical grating based x-ray Talbot interferometry

PubMed Central

Cong, Wenxiang; Xi, Yan; Wang, Ge

2015-01-01

Purpose: Grating interferometry is a state-of-the-art x-ray imaging approach, which can acquire information on x-ray attenuation, phase shift, and small-angle scattering simultaneously. Phase-contrast imaging and dark-field imaging are very sensitive to microstructural variation and offers superior contrast resolution for biological soft tissues. However, a common x-ray tube is a point-like source. As a result, the popular planar grating imaging configuration seriously restricts the flux of photons and decreases the visibility of signals, yielding a limited field of view. The purpose of this study is to extend the planar x-ray grating imaging theory and methods to a spherical grating scheme for a wider range of preclinical and clinical applications. Methods: A spherical grating matches the wave front of a point x-ray source very well, allowing the perpendicular incidence of x-rays on the grating to achieve a higher visibility over a larger field of view than the planer grating counterpart. A theoretical analysis of the Talbot effect for spherical grating imaging is proposed to establish a basic foundation for x-ray spherical gratings interferometry. An efficient method of spherical grating imaging is also presented to extract attenuation, differential phase, and dark-field images in the x-ray spherical grating interferometer. Results: Talbot self-imaging with spherical gratings is analyzed based on the Rayleigh–Sommerfeld diffraction formula, featuring a periodic angular distribution in a polar coordinate system. The Talbot distance is derived to reveal the Talbot self-imaging pattern. Numerical simulation results show the self-imaging phenomenon of a spherical grating interferometer, which is in agreement with the theoretical prediction. Conclusions: X-ray Talbot interferometry with spherical gratings has a significant practical promise. Relative to planar grating imaging, spherical grating based x-ray Talbot interferometry has a larger field of view and improves both signal visibility and dose utilization for pre-clinical and clinical applications. PMID:26520741

Spherical grating based x-ray Talbot interferometry

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

Cong, Wenxiang, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu; Xi, Yan, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu; Wang, Ge, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu

2015-11-15

Purpose: Grating interferometry is a state-of-the-art x-ray imaging approach, which can acquire information on x-ray attenuation, phase shift, and small-angle scattering simultaneously. Phase-contrast imaging and dark-field imaging are very sensitive to microstructural variation and offers superior contrast resolution for biological soft tissues. However, a common x-ray tube is a point-like source. As a result, the popular planar grating imaging configuration seriously restricts the flux of photons and decreases the visibility of signals, yielding a limited field of view. The purpose of this study is to extend the planar x-ray grating imaging theory and methods to a spherical grating scheme formore » a wider range of preclinical and clinical applications. Methods: A spherical grating matches the wave front of a point x-ray source very well, allowing the perpendicular incidence of x-rays on the grating to achieve a higher visibility over a larger field of view than the planer grating counterpart. A theoretical analysis of the Talbot effect for spherical grating imaging is proposed to establish a basic foundation for x-ray spherical gratings interferometry. An efficient method of spherical grating imaging is also presented to extract attenuation, differential phase, and dark-field images in the x-ray spherical grating interferometer. Results: Talbot self-imaging with spherical gratings is analyzed based on the Rayleigh–Sommerfeld diffraction formula, featuring a periodic angular distribution in a polar coordinate system. The Talbot distance is derived to reveal the Talbot self-imaging pattern. Numerical simulation results show the self-imaging phenomenon of a spherical grating interferometer, which is in agreement with the theoretical prediction. Conclusions: X-ray Talbot interferometry with spherical gratings has a significant practical promise. Relative to planar grating imaging, spherical grating based x-ray Talbot interferometry has a larger field of view and improves both signal visibility and dose utilization for pre-clinical and clinical applications.« less

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Interpolation and Polynomial Curve Fitting

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2014-01-01

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

A note on the zeros of Freud-Sobolev orthogonal polynomials

NASA Astrophysics Data System (ADS)

Moreno-Balcazar, Juan J.

2007-10-01

We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.

Optimal Chebyshev polynomials on ellipses in the complex plane

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland

1989-01-01

The design of iterative schemes for sparse matrix computations often leads to constrained polynomial approximation problems on sets in the complex plane. For the case of ellipses, we introduce a new class of complex polynomials which are in general very good approximations to the best polynomials and even optimal in most cases.

Fabrication and Testing of Binary-Phase Fourier Gratings for Nonuniform Array Generation

NASA Technical Reports Server (NTRS)

Keys, Andrew S.; Crow, Robert W.; Ashley, Paul R.; Nelson, Tom R., Jr.; Parker, Jack H.; Beecher, Elizabeth A.

2004-01-01

This effort describes the fabrication and testing of binary-phase Fourier gratings designed to generate an incoherent array of output source points with nonuniform user-defined intensities, symmetric about the zeroth order. Like Dammann fanout gratings, these binary-phase Fourier gratings employ only two phase levels to generate a defined output array. Unlike Dammann fanout gratings, these gratings generate an array of nonuniform, user-defined intensities when projected into the far-field regime. The paper describes the process of design, fabrication, and testing for two different version of the binary-phase grating; one designed for a 12 micron wavelength, referred to as the Long-Wavelength Infrared (LWIR) grating, and one designed for a 5 micron wavelength, referred to as the Mid-Wavelength Infrared Grating (MWIR).

A FAST POLYNOMIAL TRANSFORM PROGRAM WITH A MODULARIZED STRUCTURE

NASA Technical Reports Server (NTRS)

Truong, T. K.

1994-01-01

This program utilizes a fast polynomial transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional convolution has many applications, particularly in image processing. Two-dimensional cyclic convolutions can be converted to a one-dimensional convolution in a polynomial ring. Traditional FPT methods decompose the one-dimensional cyclic polynomial into polynomial convolutions of different lengths. This program will decompose a cyclic polynomial into polynomial convolutions of the same length. Thus, only FPTs and Fast Fourier Transforms of the same length are required. This modular approach can save computational resources. To further enhance its appeal, the program is written in the transportable 'C' language. The steps in the algorithm are: 1) formulate the modulus reduction equations, 2) calculate the polynomial transforms, 3) multiply the transforms using a generalized fast Fourier transformation, 4) compute the inverse polynomial transforms, and 5) reconstruct the final matrices using the Chinese remainder theorem. Input to this program is comprised of the row and column dimensions and the initial two matrices. The matrices are printed out at all steps, ending with the final reconstruction. This program is written in 'C' for batch execution and has been implemented on the IBM PC series of computers under DOS with a central memory requirement of approximately 18K of 8 bit bytes. This program was developed in 1986.

Novel gratings for next-generation instruments of astronomical observations

NASA Astrophysics Data System (ADS)

Ebizuka, N.; Okamoto, T.; Takeda, M.; Hosobata, T.; Yamagata, Y.; Sasaki, M.; Uomoto, M.; Shimatsu, T.; Sato, S.; Hashimoto, N.; Tanaka, I.; Hattori, T.; Ozaki, S.; Aoki, W.

2017-05-01

We will introduce current status of development of a birefringence volume phase holographic (B-VPH) grating, volume binary (VB) grating and reflector facet transmission (RFT) grating developing as the novel dispersive optical element for astronomical instruments for the 8.2m Subaru Telescope, for next generation 30 m class huge ground-based telescopes and for next generation large space-bone telescopes. We will also introduce a hybrid grism developed for MOIRCS (Multi-Object InfraRed Camera and Spectrograph) of the Subaru Telescope and a quasi-Bragg (QB) immersion grating. Test fabrication of B-VPH gratings with a liquid crystal (LC) of UV curable and normal LCs or a resin of visible light curable are performed. We successfully fabricated VB gratings of silicon as a mold with ridges of a high aspect ratio by means of the cycle etching process, oxidation and removal of silicon oxide. The RFT grating which is a surface-relief (SR) transmission grating with sawtooth shaped ridges of an acute vertex angle. The hybrid grism, as a prototype of the RFT grating, combines a high-index prism and SR transmission grating with sawtooth shape ridges of an acute vertex angle. The mold of the SR grating for the hybrid grism on to a work of Ni-P alloy of non-electrolysic plating successfully fabricated by using our ultra-precision machine and a single-crystal diamond bite. The QB immersion grating was fabricated by a combination of an inclined QB grating, Littrow prism and surface reflection mirror.

AKLSQF - LEAST SQUARES CURVE FITTING

NASA Technical Reports Server (NTRS)

Kantak, A. V.

1994-01-01

The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.

Nanointaglio fabrication of optical lipid multilayer diffraction gratings with applications in biosensing

NASA Astrophysics Data System (ADS)

Lowry, Troy Warren

The dynamic self-organization of lipids in biological systems is a highly regulated process that enables the compartmentalization of living systems at microscopic and nanoscopic levels. Exploiting the self-organization and innate biofunctionality of lyotropic liquid crystalline phospholipids, a novel nanofabrication process called "nanointaglio" was invented in order to rapidly and scalably integrate lipid nanopatterns onto the surface. The work presented here focuses on using nanointaglio fabricated lipid diffraction micro- and nanopatterns for the development of new sensing and bioactivity studies. The lipids are patterned as diffraction gratings for sensor functionality. The lipid multilayer gratings operate as nanomechanical sensor elements that are capable of transducing molecular binding to fluid lipid multilayers into optical signals in a label free manner due to shape changes in the lipid nanostructures. To demonstrate the label free detection capabilities, lipid nanopatterns are shown to be suitable for the integration of chemically different lipid multilayer gratings into a sensor array capable of distinguishing vapors by means of an optical nose. Sensor arrays composed of six different lipid formulations are integrated onto a surface and their optical response to three different vapors (water, ethanol and acetone) in air as well as pH under water is monitored as a function of time. Principal component analysis of the array response results in distinct clustering, indicating the suitability of the arrays for distinguishing these analytes. Importantly, the nanointaglio process used is capable of producing lipid gratings out of different materials with sufficiently uniform heights for the fabrication of an optical nose. A second main application is demonstrated for the study of membrane binding proteins. Although in vitro methods for assaying the catalytic activity of individual enzymes are well established, quantitative methods for assaying the kinetics of supramolecular remodeling such as vesicle formation from planar lipid bilayers or multilayers are needed to understand cellular self-organization. Presented next is a nanointaglio based method for quantitative measurements of lipid-protein interactions and its suitability for quantifying the membrane binding, inflation, and budding activity of the membrane-remodeling protein Sar1. Optical diffraction gratings composed of lipids are printed on surfaces using nanointaglio, resulting in lipid multilayer gratings. Exposure of lipid multilayer gratings to Sar1 results in the inflation of lipid multilayers into unilamellar structures, the kinetics of which can be detected in a label-free manner by monitoring the diffraction of white light through an optical microscope. Local variations in lipid multilayer volume on the surface can be used to vary substrate availability in a microarray format, allowing kinetic and thermodynamic data to be obtained from a single experiment without the need for varying enzyme concentration. A quantitative model is developed and fits to the data allow measurements of both binding affinity (KD) and kinetics (kon and koff). Importantly, this assay is uniquely capable of quantifying membrane remodeling. Upon Sar1 induced inflation of single bilayers from surface supported multilayers, the semi-cylindrical grating lines are observed to remodel into semi-spherical buds when a critical radius of curvature equal to 300 nm is reached, which is explained in terms of a Rayleigh type instability.

Fringe stabilizers and their application to telecommunication device manufacturing

NASA Astrophysics Data System (ADS)

Odhner, Jefferson E.

2000-10-01

The ability to create stable holographic grating is an important part of the production of many telecommunication products. The stability problem is increased by the need to use ultra-violet light for close fringe spacing and long exposure times on phot-resist - a relatively low sensitivity material. Active fringe locking increases the modulation depth and efficiency of these holographic gratings. A discussion of how fringe lockers work and how they can be incorporated into a manufacturing set-up is followed by results of using fringe lockers in the manufacturing of some telecommunication devices.

PWAS EMIS-ECIS Active Carbon Filter Residual Life Estimation Methodology

DTIC Science & Technology

2013-09-23

change in the EMIS spectrum. This method is similar to the full width at half maximum (FWHM) method implemented in the fiber Bragg grating ( FBG ), where...the intensity of the light reflected by the FBG at the half peak frequency is used to detect the strain change in the FBG . 4 W911NF-11-1-0210...grating ( FBG ), where the intensity of the light reflected by the FBG at the half peak frequency is used to detect the strain change in the FBG . A brief

Sandia Higher Order Elements (SHOE) v 0.5 alpha

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

2013-09-24

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likelymore » exist.« less

Features of Talbot effect on phase diffraction grating

NASA Astrophysics Data System (ADS)

Brazhnikov, Denis G.; Danko, Volodymyr P.; Kotov, Myhaylo M.; Kovalenko, Andriy V.

2018-01-01

The features of the Talbot effect using the phase diffraction gratings have been considered. A phase grating, unlike an amplitude grating, gives a constant light intensity in the observation plane at a distance multiple to half of the Talbot length ZT. In this case, the subject of interest consists in so-called fractional Talbot effect with the periodic intensity distribution observed in planes shifted from the position nZT/2 (the so-called Fresnel images). Binary phase diffraction gratings with varying phase steps have been investigated. Gratings were made photographically on holographic plates PFG-01. The phase shift was obtained by modulating the emulsion refraction index of the plates. Two types of gratings were used: a square grating with a fill factor of 0.5 and a checkerwise grating (square areas with a bigger and lower refractive index alternate in a checkerboard pattern). By the example of these gratings, the possibility of obtaining in the observation plane an image of a set of equidistant spots with a size smaller than the size of the phase-shifting elements of the grating (the so-called Talbot focusing) has been shown. Clear images of spots with a sufficient signal-to-noise ratio have been obtained for a square grating. Their period was equal to the period of the grating. For a grating with a checkerwise distribution of the refractive index, the spots have been located in positions corresponding to the centres of cells. In addition, the quality of the resulting pattern strongly depended on the magnitude of a grating phase step. As a result of the work, the possibility to obtain Talbot focusing has been shown and the use of this effect to wavefront investigation with a gradient sensor has been demonstrated.

Trapezius muscle activity increases during near work activity regardless of accommodation/vergence demand level.

PubMed

Richter, H O; Zetterberg, C; Forsman, M

2015-07-01

To investigate if trapezius muscle activity increases over time during visually demanding near work. The vision task consisted of sustained focusing on a contrast-varying black and white Gabor grating. Sixty-six participants with a median age of 38 (range 19-47) fixated the grating from a distance of 65 cm (1.5 D) during four counterbalanced 7-min periods: binocularly through -3.5 D lenses, and monocularly through -3.5 D, 0 D and +3.5 D. Accommodation, heart rate variability and trapezius muscle activity were recorded in parallel. General estimating equation analyses showed that trapezius muscle activity increased significantly over time in all four lens conditions. A concurrent effect of accommodation response on trapezius muscle activity was observed with the minus lenses irrespective of whether incongruence between accommodation and convergence was present or not. Trapezius muscle activity increased significantly over time during the near work task. The increase in muscle activity over time may be caused by an increased need of mental effort and visual attention to maintain performance during the visual tasks to counteract mental fatigue.

Enhanced Raman scattering in porous silicon grating.

PubMed

Wang, Jiajia; Jia, Zhenhong; Lv, Changwu

2018-03-19

The enhancement of Raman signal on monocrystalline silicon gratings with varying groove depths and on porous silicon grating were studied for a highly sensitive surface enhanced Raman scattering (SERS) response. In the experiment conducted, porous silicon gratings were fabricated. Silver nanoparticles (Ag NPs) were then deposited on the porous silicon grating to enhance the Raman signal of the detective objects. Results show that the enhancement of Raman signal on silicon grating improved when groove depth increased. The enhanced performance of Raman signal on porous silicon grating was also further improved. The Rhodamine SERS response based on Ag NPs/ porous silicon grating substrates was enhanced relative to the SERS response on Ag NPs/ porous silicon substrates. Ag NPs / porous silicon grating SERS substrate system achieved a highly sensitive SERS response due to the coupling of various Raman enhancement factors.

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

Degenerate r-Stirling Numbers and r-Bell Polynomials

NASA Astrophysics Data System (ADS)

Kim, T.; Yao, Y.; Kim, D. S.; Jang, G.-W.

2018-01-01

The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.

From Chebyshev to Bernstein: A Tour of Polynomials Small and Large

ERIC Educational Resources Information Center

Boelkins, Matthew; Miller, Jennifer; Vugteveen, Benjamin

2006-01-01

Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.

A Sliding-Mode Triboelectric Nanogenerator with Chemical Group Grated Structure by Shadow Mask Reactive Ion Etching.

PubMed

Shang, Wanyu; Gu, Guang Qin; Yang, Feng; Zhao, Lei; Cheng, Gang; Du, Zu-Liang; Wang, Zhong Lin

2017-09-26

The sliding-mode triboelectric nanogenerator (S-TENG) with grated structure has important applications in energy harvest and active sensors; however its concavo-convex structure leads to large frictional resistance and abrasion. Here, we developed a S-TENG with a chemical group grated structure (S-TENG-CGG), in which the triboelectric layer's triboelectric potential has a positive-negative alternating charged structure. The triboelectric layer of the S-TENG-CGG was fabricated through a reactive ion etching process with a metal shadow mask with grated structure. In the etched region, the nylon film, originally positively charged as in friction with stainless steel, gained opposite triboelectric potential and became negatively charged because of the change of surface functional groups. The output signals of the S-TENG-CGG are alternating and the frequency is determined by both the segment numbers and the moving speed. The applications of the S-TENG-CGG in the charging capacitor and driving calculator are demonstrated. In the S-TENG-CGG, since there is no concavo-convex structure, the frictional resistance and abrasion are largely reduced, which enhances its performances in better stability and longer working time.

Multiple Optical Traps with a Single-Beam Optical Tweezer Utilizing Surface Micromachined Planar Curved Grating

NASA Astrophysics Data System (ADS)

Kuo, Ju-Nan; Chen, Kuan-Yu

2010-11-01

In this paper, we present a single-beam optical tweezer integrated with a planar curved diffraction grating for microbead manipulation. Various curvatures of the surface micromachined planar curved grating are systematically investigated. The planar curved grating was fabricated using multiuser micro-electro-mechanical-system (MEMS) processes (MUMPs). The angular separation and the number of diffracted orders were determined. Experimental results indicate that the diffraction patterns and curvature of the planar curved grating are closely related. As the curvature of the planar curved grating increases, the vertical diffraction angle increases, resulting in the strip patterns of the planar curved grating. A single-beam optical tweezer integrated with a planar curved diffraction grating was developed. We demonstrate a technique for creating multiple optical traps from a single laser beam using the developed planar curved grating. The strip patterns of the planar curved grating that resulted from diffraction were used to trap one row of polystyrene beads.

Grating array systems having a plurality of gratings operative in a coherently additive mode and methods for making such grating array systems

DOEpatents

Kessler, Terrance J [Mendon, NY; Bunkenburg, Joachim [Victor, NY; Huang, Hu [Pittsford, NY

2007-02-13

A plurality of gratings (G1, G2) are arranged together with a wavefront sensor, actuators, and feedback system to align the gratings in such a manner, that they operate like a single, large, monolithic grating. Sub-wavelength-scale movements in the mechanical mounting, due to environmental influences, are monitored by an interferometer (28), and compensated by precision actuators (16, 18, 20) that maintain the coherently additive mode. The actuators define the grating plane, and are positioned in response to the wavefronts from the gratings and a reference flat, thus producing the interferogram that contains the alignment information. Movement of the actuators is also in response to a diffraction-limited spot on the CCD (36) to which light diffracted from the gratings is focused. The actuator geometry is implemented to take advantage of the compensating nature of the degrees of freedom between gratings, reducing the number of necessary control variables.

Fabrication of thermal-resistant gratings for high-temperature measurements using geometric phase analysis.

PubMed

Zhang, Q; Liu, Z; Xie, H; Ma, K; Wu, L

2016-12-01

Grating fabrication techniques are crucial to the success of grating-based deformation measurement methods because the quality of the grating will directly affect the measurement results. Deformation measurements at high temperatures entail heating and, perhaps, oxidize the grating. The contrast of the grating lines may change during the heating process. Thus, the thermal-resistant capability of the grating becomes a point of great concern before taking measurements. This study proposes a method that combines a laser-engraving technique with the processes of particle spraying and sintering for fabricating thermal-resistant gratings. The grating fabrication technique is introduced and discussed in detail. A numerical simulation with a geometric phase analysis (GPA) is performed for a homogeneous deformation case. Then, the selection scheme of the grating pitch is suggested. The validity of the proposed technique is verified by fabricating a thermal-resistant grating on a ZrO 2 specimen and measuring its thermal strain at high temperatures (up to 1300 °C). Images of the grating before and after deformation are used to obtain the thermal-strain field by GPA and to compare the results with well-established reference data. The experimental results indicate that this proposed technique is feasible and will offer good prospects for further applications.

Diffraction efficiency of radially-profiled off-plane reflection gratings

NASA Astrophysics Data System (ADS)

Miles, Drew M.; Tutt, James H.; DeRoo, Casey T.; Marlowe, Hannah; Peterson, Thomas J.; McEntaffer, Randall L.; Menz, Benedikt; Burwitz, Vadim; Hartner, Gisela; Laubis, Christian; Scholze, Frank

2015-09-01

Future X-ray missions will require gratings with high throughput and high spectral resolution. Blazed off-plane reflection gratings are capable of meeting these demands. A blazed grating profile optimizes grating efficiency, providing higher throughput to one side of zero-order on the arc of diffraction. This paper presents efficiency measurements made in the 0.3 - 1.5 keV energy band at the Physikalisch-Technische Bundesanstalt (PTB) BESSY II facility for three holographically-ruled gratings, two of which are blazed. Each blazed grating was tested in both the Littrow configuration and anti-Littrow configuration in order to test the alignment sensitivity of these gratings with regard to throughput. This paper outlines the procedure of the grating experiment performed at BESSY II and discuss the resulting efficiency measurements across various energies. Experimental results are generally consistent with theory and demonstrate that the blaze does increase throughput to one side of zero-order. However, the total efficiency of the non-blazed, sinusoidal grating is greater than that of the blazed gratings, which suggests that the method of manufacturing these blazed profiles fails to produce facets with the desired level of precision. Finally, evidence of a successful blaze implementation from first diffraction results of prototype blazed gratings produce via a new fabrication technique at the University of Iowa are presented.

On the robustness of bucket brigade quantum RAM

NASA Astrophysics Data System (ADS)

Arunachalam, Srinivasan; Gheorghiu, Vlad; Jochym-O'Connor, Tomas; Mosca, Michele; Varshinee Srinivasan, Priyaa

2015-12-01

We study the robustness of the bucket brigade quantum random access memory model introduced by Giovannetti et al (2008 Phys. Rev. Lett.100 160501). Due to a result of Regev and Schiff (ICALP ’08 733), we show that for a class of error models the error rate per gate in the bucket brigade quantum memory has to be of order o({2}-n/2) (where N={2}n is the size of the memory) whenever the memory is used as an oracle for the quantum searching problem. We conjecture that this is the case for any realistic error model that will be encountered in practice, and that for algorithms with super-polynomially many oracle queries the error rate must be super-polynomially small, which further motivates the need for quantum error correction. By contrast, for algorithms such as matrix inversion Harrow et al (2009 Phys. Rev. Lett.103 150502) or quantum machine learning Rebentrost et al (2014 Phys. Rev. Lett.113 130503) that only require a polynomial number of queries, the error rate only needs to be polynomially small and quantum error correction may not be required. We introduce a circuit model for the quantum bucket brigade architecture and argue that quantum error correction for the circuit causes the quantum bucket brigade architecture to lose its primary advantage of a small number of ‘active’ gates, since all components have to be actively error corrected.

Umbral orthogonal polynomials

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

Lopez-Sendino, J. E.; del Olmo, M. A.

2010-12-23

We present an umbral operator version of the classical orthogonal polynomials. We obtain three families which are the umbral counterpart of the Jacobi, Laguerre and Hermite polynomials in the classical case.

Simple design of slanted grating with simplified modal method.

PubMed

Li, Shubin; Zhou, Changhe; Cao, Hongchao; Wu, Jun

2014-02-15

A simplified modal method (SMM) is presented that offers a clear physical image for subwavelength slanted grating. The diffraction characteristic of the slanted grating under Littrow configuration is revealed by the SMM as an equivalent rectangular grating, which is in good agreement with rigorous coupled-wave analysis. Based on the equivalence, we obtained an effective analytic solution for simplifying the design and optimization of a slanted grating. It offers a new approach for design of the slanted grating, e.g., a 1×2 beam splitter can be easily designed. This method should be helpful for designing various new slanted grating devices.

Sensored fiber reinforced polymer grate

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

Ross, Michael P.; Mack, Thomas Kimball

Various technologies described herein pertain to a sensored grate that can be utilized for various security fencing applications. The sensored grate includes a grate framework and an embedded optical fiber. The grate framework is formed of a molded polymer such as, for instance, molded fiber reinforced polymer. Further, the grate framework includes a set of elongated elements, where the elongated elements are spaced to define apertures through the grate framework. The optical fiber is embedded in the elongated elements of the grate framework. Moreover, bending or breaking of one or more of the elongated elements can be detected based onmore » a change in a characteristic of input light provided to the optical fiber compared to output light received from the optical fiber.« less

Output characteristics of a 0.14 THz dual sheet beam backward wave oscillator based on a hole-grating slow wave structure

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

Tang, Xiaopin; Yang, Ziqiang; Shi, Zongjun

A novel backward wave oscillator (BWO) based on a hole-grating slow wave structure is proposed as a dual sheet beam millimeter wave radiation source. In this paper, we focus on the output characteristics of a 0.14 THz hole-grating BWO. The output characteristics of the hole-grating BWO, the conventional single-beam grating BWO, and the dual-beam grating BWO are contrasted in detail. 3-D particle-in-cell results indicate that the hole-grating slow wave structure can help to increase the maximum output power as well as lower the operating current density. Meanwhile, the hole-grating BWO shows good insensitivity to the differences between two sheet electronmore » beams. These characteristics make the hole-grating BWO feasible to be a stable millimeter wave radiation source with higher output power.« less

Excitation of multiple surface-plasmon-polariton waves using a compound surface-relief grating

NASA Astrophysics Data System (ADS)

Faryad, Muhammad; Lakhtakia, Akhlesh

2012-01-01

The excitation of multiple surface-plasmon-polariton waves, all of the same frequency but different polarization states, phase speeds, spatial profiles and degrees of localization, by a compound surface-relief grating formed by a metal and a rugate filter, both of finite thickness, was studied using the rigorous coupled-wave approach. Each period of the compound surface-relief grating was chosen to have an integral number of periods of two different simple surface-relief gratings. The excitation of different SPP waves was inferred from the absorptance peaks that were independent of the thickness of the rugate filter. The excitation of each SPP wave could be attributed to either a simple surface-relief grating present in the compound surface-relief grating or to the compound surface-relief grating itself. However, the excitation of SPP waves was found to be less efficient with the compound surface-relief grating than with a simple surface-relief grating.

Binary-Phase Fourier Gratings for Nonuniform Array Generation

NASA Technical Reports Server (NTRS)

Keys, Andrew S.; Crow, Robert W.; Ashley, Paul R.

2003-01-01

We describe a design method for a binary-phase Fourier grating that generates an array of spots with nonuniform, user-defined intensities symmetric about the zeroth order. Like the Dammann fanout grating approach, the binary-phase Fourier grating uses only two phase levels in its grating surface profile to generate the final spot array. Unlike the Dammann fanout grating approach, this method allows for the generation of nonuniform, user-defined intensities within the final fanout pattern. Restrictions governing the specification and realization of the array's individual spot intensities are discussed. Design methods used to realize the grating employ both simulated annealing and nonlinear optimization approaches to locate optimal solutions to the grating design problem. The end-use application driving this development operates in the near- to mid-infrared spectrum - allowing for higher resolution in grating specification and fabrication with respect to wavelength than may be available in visible spectrum applications. Fabrication of a grating generating a user-defined nine spot pattern is accomplished in GaAs for the near-infrared. Characterization of the grating is provided through the measurement of individual spot intensities, array uniformity, and overall efficiency. Final measurements are compared to calculated values with a discussion of the results.

System Construction for the Measurement of Bragg Grating Characteristics in Optical Fibers

NASA Technical Reports Server (NTRS)

West, Douglas P.

1995-01-01

Bragg gratings are used to measure strain in optical fibers. To measure strain they are sometimes used as a smart structure. They must be characterized after they are written to determine their spectral response. This paper deals with the test setup to characterize Bragg grating spectral responses.Bragg gratings are a photo-induced phenomena in optical fibers. The gratings can be used to measure strain by measuring the shift in wavelength. They placed the fibers into a smart structure to measure the stress and strain produced on support columns placed in bridges. As the cable is subjected to strain the grating causes a shift to a longer wavelength if the fiber is stretched and a shift to a shorter wavelength shift if the fiber is compacted. Our applications involve using the fibers to measure stress and strain on airborne systems. There are many ways to write Bragg gratings into optical fibers. Our focus is on side writing the grating. Our capabilities are limited in the production rate of the gratings. The Bragg grating is written into a fiber and becomes a permanent fixture. We are writing the grating to be centered at 1300 nm because that is the standard phase mask wavelength.

Speed and the coherence of superimposed chromatic gratings.

PubMed

Bosten, J M; Smith, L; Mollon, J D

2016-05-01

On the basis of measurements of the perceived coherence of superimposed drifting gratings, Krauskopf and Farell (1990) proposed that motion is analysed independently in different chromatic channels. They found that two gratings appeared to slip if each modulated one of the two 'cardinal' color mechanisms S/(L+M) and L/(L+M). If the gratings were defined along intermediate color directions, observers reported a plaid, moving coherently. We hypothesised that slippage might occur in chromatic gratings if the motion signal from the S/(L+M) channel is weak and equivalent to a lower speed. We asked observers to judge coherence in two conditions. In one, S/(L+M) and L/(L+M) gratings were physically the same speed. In the other, the two gratings had perceptually matched speeds. We found that the relative incoherence of cardinal gratings is the same whether gratings are physically or perceptually matched in speed. Thus our hypothesis was firmly contradicted. In a control condition, observers were asked to judge the coherence of stationary gratings. Interestingly, the difference in judged coherence between cardinal and intermediate gratings remained as strong as it was when the gratings moved. Our results suggest a possible alternative interpretation of Krauskopf and Farell's result: the processes of object segregation may precede the analysis of the motion of chromatic gratings, and the same grouping signals may prompt object segregation in the stationary and moving cases. Copyright © 2016 Elsevier Ltd. All rights reserved.

Critical-angle transmission grating technology development for high resolving power soft x-ray spectrometers on Arcus and Lynx

NASA Astrophysics Data System (ADS)

Heilmann, Ralf K.; Bruccoleri, Alexander R.; Song, Jungki; Kolodziejczak, Jeffery; Gaskin, Jessica A.; O'Dell, Stephen L.; Cheimetz, Peter; Hertz, Edward; Smith, Randall K.; Burwitz, Vadim; Hartner, Gisela; La Caria, Marlis-Madeleine; Schattenburg, Mark L.

2017-08-01

Soft x-ray spectroscopy with high resolving power (R = λ/Δλ) and large effective area (A) addresses numerous unanswered science questions about the physical laws that lead to the structure of our universe. In the soft x-ray band R > 1000 can currently only be achieved with diffraction grating-based spectroscopy. Criticalangle transmission (CAT) gratings combine the advantages of blazed reflection gratings (high efficiency, use of higher diffraction orders) with those of conventional transmission gratings (relaxed alignment tolerances and temperature requirements, transparent at higher energies, low mass), resulting in minimal mission resource requirements, while greatly improving figures of merit. Diffraction efficiency > 33% and R > 10, 000 have been demonstrated for CAT gratings. Last year the technology has been certified at Technology Readiness Level 4 based on a probe class mission concept. The Explorer-scale (A > 450 cm2 , R > 2500) grating spectroscopy Arcus mission can be built with today's CAT grating technology and has been selected in the current Explorer round for a Phase A concept study. Its figure of merit for the detection of weak absorption lines will be an order of magnitude larger than current instruments on Chandra and XMM-Newton. Further CAT grating technology development and improvements in the angular resolution of x-ray optics can provide another order of magnitude improvement in performance, as is envisioned for the X-ray Surveyor/Lynx mission concept currently under development for input into the 2020 Decadal Survey. For Arcus we have tested CAT gratings in a spectrometer setup in combination with silicon pore optics (SPO) and obtained resolving power results that exceed Arcus requirements before and after environmental testing of the gratings. We have recently fabricated the largest (32 mm x 32 mm) CAT gratings to date, and plan to increase grating size further. We mounted two of these large gratings to frames and aligned them in the roll direction using a laser-based technique. Simultaneous x-ray illumination of both gratings with an SPO module demonstrated that we can exceed Arcus grating-to-grating alignment requirements without x rays.

Transmission Grating and Optics Technology Development for the Arcus Explorer Mission

NASA Astrophysics Data System (ADS)

Heilmann, Ralf; Arcus Team

2018-01-01

Arcus is a high-resolution x-ray spectroscopy MIDEX mission selected for a Phase A concept study. It is designed to explore structure formation through measurements of hot baryon distributions, feedback from black holes, and the formation and evolution of stars, disks, and exoplanet atmospheres. The design provides unprecedented sensitivity in the 1.2-5 nm wavelength band with effective area above 450 sqcm and spectral resolution R > 2500. The Arcus technology is based on 12 m-focal length silicon pore optics (SPO) developed for the European Athena mission, and critical-angle transmission (CAT) x-ray diffraction gratings and x-ray CCDs developed at MIT. The modular design consists of four parallel channels, each channel holding an optics petal, followed by a grating petal. CAT gratings are lightweight, alignment insensitive, high-efficiency x-ray transmission gratings that blaze into high diffraction orders, leading to high spectral resolution. Each optics petal represents an azimuthal sub-aperture of a full Wolter optic. The sub-aperturing effect increases spectral resolving power further. Two CCD readout strips receive photons from each channel, including higher-energy photons in 0th order. Each optics petal holds 34 SPO modules. Each grating petal holds 34 grating windows, and each window holds 4-6 grating facets. A grating facet consists of a silicon grating membrane, bonded to a flexure frame that interfaces with the grating window. We report on a sequence of tests with increasing complexity that systematically increase the Technology Readiness Level (TRL) for the combination of CAT gratings and SPOs towards TLR 6. CAT gratings have been evaluated in x rays for diffraction efficiency (> 30% at 2.5 nm) and for resolving power (R> 10,000). A CAT grating/SPO combination was measured at R ~ 3100 at blaze angles smaller than design values, exceeding Arcus requirements. Efficiency and resolving power were not impacted by vibration and thermal testing of gratings. A pair of large (32 mm x 32 mm) gratings was aligned using laser metrology, and alignment was verified under x rays. We present results on simultaneous illumination of the aligned grating pair, and describe our progress towards further tests.

Design and Use of a Learning Object for Finding Complex Polynomial Roots

ERIC Educational Resources Information Center

Benitez, Julio; Gimenez, Marcos H.; Hueso, Jose L.; Martinez, Eulalia; Riera, Jaime

2013-01-01

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

Extending a Property of Cubic Polynomials to Higher-Degree Polynomials

ERIC Educational Resources Information Center

Miller, David A.; Moseley, James

2012-01-01

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

Computing Galois Groups of Eisenstein Polynomials Over P-adic Fields

NASA Astrophysics Data System (ADS)

Milstead, Jonathan

The most efficient algorithms for computing Galois groups of polynomials over global fields are based on Stauduhar's relative resolvent method. These methods are not directly generalizable to the local field case, since they require a field that contains the global field in which all roots of the polynomial can be approximated. We present splitting field-independent methods for computing the Galois group of an Eisenstein polynomial over a p-adic field. Our approach is to combine information from different disciplines. We primarily, make use of the ramification polygon of the polynomial, which is the Newton polygon of a related polynomial. This allows us to quickly calculate several invariants that serve to reduce the number of possible Galois groups. Algorithms by Greve and Pauli very efficiently return the Galois group of polynomials where the ramification polygon consists of one segment as well as information about the subfields of the stem field. Second, we look at the factorization of linear absolute resolvents to further narrow the pool of possible groups.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

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

Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei

The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl{sub -1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from the q{yields}-1 limit of the dual q-Hahn polynomials. The Hopf algebra sl{sub -1}(2) has four generators including an involution, it is also a q{yields}-1 limit of the quantum algebra sl{sub q}(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter generalization of u(2) with an involution as additional generator, is first derived from the recurrence relation of themore » -1 Hahn polynomials. It is then shown that H can be realized in terms of the generators of two added sl{sub -1}(2) algebras, so that the Clebsch-Gordan coefficients of sl{sub -1}(2) are dual -1 Hahn polynomials. An irreducible representation of H involving five-diagonal matrices and connected to the difference equation of the dual -1 Hahn polynomials is constructed.« less

Attention improves encoding of task-relevant features in the human visual cortex.

PubMed

Jehee, Janneke F M; Brady, Devin K; Tong, Frank

2011-06-01

When spatial attention is directed toward a particular stimulus, increased activity is commonly observed in corresponding locations of the visual cortex. Does this attentional increase in activity indicate improved processing of all features contained within the attended stimulus, or might spatial attention selectively enhance the features relevant to the observer's task? We used fMRI decoding methods to measure the strength of orientation-selective activity patterns in the human visual cortex while subjects performed either an orientation or contrast discrimination task, involving one of two laterally presented gratings. Greater overall BOLD activation with spatial attention was observed in visual cortical areas V1-V4 for both tasks. However, multivariate pattern analysis revealed that orientation-selective responses were enhanced by attention only when orientation was the task-relevant feature and not when the contrast of the grating had to be attended. In a second experiment, observers discriminated the orientation or color of a specific lateral grating. Here, orientation-selective responses were enhanced in both tasks, but color-selective responses were enhanced only when color was task relevant. In both experiments, task-specific enhancement of feature-selective activity was not confined to the attended stimulus location but instead spread to other locations in the visual field, suggesting the concurrent involvement of a global feature-based attentional mechanism. These results suggest that attention can be remarkably selective in its ability to enhance particular task-relevant features and further reveal that increases in overall BOLD amplitude are not necessarily accompanied by improved processing of stimulus information.

Interbasis expansions in the Zernike system

NASA Astrophysics Data System (ADS)

Atakishiyev, Natig M.; Pogosyan, George S.; Wolf, Kurt Bernardo; Yakhno, Alexander

2017-10-01

The differential equation with free boundary conditions on the unit disk that was proposed by Frits Zernike in 1934 to find Jacobi polynomial solutions (indicated as I) serves to define a classical system and a quantum system which have been found to be superintegrable. We have determined two new orthogonal polynomial solutions (indicated as II and III) that are separable and involve Legendre and Gegenbauer polynomials. Here we report on their three interbasis expansion coefficients: between the I-II and I-III bases, they are given by F32(⋯|1 ) polynomials that are also special su(2) Clebsch-Gordan coefficients and Hahn polynomials. Between the II-III bases, we find an expansion expressed by F43(⋯|1 ) 's and Racah polynomials that are related to the Wigner 6j coefficients.

Novel hybrid laser modes in composite VCSEL-DFB microcavities (Conference Presentation)

NASA Astrophysics Data System (ADS)

Mischok, Andreas; Wagner, Tim; Sudzius, Markas; Brückner, Robert; Fröb, Hartmut; Lyssenko, Vadim G.; Leo, Karl

2017-02-01

Two of the most successful microcresonator concepts are the vertical cavity surface emitting laser (VCSEL), where light is confined between distributed Bragg reflectors (DBRs), and the distributed feedback (DFB) laser, where a periodic grating provides positive optical feedback to selected modes in an active waveguide (WG) layer. Our work concerns the combination of both into a composite device, facilitating coherent interaction between both regimes and giving rise to novel laser modes in the system. In a first realization, a full VCSEL stack with an organic active layer is evaporated on top of a diffraction grating with a large period (approximately 1 micron), leading to diffraction of waveguided modes into the surface emission of the device. Here, the coherent interaction between VCSEL and WG modes, as observed in an anticrossing of the dispersion lines, facilitates novel hybrid lasing modes with macroscopic in-plane coherence [1]. In further studies, we decrease the grating period of such devices to realise DFB conditions in a second-order Bragg grating which strongly couples photons via first-order light diffraction to the VCSEL. This efficient coupling can be compared to more classical cascade-coupled cavities and is successfully described by a coupled oscillator model [2]. When both resonators are non-degenerate, they are able to function as independent structures without substantial diffraction losses. The realization of such novel devices provides a promising platform for photonic circuits based on organic microlasers. [1] A. Mischok et al., Adv. Opt. Mater., early online, DOI: 10.1002/adom.201600282, (2016) [2] T. Wagner et al., Appl. Phys. Lett., accepted, in production, (2016)

Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

NASA Astrophysics Data System (ADS)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2009-12-01

We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula.

PubMed

Haglund, J; Haiman, M; Loehr, N

2005-02-22

Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H(mu). We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H(mu). As corollaries, we obtain the cocharge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials J(mu), a formula for H(mu) in terms of Lascoux-Leclerc-Thibon polynomials, and combinatorial expressions for the Kostka-Macdonald coefficients K(lambda,mu) when mu is a two-column shape.

Multi-indexed (q-)Racah polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2012-09-01

As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by the multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of ‘virtual state’ vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the ‘solutions’ of the matrix Schrödinger equation with negative ‘eigenvalues’, except for one of the two boundary points.

Fiber facet gratings for high power fiber lasers

NASA Astrophysics Data System (ADS)

Vanek, Martin; Vanis, Jan; Baravets, Yauhen; Todorov, Filip; Ctyroky, Jiri; Honzatko, Pavel

2017-12-01

We numerically investigated the properties of diffraction gratings designated for fabrication on the facet of an optical fiber. The gratings are intended to be used in high-power fiber lasers as mirrors either with a low or high reflectivity. The modal reflectance of low reflectivity polarizing grating has a value close to 3% for TE mode while it is significantly suppressed for TM mode. Such a grating can be fabricated on laser output fiber facet. The polarizing grating with high modal reflectance is designed as a leaky-mode resonant diffraction grating. The grating can be etched in a thin layer of high index dielectric which is sputtered on fiber facet. We used refractive index of Ta2O5 for such a layer. We found that modal reflectance can be close to 0.95 for TE polarization and polarization extinction ratio achieves 18 dB. Rigorous coupled wave analysis was used for fast optimization of grating parameters while aperiodic rigorous coupled wave analysis, Fourier modal method and finite difference time domain method were compared and used to compute modal reflectance of designed gratings.

Kinesthetic information disambiguates visual motion signals.

PubMed

Hu, Bo; Knill, David C

2010-05-25

Numerous studies have shown that extra-retinal signals can disambiguate motion information created by movements of the eye or head. We report a new form of cross-modal sensory integration in which the kinesthetic information generated by active hand movements essentially captures ambiguous visual motion information. Several previous studies have shown that active movement can bias observers' percepts of bi-stable stimuli; however, these effects seem to be best explained by attentional mechanisms. We show that kinesthetic information can change an otherwise stable perception of motion, providing evidence of genuine fusion between visual and kinesthetic information. The experiments take advantage of the aperture problem, in which the motion of a one-dimensional grating pattern behind an aperture, while geometrically ambiguous, appears to move stably in the grating normal direction. When actively moving the pattern, however, the observer sees the motion to be in the hand movement direction. Copyright 2010 Elsevier Ltd. All rights reserved.

Monolithic thulium-doped fiber laser

NASA Astrophysics Data System (ADS)

Aubrecht, J.; Peterka, P.; Honzátko, P.; Todorov, F.; Podrazký, O.; Kamrádek, M.; Proboštová, J.; Kašík, I.

2017-12-01

In this contribution we report and discuss the results of laser characterizations of experimental thulium-doped optical fibers. These active fibers were fabricated in house and were tested in two laser systems to verify their characteristics. The first one, a monolithic fiber laser, was of great interest to us due to its potentially lower overall resonator losses, improved laser lifetime and better robustness. The compact laser cavities with a Bragg gratings inscribed directly into the active optical fiber differs to the second laser system where the Bragg gratings were inscribed into a passive fiber which had to be spliced to the active fiber. The tested fibers were manufactured by the modified chemical vapor deposition method and a solution-doping of thulium ions with Al2O3 or alumina nanoparticles, respectively. We focused on comparison of laser output powers, slope efficiencies, and laser thresholds for particular thulium-doped fiber in different laser configurations.

Curved VPH gratings for novel spectrographs

NASA Astrophysics Data System (ADS)

Clemens, J. Christopher; O'Donoghue, Darragh; Dunlap, Bart H.

2014-07-01

The introduction of volume phase holographic (VPH) gratings into astronomy over a decade ago opened new possibilities for instrument designers. In this paper we describe an extension of VPH grating technology that will have applications in astronomy and beyond: curved VPH gratings. These devices can disperse light while simultaneously correcting aberrations. We have designed and manufactured two different kinds of convex VPH grating prototypes for use in off-axis reflecting spectrographs. One type functions in transmission and the other in reflection, enabling Offnerstyle spectrographs with the high-efficiency and low-cost advantages of VPH gratings. We will discuss the design process and the tools required for modelling these gratings along with the recording layout and process steps required to fabricate them. We will present performance data for the first convex VPH grating produced for an astronomical spectrograph.

Design and fabrication of a polarization-independent two-port beam splitter.

PubMed

Feng, Jijun; Zhou, Changhe; Zheng, Jiangjun; Cao, Hongchao; Lv, Peng

2009-10-10

We design and manufacture a fused-silica polarization-independent two-port beam splitter grating. The physical mechanism of this deeply etched grating can be shown clearly by using the simplified modal method with consideration of corresponding accumulated phase difference of two excited propagating grating modes, which illustrates that the binary-phase fused-silica grating structure depends little on the incident wavelength, but mainly on the ratio of groove depth to grating period and the ratio of incident wavelength to grating period. These analytic results would also be very helpful for wavelength bandwidth analysis. The exact grating profile is optimized by using the rigorous coupled-wave analysis. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results agree well with the theoretical values.

Dual-function beam splitter of a subwavelength fused-silica grating.

PubMed

Feng, Jijun; Zhou, Changhe; Zheng, Jiangjun; Cao, Hongchao; Lv, Peng

2009-05-10

We present the design and fabrication of a novel dual-function subwavelength fused-silica grating that can be used as a polarization-selective beam splitter. For TM polarization, the grating can be used as a two-port beam splitter at a wavelength of 1550 nm with a total diffraction efficiency of 98%. For TE polarization, the grating can function as a high-efficiency grating, and the diffraction efficiency of the -1st order is 95% under Littrow mounting. This dual-function grating design is based on a simplified modal method. By using the rigorous coupled-wave analysis, the optimum grating parameters can be determined. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results are in agreement with the theoretical values.

Conformal Galilei algebras, symmetric polynomials and singular vectors

NASA Astrophysics Data System (ADS)

Křižka, Libor; Somberg, Petr

2018-01-01

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras cga_ℓ (d,C) with d=1 for any integer value ℓ \\in N. The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.

Identities associated with Milne-Thomson type polynomials and special numbers.

PubMed

Simsek, Yilmaz; Cakic, Nenad

2018-01-01

The purpose of this paper is to give identities and relations including the Milne-Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers. By using fermionic and bosonic p -adic integrals, we derive some new relations and formulas related to these numbers and polynomials, and also the combinatorial sums.

Determination of modulation transfer function of a printer by measuring the autocorrelation of the transmission function of a printed Ronchi grating

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

Madanipour, Khosro; Tavassoly, Mohammad T

2009-02-01

We show theoretically and verify experimentally that the modulation transfer function (MTF) of a printing system can be determined by measuring the autocorrelation of a printed Ronchi grating. In practice, two similar Ronchi gratings are printed on two transparencies and the transparencies are superimposed with parallel grating lines. Then, the gratings are uniformly illuminated and the transmitted light from a large section is measured versus the displacement of one grating with respect to the other in a grating pitch interval. This measurement provides the required autocorrelation function for determination of the MTF.

Hidden symmetries in plasmonic gratings

NASA Astrophysics Data System (ADS)

Huidobro, P. A.; Chang, Y. H.; Kraft, M.; Pendry, J. B.

2017-04-01

Plasmonic gratings constitute a paradigmatic instance of the wide range of applications enabled by plasmonics. While subwavelength metal gratings find applications in optical biosensing and photovoltaics, atomically thin gratings achieved by periodically doping a graphene monolayer perform as metasurfaces for the control of terahertz radiation. In this paper we show how these two instances of plasmonic gratings inherit their spectral properties from an underlying slab with translational symmetry. We develop an analytical formalism to accurately derive the mode spectrum of the gratings that provides a great physical insight.

Diffraction Efficiency Testing of Sinusoidal and Blazed Off-Plane Reflection Gratings

NASA Astrophysics Data System (ADS)

Tutt, James H.; McEntaffer, Randall L.; Marlowe, Hannah; Miles, Drew M.; Peterson, Thomas J.; Deroo, Casey T.; Scholze, Frank; Laubis, Christian

2016-09-01

Reflection gratings in the off-plane mount have the potential to enhance the performance of future high resolution soft X-ray spectrometers. Diffraction efficiency can be optimized through the use of blazed grating facets, achieving high-throughput on one side of zero-order. This paper presents the results from a comparison between a grating with a sinusoidally grooved profile and two gratings that have been blazed. The results show that the blaze does increase throughput to one side of zero-order; however, the total throughput of the sinusoidal gratings is greater than the blazed gratings, suggesting the method of manufacturing the blazed gratings does not produce precise facets. The blazed gratings were also tested in their Littrow and anti-Littrow configurations to quantify diffraction efficiency sensitivity to rotations about the grating normal. Only a small difference in the energy at which efficiency is maximized between the Littrow and anti-Littrow configurations is seen with a small shift in peak efficiency towards higher energies in the anti-Littrow case. This is due to a decrease in the effective blaze angle in the anti-Littrow mounting. This is supported by PCGrate-SX V6.1 modeling carried out for each blazed grating which predicts similar response trends in the Littrow and anti-Littrow orientations.

Fabrication et applications des reseaux de Bragg ultra-longs

NASA Astrophysics Data System (ADS)

Gagne, Mathieu

This thesis presents the principal accomplishments realized during the PhD project. The thesis is presented by publication format and is a collection of four published articles having fiber Bragg gratings as a central theme. First achieved in 1978, UV writing of fiber Bragg gratings is nowadays a common and mature technology being present in both industry and academia. The property of reflecting light guided by optical fibers lead to diverse applications in telecommunication, lasers as well as several types of sensors. The conventional fabrication technique is generally based on the use of generally expensive phase masks which determine the obtained characteristics of the fiber Bragg grating. The fiber being photosensitive at those wavelengths, a periodic pattern can be written into it. The maximal length, the period, the chirp, the index contrast and the apodisation are all characteristics that depend on the phase mask. The first objective of the research project is to be able to go beyond this strong dependance on the phase mask without deteriorating grating quality. This is what really sets apart the technique presented in this thesis from other long fiber Bragg grating fabrication techniques available in the literature. The fundamental approach to obtain ultra long fiber Bragg gratings of arbitrary profile is to replace the scheme of scanning a UV beam across a phase mask to expose a fixed fiber by a scheme where the UV beam and phase mask are fixed and where the fiber is moving instead. To obtain a periodic index variation, the interference pattern itself must be synchronized with the moving fiber. Two variations of this scheme were implanted: the first one using electro-optical phase modulator placed in each arm of a Talbot interferometer and the second one using a phase mask mounted on a piezo electric actuator. A new scheme that imparts fine movements of the interferometer is also implemented for the first time and showed to be essential to achieve high quality ultra long fiber Bragg gratings. High quality theory matching ultra long fiber Bragg gratings up to 1 meter long are obtained for the first time. The possibility of fabricating high quality ultra long fiber Bragg grating of more than 10 cm (approximately the maximal phase mask length) opens a variety of new applications otherwise impossible with short fiber Bragg grating technology. Ultra long fiber Bragg gratings have unique characteristics such as high reflectivity, high dispersion and ultra narrow bandwidth. Those characteristics can be used to do advanced signal processing, non linear propagation experiments, distributed feedback fiber lasers and dispersion compensator for telecommunication or optical tomography. The second objective of this project is to use these ultra-long fiber Bragg gratings as an optical cavity for fiber lasers. Alot of research in the past years have been concentrated on those lasers, particularly on distributed feedback fiber lasers where the gratings spans all the gain media. A new random fiber laser configuration is presented. It is based on passive or active insertion of phase shifts along the Bragg grating to obtained a phenomenon called light localization which is the optical equivalent of Anderson localization. This complex wave phenomenon has the unique property to mimic the reflection of a uniform photonic crystal with the random diffusion of light among the elements of a random media. Being commonly obtained in fine powders which must respect a certain set of rules, the realization of 1D structures is vastly simplified in optical fibers. Two random fiber laser schemes based on light localization, one using erbium dopant and the other one Raman scattering, are demonstrated for the first time and compared to traditional distributed feedback fiber lasers.

Phasor Analysis of Binary Diffraction Gratings with Different Fill Factors

ERIC Educational Resources Information Center

Martinez, Antonio; Sanchez-Lopez, Ma del Mar; Moreno, Ignacio

2007-01-01

In this work, we present a simple analysis of binary diffraction gratings with different slit widths relative to the grating period. The analysis is based on a simple phasor technique directly derived from the Huygens principle. By introducing a slit phasor and a grating phasor, the intensity of the diffracted orders and the grating's resolving…

Approximating smooth functions using algebraic-trigonometric polynomials

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

Sharapudinov, Idris I

2011-01-14

The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form p{sub n}(t)+{tau}{sub m}(t), where p{sub n}(t) is an algebraic polynomial of degree n and {tau}{sub m}(t)=a{sub 0}+{Sigma}{sub k=1}{sup m}a{sub k} cos k{pi}t + b{sub k} sin k{pi}t is a trigonometric polynomial of order m. The precise order of approximation by such polynomials in the classes W{sup r}{sub {infinity}(}M) and an upper bound for similar approximations in the class W{sup r}{sub p}(M) with 4/3

Parameter reduction in nonlinear state-space identification of hysteresis

NASA Astrophysics Data System (ADS)

Fakhrizadeh Esfahani, Alireza; Dreesen, Philippe; Tiels, Koen; Noël, Jean-Philippe; Schoukens, Johan

2018-05-01

Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50%, while maintaining a comparable output error level.

Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm

NASA Astrophysics Data System (ADS)

Cao, Hongchao; Zhou, Changhe; Feng, Jijun; Lv, Peng; Ma, Jianyong

2010-11-01

We describe polarization-independent triangular-groove fused-silica gratings illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. The physical mechanisms of the grating can be shown clearly by using the simplified modal method with consideration of the corresponding accumulated average phase difference of two excited propagating grating modes, which illustrates that the grating structure depends mainly on the ratio of the average effective indices difference to the incident wavelength. Exact grating profile is optimized by using the rigorous coupled-wave analysis (RCWA). With the optimized grating parameters, the grating exhibits diffraction efficiencies of greater than 90% under TE- and TM-polarized incident lights for 101 nm spectral bandwidths (1500-1601 nm) and it can reach an efficiency of more than 99% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, coating of dielectric film layers, the designed triangular-groove fused-silica grating should be of great interest for DWDM application.

Design and analysis of a worm gear turntable off-axis assembly method in a three-grating monochromator.

PubMed

Chen, Jianjun; Cui, Jicheng; Yao, Xuefeng; Liu, Jianan; Sun, Ci

2018-04-01

To solve the problem where the actual grating aperture decreases with an increasing scanning angle during the scanning of a three-grating monochromator, we propose an off-axis assembly method for the worm gear turntable that makes it possible to suppress this aperture reduction. We simulated and compared the traditional assembly method with the off-axis assembly method in the three-grating monochromator. Results show that the actual grating aperture can be improved by the off-axis assembly method. In fact, for any one of the three gratings, when the monochromator outputs the longest wavelength in the corresponding wavelength band, the actual grating aperture increases by 45.93%. Over the entire monochromator output band, the actual grating aperture increased by an average of 32.56% and can thus improve the monochromator's output energy. Improvement of the actual grating aperture can also reduce the stray light intensity in the monochromator and improve its output signal-to-noise ratio.

Using a cover layer to improve the damage resistance of gold-coated gratings induced by a picosecond pulsed laser

NASA Astrophysics Data System (ADS)

Xia, Zhilin; Wu, Yihan; Kong, Fanyu; Jin, Yunxia

2018-04-01

The chirped pulse amplification (CPA) technology is the main approach to achieve high-intensity short-pulse laser. Diffraction gratings are good candidates for stretching and compressing laser pulses in CPA. In this paper, a kind of gold-coated grating has been prepared and its laser damage experiment has been performed. The results reflect that the gratings laser damage was dominated by thermal ablation due to gold films or inclusions absorption and involved the deformation or eruption of the gold film. Based on these damage phenomena, a method of using a cover layer to prevent gold films from deforming and erupting has been adopted to improve the gold-coated gratings laser damage threshold. Since the addition of a cover layer changes the gratings diffraction efficiency, the gratings structure has been re-optimized. Furthermore, according to the calculated thermal stress distributions in gratings with optimized structures, the cover layer was demonstrated to be helpful for improving the gratings laser damage resistance if it is thick enough.

Theoretical investigation and optimization of fiber grating based slow light

NASA Astrophysics Data System (ADS)

Wang, Qi; Wang, Peng; Du, Chao; Li, Jin; Hu, Haifeng; Zhao, Yong

2017-07-01

On the edge of bandgap in a fiber grating, narrow peaks of high transimittivity exist at frequencies where light interferes constructively in the forward direction. In the vicinity of these transmittivity peaks, light reflects back and forth numerous times across the periodic structure and experiences a large group delay. In order to generate the extremely slow light in fiber grating for applications, in this research, the common sense of formation mechanism of slow light in fiber grating was introduced. The means of producing and operating fiber grating was studied to support structural slow light with a group index that can be in principle as high as several thousand. The simulations proceeded by transfer matrix method in the paper were presented to elucidate how the fiber grating parameters effect group refractive index. The main parameters that need to be optimized include grating length, refractive index contrast, grating period, loss coefficient, chirp and apodization functions, those can influence fiber grating characteristics.

Stratified Diffractive Optic Approach for Creating High Efficiency Gratings

NASA Technical Reports Server (NTRS)

Chambers, Diana M.; Nordin, Gregory P.

1998-01-01

Gratings with high efficiency in a single diffracted order can be realized with both volume holographic and diffractive optical elements. However, each method has limitations that restrict the applications in which they can be used. For example, high efficiency volume holographic gratings require an appropriate combination of thickness and permittivity modulation throughout the bulk of the material. Possible combinations of those two characteristics are limited by properties of currently available materials, thus restricting the range of applications for volume holographic gratings. Efficiency of a diffractive optic grating is dependent on its approximation of an ideal analog profile using discrete features. The size of constituent features and, consequently, the number that can be used within a required grating period restricts the applications in which diffractive optic gratings can be used. These limitations imply that there are applications which cannot be addressed by either technology. In this paper we propose to address a number of applications in this category with a new method of creating high efficiency gratings which we call stratified diffractive optic gratings. In this approach diffractive optic techniques are used to create an optical structure that emulates volume grating behavior. To illustrate the stratified diffractive optic grating concept we consider a specific application, a scanner for a space-based coherent wind lidar, with requirements that would be difficult to meet by either volume holographic or diffractive optic methods. The lidar instrument design specifies a transmissive scanner element with the input beam normally incident and the exiting beam deflected at a fixed angle from the optical axis. The element will be rotated about the optical axis to produce a conical scan pattern. The wavelength of the incident beam is 2.06 microns and the required deflection angle is 30 degrees, implying a grating period of approximately 4 microns. Creating a high efficiency volume grating with these parameters would require a grating thickness that cannot be attained with current photosensitive materials. For a diffractive optic grating, the number of binary steps necessary to produce high efficiency combined with the grating period requires feature sizes and alignment tolerances that are also unattainable with current techniques. Rotation of the grating and integration into a space-based lidar system impose the additional requirements that it be insensitive to polarization orientation, that its mass be minimized and that it be able to withstand launch and space environments.

Study of distributed fiber-optic laser-ultrasound generation based on ghost-mode of tilted fiber Bragg gratings

NASA Astrophysics Data System (ADS)

Tian, Jiajun; Zhang, Qi; Han, Ming

2013-05-01

Fiber-optic ultrasonic transducers are an important component of an active ultrasonic testing system for structural health monitoring. Fiber-optic transducers have several advantages such as small size, light weight, and immunity to electromagnetic interference that make them much more attractive than the current available piezoelectric transducers, especially as embedded and permanent transducers in active ultrasonic testing for structural health monitoring. In this paper, a distributed fiber-optic laser-ultrasound generation based on the ghost-mode of tilted fiber Bragg gratings is studied. The influences of the laser power and laser pulse duration on the laser-ultrasound generation are investigated. The results of this paper are helpful to understand the working principle of this laser-ultrasound method and improve the ultrasonic generation efficiency.

Multimode Surface Plasmon Excitations on Organic Thin Film/Metallic Diffraction Grating

NASA Astrophysics Data System (ADS)

Baba, Akira; Kanda, Kenji; Ohno, Tsutomu; Ohdaira, Yasuo; Shinbo, Kazunari; Kato, Keizo; Kaneko, Futao

2010-01-01

In this work, we demonstrate multimode surface plasmon (SP) excitations by white light irradiation on metallic diffraction grating/plastic substrates. Recordable compact discs were used as the diffraction grating substrates on which silver films were deposited by vacuum evaporation. Since the grating pitch (1.6 µm) was larger than that of diffraction gratings commonly used for the excitation of SPs, multimode SP excitations due to several diffraction orders were observed simultaneously in the wavelength region from 400 to 800 nm. The obtained SP excitations were then compared with the calculated SP dispersion on the grating. The multimode SP excitations were further studied on spin-coated poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) thin film/silver grating substrates. An increased photoluminescence intensity due to SP excitations was observed on MEH-PPV/silver grating surfaces.

Grateful parents raising grateful children: Niche selection and the socialization of child gratitude

PubMed Central

Rothenberg, William A.; Hussong, Andrea M.; Langley, Hillary A.; Egerton, Gregory A.; Halberstadt, Amy G.; Coffman, Jennifer L.; Mokrova, Irina; Costanzo, Philip R.

2016-01-01

Given that children’s exposure to gratitude-related activities may be one way that parents can socialize gratitude in their children, we examined whether parents’ niche selection (i.e., tendency to choose perceived gratitude-inducing activities for their children) mediates the association between parents’ reports of their own and their children's gratitude. Parent-child dyads (N =101; children aged 6-9; 52% girls; 80% Caucasian; 85% mothers) participated in a laboratory visit and parents also completed a seven-day online diary regarding children’s gratitude. Decomposing specific indirect effects within a structural equation model, we found that parents high in gratitude were more likely to set goals to use niche selection as a gratitude socialization strategy, and thereby more likely to place their children in gratitude-related activities. Placement in these activities, in turn, was associated with more frequent expression of gratitude in children. We describe future directions for research on parents’ role in socializing gratitude in their children. PMID:28943753

Grateful parents raising grateful children: Niche selection and the socialization of child gratitude.

PubMed

Rothenberg, William A; Hussong, Andrea M; Langley, Hillary A; Egerton, Gregory A; Halberstadt, Amy G; Coffman, Jennifer L; Mokrova, Irina; Costanzo, Philip R

2017-01-01

Given that children's exposure to gratitude-related activities may be one way that parents can socialize gratitude in their children, we examined whether parents' niche selection (i.e., tendency to choose perceived gratitude-inducing activities for their children) mediates the association between parents' reports of their own and their children's gratitude. Parent-child dyads ( N =101; children aged 6-9; 52% girls; 80% Caucasian; 85% mothers) participated in a laboratory visit and parents also completed a seven-day online diary regarding children's gratitude. Decomposing specific indirect effects within a structural equation model, we found that parents high in gratitude were more likely to set goals to use niche selection as a gratitude socialization strategy, and thereby more likely to place their children in gratitude-related activities. Placement in these activities, in turn, was associated with more frequent expression of gratitude in children. We describe future directions for research on parents' role in socializing gratitude in their children.

Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach.

PubMed

Lam, H K

2012-02-01

This paper investigates the stability of sampled-data output-feedback (SDOF) polynomial-fuzzy-model-based control systems. Representing the nonlinear plant using a polynomial fuzzy model, an SDOF fuzzy controller is proposed to perform the control process using the system output information. As only the system output is available for feedback compensation, it is more challenging for the controller design and system analysis compared to the full-state-feedback case. Furthermore, because of the sampling activity, the control signal is kept constant by the zero-order hold during the sampling period, which complicates the system dynamics and makes the stability analysis more difficult. In this paper, two cases of SDOF fuzzy controllers, which either share the same number of fuzzy rules or not, are considered. The system stability is investigated based on the Lyapunov stability theory using the sum-of-squares (SOS) approach. SOS-based stability conditions are obtained to guarantee the system stability and synthesize the SDOF fuzzy controller. Simulation examples are given to demonstrate the merits of the proposed SDOF fuzzy control approach.

Quasi-kernel polynomials and convergence results for quasi-minimal residual iterations

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1992-01-01

Recently, Freund and Nachtigal have proposed a novel polynominal-based iteration, the quasi-minimal residual algorithm (QMR), for solving general nonsingular non-Hermitian linear systems. Motivated by the QMR method, we have introduced the general concept of quasi-kernel polynomials, and we have shown that the QMR algorithm is based on a particular instance of quasi-kernel polynomials. In this paper, we continue our study of quasi-kernel polynomials. In particular, we derive bounds for the norms of quasi-kernel polynomials. These results are then applied to obtain convergence theorems both for the QMR method and for a transpose-free variant of QMR, the TFQMR algorithm.

On universal knot polynomials

NASA Astrophysics Data System (ADS)

Mironov, A.; Mkrtchyan, R.; Morozov, A.

2016-02-01

We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

Zernike Basis to Cartesian Transformations

NASA Astrophysics Data System (ADS)

Mathar, R. J.

2009-12-01

The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle) defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.

High-Performance, Large Format Surfaces for Surface-Enhanced Raman Spectroscopy: Increasing the Accessibility of an Analytical Platform

NASA Astrophysics Data System (ADS)

Kanipe, Katherine Nicole

Although surface-enhanced Raman spectroscopy (SERS) is a spectroscopic technique with unusually high sensitivity and molecular specificity, few practical analytical applications have been implemented that take advantage of its power. Based on what is understood about SERS from the experimental and theoretical research of the past forty years, we developed a few well-defined design principles on the basis of which a reliable and reproducibly manufacturable SERS-active substrate could be fabricated that is highly enhancing, highly uniform, stable, and based on a broad range of metals so that various chemical processes could be probed. Finally, we restricted ourselves to using only readily scalable fabrication techniques. The resulting SERS-active device was a metal over silica, two-dimensional nano-grating that was shown to produce enhancements of ˜107 when compared to a smooth surface of the same metal. This SERS substrate also shows unprecedented signal uniformity over square centimeters, and is fabricated using commonly-available foundry-based approaches exclusively. Initially, we explored the properties of a gold-coated substrates in which a first-order grating resonance due to long-range symmetry is augmented by a local resonance due to the individual core-shell grating elements. The SERS properties of such grating systems were systematically studied as a function of various structural parameters such as the grating pitch, the inter-element gap and the thickness of the metal layer. The most enhancing substrates were found to have a grating parameter with a radiative, rather than evanescent, first-order resonance; a sufficiently small gap between nearest neighbor grating elements to produce near-field interactions; and a gold layer whose thickness was larger than the electronic mean-free-path of the conduction electrons, so as to ensure a high conductivity for the metal layer to sustain strong surface plasmons. We applied these same architectural principles to metals other than gold, and concluded that every workable metal (and virtually any material with sufficiently high electrical conductivity) when appropriately nanostructured, has the potential to be an efficient SERS substrate. The use of materials for SERS beyond silver and gold, has significant advantages, most importantly, allowing SERS to be used to study the surface chemistry and catalysis taking place on metals with more interesting chemistries than those of Au and Ag. Additionally, SERS substrates can be fabricated from high natural abundance, low cost materials. This was illustrated by producing SERS substrates using copper, aluminum, and nickel in addition to silver and gold which were used as benchmarks. All five metals were found to yield high SERS intensities. The variation of the SERS enhancement among them is ascribed mainly to local field effects, with the (larger) grating-based enhancement making an approximately equivalent contribution to the SERS enhancement of the five metals. This conclusion is supported by local electric field simulations. The utility of these new grating-based SERS substrates was demonstrated by implementing them in chemical analysis in both aqueous and gas phases for which, for example, we were able to readily detect opioids such as fentanyl and morphine at concentrations as low as less than one part per billion. Additionally, we have made good progress toward integration of this substrate architecture into a microfluidic channel for a higher degree of sample workup and control.

Optimization of top coupling grating for very long wavelength QWIP based on surface plasmon

NASA Astrophysics Data System (ADS)

Wang, Guodong; Shen, Junling; Liu, Xiaolian; Ni, Lu; Wang, Saili

2017-09-01

The relative coupling efficiency of two-dimensional (2D) grating based on surface plasmon for very long wavelength quantum well infrared detector is analyzed by using the three-dimensional finite-difference time domain (3D-FDTD) method algorithm. The relative coupling efficiency with respect to the grating parameters, such as grating pitch, duty ratio, and grating thickness, is analyzed. The calculated results show that the relative coupling efficiency would reach the largest value for the 14.5 μm incident infrared light when taking the grating pitch as 4.4 μm, the duty ratio as 0.325, and the grating thickness as 0.07 μm, respectively.

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Fabrication of Polymer Optical Fibre (POF) Gratings

PubMed Central

Luo, Yanhua; Yan, Binbin; Zhang, Qijin; Peng, Gang-Ding; Wen, Jianxiang; Zhang, Jianzhong

2017-01-01

Gratings inscribed in polymer optical fibre (POF) have attracted remarkable interest for many potential applications due to their distinctive properties. This paper overviews the current state of fabrication of POF gratings since their first demonstration in 1999. In particular we summarize and discuss POF materials, POF photosensitivity, techniques and issues of fabricating POF gratings, as well as various types of POF gratings. PMID:28273844

High-mechanical-strength single-pulse draw tower gratings

NASA Astrophysics Data System (ADS)

Rothhardt, Manfred W.; Chojetzki, Christoph; Mueller, Hans Rainer

2004-11-01

The inscription of fiber Bragg gratings during the drawing process is a very useful method to realize sensor arrays with high numbers of gratings and excellent mechanical strength and also type II gratings with high temperature stability. Results of single pulse grating arrays with numbers up to 100 and definite wavelengths and positions for sensor applications were achieved at 1550 nm and 830 nm using new photosensitive fibers developed in IPHT. Single pulse type I gratings at 1550 nm with more than 30% reflectivity were shown first time to our knowledge. The mechanical strength of this fiber with an Ormocer coating with those single pulse gratings is the same like standard telecom fibers. Weibull plots of fiber tests will be shown. At 830 nm we reached more than 10% reflectivity with single pulse writing during the fiber drawing in photosensitive fibers with less than 16 dB/km transmission loss. These gratings are useful for stress and vibration sensing applications. Type II gratings with reflectivity near 100% and smooth spectral shape and spectral width of about 1 nm are temperature stable up to 1200 K for short time. They are also realized in the fiber drawing process. These gratings are useful for temperature sensor applications.

Astronomical large Ge immersion grating by Canon

NASA Astrophysics Data System (ADS)

Sukegawa, Takashi; Suzuki, Takeshi; Kitamura, Tsuyoshi

2016-07-01

Immersion grating is a powerful optical device for thee infrared high-resolution spectroscope. Germanium (GGe) is the best material for a mid-infrared immersion grating because of Ge has very large reflective index (n=4.0). On the other hands, there is no practical Ge immersion grating under 5umm use. It was very difficult for a fragile IR crystal to manufacture a diffraction grating precisely. Our original free-forming machine has accuracy of a few nano-meter in positioning and stability. We already fabricated the large CdZnTe immersion grating. (Sukegawa et al. (2012), Ikeda et al. (2015)) Wee are developing Ge immersion grating that can be a good solution for high-resolution infrared spectroscopy with the large ground-based/space telescopes. We succeeded practical Ge immersion grating with the grooved area off 75mm (ruled direction) x 119mm (grove width) and the blaze angle of 75 degrees. Our astronomical large Ge immersion grating has the grooved area of 155mm (ruled direction) x 41mmm (groove width) and groove pitch off 91.74um. We also report optical performance of astronomical large Ge immersion grating with a metal coating on the diffraction surface.

Universal Racah matrices and adjoint knot polynomials: Arborescent knots

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2016-04-01

By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.

Imaging characteristics of Zernike and annular polynomial aberrations.

PubMed

Mahajan, Virendra N; Díaz, José Antonio

2013-04-01

The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.

[Design method of convex master gratings for replicating flat-field concave gratings].

PubMed

Zhou, Qian; Li, Li-Feng

2009-08-01

Flat-field concave diffraction grating is the key device of a portable grating spectrometer with the advantage of integrating dispersion, focusing and flat-field in a single device. It directly determines the quality of a spectrometer. The most important two performances determining the quality of the spectrometer are spectral image quality and diffraction efficiency. The diffraction efficiency of a grating depends mainly on its groove shape. But it has long been a problem to get a uniform predetermined groove shape across the whole concave grating area, because the incident angle of the ion beam is restricted by the curvature of the concave substrate, and this severely limits the diffraction efficiency and restricts the application of concave gratings. The authors present a two-step method for designing convex gratings, which are made holographically with two exposure point sources placed behind a plano-convex transparent glass substrate, to solve this problem. The convex gratings are intended to be used as the master gratings for making aberration-corrected flat-field concave gratings. To achieve high spectral image quality for the replicated concave gratings, the refraction effect at the planar back surface and the extra optical path lengths through the substrate thickness experienced by the two divergent recording beams are considered during optimization. This two-step method combines the optical-path-length function method and the ZEMAX software to complete the optimization with a high success rate and high efficiency. In the first step, the optical-path-length function method is used without considering the refraction effect to get an approximate optimization result. In the second step, the approximate result of the first step is used as the initial value for ZEMAX to complete the optimization including the refraction effect. An example of design problem was considered. The simulation results of ZEMAX proved that the spectral image quality of a replicated concave grating is comparable with that of a directly recorded concave grating.

Fabrication of 200 nanometer period centimeter area hard x-ray absorption gratings by multilayer deposition

PubMed Central

Lynch, S K; Liu, C; Morgan, N Y; Xiao, X; Gomella, A A; Mazilu, D; Bennett, E E; Assoufid, L; de Carlo, F; Wen, H

2012-01-01

We describe the design and fabrication trials of x-ray absorption gratings of 200 nm period and up to 100:1 depth-to-period ratios for full-field hard x-ray imaging applications. Hard x-ray phase-contrast imaging relies on gratings of ultra-small periods and sufficient depth to achieve high sensitivity. Current grating designs utilize lithographic processes to produce periodic vertical structures, where grating periods below 2.0 μm are difficult due to the extreme aspect ratios of the structures. In our design, multiple bilayers of x-ray transparent and opaque materials are deposited on a staircase substrate, and mostly on the floor surfaces of the steps only. When illuminated by an x-ray beam horizontally, the multilayer stack on each step functions as a micro-grating whose grating period is the thickness of a bilayer. The array of micro-gratings over the length of the staircase works as a single grating over a large area when continuity conditions are met. Since the layers can be nanometers thick and many microns wide, this design allows sub-micron grating periods and sufficient grating depth to modulate hard x-rays. We present the details of the fabrication process and diffraction profiles and contact radiography images showing successful intensity modulation of a 25 keV x-ray beam. PMID:23066175

Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime

NASA Astrophysics Data System (ADS)

Shui, Tao; Yang, Wen-Xing; Liu, Shaopeng; Li, Ling; Zhu, Zhonghu

2018-03-01

We propose and analyze an efficient scheme for the lopsided Raman-Nath diffraction of one-dimensional (1 D ) and two-dimensional (2 D ) atomic gratings with periodic parity-time (PT )-symmetric refractive index. The atomic grating is constructed by the cold-atomic vapor with two isotopes of rubidium, which is driven by weak probe field and space-dependent control field. Using experimentally achievable parameters, we identify the conditions under which PT -symmetric refractive index allows us to observe the lopsided Raman-Nath diffraction phenomenon and improve the diffraction efficiencies beyond what is achievable in a conventional atomic grating. The nontrivial atomic grating is a superposition of an amplitude grating and a phase grating. It is found that the lopsided Raman-Nath diffraction at the exceptional point (EP) of PT -symmetric grating originates from constructive and destructive interferences between the amplitude and phase gratings. Furthermore, we show that the PT -phase transition from unbroken to broken PT -symmetric regimes can modify the asymmetric distribution of the diffraction spectrum and that the diffraction efficiencies in the non-negative diffraction orders can be significantly enhanced when the atomic grating is pushed into a broken PT -symmetric phase. In addition, we also analyze the influence of the grating thickness on the diffraction spectrum. Our scheme may provide the possibility to design a gain-beam splitter with tunable splitting ratio and other optical components in integrated optics.

[Development of X-ray Reflection Grating Technology for the Constellation-X Mission

NASA Technical Reports Server (NTRS)

Schattenburg, Mark L.

2005-01-01

This Grant supports MIT technology development of x-ray reflection gratings for the Constellation-X Reflection Grating Spectrometer (RGS). Since the start of the Grant MIT has extended its previously-developed patterning and super-smooth, blazed grating fabrication technology to ten-times smaller grating periods and ten-times larger blaze angles to demonstrate feasibility and performance in the off-plane grating geometry. In the past year we have focused our efforts on extending our Nanoruler grating fabrication tool to enable it to perform variable-period scanning-beam interference lithography (VP-SBIL). This new capability required extensive optical and mechanical improvements to the system. The design phase of this work is largely completed and key components are now on order and assembly has begun. Over the next several months the new VP-SBIL Nanoruler system will be completed and testing begun. We have also demonstrated a new technique for patterning gratings using the Nanoruler called Doppler mode, which will be important for patterning the radial groove gratings for the RGS using the new VP-SBIL system. Flat and thin grating substrates will be critical for the RGS. In the last year we demonstrated a new technique for flattening thin substrates using magneto-rheologic fluid polishing (MRF) and achieved 2 arcsecond flatness with a 0.5 mm-thick substrate-a world's record. This meets the Con X requirement for grating substrate flatness.

Applications of polynomial optimization in financial risk investment

NASA Astrophysics Data System (ADS)

Zeng, Meilan; Fu, Hongwei

2017-09-01

Recently, polynomial optimization has many important applications in optimization, financial economics and eigenvalues of tensor, etc. This paper studies the applications of polynomial optimization in financial risk investment. We consider the standard mean-variance risk measurement model and the mean-variance risk measurement model with transaction costs. We use Lasserre's hierarchy of semidefinite programming (SDP) relaxations to solve the specific cases. The results show that polynomial optimization is effective for some financial optimization problems.

A Stochastic Mixed Finite Element Heterogeneous Multiscale Method for Flow in Porous Media

DTIC Science & Technology

2010-08-01

applicable for flow in porous media has drawn significant interest in the last few years. Several techniques like generalized polynomial chaos expansions (gPC...represents the stochastic solution as a polynomial approxima- tion. This interpolant is constructed via independent function calls to the de- terministic...of orthogonal polynomials [34,38] or sparse grid approximations [39–41]. It is well known that the global polynomial interpolation cannot resolve lo

A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or 6 - j Symbols.

DTIC Science & Technology

1978-03-01

Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. [11] D. Stanton, Some basic hypergeometric polynomials arising from... Some bas ic hypergeometr ic an a logues of the classical orthogonal polynomials and applications , to appear. [3] C. de Boor and G. H. Golub , The...Report #1833 A SET OF ORTHOGONAL POLYNOMIALS THAT GENERALIZE THE RACAR COEFFICIENTS OR 6 — j SYMBOLS Richard Askey and James Wilson •

DIFFERENTIAL CROSS SECTION ANALYSIS IN KAON PHOTOPRODUCTION USING ASSOCIATED LEGENDRE POLYNOMIALS

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

P. T. P. HUTAURUK, D. G. IRELAND, G. ROSNER

2009-04-01

Angular distributions of differential cross sections from the latest CLAS data sets,6 for the reaction γ + p→K+ + Λ have been analyzed using associated Legendre polynomials. This analysis is based upon theoretical calculations in Ref. 1 where all sixteen observables in kaon photoproduction can be classified into four Legendre classes. Each observable can be described by an expansion of associated Legendre polynomial functions. One of the questions to be addressed is how many associated Legendre polynomials are required to describe the data. In this preliminary analysis, we used data models with different numbers of associated Legendre polynomials. We thenmore » compared these models by calculating posterior probabilities of the models. We found that the CLAS data set needs no more than four associated Legendre polynomials to describe the differential cross section data. In addition, we also show the extracted coefficients of the best model.« less

Tutte polynomial in functional magnetic resonance imaging

NASA Astrophysics Data System (ADS)

García-Castillón, Marlly V.

2015-09-01

Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

Influence of dielectric protective layer on laser damage resistance of gold coated gratings

NASA Astrophysics Data System (ADS)

Wu, Kepeng; Ma, Ping; Pu, Yunti; Xia, Zhilin

2016-03-01

Aiming at the problem that the damage threshold of gold coated grating is relatively low, a dielectric film is considered on the gold coated gratings as a protective layer. The thickness range of the protective layer is determined under the prerequisite that the diffraction efficiency of the gold coated grating is reduced to an acceptable degree. In this paper, the electromagnetic field, the temperature field and the stress field distribution in the grating are calculated when the silica and hafnium oxide are used as protective layers, under the preconditions of the electromagnetic field distribution of the gratings known. The results show that the addition of the protective layer changes the distribution of the electromagnetic field, temperature field and stress field in the grating, and the protective layer with an appropriate thickness can improve the laser damage resistance of the grating.

Nanostructure Diffraction Gratings for Integrated Spectroscopy and Sensing

NASA Technical Reports Server (NTRS)

Guo, Junpeng (Inventor)

2015-01-01

The present disclosure pertains to metal or dielectric nanostructures of the subwavelength scale within the grating lines of optical diffraction gratings. The nanostructures have surface plasmon resonances or non-plasmon optical resonances. A linear photodetector array is used to capture the resonance spectra from one of the diffraction orders. The combined nanostructure super-grating and photodetector array eliminates the use of external optical spectrometers for measuring surface plasmon or optical resonance frequency shift caused by the presence of chemical and biological agents. The nanostructure super-gratings can be used for building integrated surface enhanced Raman scattering (SERS) spectrometers. The nanostructures within the diffraction grating lines enhance Raman scattering signal light while the diffraction grating pattern of the nanostructures diffracts Raman scattering light to different directions of propagation according to their wavelengths. Therefore, the nanostructure super-gratings allows for the use of a photodetector array to capture the surface enhanced Raman scattering spectra.

Nanostructure Diffraction Gratings for Integrated Spectroscopy and Sensing

NASA Technical Reports Server (NTRS)

Guo, Junpeng (Inventor)

2016-01-01

The present disclosure pertains to metal or dielectric nanostructures of the subwavelength scale within the grating lines of optical diffraction gratings. The nanostructures have surface plasmon resonances or non-plasmon optical resonances. A linear photodetector array is used to capture the resonance spectra from one of the diffraction orders. The combined nanostructure super-grating and photodetector array eliminates the use of external optical spectrometers for measuring surface plasmon or optical resonance frequency shift caused by the presence of chemical and biological agents. The nanostructure super-gratings can be used for building integrated surface enhanced Raman scattering (SERS) spectrometers. The nanostructures within the diffraction grating lines enhance Raman scattering signal light while the diffraction grating pattern of the nanostructures diffracts Raman scattering light to different directions of propagation according to their wavelengths. Therefore, the nanostructure super-gratings allows for the use of a photodetector array to capture the surface enhanced Raman scattering spectra.

Resonant quantum efficiency enhancement of midwave infrared nBn photodetectors using one-dimensional plasmonic gratings

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

Nolde, Jill A., E-mail: jill.nolde@nrl.navy.mil; Kim, Chul Soo; Jackson, Eric M.

2015-06-29

We demonstrate up to 39% resonant enhancement of the quantum efficiency (QE) of a low dark current nBn midwave infrared photodetector with a 0.5 μm InAsSb absorber layer. The enhancement was achieved by using a 1D plasmonic grating to couple incident light into plasmon modes propagating in the plane of the device. The plasmonic grating is composed of stripes of deposited amorphous germanium overlaid with gold. Devices with and without gratings were processed side-by-side for comparison of their QEs and dark currents. The peak external QE for a grating device was 29% compared to 22% for a mirror device when themore » illumination was polarized perpendicularly to the grating lines. Additional experiments determined the grating coupling efficiency by measuring the reflectance of analogous gratings deposited on bare GaSb substrates.« less

Spatio-temporal modeling and optimization of a deformable-grating compressor for short high-energy laser pulses

DOE PAGES

Qiao, Jie; Papa, J.; Liu, X.

2015-09-24

Monolithic large-scale diffraction gratings are desired to improve the performance of high-energy laser systems and scale them to higher energy, but the surface deformation of these diffraction gratings induce spatio-temporal coupling that is detrimental to the focusability and compressibility of the output pulse. A new deformable-grating-based pulse compressor architecture with optimized actuator positions has been designed to correct the spatial and temporal aberrations induced by grating wavefront errors. An integrated optical model has been built to analyze the effect of grating wavefront errors on the spatio-temporal performance of a compressor based on four deformable gratings. Moreover, a 1.5-meter deformable gratingmore » has been optimized using an integrated finite-element-analysis and genetic-optimization model, leading to spatio-temporal performance similar to the baseline design with ideal gratings.« less

A simple mathematical model based on biomarkers in stress-resistant catfish species, Sciades herzbergii (Pisces, Ariidae), in São Marcos Bay, Brazil.

PubMed

Carvalho Neta, Raimunda Nonata Fortes; Torres Junior, Audalio Rebelo; Silva, Dilson; Cortez, Célia Martins

2014-12-01

We present a refinement of our model describing the association between enzyme activity and histopathological lesions in the catfish, Sciades herzbergii from a polluted port. The fish were sampled from a port known to be contaminated with heavy metals and organic compounds and from a natural reserve in São Marcos Bay, Brazil. Two biomarkers, hepatic glutathione S-transferase (GST) activity and histopathological lesions, in gills and liver tissue were measured. The values for GST activity were modeled with the occurrence of branchial and hepatic lesions by fitting a third-order polynomial. Results from the mathematical model indicate that GST activity has a strong polynomial relationship with the occurrence of branchial and hepatic lesions in both wet and the dry seasons but only at the polluted port site. The model developed in this study indicates that branchial and hepatic lesions are initiated when GST activity reaches 2.17 μmol min(-1) mg protein(-1). Beyond this limit, GST activity decreased to very low levels and irreversible histopathological lesions occurred. This mathematical model based on two biomarkers (histopathological lesions and enzyme activity) in catfish provides a realistic approach to analyze stress induced by contaminants.

Inverted Ultrathin Organic Solar Cells with a Quasi-Grating Structure for Efficient Carrier Collection and Dip-less Visible Optical Absorption.

PubMed

In, Sungjun; Park, Namkyoo

2016-02-23

We propose a metallic-particle-based two-dimensional quasi-grating structure for application to an organic solar cell. With the use of oblate spheroidal nanoparticles in contact with an anode of inverted, ultrathin organic solar cells (OSCs), the quasi-grating structure offers strong hybridization between localized surface plasmons and plasmonic gap modes leading to broadband (300~800 nm) and uniform (average ~90%) optical absorption spectra. Both strong optical enhancement in extreme confinement within the active layer (90 nm) and improved hole collection are thus realized. A coupled optical-electrical multi-physics optimization shows a large (~33%) enhancement in the optical absorption (corresponding to an absorption efficiency of ~47%, AM1.5G weighted, visible) when compared to a control OSC without the quasi-grating structure. That translates into a significant electrical performance gain of ~22% in short circuit current and ~15% in the power conversion efficiency (PCE), leading to an energy conversion efficiency (~6%) which is comparable to that of optically-thick inverted OSCs (3-7%). Detailed analysis on the influences of mode hybridization to optical field distributions, exciton generation rate, charge carrier collection efficiency and electrical conversion efficiency is provided, to offer an integrated understanding on the coupled optical-electrical optimization of ultrathin OSCs.

Imaging Grating Spectrometer (I-GRASP) for Solar Soft X-Ray Spectral Measurements in Critically Under-Observed 0.5 - 7 nm Spectral Range

NASA Astrophysics Data System (ADS)

Didkovsky, L. V.; Wieman, S. R.; Chao, W.; Woods, T. N.; Jones, A. R.; Thiemann, E.; Mason, J. P.

2016-12-01

We discuss science and technology advantages of the Imaging Grating Spectrometer (I-GRASP) based on a novel transmission diffracting grating (TDG) made possible by technology for fabricating Fresnel zone plates (ZPs) developed at the Lawrence Berkeley National Laboratory (LBNL). Older version TDGs with 200 nm period available in the 1990s became a proven technology for providing 21 years of regular measurements of solar EUV irradiance. I-GRASP incorporates an advanced TDG with a grating period of 50 nm providing four times better diffraction dispersion than the 200 nm period gratings used in the SOHO/CELIAS/SEM, the SDO/EVE/ESP flight spectrophotometers, and the EVE/SAM sounding rocket channel. Such new technology for the TDG combined with a back-illuminated 2000 x 1504 CMOS image sensor with 7 micron pixels, will provide spatially-and-spectrally resolved images and spectra from individual Active Regions (ARs) and solar flares with high (0.15 nm) spectral resolution. Such measurements are not available in the spectral band from about 2 to 6 nm from existing or planned spectrographs and will be significantly important to study ARs and solar flare temperatures and dynamics, to improve existing spectral models, e.g. CHIANTI, and to better understand processes in the Earth's atmosphere processes. To test this novel technology, we have proposed to the NASA LCAS program an I-GRASP version for a sounding rocket flight to increase the TDG TRL to a level appropriate for future CubeSat projects.

Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

NASA Astrophysics Data System (ADS)

Recchioni, Maria Cristina

2001-12-01

This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography.

PubMed

Cazac, V; Meshalkin, A; Achimova, E; Abashkin, V; Katkovnik, V; Shevkunov, I; Claus, D; Pedrini, G

2018-01-20

Surface relief gratings and refractive index gratings are formed by direct holographic recording in amorphous chalcogenide nanomultilayer structures As 2 S 3 -Se and thin films As 2 S 3 . The evolution of the grating parameters, such as the modulation of refractive index and relief depth in dependence of the holographic exposure, is investigated. Off-axis digital holographic microscopy is applied for the measurement of the photoinduced phase gratings. For the high-accuracy reconstruction of the wavefront (amplitude and phase) transmitted by the fabricated gratings, we used a computational technique based on the sparse modeling of phase and amplitude. Both topography and refractive index maps of recorded gratings are revealed. Their separated contribution in diffraction efficiency is estimated.

Fabrication of absorption gratings with X-ray lithography for X-ray phase contrast imaging

NASA Astrophysics Data System (ADS)

Wang, Bo; Wang, Yu-Ting; Yi, Fu-Ting; Zhang, Tian-Chong; Liu, Jing; Zhou, Yue

2018-05-01

Grating-based X-ray phase contrast imaging is promising especially in the medical area. Two or three gratings are involved in grating-based X-ray phase contrast imaging in which the absorption grating of high-aspect-ratio is the most important device and the fabrication process is a great challenge. The material with large atomic number Z is used to fabricate the absorption grating for excellent absorption of X-ray, and Au is usually used. The fabrication process, which involves X-ray lithography, development and gold electroplating, is described in this paper. The absorption gratings with 4 μm period and about 100 μm height are fabricated and the high-aspect-ratio is 50.

Ultrafast transient grating radiation to optical image converter

DOEpatents

Stewart, Richard E; Vernon, Stephen P; Steel, Paul T; Lowry, Mark E

2014-11-04

A high sensitivity transient grating ultrafast radiation to optical image converter is based on a fixed transmission grating adjacent to a semiconductor substrate. X-rays or optical radiation passing through the fixed transmission grating is thereby modulated and produces a small periodic variation of refractive index or transient grating in the semiconductor through carrier induced refractive index shifts. An optical or infrared probe beam tuned just below the semiconductor band gap is reflected off a high reflectivity mirror on the semiconductor so that it double passes therethrough and interacts with the radiation induced phase grating therein. A small portion of the optical beam is diffracted out of the probe beam by the radiation induced transient grating to become the converted signal that is imaged onto a detector.

Integrated optic head for sensing a two-dimensional displacement of a grating scale

NASA Astrophysics Data System (ADS)

Ura, Shogo; Endoh, Toshiaki; Suhara, Toshiaki; Nishihara, Hiroshi

1996-11-01

An integrated optic sensor head was proposed for sensing a two-dimensional displacement of a scale consisting of crossed gratings. Two interferometers, crossing each other, are constructed by the integration of two pairs of linearly focusing grating couplers (LFGC's) and two pairs of photodiodes (PD's) on a Si substrate. Four beams radiated by the LFGC's from the sensor head overlap on the grating scale, and the beams are diffracted by the grating scale and interfere on the PD's. The period of the interference signal variation is just half of the scale grating period. The device was designed and fabricated with a grating scale of 3.2- mu m period, and the sensing principle was experimentally confirmed.

Experimental demonstration of high sensitivity for silver rectangular grating-coupled surface plasmon resonance (SPR) sensing

NASA Astrophysics Data System (ADS)

Dai, Yanqiu; Xu, Huimei; Wang, Haoyu; Lu, Yonghua; Wang, Pei

2018-06-01

We experimentally demonstrated a high sensitivity of surface plasmon resonance (SPR) sensor with silver rectangular grating coupling. The reflection spectra of the silver gratings indicated that surface plasmon resonance can be excited by either positive or negative order diffraction of the grating, depending on the period of the gratings. Comparing to prism-coupled SPR sensor, the sensitivities are higher for negative order diffraction coupling in bigger coupling angle, but much smaller for positive order diffraction coupling of the gratings. High sensitivity of 254.13 degree/RIU is experimentally realized by grating-based SPR sensor in the negative diffraction excitation mode. Our work paves the way for compact and sensitive SPR sensor in the applications of biochemical and gas sensing.

[Research on the photoelectric conversion efficiency of grating antireflective layer solar cells].

PubMed

Zhong, Hui; Gao, Yong-Yi; Zhou, Ren-Long; Zhou, Bing-ju; Tang, Li-qiang; Wu, Ling-xi; Li, Hong-jian

2011-07-01

A numerical investigation of the effect of grating antireflective layer structure on the photoelectric conversion efficiency of solar cells was carried out by the finite-difference time-domain method. The influence of grating shape, height and the metal film thickness coated on grating surface on energy storage was analyzed in detail. It was found that the comparison between unoptimized and optimized surface grating structure on solar cells shows that the optimization of surface by grating significantly increases the energy storage capability and greatly improves the efficiency, especially of the photoelectric conversion efficiency and energy storage of the triangle grating. As the film thickness increases, energy storage effect increases, while as the film thickness is too thick, energy storage effect becomes lower and lower.

Echelle grating multi-order imaging spectrometer utilizing a catadioptric lens

DOEpatents

Chrisp, Michael P; Bowers, Joel M

2014-05-27

A cryogenically cooled imaging spectrometer that includes a spectrometer housing having a first side and a second side opposite the first side. An entrance slit is on the first side of the spectrometer housing and directs light to a cross-disperser grating. An echelle immersions grating and a catadioptric lens are positioned in the housing to receive the light. A cryogenically cooled detector is located in the housing on the second side of the spectrometer housing. Light from the entrance slit is directed to the cross-disperser grating. The light is directed from the cross-disperser grating to the echelle immersions grating. The light is directed from the echelle immersions grating to the cryogenically cooled detector on the second side of the spectrometer housing.

X-ray verification of an optically aligned off-plane grating module

NASA Astrophysics Data System (ADS)

Donovan, Benjamin D.; McEntaffer, Randall L.; Tutt, James H.; DeRoo, Casey T.; Allured, Ryan; Gaskin, Jessica A.; Kolodziejczak, Jeffery J.

2018-01-01

Off-plane x-ray reflection gratings are theoretically capable of achieving high resolution and high diffraction efficiencies over the soft x-ray bandpass, making them an ideal technology to implement on upcoming x-ray spectroscopy missions. To achieve high effective area, these gratings must be aligned into grating modules. X-ray testing was performed on an aligned grating module to assess the current optical alignment methods. Results indicate that the grating module achieved the desired alignment for an upcoming x-ray spectroscopy suborbital rocket payload with modest effective area and resolving power. These tests have also outlined a pathway towards achieving the stricter alignment tolerances of future x-ray spectrometer payloads, which require improvements in alignment metrology, grating fabrication, and testing techniques.

D-shaped fiber grating refractive index sensor induced by an ultrashort pulse laser.

PubMed

Liao, Changrui; Wang, Qiao; Xu, Lei; Liu, Shen; He, Jun; Zhao, Jing; Li, Zhengyong; Wang, Yiping

2016-03-01

The fabrication of fiber Bragg gratings was here demonstrated using ultrashort pulse laser point-by-point inscription. This is a very convenient means of creating fiber Bragg gratings with different grating periods and works by changing the translation speed of the fiber. The laser energy was first optimized in order to improve the spectral properties of the fiber gratings. Then, fiber Bragg gratings were formed into D-shaped fibers for use as refractive index sensors. A nonlinear relationship was observed between the Bragg wavelength and liquid refractive index, and a sensitivity of ∼30  nm/RIU was observed at 1.450. This shows that D-shaped fiber Bragg gratings might be used to develop promising biochemical sensors.

NASA Astrophysics Data System (ADS)

Schattenburg, Mark

Development of a Critical Angle Transmission Grating Spectrometer With APRA and SAT support, MIT has developed a unique blazed soft x-ray diffraction grating called the critical-angle transmission (CAT) grating. This device combines the high diffraction efficiency and resolving power of blazed reflection gratings with the low mass, low power, compact packaging and simple alignment of transmission gratings. We have shown that a spectrometer based on CAT gratings represents a huge leap forward in instrument scientific performance compared to previous missions, leading to much increased collecting area and spectral resolving power, which in turn results in orders-ofmagnitude improvement in figures-of-merit for emission and absorption line spectroscopy. MIT proposes to bring CAT x-ray grating spectrometer (CATXGS) technology to a higher Technology Readiness Level (TRL). We will increase fabrication yield and grating performance, and develop bonding techniques for grating membranes and alignment techniques for grating arrays. We will build and test robust grating arrays for space deployment, and perform thorough environmental testing. We are very close to achieving TRL4 and ready to move on to TRL5, which we can achieve within the period covered by this proposal. Our rapid progress over the last year was made possible by significant prior investments in our infrastructure, but further progress will require further investments. Since 2007 we have - with NASA support - demonstrated the CAT grating principle, and prototypes of increasing quality and size have verified theoretical predictions, putting the technology at a solid TRL3. Recent NASA and MIT investments in fabrication and metrology infrastructure has been justified by our rapid progress during the last year: the fabrication of practically defect-free CAT gratings with record diffraction efficiency, the demonstration of extended bandpass CAT gratings using conformal deposition of thin metal films via atomic layer deposition (ALD), and the demonstration of record-setting resolving power for an XGS on the order of R = 10,000, which exceeds the requirements for all currently proposed mission concepts. Grating fabrication still consumes the lion's share of our efforts and time. In order to maintain momentum and continue progress towards TRL5 in an efficient manner we need to improve our fabrication infrastructure further to accelerate grating fabrication and increase yield, so we can devote more resources to the new work required for reaching TRL5.

Two-port connecting-layer-based sandwiched grating by a polarization-independent design.

PubMed

Li, Hongtao; Wang, Bo

2017-05-02

In this paper, a two-port connecting-layer-based sandwiched beam splitter grating with polarization-independent property is reported and designed. Such the grating can separate the transmission polarized light into two diffraction orders with equal energies, which can realize the nearly 50/50 output with good uniformity. For the given wavelength of 800 nm and period of 780 nm, a simplified modal method can design a optimal duty cycle and the estimation value of the grating depth can be calculated based on it. In order to obtain the precise grating parameters, a rigorous coupled-wave analysis can be employed to optimize grating parameters by seeking for the precise grating depth and the thickness of connecting layer. Based on the optimized design, a high-efficiency two-port output grating with the wideband performances can be gained. Even more important, diffraction efficiencies are calculated by using two analytical methods, which are proved to be coincided well with each other. Therefore, the grating is significant for practical optical photonic element in engineering.

On a Family of Multivariate Modified Humbert Polynomials

PubMed Central

Aktaş, Rabia; Erkuş-Duman, Esra

2013-01-01

This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials. PMID:23935411

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

Lue Xing; Sun Kun; Wang Pan

In the framework of Bell-polynomial manipulations, under investigation hereby are three single-field bilinearizable equations: the (1+1)-dimensional shallow water wave model, Boiti-Leon-Manna-Pempinelli model, and (2+1)-dimensional Sawada-Kotera model. Based on the concept of scale invariance, a direct and unifying Bell-polynomial scheme is employed to achieve the Baecklund transformations and Lax pairs associated with those three soliton equations. Note that the Bell-polynomial expressions and Bell-polynomial-typed Baecklund transformations for those three soliton equations can be, respectively, cast into the bilinear equations and bilinear Baecklund transformations with symbolic computation. Consequently, it is also shown that the Bell-polynomial-typed Baecklund transformations can be linearized into the correspondingmore » Lax pairs.« less

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1989-01-01

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

Factor affecting happiness among nursing students in South Korea.

PubMed

Jun, W H; Jo, M J

2016-08-01

WHAT IS KNOWN ON THE SUBJECT?: Despite the increased interest in nursing students' happiness in South Korea, few studies have attempted to identify factors influencing their happiness. Therefore, nursing educators should consistently investigate the factors influencing happiness and develop strategies to improve happiness among Korean nursing students. WHAT THIS PAPER ADDS TO EXISTING KNOWLEDGE?: This study confirmed that there were positive correlations between grateful disposition, social support and happiness. In addition, grateful disposition and support from intimate people were identified as predictors of happiness in Korean nursing students. WHAT ARE THE IMPLICATIONS FOR PRACTICE?: Development of intervention programmes to help nursing students increase grateful disposition and support from intimate people may be helpful for improving happiness. These programmes can include activity, such as writing a gratitude journal, and extracurricular programmes, such as mentoring programmes between seniors and juniors and/or professor and student. Introduction Happiness is very important in the training and development of nursing students as future nurses. However, nursing students experience a high level of stress and low level of happiness in South Korea. Aim This study aimed to investigate factors that affect happiness among nursing students in South Korea. Method Data were collected from a total of 241 nursing enrolled in two 4-year baccalaureate nursing programmes in South Korea, using a self-administrated questionnaire. To identify predictors of happiness, stepwise regression analysis was conducted. Results The results indicated that grateful disposition and support from intimate people significantly predict happiness among Korean nursing students. These two factors accounted for 38.0% of the variance in happiness. Discussion This study indicated grateful disposition and support from intimate people as factors promoting happiness in nursing students. The findings highlight grateful disposition and support from intimate people as important factors when developing effective interventions that foster nursing students' happiness. © 2016 John Wiley & Sons Ltd.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

Writing and applications of fiber Bragg grating arrays

NASA Astrophysics Data System (ADS)

LaRochelle, Sophie; Cortes, Pierre-Yves; Fathallah, H.; Rusch, Leslie A.; Jaafar, H. B.

2000-12-01

Multiple Bragg gratings are written in a single fibre strand with accurate positioning to achieve predetermined time delays between optical channels. Applications of fibre Bragg grating arrays include encoders/decoders with series of identical gratings for optical code-division multiple access.

Grazing-incidence grating compressor for applications to free-electron-lasers

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

Frassetto, Fabio, E-mail: fabio.frassetto@pd.ifn.cnr.it; Miotti, Paolo; Poletto, Luca, E-mail: luca.poletto@ifn.cnr.it

2016-07-27

The design of a grating compressor for FEL pulses is discussed here. The design is based on the use of two grazing-incidence gratings. The available grating geometries, the classical diffraction mount and the off-plane one, are discussed.

A novel dispersion compensating fiber grating with a large chirp parameter and period sampled distribution

NASA Astrophysics Data System (ADS)

Xia, Li; Li, Xuhui; Chen, Xiangfei; Xie, Shizhong

2003-11-01

A novel fiber grating structure is proposed for the purpose of dispersion compensation. This kind of grating can be produced with a large chirp parameter and period sampled distribution along the grating length. There are multiple channels in the wide bandwidth and each channel has totally different dispersion and bandwidth. The dispersion compensation effect of this special designed grating is verified through system simulation.

Multilayer dielectric diffraction gratings

DOEpatents

Perry, Michael D.; Britten, Jerald A.; Nguyen, Hoang T.; Boyd, Robert; Shore, Bruce W.

1999-01-01

The design and fabrication of dielectric grating structures with high diffraction efficiency used in reflection or transmission is described. By forming a multilayer structure of alternating index dielectric materials and placing a grating structure on top of the multilayer, a diffraction grating of adjustable efficiency, and variable optical bandwidth can be obtained. Diffraction efficiency into the first order in reflection varying between 1 and 98 percent has been achieved by controlling the design of the multilayer and the depth, shape, and material comprising the grooves of the grating structure. Methods for fabricating these gratings without the use of ion etching techniques are described.

Multilayer dielectric diffraction gratings

DOEpatents

Perry, M.D.; Britten, J.A.; Nguyen, H.T.; Boyd, R.; Shore, B.W.

1999-05-25

The design and fabrication of dielectric grating structures with high diffraction efficiency used in reflection or transmission is described. By forming a multilayer structure of alternating index dielectric materials and placing a grating structure on top of the multilayer, a diffraction grating of adjustable efficiency, and variable optical bandwidth can be obtained. Diffraction efficiency into the first order in reflection varying between 1 and 98 percent has been achieved by controlling the design of the multilayer and the depth, shape, and material comprising the grooves of the grating structure. Methods for fabricating these gratings without the use of ion etching techniques are described. 7 figs.

Parameter-tolerant design of high contrast gratings

NASA Astrophysics Data System (ADS)

Chevallier, Christyves; Fressengeas, Nicolas; Jacquet, Joel; Almuneau, Guilhem; Laaroussi, Youness; Gauthier-Lafaye, Olivier; Cerutti, Laurent; Genty, Frédéric

2015-02-01

This work is devoted to the design of high contrast grating mirrors taking into account the technological constraints and tolerance of fabrication. First, a global optimization algorithm has been combined to a numerical analysis of grating structures (RCWA) to automatically design HCG mirrors. Then, the tolerances of the grating dimensions have been precisely studied to develop a robust optimization algorithm with which high contrast gratings, exhibiting not only a high efficiency but also large tolerance values, could be designed. Finally, several structures integrating previously designed HCGs has been simulated to validate and illustrate the interest of such gratings.

Fiber-bragg grating-loop ringdown method and apparatus

DOEpatents

Wang, Chuji [Starkville, MS

2008-01-29

A device comprising a fiber grating loop ringdown (FGLRD) system of analysis is disclosed. A fiber Bragg grating (FBG) or Long-Period grating (LPG) written in a section of single mode fused silica fiber is incorporated into a fiber loop. By utilizing the wing areas of the gratings' bandwidth as a wavelength dependent attenuator of the light transmission, a fiber grating loop ringdown concept is formed. One aspect of the present invention is temperature sensing, which has been demonstrated using the disclosed device. Temperature measurements in the areas of accuracy, stability, high temperature, and dynamic range are also described.

Three-port beam splitter of a binary fused-silica grating.

PubMed

Feng, Jijun; Zhou, Changhe; Wang, Bo; Zheng, Jiangjun; Jia, Wei; Cao, Hongchao; Lv, Peng

2008-12-10

A deep-etched polarization-independent binary fused-silica phase grating as a three-port beam splitter is designed and manufactured. The grating profile is optimized by use of the rigorous coupled-wave analysis around the 785 nm wavelength. The physical explanation of the grating is illustrated by the modal method. Simple analytical expressions of the diffraction efficiencies and modal guidelines for the three-port beam splitter grating design are given. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results are in good agreement with the theoretical values.

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

NASA Astrophysics Data System (ADS)

Janicijevic, Ljiljana; Topuzoski, Suzana

2007-04-01

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

Innovative diffraction gratings for high-resolution resonant inelastic soft x-ray scattering spectroscopy

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

Voronov, D.L.; Warwick, T.; Gullikson, E. M.

2016-07-27

High-resolution Resonant Inelastic X-ray Scattering (RIXS) requires diffraction gratings with very exacting characteristics. The gratings should provide both very high dispersion and high efficiency which are conflicting requirements and extremely challenging to satisfy in the soft x-ray region for a traditional grazing incidence geometry. To achieve high dispersion one should increase the groove density of a grating; this however results in a diffraction angle beyond the critical angle range and results in drastic efficiency loss. The problem can be solved by use of multilayer coated blazed gratings (MBG). In this work we have investigated the diffraction characteristics of MBGs viamore » numerical simulations and have developed a procedure for optimization of grating design for a multiplexed high resolution imaging spectrometer for RIXS spectroscopy to be built in sector 6 at the Advanced Light Source (ALS). We found that highest diffraction efficiency can be achieved for gratings optimized for 4{sup th} or 5{sup th} order operation. Fabrication of such gratings is an extremely challenging technological problem. We present a first experimental prototype of these gratings and report its performance. High order and high line density gratings have the potential to be a revolutionary new optical element that should have great impact in the area of soft x-ray RIXS.« less

Chiral fiber sensors

NASA Astrophysics Data System (ADS)

Kopp, Victor I.; Churikov, Victor M.; Singer, Jonathan; Neugroschl, Daniel; Genack, Azriel Z.

2010-04-01

We have fabricated a variety of chiral fiber sensors by twisting one or more standard or custom optical fibers with noncircular or nonconcentric core as they pass though a miniature oven. The resulting structures are as stable as the glass material and can be produced with helical pitch ranging from microns to hundreds of microns. The polarization selectivity of the chiral gratings is determined by the geometry of the fiber cross section. Single helix structures are polarization insensitive, while double helix gratings interact only with a single optical polarization component. Both single and double helix gratings may function as a fiber long period grating, coupling core and cladding modes or as a diffraction grating scattering light from the fiber core out of the fiber. The resulting dips in the transmission spectrum are sensitive to fiber elongation, twist and temperature, and (in the case of the long period gratings) to the refractive index of the surrounding medium. The suitability of chiral gratings for sensing temperature, elongation, twist and liquid levels will be discussed. Gratings made of radiation sensitive glass can be used to measure the cumulative radiation dose, while gratings made of radiation-hardened glass are suitable for stable sensing of the environment in nuclear power plants. Excellent temperature stability up to 900°C is found in pure silica chiral diffraction grating sensors.

Diffraction Gratings for High-Intensity Laser Applications

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

Britten, J

The scattering of light into wavelength-dependent discrete directions (orders) by a device exhibiting a periodic modulation of a physical attribute on a spatial scale similar to the wavelength of light has been the subject of study for over 200 years. Such a device is called a diffraction grating. Practical applications of diffraction gratings, mainly for spectroscopy, have been around for over 100 years. The importance of diffraction gratings in spectroscopy for the measurement of myriad properties of matter can hardly be overestimated. Since the advent of coherent light sources (lasers) in the 1960's, applications of diffraction gratings in spectroscopy havemore » further exploded. Lasers have opened a vast application space for gratings, and apace, gratings have enabled entirely new classes of laser systems. Excellent reviews of the history, fundamental properties, applications and manufacturing techniques of diffraction gratings up to the time of their publication can be found in the books by Hutley (1) and more recently Loewen and Popov (2). The limited scope of this chapter can hardly do justice to such a comprehensive subject, so the focus here will be narrowly limited to characteristics required for gratings suitable for high-power laser applications, and methods to fabricate them. A particular area of emphasis will be on maximally-efficient large-aperture gratings for short-pulse laser generation.« less

Cross-fiber Bragg grating transducer

NASA Technical Reports Server (NTRS)

Albin, Sacharia (Inventor); Zheng, Jianli (Inventor); Lavarias, Arnel (Inventor)

2000-01-01

A transducer has been invented that uses specially-oriented gratings in waveguide a manner that allows the simultaneous measurement of physical phenomena (such as shear force, strain and temperature) in a single sensing element. The invention has a highly sensitive, linear response and also has directional sensitivity with regard to strain. The transducer has a waveguide with a longitudinal axis as well as two Bragg gratings. The transducer has a first Bragg grating associated with the waveguide that has an angular orientation .theta..sub.a relative to a perpendicular to the longitudinal axis such that 0.degree.<.theta..sub.a <.theta..sub.max. The second Bragg grating is associated with the waveguide in such a way that the angular orientation .theta..sub.b of the grating relative to a perpendicular to the longitudinal axis is (360.degree.-.theta..sub.max)<.theta..sub.b <360.degree.. The first Bragg grating can have a periodicity .LAMBDA..sub.a and the second Bragg grating can have a periodicity .LAMBDA..sub.b such that the periodicity .LAMBDA..sub.a of the first Bragg grating does not equal the periodicity .LAMBDA..sub.b of the second Bragg grating. The angle of the gratings can be such that .theta..sub.a =360.degree.-.theta..sub.b. The waveguide can assume a variety of configurations, including an optical fiber, a rectangular waveguide and a planar waveguide. The waveguide can be fabricated of a variety of materials, including silica and polymer material.

Evaluation of catch basin grates : final report.

DOT National Transportation Integrated Search

1972-10-01

The Louisiana Department of Highways has adopted new designs for the Standard Plans for the RCB 22X catch basin to replace the old standard cast iron grate with either a welded bar steel grate or an alternate riveted steel reticuline grate. This revi...

A user-friendly LabVIEW software platform for grating based X-ray phase-contrast imaging.

PubMed

Wang, Shenghao; Han, Huajie; Gao, Kun; Wang, Zhili; Zhang, Can; Yang, Meng; Wu, Zhao; Wu, Ziyu

2015-01-01

X-ray phase-contrast imaging can provide greatly improved contrast over conventional absorption-based imaging for weakly absorbing samples, such as biological soft tissues and fibre composites. In this study, we introduced an easy and fast way to develop a user-friendly software platform dedicated to the new grating-based X-ray phase-contrast imaging setup at the National Synchrotron Radiation Laboratory of the University of Science and Technology of China. The control of 21 motorized stages, of a piezoelectric stage and of an X-ray tube are achieved with this software, it also covers image acquisition with a flat panel detector for automatic phase stepping scan. Moreover, a data post-processing module for signals retrieval and other custom features are in principle available. With a seamless integration of all the necessary functions in one software package, this platform greatly facilitate users' activities during experimental runs with this grating based X-ray phase contrast imaging setup.

Stability test of the silicon Fiber Bragg Grating embroidered on textile for joint angle measurement

NASA Astrophysics Data System (ADS)

Apiwattanadej, Thanit; Chun, Byung Jae; Lee, Hyub; Li, King Ho Holden; Kim, Young-Jin

2017-06-01

Recently, Fiber Bragg Grating (FBG) sensors are being used for motion tracking applications. However, the sensitivity, linearity and stability of the systems have not been fully studied. Herein, an embroidered optical Fiber Bragg Grating (FBG) on a stretchable supportive textile for elbow movement measurement was developed. The sensing principle of this system is based on the alteration of Bragg wavelength due to strain from the elbow movements. The relationship between elbow movements and reflected Bragg wavelength was found to be linear. The dynamic range of FBG sensor on elbow support is between 0 and 120 degree. Finally, the stability of the FBG sensor on the supportive textile was tested during the exercise and the cleaning process with water. The sensitivity of FBG sensors for joint angle measurement and the effect of the movement and cleaning process to signals from FBG sensors after using in the real activity will be the basis knowledge for design and actual implementation of future optical fiber based wearable devices.

Polynomial time blackbox identity testers for depth-3 circuits : the field doesn't matter.

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

Seshadhri, Comandur; Saxena, Nitin

Let C be a depth-3 circuit with n variables, degree d and top fanin k (called {Sigma}{Pi}{Sigma}(k, d, n) circuits) over base field F. It is a major open problem to design a deterministic polynomial time blackbox algorithm that tests if C is identically zero. Klivans & Spielman (STOC 2001) observed that the problem is open even when k is a constant. This case has been subjected to a serious study over the past few years, starting from the work of Dvir & Shpilka (STOC 2005). We give the first polynomial time blackbox algorithm for this problem. Our algorithm runsmore » in time poly(n)d{sup k}, regardless of the base field. The only field for which polynomial time algorithms were previously known is F = Q (Kayal & Saraf, FOCS 2009, and Saxena & Seshadhri, FOCS 2010). This is the first blackbox algorithm for depth-3 circuits that does not use the rank based approaches of Karnin & Shpilka (CCC 2008). We prove an important tool for the study of depth-3 identities. We design a blackbox polynomial time transformation that reduces the number of variables in a {Sigma}{Pi}{Sigma}(k, d, n) circuit to k variables, but preserves the identity structure. Polynomial identity testing (PIT) is a major open problem in theoretical computer science. The input is an arithmetic circuit that computes a polynomial p(x{sub 1}, x{sub 2},..., x{sub n}) over a base field F. We wish to check if p is the zero polynomial, or in other words, is identically zero. We may be provided with an explicit circuit, or may only have blackbox access. In the latter case, we can only evaluate the polynomial p at various domain points. The main goal is to devise a deterministic blackbox polynomial time algorithm for PIT.« less

Double sided grating fabrication for high energy X-ray phase contrast imaging

DOE PAGES

Hollowell, Andrew E.; Arrington, Christian L.; Finnegan, Patrick; ...

2018-04-19

State of the art grating fabrication currently limits the maximum source energy that can be used in lab based x-ray phase contrast imaging (XPCI) systems. In order to move to higher source energies, and image high density materials or image through encapsulating barriers, new grating fabrication methods are needed. In this work we have analyzed a new modality for grating fabrication that involves precision alignment of etched gratings on both sides of a substrate, effectively doubling the thickness of the grating. Furthermore, we have achieved a front-to-backside feature alignment accuracy of 0.5 µm demonstrating a methodology that can be appliedmore » to any grating fabrication approach extending the attainable aspect ratios allowing higher energy lab based XPCI systems.« less

Correcting groove error in gratings ruled on a 500-mm ruling engine using interferometric control.

PubMed

Mi, Xiaotao; Yu, Haili; Yu, Hongzhu; Zhang, Shanwen; Li, Xiaotian; Yao, Xuefeng; Qi, Xiangdong; Bayinhedhig; Wan, Qiuhua

2017-07-20

Groove error is one of the most important factors affecting grating quality and spectral performance. To reduce groove error, we propose a new ruling-tool carriage system based on aerostatic guideways. We design a new blank carriage system with double piezoelectric actuators. We also propose a completely closed-loop servo-control system with a new optical measurement system that can control the position of the diamond relative to the blank. To evaluate our proposed methods, we produced several gratings, including an echelle grating with 79  grooves/mm, a grating with 768  grooves/mm, and a high-density grating with 6000  grooves/mm. The results show that our methods effectively reduce groove error in ruled gratings.

Compact cross-dispersion device based on a prism and a plane transmission grating

NASA Astrophysics Data System (ADS)

Yang, Qinghua; Wang, Weiqiang

2018-05-01

This paper presents a cross-dispersion prism-grating device using a plane transmission grating attached directly to a prism, which is different from traditional cross-dispersion grating-prism systems that are based on the reflection grating. Unlike conventional direct-vision grism or constant-dispersion grism in which both the prism and grating have the same dispersion direction, for this device the dispersion directions of the prism and grating are different. The analytical expressions for the cross-dispersion of this device are derived in detail and the formulas of the footprint of the dispersed spectra are given. The numerical results and ray-tracing simulations by ZEMAX are shown. The device provides a compact, small-sized and broadband cross-dispersion device used for the medium resolution spectrometer.

Double sided grating fabrication for high energy X-ray phase contrast imaging

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

Hollowell, Andrew E.; Arrington, Christian L.; Finnegan, Patrick

State of the art grating fabrication currently limits the maximum source energy that can be used in lab based x-ray phase contrast imaging (XPCI) systems. In order to move to higher source energies, and image high density materials or image through encapsulating barriers, new grating fabrication methods are needed. In this work we have analyzed a new modality for grating fabrication that involves precision alignment of etched gratings on both sides of a substrate, effectively doubling the thickness of the grating. Furthermore, we have achieved a front-to-backside feature alignment accuracy of 0.5 µm demonstrating a methodology that can be appliedmore » to any grating fabrication approach extending the attainable aspect ratios allowing higher energy lab based XPCI systems.« less

Analysis on the misalignment errors between Hartmann-Shack sensor and 45-element deformable mirror

NASA Astrophysics Data System (ADS)

Liu, Lihui; Zhang, Yi; Tao, Jianjun; Cao, Fen; Long, Yin; Tian, Pingchuan; Chen, Shangwu

2017-02-01

Aiming at 45-element adaptive optics system, the model of 45-element deformable mirror is truly built by COMSOL Multiphysics, and every actuator's influence function is acquired by finite element method. The process of this system correcting optical aberration is simulated by making use of procedure, and aiming for Strehl ratio of corrected diffraction facula, in the condition of existing different translation and rotation error between Hartmann-Shack sensor and deformable mirror, the system's correction ability for 3-20 Zernike polynomial wave aberration is analyzed. The computed result shows: the system's correction ability for 3-9 Zernike polynomial wave aberration is higher than that of 10-20 Zernike polynomial wave aberration. The correction ability for 3-20 Zernike polynomial wave aberration does not change with misalignment error changing. With rotation error between Hartmann-Shack sensor and deformable mirror increasing, the correction ability for 3-20 Zernike polynomial wave aberration gradually goes down, and with translation error increasing, the correction ability for 3-9 Zernike polynomial wave aberration gradually goes down, but the correction ability for 10-20 Zernike polynomial wave aberration behave up-and-down depression.

Stability analysis of fuzzy parametric uncertain systems.

PubMed

Bhiwani, R J; Patre, B M

2011-10-01

In this paper, the determination of stability margin, gain and phase margin aspects of fuzzy parametric uncertain systems are dealt. The stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. A complexity reduced technique for determining the stability margin for FPUS is proposed. The method suggested is dependent on the order of the characteristic polynomial. In order to find the stability margin of interval polynomials of order less than 5, it is not always necessary to determine and check all four Kharitonov's polynomials. It has been shown that, for determining stability margin of FPUS of order five, four, and three we require only 3, 2, and 1 Kharitonov's polynomials respectively. Only for sixth and higher order polynomials, a complete set of Kharitonov's polynomials are needed to determine the stability margin. Thus for lower order systems, the calculations are reduced to a large extent. This idea has been extended to determine the stability margin of fuzzy interval polynomials. It is also shown that the gain and phase margin of FPUS can be determined analytically without using graphical techniques. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2004-08-01

A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed.

A general theory of interference fringes in x-ray phase grating imaging.

PubMed

Yan, Aimin; Wu, Xizeng; Liu, Hong

2015-06-01

The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need. In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance. The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints. In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers.

Formation of surface relief grating in polymers with pendant azobenzene chromophores as studied by AFM/UFM

NASA Astrophysics Data System (ADS)

Kulikovska, Olga; Gharagozloo-Hubmann, Kati; Stumpe, Joachim; Huey, Bryan D.; Bliznyuk, Valery N.

2012-12-01

We studied peculiarities of the structural reconstruction within holographically recorded gratings on the surface of several different amorphous azobenzene-containing polymers. Under illumination with a light interference pattern, two processes take place in this type of polymer. The first process is the light-induced orientation of azobenzene units perpendicular to the polarization plane of the incident light. The second one is a transfer of macromolecules along the grating vector (i.e. perpendicular to the grating lines). These two processes result in the creation of a volume orientation grating (alternating regions of different direction or degree of molecular orientation) and a surface relief grating (SRG)—i.e. modulation of film thickness. One can assume that both orientation of molecules and their movement might change the local mechanical properties of the material. Therefore, formation of the SRG is expected to result also in modulation of the local stiffness of the polymer film. To reveal and investigate these stiffness changes within the grating, spin-coated polymer films were prepared and the gratings were recorded on them in two different ways: with an orthogonal circular or orthogonal linear polarization of two recording light beams. A combination of atomic force microscopy (AFM) and ultrasonic force microscopy (UFM) techniques was applied for SRG development monitoring. We demonstrate that formation of the phase gratings depends on the chemical structure of polymers being used, polymer film thickness, and recording parameters, with the height of grating structures (depth of modulation) increasing with both the exposure time and the film thickness. UFM images suggest that the slopes of the topographic peaks in the phase gratings exhibit an increased stiffness with respect to the grating depressions.

Chirped Grating Tunable Lasers for the Infrared Molecular Fingerprint Spectral Region

DTIC Science & Technology

2013-09-01

lasers with chirped gratings and compare both normal DFB (pump stripe perpendicular to grating) and -DFB (pump stripe perpendicular to facets...structure. Because the period of grating increases gradually laterally, wavelength tuning is implemented by shifting pump stripe to different positions on...tilted with respect to facets and adjusting the pump stripe normal to the grating. Continuous tuning of 30 nm around 3.1 µm with 320 mW single facet

On the coefficients of differentiated expansions of ultraspherical polynomials

NASA Technical Reports Server (NTRS)

Karageorghis, Andreas; Phillips, Timothy N.

1989-01-01

A formula expressing the coefficients of an expression of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved. The particular examples of Chebyshev and Legendre polynomials are considered.

On Polynomial Solutions of Linear Differential Equations with Polynomial Coefficients

ERIC Educational Resources Information Center

Si, Do Tan

1977-01-01

Demonstrates a method for solving linear differential equations with polynomial coefficients based on the fact that the operators z and D + d/dz are known to be Hermitian conjugates with respect to the Bargman and Louck-Galbraith scalar products. (MLH)

Algorithms for computing solvents of unilateral second-order matrix polynomials over prime finite fields using lambda-matrices

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-01-01

The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.

On the Analytical and Numerical Properties of the Truncated Laplace Transform I

DTIC Science & Technology

2014-09-05

contains generalizations and conclusions. 2 2 Preliminaries 2.1 The Legendre Polynomials In this subsection we summarize some of the properties of the the...standard Legendre Polynomi - als, and restate these properties for shifted and normalized forms of the Legendre Polynomials . We define the Shifted... Legendre Polynomial of degree k = 0, 1, ..., which we will be denoting by P ∗k , by the formula P ∗k (x) = Pk(2x− 1), (5) where Pk is the Legendre

Development of Fast Deterministic Physically Accurate Solvers for Kinetic Collision Integral for Applications of Near Space Flight and Control Devices

DTIC Science & Technology

2015-08-31

following functions were used: where are the Legendre polynomials of degree . It is assumed that the coefficient standing with has the form...enforce relaxation rates of high order moments, higher order polynomial basis functions are used. The use of high order polynomials results in strong...enforced while only polynomials up to second degree were used in the representation of the collision frequency. It can be seen that the new model

Effects of Air Drag and Lunar Third-Body Perturbations on Motion Near a Reference KAM Torus

DTIC Science & Technology

2011-03-01

body m 1) mass of satellite; 2) order of associated Legendre polynomial n 1) mean motion; 2) degree of associated Legendre polynomial n3 mean motion...physical momentum pi ith physical momentum Pmn associated Legendre polynomial of order m and degree n q̇ physical coordinate derivatives vector, [q̇1...are constants specifying the shape of the gravitational field; and Pmn are associated Legendre polynomials . When m = n = 0, the geopotential function

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

NASA Astrophysics Data System (ADS)

Gautschi, Walter; Giordano, Carla

2008-12-01

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

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Beam splitting of low-contrast binary gratings under second Bragg angle incidence.

PubMed

Zheng, Jiangjun; Zhou, Changhe; Wang, Bo; Feng, Jijun

2008-05-01

Beam splitting of low-contrast rectangular gratings under second Bragg angle incidence is studied. The grating period is between lambda and 2lambda. The diffraction behaviors of the three transmitted propagating orders are illustrated by analyzing the first three propagating grating modes. From a simplified modal approach, the design conditions of gratings as a high-efficiency element with most of its energy concentrated in the -2nd transmitted order (~90%) and of gratings as a 1 x 2 beam splitter with a total efficiency over 90% are derived. The grating parameters for achieving exactly the splitting pattern by use of rigorous coupled-wave analysis verified the design method. A 1 x 3 beam splitter is also demonstrated. Moreover, the polarization-dependent diffraction behaviors are investigated, which suggest the possibility of designing polarization-selective elements under such a configuration. The proposed concept of using the second Bragg angle should be helpful for developing new grating-based devices.

Ultra-broadband and wide-angle perfect absorber based on composite metal-semiconductor grating

NASA Astrophysics Data System (ADS)

Li, Xu; Wang, Zongpeng; Hou, Yumin

2018-01-01

In this letter, we present an ultra-broadband and wide-angle perfect absorber based on composite Ge-Ni grating. Near perfect absorption above 90% is achieved in a wide frequency range from 150 nm to 4200 nm, which covers almost the full spectrum of solar radiation. The absorption keeps robust in a wide range of incident angle from 0º to 60º. The upper triangle Ge grating works as an antireflection coating. The lower Ni grating works as a reflector and an effective energy trapper. The guided modes inside Ge grating are excited due to reflection of the lower Ni grating surface. In longer wavelength band, gap surface plasmons (GSPs) in the Ni grating are excited and couple with the guided modes inside the Ge grating. The coupled modes extend the perfect absorption band to the near-infrared region (150 nm-4200 nm). This design has potential application in photovoltaic devices and thermal emitters.

An application of neural network for Structural Health Monitoring of an adaptive wing with an array of FBG sensors

NASA Astrophysics Data System (ADS)

Mieloszyk, Magdalena; Krawczuk, Marek; Skarbek, Lukasz; Ostachowicz, Wieslaw

2011-07-01

This paper presents an application of neural networks to determinate the level of activation of shape memory alloy actuators of an adaptive wing. In this concept the shape of the wing can be controlled and altered thanks to the wing design and the use of integrated shape memory alloy actuators. The wing is assumed as assembled from a number of wing sections that relative positions can be controlled independently by thermal activation of shape memory actuators. The investigated wing is employed with an array of Fibre Bragg Grating sensors. The Fibre Bragg Grating sensors with combination of a neural network have been used to Structural Health Monitoring of the wing condition. The FBG sensors are a great tool to control the condition of composite structures due to their immunity to electromagnetic fields as well as their small size and weight. They can be mounted onto the surface or embedded into the wing composite material without any significant influence on the wing strength. The paper concentrates on analysis of the determination of the twisting moment produced by an activated shape memory alloy actuator. This has been analysed both numerically using the finite element method by a commercial code ABAQUS® and experimentally using Fibre Bragg Grating sensor measurements. The results of the analysis have been then used by a neural network to determine twisting moments produced by each shape memory alloy actuator.

Second Chandra Instrument Activated August 28

NASA Astrophysics Data System (ADS)

1999-08-01

Cambridge, MA--NASA's Chandra X-ray Observatory opened a new era in astronomy Saturday, August 28, by making the most precise measurements ever recorded of the energy output from the 10 million degree corona of a star. Last weekend's observations came after the successful activation of an instrument developed by MIT that will allow a one-thousand-fold improvement in the capability to measure X-ray spectra from space. The new measurements, made with the High Energy Transmission Grating Spectrometer, join spectacular images taken last week by Chandra of the aftermath of a gigantic stellar explosion. The spectrometer is one of four key instruments aboard Chandra, and the second to be activated. The others will be turned on over the next two weeks. The spectrometer activated yesterday spreads the X-rays from Chandra's mirrors into a spectrum, much as a prism spreads light into its colors. The spectrum then can be read by Chandra's imaging detectors like a kind of cosmic bar code from which scientists can deduce the chemical composition and temperature of the corona. A corona is a region of hot gas and magnetic loops that extend hundreds of thousands of miles above the star's visible surface and is best studied with X-rays. "The success of the new spectrometer is definitely a major milestone for modern astronomy," said MIT Professor Claude R. Canizares, principal investigator for the instrument and associate director of the Chandra X-ray Observatory Center (CXC). "Within the first hour we had obtained the best X-ray spectrum ever recorded for a celestial source. We can already see unexpected features that will teach us new things about stars and about matter at high temperatures." The spectrometer measured X-rays from the star Capella, which is 40 light years away in the constellation Auriga. Capella is actually two stars orbiting one another and possibly interacting in ways that pump extra heat into the corona, which appears more active than that of the Sun. How a star manages to heat its corona to temperatures a thousand times higher than its own surface is still a puzzle, which astronomers hope can be solved by observations like this one. Other prime targets for Chandra's spectrometers over the next few months include black holes, quasars and supernova explosions. The grating spectrometer consists of hundreds of gold gratings, each about the size of a postage stamp. The surface of each grating resembles a precise picket fence, with microscopic gold pickets 500 times thinner than a human hair. These are spaced every 2000 angstroms, or less than half the wavelength of visible light. The instrument was developed at MIT's Center for Space Research, which Professor Canizares directs, by adapting techniques usually used to make computer chips. Some of these adaptations have found their way back as improvements in the chip-making industry. The grating spectrometer is one of two such devices carried by Chandra. The other, a low-energy grating built by a Dutch-German team, will be activated next week. Chandra also contains two detectors. One, built by researchers at Pennsylvania State University and MIT, was turned on two weeks ago and has recorded all the images and spectra seen so far. The second, built by the Smithsonian Astrophysical Observatory, is being activated this week. Dr. Stephen Murray of the Harvard-Smithsonian Center for Astrophysics summarized the expected impact of Chandra's high resolution X-ray spectroscopy with these words: "A picture is worth a thousand words, a spectrum is worth a million." Capella's spectrum and further information about Chandra's High Energy Transmission Grating Spectrometer may be found at: http://space.mit.edu/CSR/hetg_info.html The Chandra X-ray Observatory Center was named in honor of the late Nobel laureate Subrahmanyan Chandrasekhar. NASA's Marshall Space Flight Center manages the Chandra program. TRW, Inc., Redondo Beach, CA, is the prime contractor for the spacecraft. The Smithsonian Astrophysical Observatory's Chandra X-ray Center controls science and flight operations from Cambridge, MA. The first Chandra images and more information on the Chandra X-ray Observatory Center are available at: http://chandra.harvard.edu and http://chandra.nasa.gov

Polynomial fuzzy observer designs: a sum-of-squares approach.

PubMed

Tanaka, Kazuo; Ohtake, Hiroshi; Seo, Toshiaki; Tanaka, Motoyasu; Wang, Hua O

2012-10-01

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.

Simulation Studies of the Dielectric Grating as an Accelerating and Focusing Structure

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

Soong, Ken; Peralta, E.A.; Byer, R.L.

A grating-based design is a promising candidate for a laser-driven dielectric accelerator. Through simulations, we show the merits of a readily fabricated grating structure as an accelerating component. Additionally, we show that with a small design perturbation, the accelerating component can be converted into a focusing structure. The understanding of these two components is critical in the successful development of any complete accelerator. The concept of accelerating electrons with the tremendous electric fields found in lasers has been proposed for decades. However, until recently the realization of such an accelerator was not technologically feasible. Recent advances in the semiconductor industry,more » as well as advances in laser technology, have now made laser-driven dielectric accelerators imminent. The grating-based accelerator is one proposed design for a dielectric laser-driven accelerator. This design, which was introduced by Plettner, consists of a pair of opposing transparent binary gratings, illustrated in Fig. 1. The teeth of the gratings serve as a phase mask, ensuring a phase synchronicity between the electromagnetic field and the moving particles. The current grating accelerator design has the drive laser incident perpendicular to the substrate, which poses a laser-structure alignment complication. The next iteration of grating structure fabrication seeks to monolithically create an array of grating structures by etching the grating's vacuum channel into a fused silica wafer. With this method it is possible to have the drive laser confined to the plane of the wafer, thus ensuring alignment of the laser-and-structure, the two grating halves, and subsequent accelerator components. There has been previous work using 2-dimensional finite difference time domain (2D-FDTD) calculations to evaluate the performance of the grating accelerator structure. However, this work approximates the grating as an infinite structure and does not accurately model a realizable structure. In this paper, we will present a 3-dimensional frequency-domain simulation of both the infinite and the finite grating accelerator structure. Additionally, we will present a new scheme for a focusing structure based on a perturbation of the accelerating structure. We will present simulations of this proposed focusing structure and quantify the quality of the focusing fields.« less

Recurrence relations for orthogonal polynomials for PDEs in polar and cylindrical geometries.

PubMed

Richardson, Megan; Lambers, James V

2016-01-01

This paper introduces two families of orthogonal polynomials on the interval (-1,1), with weight function [Formula: see text]. The first family satisfies the boundary condition [Formula: see text], and the second one satisfies the boundary conditions [Formula: see text]. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can efficiently compute the corresponding recurrences for generalized Jacobi polynomials that satisfy the same boundary conditions.

Gaussian quadrature for multiple orthogonal polynomials

NASA Astrophysics Data System (ADS)

Coussement, Jonathan; van Assche, Walter

2005-06-01

We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.

Frequency domain system identification methods - Matrix fraction description approach

NASA Technical Reports Server (NTRS)

Horta, Luca G.; Juang, Jer-Nan

1993-01-01

This paper presents the use of matrix fraction descriptions for least-squares curve fitting of the frequency spectra to compute two matrix polynomials. The matrix polynomials are intermediate step to obtain a linearized representation of the experimental transfer function. Two approaches are presented: first, the matrix polynomials are identified using an estimated transfer function; second, the matrix polynomials are identified directly from the cross/auto spectra of the input and output signals. A set of Markov parameters are computed from the polynomials and subsequently realization theory is used to recover a minimum order state space model. Unevenly spaced frequency response functions may be used. Results from a simple numerical example and an experiment are discussed to highlight some of the important aspect of the algorithm.

X-ray/VUV transmission gratings for astrophysical and laboratory applications

NASA Technical Reports Server (NTRS)

Schattenburg, M. L.; Anderson, E. H.; Smith, Henry I.

1990-01-01

This paper describes the techniques used to fabricate deep-submicron-period transmission gratings for astrophysical and laboratory applications, with special attention given to the major steps involved in the transmission grating fabrication. These include the holographic lithography procedure used to pattern the master transmission grating, the fabrication of X-ray mask, the X-ray lithography step used to transfer the X-ray mask pattern into a substrate, and the electroplating of the substrate to form the final grating pattern. The various ways in which transmission gratings can be used in X-ray and VUV spectroscopy are discussed together with some examples of experiments reported in the literature.

Metrology measurements for large-aperture VPH gratings

NASA Astrophysics Data System (ADS)

Zheng, Jessica R.; Gers, Luke; Heijmans, Jeroen

2013-09-01

The High Efficiency and Resolution Multi Element Spectrograph (HERMES) for the Australian Astronomical Observatory (AAO) uses four large aperture, high angle of incidence volume phase holographic gratings (VPHG) for high resolution `Galactic archaeology' spectroscopy. The large clear aperture, the high diffraction efficiency, the line frequency homogeneity, and mosaic alignment made manufacturing and testing challenging. We developed new metrology systems at the AAO to verify the performance of these VPH gratings. The measured diffraction efficiencies and line frequency of the VPH gratings received so far meet the vendor's provided data. The wavefront quality for the Blue VPH grating is good but the Green and Red VPH gratings need to be post polishing.

Performance characteristics of advanced volume phase holographic gratings for operation in the near infrared

NASA Astrophysics Data System (ADS)

Arns, James A.

2016-07-01

Volume phase holographic (VPH) gratings are proven dispersing elements in astronomical spectrographs over the visible spectrum. VPH gratings have also been successfully deployed for use at cryogenic temperatures. Recent advances in production technology now permit the production of gratings for use in the near infrared up to 2450 nm at cryogenic conditions. This paper describes the requirements of VPH gratings for use in the H (wavelengths from 1500 nm to 1800 nm) and K (wavelengths from 1950 nm to 2450 nm) bands, gives the theoretical performances of diffraction efficiency for the production designs and presents the measured performances on the production gratings

Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory

DOE PAGES

Feng, Hao; Ashkar, Rana; Steinke, Nina; ...

2018-02-01

A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography.more » Additionally, it is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. Finally, while the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.« less

Talbot effect of the defective grating in deep Fresnel region

NASA Astrophysics Data System (ADS)

Teng, Shuyun; Wang, Junhong; Zhang, Wei; Cui, Yuwei

2015-02-01

Talbot effect of the grating with different defect is studied theoretically and experimentally in this paper. The defects of grating include the loss of the diffraction unit, the dislocation of the diffraction unit and the modulation of the unit separation. The exact diffraction distributions of three kinds of defective gratings are obtained according to the finite-difference time-domain (FDTD) method. The calculation results show the image of the missing or dislocating unit appears at the Talbot distance (as mentioned in K. Patorski Prog. Opt., 27, 1989, pp.1-108). This is the so-called self-repair ability of grating imaging. In addition, some more phenomena are discovered. The loss or the dislocation of diffraction unit causes the diffraction distortion within a certain radial angle. The regular modulation of unit separation changes the original diffraction, but the new periodicity of the diffraction distribution rebuilds. The self-imaging of grating with smaller random modulation still keeps the partial self-repair ability, and yet this characteristic depends on the modulation degree of defective grating. These diffraction phenomena of the defective gratings are explained by use of the diffraction theory of grating. The practical experiment is also performed and the experimental results confirm the theoretic predictions.

Substrate Oxide Layer Thickness Optimization for a Dual-Width Plasmonic Grating for Surface-Enhanced Raman Spectroscopy (SERS) Biosensor Applications

PubMed Central

Bauman, Stephen J.; Brawley, Zachary T.; Darweesh, Ahmad A.; Herzog, Joseph B.

2017-01-01

This work investigates a new design for a plasmonic SERS biosensor via computational electromagnetic models. It utilizes a dual-width plasmonic grating design, which has two different metallic widths per grating period. These types of plasmonic gratings have shown larger optical enhancement than standard single-width gratings. The new structures have additional increased enhancement when the spacing between the metal decreases to sub-10 nm dimensions. This work integrates an oxide layer to improve the enhancement even further by carefully studying the effects of the substrate oxide thickness on the enhancement and reports ideal substrate parameters. The combined effects of varying the substrate and the grating geometry are studied to fully optimize the device’s enhancement for SERS biosensing and other plasmonic applications. The work reports the ideal widths and substrate thickness for both a standard and a dual-width plasmonic grating SERS biosensor. The ideal geometry, comprising a dual-width grating structure atop an optimal SiO2 layer thickness, improves the enhancement by 800%, as compared to non-optimized structures with a single-width grating and a non-optimal oxide thickness. PMID:28665308

Diffraction efficiency of plasmonic gratings fabricated by electron beam lithography using a silver halide film

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

Sudheer,, E-mail: sudheer@rrcat.gov.in, E-mail: sudheer.rrcat@gmail.com; Tiwari, P.; Srivastava, Himanshu

2016-07-28

The silver nanoparticle surface relief gratings of ∼10 μm period are fabricated using electron beam lithography on the silver halide film substrate. Morphological characterization of the gratings shows that the period, the shape, and the relief depth in the gratings are mainly dependent on the number of lines per frame, the spot size, and the accelerating voltage of electron beam raster in the SEM. Optical absorption of the silver nanoparticle gratings provides a broad localized surface plasmon resonance peak in the visible region, whereas the intensity of the peaks depends on the number density of silver nanoparticles in the gratings. Themore » maximum efficiency of ∼7.2% for first order diffraction is observed for the grating fabricated at 15 keV. The efficiency is peaking at 560 nm with ∼380 nm bandwidth. The measured profiles of the diffraction efficiency for the gratings are found in close agreement with the Raman-Nath diffraction theory. This technique provides a simple and efficient method for the fabrication of plasmonic nanoparticle grating structures with high diffraction efficiency having broad wavelength tuning.« less

Overview on grating developments at ESA

NASA Astrophysics Data System (ADS)

Guldimann, B.; Deep, A.; Vink, R.; Harnisch, B.; Kraft, S.; Sierk, B.; Bazalgette, G.; Bézy, J.-L.

2017-11-01

In the frame of recent studies and missions, ESA has been performing various pre-developments of optical gratings for instruments operating at wavelengths from the UV up to the SWIR. The instrument requirements of Sentinel-4, Sentinel-5, CarbonSat and FLEX are driving the need for advanced designs and technologies leading to gratings with high efficiency, high spectral resolution, low stray light and low polarization sensitivities. Typical ESA instruments (e.g. Sciamachy, GOME, MERIS, OLCI, NIRSpec) were and are based on ruled gratings or gratings manufactured with one holographic photoresist mask layer which is transferred to an optical substrate (e.g. glass, glass ceramic) with dry etching methods and subsequently either coated with a reflective coating or used as a mold for replication. These manufacturing methods lead to blazed grating profiles with a metallic reflective surface. The vast majority of spectrometers on ground are still based on such gratings. In general, gratings based on grooved metallic surfaces tend for instance to polarize the incoming light significantly and are therefore not always suitable for ESA's needs of today. Gratings made for space therefore evolved to many other designs and concepts which will be reported in this paper.

Embedded high-contrast distributed grating structures

DOEpatents

Zubrzycki, Walter J.; Vawter, Gregory A.; Allerman, Andrew A.

2002-01-01

A new class of fabrication methods for embedded distributed grating structures is claimed, together with optical devices which include such structures. These new methods are the only known approach to making defect-free high-dielectric contrast grating structures, which are smaller and more efficient than are conventional grating structures.

A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithm

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, I. S.; Eastman, W. L.; Reed, I. S.

1987-01-01

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code.

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

PubMed

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

Minimum Sobolev norm interpolation of scattered derivative data

NASA Astrophysics Data System (ADS)

Chandrasekaran, S.; Gorman, C. H.; Mhaskar, H. N.

2018-07-01

We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data of the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two variables with total degree ≤n given the values of the polynomial and some of its derivatives at exactly the same number of points as the dimension of the polynomial space is sometimes impossible, we show that such a problem always has a solution in a very general situation if the degree of the polynomials is sufficiently large. We give estimates on how large the degree should be, and give explicit constructions for such a polynomial even in a far more general case. As the number of sampling points at which the data is available increases, our polynomials converge to the target function on the set where the sampling points are dense. Numerical examples in single and double precision show that this method is stable, efficient, and of high-order.

Deformable silicone grating fabricated with a photo-imprinted polymer mold

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

Yamada, Itsunari, E-mail: yamada.i@e.usp.ac.jp; Nishii, Junji; Saito, Mitsunori

A tunable transmission grating was fabricated by molding a silicone elastomer (polydimethylsiloxane). Its optical characteristics were then evaluated during compression. For fabrication, a glass plate with a photoimprinted polymer grating film was used as a mold. Both the grating period and diffraction transmittance of the molded elastomer were functions of the compressive stress. The grating period changed from 3.02 to 2.86 μm during compressing the elastomer in the direction perpendicular to the grooves.

High-resolution absolute position detection using a multiple grating

NASA Astrophysics Data System (ADS)

Schilling, Ulrich; Drabarek, Pawel; Kuehnle, Goetz; Tiziani, Hans J.

1996-08-01

To control electro-mechanical engines, high-resolution linear and rotary encoders are needed. Interferometric methods (grating interferometers) promise a resolution of a few nanometers, but have an ambiguity range of some microns. Incremental encoders increase the absolute measurement range by counting the signal periods starting from a defined initial point. In many applications, however, it is not possible to move to this initial point, so that absolute encoders have to be used. Absolute encoders generally have a scale with two or more tracks placed next to each other. Therefore, they use a two-dimensional grating structure to measure a one-dimensional position. We present a new method, which uses a one-dimensional structure to determine the position in one dimension. It is based on a grating with a large grating period up to some millimeters, having the same diffraction efficiency in several predefined diffraction orders (multiple grating). By combining the phase signals of the different diffraction orders, it is possible to establish the position in an absolute range of the grating period with a resolution like incremental grating interferometers. The principal functionality was demonstrated by applying the multiple grating in a heterodyne grating interferometer. The heterodyne frequency was generated by a frequency modulated laser in an unbalanced interferometer. In experimental measurements an absolute range of 8 mm was obtained while achieving a resolution of 10 nm.

Electromagnetic resonance modes on a two-dimensional tandem grating and its application for broadband absorption in the visible spectrum.

PubMed

Han, Sunwoo; Lee, Bong Jae

2016-01-25

In this work, we numerically investigate the electromagnetic resonances on two-dimensional tandem grating structures. The base of a tandem grating consists of an opaque Au substrate, a SiO(2) spacer, and a Au grating (concave type); that is, a well-known fishnet structure forming Au/SiO(2)/Au stack. A convex-type Au grating (i.e., topmost grating) is then attached on top of the base fishnet structure with or without additional SiO(2) spacer, resulting in two types of tandem grating structures. In order to calculate the spectral reflectance and local magnetic field distribution, the finite-difference time-domain method is employed. When the topmost Au grating is directly added onto the base fishnet structure, the surface plasmon and magnetic polariton in the base structure are branched out due to the geometric asymmetry with respect to the SiO(2) spacer. If additional SiO(2) spacer is added between the topmost Au grating and the base fishnet structure, new magnetic resonance modes appear due to coupling between two vertically aligned Au/SiO(2)/Au stacks. With the understanding of multiple electromagnetic resonance modes on the proposed tandem grating structures, we successfully design a broadband absorber made of Au and SiO(2) in the visible spectrum.

Polarization-independent broadband dielectric bilayer gratings for spectral beam combining system

NASA Astrophysics Data System (ADS)

Li, Linxin; Liu, Quan; Chen, Junming; Wang, Leilei; Jin, Yunxia; Yang, Yifeng; Shao, Jianda

2017-02-01

We report on a polarization-independent all-dielectric trapezoidal bilayer grating with broadband and high diffraction efficiency. The bilayer trapezoidal grating ridge on a reflector consists of an HfO2 layer and a SiO2 layer. The theoretical -1st order efficiencies of the grating are more than 95% with wavelength range from 1010 nm to 1080 nm for both TE and TM polarizations. The fabrication tolerances depending on the HfO2 and SiO2 layer grating ridge depths are enough to obtain the designed grating using current craft. The fabricated grating with exceeding 94% efficiency from 1000 nm to 1085 nm measured by a non-polarization laser has been fabricated and applied in a spectral beam combining external cavity to combine eight beams into one beam output with 10.77 kW.

An on-chip colloidal magneto-optical grating

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

Prikockis, M.; Wijesinghe, H.; Chen, A.

2016-04-18

Interacting nano- and micro-particles provide opportunities to create a wide range of useful colloidal and soft matter constructs. In this letter, we examine interacting superparamagnetic polymeric particles residing on designed permalloy (Ni{sub 0.8} Fe{sub 0.2}) shapes that are subject to weak time-orbiting magnetic fields. The precessing field and magnetic barriers that ensue along the outer perimeter of the shapes allow for containment concurrent with independent field-tunable ordering of the dipole-coupled particles. These remotely activated arrays with inter-particle spacing comparable to the wavelength of light yield microscopic on-chip surface gratings for beam steering and magnetically regulated light diffraction applications.

Tunable Stable Levitation Based on Casimir Interaction between Nanostructures

NASA Astrophysics Data System (ADS)

Liu, Xianglei; Zhang, Zhuomin M.

2016-03-01

Quantum levitation enabled by repulsive Casimir force has been desirable due to the potential exciting applications in passive-suspension devices and frictionless bearings. In this paper, dynamically tunable stable levitation is theoretically demonstrated based on the configuration of dissimilar gratings separated by an intervening fluid using exact scattering theory. The levitation position is insensitive to temperature variations and can be actively tuned by adjusting the lateral displacement between the two gratings. This work investigates the possibility of applying quantum Casimir interactions into macroscopic mechanical devices working in a noncontact and low-friction environment for controlling the position or transducing lateral movement into vertical displacement at the nanoscale.

Stimulus-induced dissociation of neuronal firing rates and local field potential gamma power and its relationship to the blood oxygen level-dependent signal in macaque primary visual cortex

PubMed Central

Bartolo, M J; Gieselmann, M A; Vuksanovic, V; Hunter, D; Sun, L; Chen, X; Delicato, L S; Thiele, A

2011-01-01

The functional magnetic resonance imaging (fMRI) blood oxygenation level-dependent (BOLD) signal is regularly used to assign neuronal activity to cognitive function. Recent analyses have shown that the local field potential (LFP) gamma power is a better predictor of the fMRI BOLD signal than spiking activity. However, LFP gamma power and spiking activity are usually correlated, clouding the analysis of the neural basis of the BOLD signal. We show that changes in LFP gamma power and spiking activity in the primary visual cortex (V1) of the awake primate can be dissociated by using grating and plaid pattern stimuli, which differentially engage surround suppression and cross-orientation inhibition/facilitation within and between cortical columns. Grating presentation yielded substantial V1 LFP gamma frequency oscillations and significant multi-unit activity. Plaid pattern presentation significantly reduced the LFP gamma power while increasing population multi-unit activity. The fMRI BOLD activity followed the LFP gamma power changes, not the multi-unit activity. Inference of neuronal activity from the fMRI BOLD signal thus requires detailed a priori knowledge of how different stimuli or tasks activate the cortical network. PMID:22081989

Similar effects of feature-based attention on motion perception and pursuit eye movements at different levels of awareness.

PubMed

Spering, Miriam; Carrasco, Marisa

2012-05-30

Feature-based attention enhances visual processing and improves perception, even for visual features that we are not aware of. Does feature-based attention also modulate motor behavior in response to visual information that does or does not reach awareness? Here we compare the effect of feature-based attention on motion perception and smooth-pursuit eye movements in response to moving dichoptic plaids--stimuli composed of two orthogonally drifting gratings, presented separately to each eye--in human observers. Monocular adaptation to one grating before the presentation of both gratings renders the adapted grating perceptually weaker than the unadapted grating and decreases the level of awareness. Feature-based attention was directed to either the adapted or the unadapted grating's motion direction or to both (neutral condition). We show that observers were better at detecting a speed change in the attended than the unattended motion direction, indicating that they had successfully attended to one grating. Speed change detection was also better when the change occurred in the unadapted than the adapted grating, indicating that the adapted grating was perceptually weaker. In neutral conditions, perception and pursuit in response to plaid motion were dissociated: While perception followed one grating's motion direction almost exclusively (component motion), the eyes tracked the average of both gratings (pattern motion). In attention conditions, perception and pursuit were shifted toward the attended component. These results suggest that attention affects perception and pursuit similarly even though only the former reflects awareness. The eyes can track an attended feature even if observers do not perceive it.

Sub-wavelength grating structure on the planar waveguide (Conference Presentation)

NASA Astrophysics Data System (ADS)

Qing-Song, Zhu; Sheng-Hui, Chen

2016-10-01

Making progress in recent years, with the technology of the grating, the grating period can be reduced to shrink the size of the light coupler on a waveguide. The working wavelength of the light coupler can be in the range from the near-infrared to visible. In this study , we used E-gun evaporation system with ion-beam-assisted deposition system to fabricate bottom cladding (SiO2), guiding layer (Ta2O5) and Distributed Bragg Reflector(DBR) of the waveguide on the silicon substrate. Electron-beam lithography is used to make sub-wavelength gratings and reflector grating on the planar waveguide which is a coupling device on the guiding layer. The best fabrication parameters were analyzed to deposit the film. The exposure and development times also influenced to fabricate the grating quality. The purpose is to reduce the device size and enhance coupling efficiency which maintain normal incidence of the light . We designed and developed the device using the Finite-Difference Time-Domain (FDTD) method. The grating period, depth, fill factor, film thickness, Distributed Bragg Reflector(DBR) numbers and reflector grating period have been discussed to enhance coupling efficiency and maintained normal incidence of the light. According to the simulation results, when the wavelength is 1300 nm, the coupling grating period is 720 nm and the Ta2O5 film is 460 nm with 360 nm of reflector grating period and 2 layers of Distributed Bragg Reflector, which had the optimum coupling efficiency and normal incidence angle. In the measurement, We successfully measured the TE wave coupling efficiency of the photoresist grating coupling device.

Modeling State-Space Aeroelastic Systems Using a Simple Matrix Polynomial Approach for the Unsteady Aerodynamics

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.

2008-01-01

A simple matrix polynomial approach is introduced for approximating unsteady aerodynamics in the s-plane and ultimately, after combining matrix polynomial coefficients with matrices defining the structure, a matrix polynomial of the flutter equations of motion (EOM) is formed. A technique of recasting the matrix-polynomial form of the flutter EOM into a first order form is also presented that can be used to determine the eigenvalues near the origin and everywhere on the complex plane. An aeroservoelastic (ASE) EOM have been generalized to include the gust terms on the right-hand side. The reasons for developing the new matrix polynomial approach are also presented, which are the following: first, the "workhorse" methods such as the NASTRAN flutter analysis lack the capability to consistently find roots near the origin, along the real axis or accurately find roots farther away from the imaginary axis of the complex plane; and, second, the existing s-plane methods, such as the Roger s s-plane approximation method as implemented in ISAC, do not always give suitable fits of some tabular data of the unsteady aerodynamics. A method available in MATLAB is introduced that will accurately fit generalized aerodynamic force (GAF) coefficients in a tabular data form into the coefficients of a matrix polynomial form. The root-locus results from the NASTRAN pknl flutter analysis, the ISAC-Roger's s-plane method and the present matrix polynomial method are presented and compared for accuracy and for the number and locations of roots.

Catwalk grate lifting tool

DOEpatents

Gunter, L.W.

1992-08-11

A device is described for lifting catwalk grates comprising an elongated bent member with a handle at one end and a pair of notched braces and a hook at the opposite end that act in conjunction with each other to lock onto the grate and give mechanical advantage in lifting the grate. 10 figs.

Polycrystalline PLZT/ITO Ceramic Electro-Optic Phase Gratings: Electro- Optically Reconfigurable Diffractive Devices for Free-Space and In-Wafer Interconnects

DTIC Science & Technology

1994-09-01

free-space and waveguide interconnects is investigated through the fabrication, testing and modeling of polycrystalline PLZT/ITO ceramic electro - optic phase...only gratings. PLZT Diffraction grating, Electro - optic diffraction grating, Optical switching, Optical interconnects, Reconfigurable interconnect

21 CFR 133.147 - Grated American cheese food.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 2 2010-04-01 2010-04-01 false Grated American cheese food. 133.147 Section 133...) FOOD FOR HUMAN CONSUMPTION CHEESES AND RELATED CHEESE PRODUCTS Requirements for Specific Standardized Cheese and Related Products § 133.147 Grated American cheese food. (a)(1) Grated American cheese food is...

21 CFR 133.146 - Grated cheeses.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 21 Food and Drugs 2 2011-04-01 2011-04-01 false Grated cheeses. 133.146 Section 133.146 Food and... CONSUMPTION CHEESES AND RELATED CHEESE PRODUCTS Requirements for Specific Standardized Cheese and Related Products § 133.146 Grated cheeses. (a) Description. Grated cheeses is the class of foods prepared by...

21 CFR 133.147 - Grated American cheese food.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 21 Food and Drugs 2 2011-04-01 2011-04-01 false Grated American cheese food. 133.147 Section 133...) FOOD FOR HUMAN CONSUMPTION CHEESES AND RELATED CHEESE PRODUCTS Requirements for Specific Standardized Cheese and Related Products § 133.147 Grated American cheese food. (a)(1) Grated American cheese food is...

Holographic Gratings for Slow-Neutron Optics

PubMed Central

Klepp, Juergen; Pruner, Christian; Tomita, Yasuo; Geltenbort, Peter; Drevenšek-Olenik, Irena; Gyergyek, Saso; Kohlbrecher, Joachim; Fally, Martin

2012-01-01

Recent progress in the development of holographic gratings for neutron-optics applications is reviewed. We summarize the properties of gratings recorded in deuterated (poly)methylmethacrylate, holographic polymer-dispersed liquid crystals and nanoparticle-polymer composites revealed by diffraction experiments with slow neutrons. Existing and anticipated neutron-optical instrumentations based on holographic gratings are discussed.

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Laser-induced transient grating setup with continuously tunable period

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

Vega-Flick, A.; Applied Physics Department, CINVESTAV-Unidad Mérida, Carretera Antigua a Progreso Km 6, Cordemex, Mérida, Yucatán 97310 Mexico; Eliason, J. K.

2015-12-15

We present a modification of the laser-induced transient grating setup enabling continuous tuning of the transient grating period. The fine control of the period is accomplished by varying the angle of the diffraction grating used to split excitation and probe beams. The setup has been tested by measuring dispersion of bulk and surface acoustic waves in both transmission and reflection geometries. The presented modification is fully compatible with optical heterodyne detection and can be easily implemented in any transient grating setup.

Design and fabrication of inverted rib waveguide Bragg grating

NASA Astrophysics Data System (ADS)

Huang, Cheng-Sheng; Wang, Wei-Chih

2009-03-01

A polymeric SU8 rib waveguide Bragg grating filterfabricated using reactive ion etching (RIE) and solvent assisted microcontact molding (SAMIM) is presented. SAMIM is one kind of soft lithography. The technique is unique in which that a composite hPDMS/PDMS stamp was used to transfer the grating pattern onto an inverted SU8 rib waveguide system. The composite grating stamp can be used repeatedly several times with degradation. Using this stamp and inverter rib waveguide structure, the Bragg grating filter fabrication can be significantly simplified.

Fractional Talbot field and of finite gratings: compact analytical formulation.

PubMed

Arrizón, V; Rojo-Velázquez, G

2001-06-01

We present a compact analytical formulation for the fractional Talbot effect at the paraxial domain of a finite grating. Our results show that laterally shifted distorted images of the grating basic cell form the Fresnel field at a fractional Talbot plane of the grating. Our formulas give the positions of those images and show that they are given by the convolution of the nondistorted cells (modulated by a quadratic phase factor) with the Fourier transform of the finite-grating pupil.

Optical system storage design with diffractive optical elements

NASA Technical Reports Server (NTRS)

Kostuk, Raymond K.; Haggans, Charles W.

1993-01-01

Optical data storage systems are gaining widespread acceptance due to their high areal density and the ability to remove the high capacity hard disk from the system. In magneto-optical read-write systems, a small rotation of the polarization state in the return signal from the MO media is the signal which must be sensed. A typical arrangement used for detecting these signals and correcting for errors in tracking and focusing on the disk is illustrated. The components required to achieve these functions are listed. The assembly and alignment of this complex system has a direct impact on cost, and also affects the size, weight, and corresponding data access rates. As a result, integrating these optical components and improving packaging techniques is an active area of research and development. Most designs of binary optic elements have been concerned with optimizing grating efficiency. However, rigorous coupled wave models for vector field diffraction from grating surfaces can be extended to determine the phase and polarization state of the diffracted field, and the design of polarization components. A typical grating geometry and the phase and polarization angles associated with the incident and diffracted fields are shown. In our current stage of work, we are examining system configurations which cascade several polarization functions on a single substrate. In this design, the beam returning from the MO disk illuminates a cascaded grating element which first couples light into the substrate, then introduces a quarter wave retardation, then a polarization rotation, and finally separates s- and p-polarized fields through a polarization beam splitter. The input coupler and polarization beam splitter are formed in volume gratings, and the two intermediate elements are zero-order elements.

Tunable dark modes in one-dimensional “diatomic” dielectric gratings

DOE PAGES

Zeng, Bo; Majumdar, Arka; Wang, Feng

2015-05-04

Recently researchers have demonstrated ultra high quality factor (Q) resonances in one-dimensional (1D) dielectric gratings. Here we theoretically investigate a new class of subwavelength 1D gratings, namely “diatomic” gratings with two nonequivalent subcells in one period, and utilize their intrinsic dark modes to achieve robust ultra high Q resonances. Such “diatomic” gratings provide extra design flexibility, and enable high Q resonators using thinner geometry with smaller filling factors compared to conventional designs like the high contrast gratings (HCGs). More importantly, we show that these high Q resonances can be efficiently tuned in situ, making the design appealing in various applicationsmore » including optical sensing, filtering and displays.« less

Surface polaritons in grating composed of left-handed materials

NASA Astrophysics Data System (ADS)

Tiwari, D. C.; Premlal, P. L.; Chaturvedi, Vandana

2018-01-01

In this work, we developed a unique mathematical model to solve dispersion relation for surface polaritons (SPs) in artificial composite materials grating. Here, we have taken two types of materials for analysis. In the first case, the grating composed of epsilon-negative (ENG) material and air interface. In second case, grating composed of left-handed materials (LHMs) and ENG medium interface is considered. The dispersion curves of both p and s polarized SPs modes are obtained analytically. In the case of ENG grating and air interface, polaritons dispersion curves exist for p-polarization only, whereas for LHM grating and ENG medium interface, the polaritons dispersion curves for both p and s polarization are observed.

Polarization sensitivity testing of off-plane reflection gratings

NASA Astrophysics Data System (ADS)

Marlowe, Hannah; McEntaffer, Randal L.; DeRoo, Casey T.; Miles, Drew M.; Tutt, James H.; Laubis, Christian; Soltwisch, Victor

2015-09-01

Off-Plane reflection gratings were previously predicted to have different efficiencies when the incident light is polarized in the transverse-magnetic (TM) versus transverse-electric (TE) orientations with respect to the grating grooves. However, more recent theoretical calculations which rigorously account for finitely conducting, rather than perfectly conducting, grating materials no longer predict significant polarization sensitivity. We present the first empirical results for radially ruled, laminar groove profile gratings in the off-plane mount which demonstrate no difference in TM versus TE efficiency across our entire 300-1500 eV bandpass. These measurements together with the recent theoretical results confirm that grazing incidence off-plane reflection gratings using real, not perfectly conducting, materials are not polarization sensitive.

Translation of Bernstein Coefficients Under an Affine Mapping of the Unit Interval

NASA Technical Reports Server (NTRS)

Alford, John A., II

2012-01-01

We derive an expression connecting the coefficients of a polynomial expanded in the Bernstein basis to the coefficients of an equivalent expansion of the polynomial under an affine mapping of the domain. The expression may be useful in the calculation of bounds for multi-variate polynomials.

On polynomial selection for the general number field sieve

NASA Astrophysics Data System (ADS)

Kleinjung, Thorsten

2006-12-01

The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.

Graphical Solution of Polynomial Equations

ERIC Educational Resources Information Center

Grishin, Anatole

2009-01-01

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

Evaluation of more general integrals involving universal associated Legendre polynomials

NASA Astrophysics Data System (ADS)

You, Yuan; Chen, Chang-Yuan; Tahir, Farida; Dong, Shi-Hai

2017-05-01

We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. We present a popular integral formula which includes universal associated Legendre polynomials and we also evaluate some important integrals involving the product of two universal associated Legendre polynomials Pl' m'(x ) , Pk' n'(x ) and x2 a(1-x2 ) -p -1, xb(1±x2 ) -p, and xc(1-x2 ) -p(1±x ) -1, where l'≠k' and m'≠n'. Their selection rules are also mentioned.

Neck curve polynomials in neck rupture model

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

Kurniadi, Rizal; Perkasa, Yudha S.; Waris, Abdul

2012-06-06

The Neck Rupture Model is a model that explains the scission process which has smallest radius in liquid drop at certain position. Old fashion of rupture position is determined randomly so that has been called as Random Neck Rupture Model (RNRM). The neck curve polynomials have been employed in the Neck Rupture Model for calculation the fission yield of neutron induced fission reaction of {sup 280}X{sub 90} with changing of order of polynomials as well as temperature. The neck curve polynomials approximation shows the important effects in shaping of fission yield curve.

More on rotations as spin matrix polynomials

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

Curtright, Thomas L.

2015-09-15

Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined.

Robust stability of fractional order polynomials with complicated uncertainty structure

PubMed Central

Şenol, Bilal; Pekař, Libor

2017-01-01

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. PMID:28662173

Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

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

Zhang, Hong-Biao, E-mail: zhanghb017@nenu.edu.cn; Lu, Lu

2013-12-15

Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators K-circumflex{sub ±} of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derivedmore » naturally from the polynomial su(1, 1) algebras built by us.« less

Polynomials to model the growth of young bulls in performance tests.

PubMed

Scalez, D C B; Fragomeni, B O; Passafaro, T L; Pereira, I G; Toral, F L B

2014-03-01

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.

Cylinder surface test with Chebyshev polynomial fitting method

NASA Astrophysics Data System (ADS)

Yu, Kui-bang; Guo, Pei-ji; Chen, Xi

2017-10-01

Zernike polynomials fitting method is often applied in the test of optical components and systems, used to represent the wavefront and surface error in circular domain. Zernike polynomials are not orthogonal in rectangular region which results in its unsuitable for the test of optical element with rectangular aperture such as cylinder surface. Applying the Chebyshev polynomials which are orthogonal among the rectangular area as an substitution to the fitting method, can solve the problem. Corresponding to a cylinder surface with diameter of 50 mm and F number of 1/7, a measuring system has been designed in Zemax based on Fizeau Interferometry. The expressions of the two-dimensional Chebyshev polynomials has been given and its relationship with the aberration has been presented. Furthermore, Chebyshev polynomials are used as base items to analyze the rectangular aperture test data. The coefficient of different items are obtained from the test data through the method of least squares. Comparing the Chebyshev spectrum in different misalignment, it show that each misalignment is independence and has a certain relationship with the certain Chebyshev terms. The simulation results show that, through the Legendre polynomials fitting method, it will be a great improvement in the efficient of the detection and adjustment of the cylinder surface test.

Generating the patterns of variation with GeoGebra: the case of polynomial approximations

NASA Astrophysics Data System (ADS)

Attorps, Iiris; Björk, Kjell; Radic, Mirko

2016-01-01

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students' learning opportunities in the study group compared with the control group.

Interlaced spin grating for optical wave filtering

NASA Astrophysics Data System (ADS)

Linget, H.; Chanelière, T.; Le Gouët, J.-L.; Berger, P.; Morvan, L.; Louchet-Chauvet, A.

2015-02-01

Interlaced spin grating is a scheme for the preparation of spectrospatial periodic absorption gratings in an inhomogeneously broadened absorption profile. It relies on the optical pumping of atoms in a nearby long-lived ground state sublevel. The scheme takes advantage of the sublevel proximity to build large contrast gratings with unlimited bandwidth and preserved average optical depth. It is particularly suited to Tm-doped crystals in the context of classical and quantum signal processing. In this paper, we study the optical pumping dynamics at play in an interlaced spin grating and describe the corresponding absorption profile shape in an optically thick atomic ensemble. We show that, in Tm:YAG, the diffraction efficiency of such a grating can reach 18.3 % in the small-angle and 11.6 % in the large-angle configuration when the excitation is made of simple pulse pairs, considerably outperforming conventional gratings.

Dopants concentration effects on the wavelength shift of long-period fiber gratings used as liquid level detectors

NASA Astrophysics Data System (ADS)

Mao, Barerem-Melgueba; Zhou, Bin

2011-12-01

Two liquid level sensors based on different long-period fiber gratings are proposed and compared. The long-period gratings have the same characteristics (length, grating period) but are fabricated in different optical fibers (photosensitive B-Ge codoped optical fibers with different dopants concentrations). The principle of this type of sensor is based on the refractive index sensitivity of long-period fiber gratings. By monitoring the resonant wavelength shifts of a given attenuation band, one can measure the immersed lengths of long-period fiber gratings and then the liquid level. The levels of two different solutions are measured. The maximum shift (7.69 nm) of the investigated resonance wavelength was observed in LPG1 (fabricated in Fibercore PS1250/1500). By controlling the fiber dopants concentrations one can improve the readouts of a fiber-optic liquid level sensor based on long-period fiber gratings.

Simulations and experiments of aperiodic and multiplexed gratings in volume holographic imaging systems

PubMed Central

Luo, Yuan; Castro, Jose; Barton, Jennifer K.; Kostuk, Raymond K.; Barbastathis, George

2010-01-01

A new methodology describing the effects of aperiodic and multiplexed gratings in volume holographic imaging systems (VHIS) is presented. The aperiodic gratings are treated as an ensemble of localized planar gratings using coupled wave methods in conjunction with sequential and non-sequential ray-tracing techniques to accurately predict volumetric diffraction effects in VHIS. Our approach can be applied to aperiodic, multiplexed gratings and used to theoretically predict the performance of multiplexed volume holographic gratings within a volume hologram for VHIS. We present simulation and experimental results for the aperiodic and multiplexed imaging gratings formed in PQ-PMMA at 488nm and probed with a spherical wave at 633nm. Simulation results based on our approach that can be easily implemented in ray-tracing packages such as Zemax® are confirmed with experiments and show proof of consistency and usefulness of the proposed models. PMID:20940823

Polarizing beam splitter of deep-etched triangular-groove fused-silica gratings.

PubMed

Zheng, Jiangjun; Zhou, Changhe; Feng, Jijun; Wang, Bo

2008-07-15

We investigated the use of a deep-etched fused-silica grating with triangular-shaped grooves as a highly efficient polarizing beam splitter (PBS). A triangular-groove PBS grating is designed at a wavelength of 1550 nm to be used in optical communication. When it is illuminated in Littrow mounting, the transmitted TE- and TM-polarized waves are mainly diffracted in the minus-first and zeroth orders, respectively. The design condition is based on the average differences of the grating mode indices, which is verified by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient over the C+L band range for both TE and TM polarizations (>97.68%). It is shown that such a triangular-groove PBS grating can exhibit a higher diffraction efficiency, a larger extinction ratio, and less reflection loss than the binary-phase fused-silica PBS grating.

A fully reconfigurable waveguide Bragg grating for programmable photonic signal processing.

PubMed

Zhang, Weifeng; Yao, Jianping

2018-04-11

Since the discovery of the Bragg's law in 1913, Bragg gratings have become important optical devices and have been extensively used in various systems. In particular, the successful inscription of a Bragg grating in a fiber core has significantly boosted its engineering applications. However, a conventional grating device is usually designed for a particular use, which limits general-purpose applications since its index modulation profile is fixed after fabrication. In this article, we propose to implement a fully reconfigurable grating, which is fast and electrically reconfigurable by field programming. The concept is verified by fabricating an integrated grating on a silicon-on-insulator platform, which is employed as a programmable signal processor to perform multiple signal processing functions including temporal differentiation, microwave time delay, and frequency identification. The availability of ultrafast and reconfigurable gratings opens new avenues for programmable optical signal processing at the speed of light.

Wavelength-division multiplexed optical integrated circuit with vertical diffraction grating

NASA Technical Reports Server (NTRS)

Lang, Robert J. (Inventor); Forouhar, Siamak (Inventor)

1994-01-01

A semiconductor optical integrated circuit for wave division multiplexing has a semiconductor waveguide layer, a succession of diffraction grating points in the waveguide layer along a predetermined diffraction grating contour, a semiconductor diode array in the waveguide layer having plural optical ports facing the succession of diffraction grating points along a first direction, respective semiconductor diodes in the array corresponding to respective ones of a predetermined succession of wavelengths, an optical fiber having one end thereof terminated at the waveguide layer, the one end of the optical fiber facing the succession of diffraction grating points along a second direction, wherein the diffraction grating points are spatially distributed along the predetermined contour in such a manner that the succession of diffraction grating points diffracts light of respective ones of the succession of wavelengths between the one end of the optical fiber and corresponding ones of the optical ports.

X-ray grating interferometry at photon energies over 180 keV

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

Ruiz-Yaniz, M., E-mail: maite.ruiz-yaniz@esrf.fr; Lehrstuhl für Biomedizinische Physik, Physik-Department and Institut für Medizintechnik, Technische Universität München, James-Franck-Str. 1, 85748 Garching; Koch, F.

2015-04-13

We report on the implementation and characterization of grating interferometry operating at an x-ray energy of 183 keV. With the possibility to use this technique at high x-ray energies, bigger specimens could be studied in a quantitative way. Also, imaging strongly absorbing specimens will benefit from the advantages of the phase and dark-field signals provided by grating interferometry. However, especially at these high photon energies the performance of the absorption grating becomes a key point on the quality of the system, because the grating lines need to keep their small width of a couple of micrometers and exhibit a greater heightmore » of hundreds of micrometers. The performance of high aspect ratio absorption gratings fabricated with different techniques is discussed. Further, a dark-field image of an alkaline multicell battery highlights the potential of high energy x-ray grating based imaging.« less

Transparent Electrochemical Gratings from a Patterned Bistable Silver Mirror.

PubMed

Park, Chihyun; Na, Jongbeom; Han, Minsu; Kim, Eunkyoung

2017-07-25

Silver mirror patterns were formed reversibly on a polystyrene (PS)-patterned electrode to produce gratings through the electrochemical reduction of silver ions. The electrochemical gratings exhibited high transparency (T > 95%), similar to a see-through window, by matching the refractive index of the grating pattern with the surrounding medium. The gratings switch to a diffractive state upon the formation of a mirror pattern (T < 5%) with a high diffraction efficiency up to 40%, providing reversible diffractive gratings. The diffraction state was maintained in the voltage-off state (V-off) for 40 min, which demonstrated bistable reversible electrochemical grating (BREG) behavior. By carefully combining the BREGs through period matching, dual-color switching was achieved within the full color region, which exhibited three distinct optical switching states between -2.5, 0, and +2.5 V. The wide range of light tenability using the metallic BREGs developed herein enabled IR modulation, NIR light reflection, and on-demand heat transfer.

Optical devices combining an organic semiconductor crystal with a two-dimensional inorganic diffraction grating

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

Kitazawa, Takenori; Yamao, Takeshi, E-mail: yamao@kit.ac.jp; Hotta, Shu

2016-02-01

We have fabricated optical devices using an organic semiconductor crystal as an emission layer in combination with a two-dimensional (2D) inorganic diffraction grating used as an optical cavity. We formed the inorganic diffraction grating by wet etching of aluminum-doped zinc oxide (AZO) under a 2D cyclic olefin copolymer (COC) diffraction grating used as a mask. The COC diffraction grating was fabricated by nanoimprint lithography. The AZO diffraction grating was composed of convex prominences arranged in a triangular lattice. The organic crystal placed on the AZO diffraction grating indicated narrowed peaks in its emission spectrum under ultraviolet light excitation. These aremore » detected parallel to the crystal plane. The peaks were shifted by rotating the optical devices around the normal to the crystal plane, which reflected the rotational symmetries of the triangular lattice through 60°.« less

Absolute S- and P-plane polarization efficiencies for high frequency holographic gratings in the VUV

NASA Technical Reports Server (NTRS)

Caruso, A. J.; Woodgate, B. E.; Mount, G. H.

1981-01-01

High frequency plane gratings (3500 and 3600 gr/mm) have been holographically ruled and blazed for the VUV spectral region. All gratings were coated with 70 nm Al + 25 nm MgF2. Absolute unpolarized and S- and P-plane polarization efficiencies have been measured for the first and second orders in the 120- to 450-nm spectral region at 18.5 and 30 deg angles of deviation. For deep grooves, anomalous features are more pronounced for the P-plane polarization efficiency than for the S-plane polarization efficiency. Holographic gratings can be tailored to produce high polarization or low polarization in the VUV. For comparison, efficiencies and polarization of the best conventional high frequency gratings were also determined. Measurements show that scattered light is significantly lower for holographic gratings in the VUV when compared with the conventional gratings.

High-throughput accurate-wavelength lens-based visible spectrometer.

PubMed

Bell, Ronald E; Scotti, Filippo

2010-10-01

A scanning visible spectrometer has been prototyped to complement fixed-wavelength transmission grating spectrometers for charge exchange recombination spectroscopy. Fast f/1.8 200 mm commercial lenses are used with a large 2160 mm(-1) grating for high throughput. A stepping-motor controlled sine drive positions the grating, which is mounted on a precision rotary table. A high-resolution optical encoder on the grating stage allows the grating angle to be measured with an absolute accuracy of 0.075 arc  sec, corresponding to a wavelength error ≤0.005 Å. At this precision, changes in grating groove density due to thermal expansion and variations in the refractive index of air are important. An automated calibration procedure determines all the relevant spectrometer parameters to high accuracy. Changes in bulk grating temperature, atmospheric temperature, and pressure are monitored between the time of calibration and the time of measurement to ensure a persistent wavelength calibration.

Grating acuity at different luminances in wild-type mice and in mice lacking rod or cone function.

PubMed

Schmucker, Christine; Seeliger, Mathias; Humphries, Pete; Biel, Martin; Schaeffel, Frank

2005-01-01

The mouse eye has become an important model in vision research. However, it is not known how visual acuity changes with luminance. Therefore, grating acuity of mice was measured at different luminances in an automated optomotor paradigm. Furthermore, mutant mice lacking either rods (RHO-/- and CNGB1-/-) or cones (CNGA3-/-), or both, were studied to determine the rod and cone contribution to visual acuity. Freely ranging individual mice were automatically tracked at a 25-Hz sampling rate with a self-programmed video system in a large rotating optomotor drum. The drum had a square-wave grating inside with adjustable spatial frequency. The angular speed of the mice with respect to the center of the drum and the angular orientation of the snout-tail body axis were analyzed. In addition, the motor activity of the wild-type mice was recorded at different luminances. The optomotor drum provided reliable data on visual input to the mouse's behavior and was convenient to use, since the experimenter's had only to place the mice individually in a Perspex cylinder. Optomotor grating acuity of the wild-type mice was limited to 0.3 to 0.4 cyc/deg. Maximum optomotor responses were obtained at 0.1 to 0.2 cyc/deg. The importance of visual input declined monotonically with decreasing luminance (30 cd/m2, 100%; 0.1 cd/m2, 76.4%; 0.005 cd/m2, 45.9%; and darkness, -9%). Mice lacking functional rods were able to resolve gratings up to 0.1 cyc/deg at 30 cd/m2. Surprisingly, mice lacking functional cones had an optomotor acuity that was similar to the wild-type. Double-knockout mice without rods and cones had no detectable grating acuity. Because the visual system of the mouse is more responsive at bright luminances, experiments in which visual input is important should be performed in photopic conditions (30 cd/m2 or even more). Apparently, spatial vision is governed by the rod system, which is not saturated in the mesopic or low photopic range. Mice lacking both rods and cones have no detectable grating acuity, indicating that the retinal melanopsin system does not contribute to spatial vision.

Optimization of fiber grating couplers on SOI using advanced search algorithms.

PubMed

Wohlfeil, Benjamin; Zimmermann, Lars; Petermann, Klaus

2014-06-01

A one-dimensional fiber grating coupler is derived from a waveguide with random etches using implementations of particle swarm and genetic algorithms. The resulting gratings yield a theoretical coupling efficiency of up to 1.1 dB and prompt clear design rules for the layout of highly efficient fiber grating couplers.

75 FR 41889 - Certain Steel Grating From China

Federal Register 2010, 2011, 2012, 2013, 2014

2010-07-19

... Steel Grating From China Determination On the basis of the record \\1\\ developed in the subject... grating from China, provided for in subheading 7308.90.70 of the Harmonized Tariff Schedule of the United... certain steel gratings from China were being subsidized within the meaning of section 703(b) of the Act...

76 FR 76368 - Certain Steel Grating From the People's Republic of China: Notice of Rescission of the 2010-2011...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-12-07

... Minmetals''), Yantai Xinke Steel Structure Co., Ltd. (``Yantai Xinke''), Sinosteel Yantai Steel Grating Co... DEPARTMENT OF COMMERCE International Trade Administration [A-570-947] Certain Steel Grating From... antidumping duty order on certain steel grating from the People's Republic of China (``PRC'') for the period...

Software Development to Assist in the Processing and Analysis of Data Obtained Using Fiber Bragg Grating Interrogation Systems

NASA Technical Reports Server (NTRS)

Hicks, Rebecca

2009-01-01

A fiber Bragg grating is a portion of a core of a fiber optic strand that has been treated to affect the way light travels through the strand. Light within a certain narrow range of wavelengths will be reflected along the fiber by the grating, while light outside that range will pass through the grating mostly undisturbed. Since the range of wavelengths that can penetrate the grating depends on the grating itself as well as temperature and mechanical strain, fiber Bragg gratings can be used as temperature and strain sensors. This capability, along with the light-weight nature of the fiber optic strands in which the gratings reside, make fiber optic sensors an ideal candidate for flight testing and monitoring in which temperature and wing strain are factors. The purpose of this project is to research the availability of software capable of processing massive amounts of data in both real-time and post-flight settings, and to produce software segments that can be integrated to assist in the task as well.

Nano-indentation and laser-induced damage testing in optical multilayer-dielectric gratings [Nanomechanics and laser-induced damage in optical multilayer dielectric gratings

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

Mehrotra, K.; Corning Research & Development Corp., Coming, NY; Taylor, B. N.

Here, we demonstrate how a nanomechanical test can be used to generate metrics to complement laser-induced–damage testing (LIDT) measurements and show that differences in optical performance of the gratings (arising from changes in cleaning process and/or fabrication methods) can be related to their mechanical reliability. Data are presented on LIDT measurements in diffractive gratings of silica deposited on optical multilayers. The nano-indentation response of the diffraction gratings is measured in a new mode that allows for the extraction of a measurable metric characterizing the brittleness of the gratings, as well as their ductility. We show that lower LIDT’s are positivelymore » correlated with an increased grating brittleness, and therefore identify a nanomechanical approach to describe LIDT’s. We present extensive numerical simulations of nano-indentation tests and identify different deformation modes including stretching, shear concentration, and bending as precursors to mechanical failure in the nano-indentation test. The effects of geometrical inhomogeneities on enhanced stress generation in these gratings are specifically examined and addressed.« less

Optimization of nonbinary slanted surface-relief gratings as high-efficiency broadband couplers for light guides.

PubMed

Bai, Benfeng; Laukkanen, Janne; Kuittinen, Markku; Siitonen, Samuli

2010-10-01

We propose and investigate the use of slanted surface-relief gratings with nonbinary profiles as high-efficiency broadband couplers for light guides. First, a Chandezon-method-based rigorous numerical formulation is presented for modeling the slanted gratings with overhanging profiles. Then, two typical types of slanted grating couplers--a sinusoidal one and a trapezoidal one--are studied and optimized numerically, both exhibiting a high coupling efficiency of over 50% over the full band of white LED under the normal illumination of unpolarized light. Reasonable structural parameters with nice tolerance have been obtained for the optimized designs. It is found that the performance of the couplers depends little on the grating profile shape, but primarily on the grating period and the slant angle of the ridge. The underlying mechanism is analyzed by the equivalence rules of gratings, which provide useful guidelines for the design and fabrication of the couplers. Preliminary investigation has been performed on the fabrication and replication of the slanted overhanging grating couplers, which shows the feasibility of fabrication with mature microfabrication techniques and the perspective for mass production.

Nano-indentation and laser-induced damage testing in optical multilayer-dielectric gratings [Nanomechanics and laser-induced damage in optical multilayer dielectric gratings

DOE PAGES

Mehrotra, K.; Corning Research & Development Corp., Coming, NY; Taylor, B. N.; ...

2017-03-16

Here, we demonstrate how a nanomechanical test can be used to generate metrics to complement laser-induced–damage testing (LIDT) measurements and show that differences in optical performance of the gratings (arising from changes in cleaning process and/or fabrication methods) can be related to their mechanical reliability. Data are presented on LIDT measurements in diffractive gratings of silica deposited on optical multilayers. The nano-indentation response of the diffraction gratings is measured in a new mode that allows for the extraction of a measurable metric characterizing the brittleness of the gratings, as well as their ductility. We show that lower LIDT’s are positivelymore » correlated with an increased grating brittleness, and therefore identify a nanomechanical approach to describe LIDT’s. We present extensive numerical simulations of nano-indentation tests and identify different deformation modes including stretching, shear concentration, and bending as precursors to mechanical failure in the nano-indentation test. The effects of geometrical inhomogeneities on enhanced stress generation in these gratings are specifically examined and addressed.« less

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

Feng, Hao; Ashkar, Rana; Steinke, Nina

A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography.more » Additionally, it is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. Finally, while the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.« less

Strategies for single-point diamond machining a large format germanium blazed immersion grating

NASA Astrophysics Data System (ADS)

Montesanti, R. C.; Little, S. L.; Kuzmenko, P. J.; Bixler, J. V.; Jackson, J. L.; Lown, J. G.; Priest, R. E.; Yoxall, B. E.

2016-07-01

A large format germanium immersion grating was flycut with a single-point diamond tool on the Precision Engineering Research Lathe (PERL) at the Lawrence Livermore National Laboratory (LLNL) in November - December 2015. The grating, referred to as 002u, has an area of 59 mm x 67 mm (along-groove and cross-groove directions), line pitch of 88 line/mm, and blaze angle of 32 degree. Based on total groove length, the 002u grating is five times larger than the previous largest grating (ZnSe) cut on PERL, and forty-five times larger than the previous largest germanium grating cut on PERL. The key risks associated with cutting the 002u grating were tool wear and keeping the PERL machine running uninterrupted in a stable machining environment. This paper presents the strategies employed to mitigate these risks, introduces pre-machining of the as-etched grating substrate to produce a smooth, flat, damage-free surface into which the grooves are cut, and reports on trade-offs that drove decisions and experimental results.

Excitation of surface waves on one-dimensional solid–fluid phononic crystals and the beam displacement effect

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

Moiseyenko, Rayisa P.; Georgia Institute of Technology, UMI Georgia Tech – CNRS, George W. Woodruff School of Mechanical Engineering, Georgia Tech Lorraine, 2 rue Marconi, 57070 Metz-Technopole; Liu, Jingfei

The possibility of surface wave generation by diffraction of pressure waves on deeply corrugated one-dimensional phononic crystal gratings is studied both theoretically and experimentally. Generation of leaky surface waves, indeed, is generally invoked in the explanation of the beam displacement effect that can be observed upon reflection on a shallow grating of an acoustic beam of finite width. True surface waves of the grating, however, have a dispersion that lies below the sound cone in water. They thus cannot satisfy the phase-matching condition for diffraction from plane waves of infinite extent incident from water. Diffraction measurements indicate that deeply corrugatedmore » one-dimensional phononic crystal gratings defined in a silicon wafer are very efficient diffraction gratings. They also confirm that all propagating waves detected in water follow the grating law. Numerical simulations however reveal that in the sub-diffraction regime, acoustic energy of a beam of finite extent can be transferred to elastic waves guided at the surface of the grating. Their leakage to the specular direction along the grating surface explains the apparent beam displacement effect.« less

Optical and x-ray alignment approaches for off-plane reflection gratings

NASA Astrophysics Data System (ADS)

Allured, Ryan; Donovan, Benjamin D.; DeRoo, Casey T.; Marlowe, Hannah R.; McEntaffer, Randall L.; Tutt, James H.; Cheimets, Peter N.; Hertz, Edward; Smith, Randall K.; Burwitz, Vadim; Hartner, Gisela; Menz, Benedikt

2015-09-01

Off-plane reflection gratings offer the potential for high-resolution, high-throughput X-ray spectroscopy on future missions. Typically, the gratings are placed in the path of a converging beam from an X-ray telescope. In the off-plane reflection grating case, these gratings must be co-aligned such that their diffracted spectra overlap at the focal plane. Misalignments degrade spectral resolution and effective area. In-situ X-ray alignment of a pair of off-plane reflection gratings in the path of a silicon pore optics module has been performed at the MPE PANTER beamline in Germany. However, in-situ X-ray alignment may not be feasible when assembling all of the gratings required for a satellite mission. In that event, optical methods must be developed to achieve spectral alignment. We have developed an alignment approach utilizing a Shack-Hartmann wavefront sensor and diffraction of an ultraviolet laser. We are fabricating the necessary hardware, and will be taking a prototype grating module to an X-ray beamline for performance testing following assembly and alignment.

Computer-generated holograms and diffraction gratings in optical security applications

NASA Astrophysics Data System (ADS)

Stepien, Pawel J.

2000-04-01

The term 'computer generated hologram' (CGH) describes a diffractive structure strictly calculated and recorded to diffract light in a desired way. The CGH surface profile is a result of the wavefront calculation rather than of interference. CGHs are able to form 2D and 3D images. Optically, variable devices (OVDs) composed of diffractive gratings are often used in security applications. There are various types of optically and digitally recorded gratings in security applications. Grating based OVDs are used to record bright 2D images with limited range of cinematic effects. These effects result form various orientations or densities of recorded gratings. It is difficult to record high quality OVDs of 3D objects using gratings. Stereo grams and analogue rainbow holograms offer 3D imaging, but they are darker and have lower resolution than grating OVDs. CGH based OVDs contains unlimited range of cinematic effects and high quality 3D images. Images recorded using CGHs are usually more noisy than grating based OVDs, because of numerical inaccuracies in CGH calculation and mastering. CGH based OVDs enable smooth integration of hidden and machine- readable features within an OVD design.

Review of rigorous coupled-wave analysis and of homogeneous effective medium approximations for high spatial-frequency surface-relief gratings

NASA Technical Reports Server (NTRS)

Glytsis, Elias N.; Brundrett, David L.; Gaylord, Thomas K.

1993-01-01

A review of the rigorous coupled-wave analysis as applied to the diffraction of electro-magnetic waves by gratings is presented. The analysis is valid for any polarization, angle of incidence, and conical diffraction. Cascaded and/or multiplexed gratings as well as material anisotropy can be incorporated under the same formalism. Small period rectangular groove gratings can also be modeled using approximately equivalent uniaxial homogeneous layers (effective media). The ordinary and extraordinary refractive indices of these layers depend on the gratings filling factor, the refractive indices of the substrate and superstrate, and the ratio of the freespace wavelength to grating period. Comparisons of the homogeneous effective medium approximations with the rigorous coupled-wave analysis are presented. Antireflection designs (single-layer or multilayer) using the effective medium models are presented and compared. These ultra-short period antireflection gratings can also be used to produce soft x-rays. Comparisons of the rigorous coupled-wave analysis with experimental results on soft x-ray generation by gratings are also included.

Fabrication and performance of efficient thin circular polarization gratings with Bragg properties using bulk photo-alignment of a liquid crystalline polymer

NASA Astrophysics Data System (ADS)

Sakhno, Oksana; Gritsai, Yuri; Sahm, Hagen; Stumpe, Joachim

2018-03-01

Thin circular polarization gratings, characterized by high diffraction efficiency and large, up to 42°, diffraction angles were created by polarization holography for the first time. The high efficiency of the gratings is the result of the specific properties of a photo-crosslinkable liquid crystalline polymer and a two-step photochemical/thermal processing procedure. A diffraction efficiency of up to 98% at 532 nm has been achieved for gratings with periods of 700 nm. In contrast to polarization gratings with larger periods these gratings exhibit Bragg properties. So one beam is either transmitted or diffracted depending on the direction of the circular polarization of the incident light, whereas the maximal diffraction efficiency is achieved only at the proper incident angle. The fabrication procedure consists of holographic exposure of the film at room temperature which provides the photo-selective cycloaddition of cinnamic ester groups. Upon subsequent thermal annealing above T g bulk photo-alignment of the LC polymer film occurs enhancing the optical anisotropy within the grating. The holographic patterning provides high spatial resolution, the arbitrary orientation of the LC director as well as high optical quality, thermal and chemical stability of the final gratings. Highly efficient symmetric and slanted circular polarization gratings were fabricated with the proposed technique.

A severe capacity limit in the consolidation of orientation information into visual short-term memory.

PubMed

Becker, Mark W; Miller, James R; Liu, Taosheng

2013-04-01

Previous research has suggested that two color patches can be consolidated into visual short-term memory (VSTM) via an unlimited parallel process. Here we examined whether the same unlimited-capacity parallel process occurs for two oriented grating patches. Participants viewed two gratings that were presented briefly and masked. In blocks of trials, the gratings were presented either simultaneously or sequentially. In Experiments 1 and 2, the presentation of the stimuli was followed by a location cue that indicated the grating on which to base one's response. In Experiment 1, participants responded whether the target grating was oriented clockwise or counterclockwise with respect to vertical. In Experiment 2, participants indicated whether the target grating was oriented along one of the cardinal directions (vertical or horizontal) or was obliquely oriented. Finally, in Experiment 3, the location cue was replaced with a third grating that appeared at fixation, and participants indicated whether either of the two test gratings matched this probe. Despite the fact that these responses required fairly coarse coding of the orientation information, across all methods of responding we found superior performance for sequential over simultaneous presentations. These findings suggest that the consolidation of oriented gratings into VSTM is severely limited in capacity and differs from the consolidation of color information.

Spectral tuning of near-field radiative heat transfer by graphene-covered metasurfaces

NASA Astrophysics Data System (ADS)

Zheng, Zhiheng; Wang, Ao; Xuan, Yimin

2018-03-01

When two gratings are respectively covered by a layer of graphene sheet, the near-field radiative heat transfer between two parallel gratings made of silica (SiO2) could be greatly improved. As the material properties of doped silicon (n-type doping concentration is 1020 cm-3, marked as Si-20) and SiO2 differ greatly, we theoretically investigate the near-field radiative heat transfer between two parallel graphene-covered gratings made of Si-20 to explore some different phenomena, especially for modulating the spectral properties. The radiative heat flux between two parallel bulks made of Si-20 can be enhanced by using gratings instead of bulks. When the two gratings are respectively covered by a layer of graphene sheet, the radiative heat flux between two gratings made of Si-20 can be further enhanced. By tuning graphene chemical potential μ and grating filling factor f, due to the interaction between surface plasmon polaritons (SPPs) of graphene sheets and grating structures, the spectral properties of the radiative heat flux between two parallel graphene-covered gratings can be effectively regulated. This work will develop and supplement the effects of materials on the near-field radiative heat transfer for this kind of system configuration, paving a way to modulate the spectral properties of near-field radiative heat transfer.

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

NASA Technical Reports Server (NTRS)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

High-resolution compact spectrometer based on a custom-printed varied-line-spacing concave blazed grating.

PubMed

Chen, Jianwei; Chen, Wang; Zhang, Guodong; Lin, Hui; Chen, Shih-Chi

2017-05-29

We present the modeling, design and characterization of a compact spectrometer, achieving a resolution better than 1.5 nm throughout the visible spectrum (360-825 nm). The key component in the spectrometer is a custom-printed varied-line-space (VLS) concave blazed grating, where the groove density linearly decreases from the center of the grating (530 g/mm) at a rate of 0.58 nm/mm to the edge (528 g/mm). Parametric models have been established to deterministically link the system performance with the VLS grating design parameters, e.g., groove density, line-space varying rate, and to minimize the system footprint. Simulations have been performed in ZEMAX to confirm the results, indicating a 15% enhancement in system resolution versus common constant line-space (CLS) gratings. Next, the VLS concave blazed grating is fabricated via our vacuum nanoimprinting system, where a polydimethylsiloxane (PDMS) stamp is non-uniformly expanded to form the varied-line-spacing pattern from a planar commercial grating master (600 g/mm) for precision imprinting. The concave blazed grating is measured to have an absolute diffraction efficiency of 43%, higher than typical holographic gratings (~30%) used in the commercial compact spectrometers. The completed compact spectrometer contains only one optical component, i.e., the VLS concave grating, as well as an entrance slit and linear photodetector array, achieving a footprint of 11 × 11 × 3 cm 3 , which makes it the most compact and resolving (1.46 nm) spectrometer of its kind.

Speed Discrimination: Multiple Stimuli Appear Better Than One

NASA Technical Reports Server (NTRS)

Verghese, Preeti; Stone, Leland S.; Null, Cynthia H. (Technical Monitor)

1995-01-01

We reported that for a 21FC task with multiple moving grating patches (Gabors) in each interval, thresholds for speed discrimination decreased with the number of patches, while increasing the area of a single grating produced no such effect. Furthermore, this decrease occurred regardless of the spacing of the patches about a circle of eccentricity 4 degrees, i.e., whether they were maximally separated or almost touching. These results suggest that it is the multiple, discrete grating patches that cause thresholds to decrease, rather than the spatial arrangement. To test this hypothesis, we measured the effect of dividing a large grating into four quadrants, by superimposing a mean-luminance cross on it. The mean speed discrimination thresholds (Weber Fractions) for four observers were 19, 15, and 11 plus or minus 2%, for the single large grating, the grating with cross, and the 4 maximally-separated, small gratings, respectively. Thus, breaking up a single large grating into multiple parts caused thresholds to improve, despite the fact that less of the original patch was visible. To investigate the possible contribution of total bounding contour length, we measured the effect of coalescing three small grating patches into a single banana-shaped patch, while keeping the total contour length constant. These two conditions were compared to a single, circular Gabor patch of equivalent area that had (necessarily) a smaller contour length. Preliminary data from 3 of 4 observers were similar for the small-grating and banana configurations, but increased for the single, large grating, suggesting that contour length might play a role. We are also investigating the role of low-level factors pertinent to the large grating, such as the pooling of signals from motion units at different eccentricities, and the stimulation of extended inhibitory motion surrounds, as well as the possible contribution of topdown influences that segment the stimulus into distinct objects.

Periodicity analysis of tourist arrivals to Banda Aceh using smoothing SARIMA approach

NASA Astrophysics Data System (ADS)

Miftahuddin, Helida, Desri; Sofyan, Hizir

2017-11-01

Forecasting the number of tourist arrivals who enters a region is needed for tourism businesses, economic and industrial policies, so that the statistical modeling needs to be conducted. Banda Aceh is the capital of Aceh province more economic activity is driven by the services sector, one of which is the tourism sector. Therefore, the prediction of the number of tourist arrivals is needed to develop further policies. The identification results indicate that the data arrival of foreign tourists to Banda Aceh to contain the trend and seasonal nature. Allegedly, the number of arrivals is influenced by external factors, such as economics, politics, and the holiday season caused the structural break in the data. Trend patterns are detected by using polynomial regression with quadratic and cubic approaches, while seasonal is detected by a periodic regression polynomial with quadratic and cubic approach. To model the data that has seasonal effects, one of the statistical methods that can be used is SARIMA (Seasonal Autoregressive Integrated Moving Average). The results showed that the smoothing, a method to detect the trend pattern is cubic polynomial regression approach, with the modified model and the multiplicative periodicity of 12 months. The AIC value obtained was 70.52. While the method for detecting the seasonal pattern is a periodic regression polynomial cubic approach, with the modified model and the multiplicative periodicity of 12 months. The AIC value obtained was 73.37. Furthermore, the best model to predict the number of foreign tourist arrivals to Banda Aceh in 2017 to 2018 is SARIMA (0,1,1)(1,1,0) with MAPE is 26%.

A general U-block model-based design procedure for nonlinear polynomial control systems

NASA Astrophysics Data System (ADS)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Two-dimensional orthonormal trend surfaces for prospecting

NASA Astrophysics Data System (ADS)

Sarma, D. D.; Selvaraj, J. B.

Orthonormal polynomials have distinct advantages over conventional polynomials: the equations for evaluating trend coefficients are not ill-conditioned and the convergence power of this method is greater compared to the least-squares approximation and therefore the approach by orthonormal functions provides a powerful alternative to the least-squares method. In this paper, orthonormal polynomials in two dimensions are obtained using the Gram-Schmidt method for a polynomial series of the type: Z = 1 + x + y + x2 + xy + y2 + … + yn, where x and y are the locational coordinates and Z is the value of the variable under consideration. Trend-surface analysis, which has wide applications in prospecting, has been carried out using the orthonormal polynomial approach for two sample sets of data from India concerned with gold accumulation from the Kolar Gold Field, and gravity data. A comparison of the orthonormal polynomial trend surfaces with those obtained by the classical least-squares method has been made for the two data sets. In both the situations, the orthonormal polynomial surfaces gave an improved fit to the data. A flowchart and a FORTRAN-IV computer program for deriving orthonormal polynomials of any order and for using them to fit trend surfaces is included. The program has provision for logarithmic transformation of the Z variable. If log-transformation is performed the predicted Z values are reconverted to the original units and the trend-surface map generated for use. The illustration of gold assay data related to the Champion lode system of Kolar Gold Fields, for which a 9th-degree orthonormal trend surface was fit, could be used for further prospecting the area.

Integrated narrowband optical filter based on embedded subwavelength resonant grating structures

DOEpatents

Grann, Eric B.; Sitter, Jr., David N.

2000-01-01

A resonant grating structure in a waveguide and methods of tuning the performance of the grating structure are described. An apparatus includes a waveguide; and a subwavelength resonant grating structure embedded in the waveguide. The systems and methods provide advantages including narrowband filtering capabilities, minimal sideband reflections, spatial control, high packing density, and tunability.

Fabrication and Characterization of Tilted Fiber Optic Bragg Grating Filters over Various Wavelengths

NASA Technical Reports Server (NTRS)

Grant, Joseph; Jackson, Kurt V.; Wang, Y.; Sharma, A.; Burdine, Robert V. (Technical Monitor)

2002-01-01

Fiber Optic Bragg Grating taps are fabricated and characterized at various wavelengths using a modified Talbot interferometric technique. Gratings are fabricated by tilting the photosensitive fiber to angles up to 45 degrees w.r.t. the writing angle. Diffraction characteristics of the tilted grating is monitored in first and second orders.

Performance characteristics of a suite of volume phase holographic gratings produced for the Subaru prime focus spectrograph

NASA Astrophysics Data System (ADS)

Arns, James A.

2016-08-01

The Subaru Prime Focus Spectrograph[1] (PFS) requires a suite of volume phase holographic (VPH) gratings that parse the observational spectrum into three sub-spectral regions. In addition, the red region has a second, higher resolution arm that includes a VPH grating that will eventually be incorporated into a grism. This paper describes the specifications of the four grating types, gives the theoretical performances of diffraction efficiency for the production designs and presents the measured performances on the gratings produced to date.

Modified tandem gratings anastigmatic imaging spectrometer with oblique incidence for spectral broadband

NASA Astrophysics Data System (ADS)

Cui, Chengguang; Wang, Shurong; Huang, Yu; Xue, Qingsheng; Li, Bo; Yu, Lei

2015-09-01

A modified spectrometer with tandem gratings that exhibits high spectral resolution and imaging quality for solar observation, monitoring, and understanding of coastal ocean processes is presented in this study. Spectral broadband anastigmatic imaging condition, spectral resolution, and initial optical structure are obtained based on geometric aberration theory. Compared with conventional tandem gratings spectrometers, this modified design permits flexibility in selecting gratings. A detailed discussion of the optical design and optical performance of an ultraviolet spectrometer with tandem gratings is also included to explain the advantage of oblique incidence for spectral broadband.

Response of CO2 laser written long period fiber gratings packaged by polymer materials

NASA Astrophysics Data System (ADS)

Wu, Zhaodi; Liu, Yunqi; Zou, Jian; Chen, Na; Pang, Fufei; Wang, Tingyun

2011-12-01

We demonstrate the packaging of CO2 laser written long-period fiber gratings (LPFGs) using different polymer materials. We use three different silicone rubber polymers to package the LPFGs by simply coating it outside the grating. After the polymer coating, the resonance wavelength of LPFG was found to shift towards shorter wavelength by about 6 nm, and the temperature sensitivity of the packaged gratings was studied experimentally. Experiments showed that the gratings packaged by different polymers have different temperature characteristics and all of them have good thermal stability.

Design of a high-efficiency seven-port beam splitter using a dual duty cycle grating structure.

PubMed

Wen, Fung Jacky; Chung, Po Sheun

2011-07-01

In this paper, we propose a compact seven-port beam splitter which is constructed using only a single-layer high-density grating with a dual duty cycle structure. The properties of this grating are investigated by a simplified modal method. The diffraction efficiency can be achieved around 10% more than conventional Dammann gratings while the uniformity can still be maintained at less than 1%. The effect of deviations from the design parameters on the performance of the grating is also presented.

Fiber optic security seal including plural Bragg gratings

DOEpatents

Forman, Peter R.

1994-01-01

An optical security system enables the integrity of a container seal to be remotely interrogated. A plurality of Bragg gratings is written holographically into the core of at least one optical fiber placed about the container seal, where each Bragg grating has a predetermined location and a known frequency for reflecting incident light. A time domain reflectometer is provided with a variable frequency light output that corresponds to the reflecting frequencies of the Bragg gratings to output a signal that is functionally related to the location and reflecting frequency of each of the Bragg gratings.

Incorporation of nanovoids into metallic gratings for broadband plasmonic organic solar cells.

PubMed

Lee, Sangjun; In, Sungjun; Mason, Daniel R; Park, Namkyoo

2013-02-25

We present investigation and optimization of a newly proposed plasmonic organic solar cell geometry based on the incorporation of nanovoids into conventional rectangular backplane gratings. Hybridization of strongly localized plasmonic modes of the nanovoids with Fabry-Perot cavity modes originating from surface plasmon reflection at the grating elements is shown to significantly boost performance in the long wavelength regime. This constitutes improved broadband operation while maintaining absorption enhancements at short wavelengths derived from conventional rectangular grating. Our calculations predict a figure of merit enhancement of up to 41% compared to when the nanovoid indented grating is absent. This is a significant improvement over the previously considered rectangular grating structures, which is further shown to be maintained over the entire angular range.

Astronomical near-infrared echelle gratings

NASA Astrophysics Data System (ADS)

Hinkle, Kenneth H.; Joyce, Richard R.; Liang, Ming

2014-07-01

High-resolution near-infrared echelle spectrographs require coarse rulings in order to match the free spectral range to the detector size. Standard near-IR detector arrays typically are 2 K x 2 K or 4 K x 4 K. Detectors of this size combined with resolutions in the range 30000 to 100000 require grating groove spacings in the range 5 to 20 lines/mm. Moderately high blaze angles are desirable to reduce instrument size. Echelle gratings with these characteristics have potential wide application in both ambient temperature and cryogenic astronomical echelle spectrographs. We discuss optical designs for spectrographs employing immersed and reflective echelle gratings. The optical designs set constraints on grating characteristics. We report on market choices for obtaining these gratings and review our experiments with custom diamond turned rulings.

Design of a variable-line-spacing grating pattern for spectrometers based on a grating Fresnel device.

PubMed

Li, Xinghui; Zhang, Jinchao; Zhou, Qian; Ni, Kai; Pang, Jinchao; Tian, Rui

2016-04-01

In this Letter, we propose a variable-line-spacing (VLS) grating pattern for a hybrid diffractive device termed a grating Fresnel (G-Fresnel) lens, which is used in spectrometers to improve spectral resolution over a wide spectral range. The VLS grating pattern disperses light of specific wavelengths with a different angle and position such that the aberration caused by the Fresnel surface can be compensated for. In this manner, high resolution can be achieved over a relatively wide spectral range. The VLS grating pattern is designed based on the least wave-change principle and simulated by ZEMAX. Results reveal that the VLS G-Fresnel device allows a subnanometer resolution over a spectral range of 200 nm.

Phase-based Bragg intragrating distributed strain sensor

NASA Astrophysics Data System (ADS)

Huang, S.; Ohn, M. M.; Measures, R. M.

1996-03-01

A strain-distribution sensing technique based on the measurement of the phase spectrum of the reflected light from a fiber-optic Bragg grating is described. When a grating is subject to a strain gradient, the grating will experience a chirp and therefore the resonant wavelength will vary along the grating, causing wavelength-dependent penetration depth. Because the group delay for each wavelength component is related to its penetration depth and the resonant wavelength is determined by strain, a measured phase spectrum can then indicate the local strain as a function of location within the grating. This phase-based Bragg grating sensing technique offers a powerful new means for studying some important effects over a few millimeters or centimeters in smart structures.

Tunable resonance-domain diffraction gratings based on electrostrictive polymers.

PubMed

Axelrod, Ramon; Shacham-Diamand, Yosi; Golub, Michael A

2017-03-01

Critical combination of high diffraction efficiency and large diffraction angles can be delivered by resonance-domain diffractive optics with high aspect ratio and wavelength-scale grating periods. To advance from static to electrically tunable resonance-domain diffraction grating, we resorted to its replication onto 2-5 μm thick P(VDF-TrFE-CFE) electrostrictive ter-polymer membranes. Electromechanical and optical computer simulations provided higher than 90% diffraction efficiency, a large continuous deflection range exceeding 20°, and capabilities for adiabatic spatial modulation of the grating period and slant. A prototype of the tunable resonance-domain diffraction grating was fabricated in a soft-stamp thermal nanoimprinting process, characterized, optically tested, and provided experimental feasibility proof for the tunable sub-micron-period gratings on electrostrictive polymers.

Modeling and empirical characterization of the polarization response of off-plane reflection gratings.

PubMed

Marlowe, Hannah; McEntaffer, Randall L; Tutt, James H; DeRoo, Casey T; Miles, Drew M; Goray, Leonid I; Soltwisch, Victor; Scholze, Frank; Herrero, Analia Fernandez; Laubis, Christian

2016-07-20

Off-plane reflection gratings were previously predicted to have different efficiencies when the incident light is polarized in the transverse-magnetic (TM) versus transverse-electric (TE) orientations with respect to the grating grooves. However, more recent theoretical calculations which rigorously account for finitely conducting, rather than perfectly conducting, grating materials no longer predict significant polarization sensitivity. We present the first empirical results for radially ruled, laminar groove profile gratings in the off-plane mount, which demonstrate no difference in TM versus TE efficiency across our entire 300-1500 eV bandpass. These measurements together with the recent theoretical results confirm that grazing incidence off-plane reflection gratings using real, not perfectly conducting, materials are not polarization sensitive.

Phase plate technology for laser marking of magnetic discs

DOEpatents

Neuman, Bill; Honig, John; Hackel, Lloyd; Dane, C. Brent; Dixit, Shamasundar

1998-01-01

An advanced design for a phase plate enables the distribution of spots in arbitrarily shaped patterns with very high uniformity and with a continuously or near-continuously varying phase pattern. A continuous phase pattern eliminates large phase jumps typically expected in a grating that provides arbitrary shapes. Large phase jumps increase scattered light outside of the desired pattern, reduce efficiency and can make the grating difficult to manufacture. When manufacturing capabilities preclude producing a fully continuous grating, the present design can be easily adapted to minimize manufacturing errors and maintain high efficiencies. This continuous grating is significantly more efficient than previously described Dammann gratings, offers much more flexibility in generating spot patterns and is easier to manufacture and replicate than a multi-level phase grating.

Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water

NASA Astrophysics Data System (ADS)

Jiménez, N.; Romero-García, V.; Picó, R.; Garcia-Raffi, L. M.; Staliunas, K.

2015-11-01

We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10-4). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.

Animating Nested Taylor Polynomials to Approximate a Function

ERIC Educational Resources Information Center

Mazzone, Eric F.; Piper, Bruce R.

2010-01-01

The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…

Polynomial Conjoint Analysis of Similarities: A Model for Constructing Polynomial Conjoint Measurement Algorithms.

ERIC Educational Resources Information Center

Young, Forrest W.

A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…

Dual exponential polynomials and linear differential equations

NASA Astrophysics Data System (ADS)

Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

2018-01-01

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

Polynomial Graphs and Symmetry

ERIC Educational Resources Information Center

Goehle, Geoff; Kobayashi, Mitsuo

2013-01-01

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

Why the Faulhaber Polynomials Are Sums of Even or Odd Powers of (n + 1/2)

ERIC Educational Resources Information Center

Hersh, Reuben

2012-01-01

By extending Faulhaber's polynomial to negative values of n, the sum of the p'th powers of the first n integers is seen to be an even or odd polynomial in (n + 1/2) and therefore expressible in terms of the sum of the first n integers.

Self-Replicating Quadratics

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo; Circi, Christian

2018-05-01

In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth-Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.

Orbifold E-functions of dual invertible polynomials

NASA Astrophysics Data System (ADS)

Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi

2016-08-01

An invertible polynomial is a weighted homogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search for mirror symmetric orbifold Landau-Ginzburg models, P. Berglund and M. Henningson considered a pair (f , G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair (f ˜ , G ˜) . We consider the so-called orbifold E-function of such a pair (f , G) which is a generating function for the exponents of the monodromy action on an orbifold version of the mixed Hodge structure on the Milnor fibre of f. We prove that the orbifold E-functions of Berglund-Henningson dual pairs coincide up to a sign depending on the number of variables and a simple change of variables. The proof is based on a relation between monomials (say, elements of a monomial basis of the Milnor algebra of an invertible polynomial) and elements of the whole symmetry group of the dual polynomial.

Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in economics.

PubMed

Su, Liyun; Zhao, Yanyong; Yan, Tianshun; Li, Fenglan

2012-01-01

Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.

Symmetric polynomials in information theory: Entropy and subentropy

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

Jozsa, Richard; Mitchison, Graeme

2015-06-15

Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantitymore » Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.« less

Recursive approach to the moment-based phase unwrapping method.

PubMed

Langley, Jason A; Brice, Robert G; Zhao, Qun

2010-06-01

The moment-based phase unwrapping algorithm approximates the phase map as a product of Gegenbauer polynomials, but the weight function for the Gegenbauer polynomials generates artificial singularities along the edge of the phase map. A method is presented to remove the singularities inherent to the moment-based phase unwrapping algorithm by approximating the phase map as a product of two one-dimensional Legendre polynomials and applying a recursive property of derivatives of Legendre polynomials. The proposed phase unwrapping algorithm is tested on simulated and experimental data sets. The results are then compared to those of PRELUDE 2D, a widely used phase unwrapping algorithm, and a Chebyshev-polynomial-based phase unwrapping algorithm. It was found that the proposed phase unwrapping algorithm provides results that are comparable to those obtained by using PRELUDE 2D and the Chebyshev phase unwrapping algorithm.

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

NASA Astrophysics Data System (ADS)

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing

2015-09-01

The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the 'hypercube' polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the 'simplex' polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.

A solver for General Unilateral Polynomial Matrix Equation with Second-Order Matrices Over Prime Finite Fields

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-03-01

The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.

Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes

DOE PAGES

Zlotnikov, Michael

2016-08-24

We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for n scattering particles into a σ-moduli multivariate polynomial of what we call the standard form. We show that a standard form polynomial must have a specific ladder type monomial structure, which has finite size at any n, with highest multivariate degree given by (n – 3)(n – 4)/2. This set of monomials spans a complete basis for polynomials with rational coefficients in kinematic data on the support of scattering equations. Subsequently, at tree and one-loop level, we employ the global residue theorem to derive amore » prescription that evaluates any CHY amplitude by means of collecting simple residues at infinity only. Furthermore, the prescription is then applied explicitly to some tree and one-loop amplitude examples.« less

Gabor-based kernel PCA with fractional power polynomial models for face recognition.

PubMed

Liu, Chengjun

2004-05-01

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

A polynomial based model for cell fate prediction in human diseases.

PubMed

Ma, Lichun; Zheng, Jie

2017-12-21

Cell fate regulation directly affects tissue homeostasis and human health. Research on cell fate decision sheds light on key regulators, facilitates understanding the mechanisms, and suggests novel strategies to treat human diseases that are related to abnormal cell development. In this study, we proposed a polynomial based model to predict cell fate. This model was derived from Taylor series. As a case study, gene expression data of pancreatic cells were adopted to test and verify the model. As numerous features (genes) are available, we employed two kinds of feature selection methods, i.e. correlation based and apoptosis pathway based. Then polynomials of different degrees were used to refine the cell fate prediction function. 10-fold cross-validation was carried out to evaluate the performance of our model. In addition, we analyzed the stability of the resultant cell fate prediction model by evaluating the ranges of the parameters, as well as assessing the variances of the predicted values at randomly selected points. Results show that, within both the two considered gene selection methods, the prediction accuracies of polynomials of different degrees show little differences. Interestingly, the linear polynomial (degree 1 polynomial) is more stable than others. When comparing the linear polynomials based on the two gene selection methods, it shows that although the accuracy of the linear polynomial that uses correlation analysis outcomes is a little higher (achieves 86.62%), the one within genes of the apoptosis pathway is much more stable. Considering both the prediction accuracy and the stability of polynomial models of different degrees, the linear model is a preferred choice for cell fate prediction with gene expression data of pancreatic cells. The presented cell fate prediction model can be extended to other cells, which may be important for basic research as well as clinical study of cell development related diseases.

Generalized Freud's equation and level densities with polynomial potential

NASA Astrophysics Data System (ADS)

Boobna, Akshat; Ghosh, Saugata

2013-08-01

We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.

FIT: Computer Program that Interactively Determines Polynomial Equations for Data which are a Function of Two Independent Variables

NASA Technical Reports Server (NTRS)

Arbuckle, P. D.; Sliwa, S. M.; Roy, M. L.; Tiffany, S. H.

1985-01-01

A computer program for interactively developing least-squares polynomial equations to fit user-supplied data is described. The program is characterized by the ability to compute the polynomial equations of a surface fit through data that are a function of two independent variables. The program utilizes the Langley Research Center graphics packages to display polynomial equation curves and data points, facilitating a qualitative evaluation of the effectiveness of the fit. An explanation of the fundamental principles and features of the program, as well as sample input and corresponding output, are included.

First Instances of Generalized Expo-Rational Finite Elements on Triangulations

NASA Astrophysics Data System (ADS)

Dechevsky, Lubomir T.; Zanaty, Peter; Laksa˚, Arne; Bang, Børre

2011-12-01

In this communication we consider a construction of simplicial finite elements on triangulated two-dimensional polygonal domains. This construction is, in some sense, dual to the construction of generalized expo-rational B-splines (GERBS). The main result is in the obtaining of new polynomial simplicial patches of the first several lowest possible total polynomial degrees which exhibit Hermite interpolatory properties. The derivation of these results is based on the theory of piecewise polynomial GERBS called Euler Beta-function B-splines. We also provide 3-dimensional visualization of the graphs of the new polynomial simplicial patches and their control polygons.

The Translated Dowling Polynomials and Numbers.

PubMed

Mangontarum, Mahid M; Macodi-Ringia, Amila P; Abdulcarim, Normalah S

2014-01-01

More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.

Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin.

PubMed

Siewert, F; Löchel, B; Buchheim, J; Eggenstein, F; Firsov, A; Gwalt, G; Kutz, O; Lemke, St; Nelles, B; Rudolph, I; Schäfers, F; Seliger, T; Senf, F; Sokolov, A; Waberski, Ch; Wolf, J; Zeschke, T; Zizak, I; Follath, R; Arnold, T; Frost, F; Pietag, F; Erko, A

2018-01-01

Blazed gratings are of dedicated interest for the monochromatization of synchrotron radiation when a high photon flux is required, such as, for example, in resonant inelastic X-ray scattering experiments or when the use of laminar gratings is excluded due to too high flux densities and expected damage, for example at free-electron laser beamlines. Their availability became a bottleneck since the decommissioning of the grating manufacture facility at Carl Zeiss in Oberkochen. To resolve this situation a new technological laboratory was established at the Helmholtz Zentrum Berlin, including instrumentation from Carl Zeiss. Besides the upgraded ZEISS equipment, an advanced grating production line has been developed, including a new ultra-precise ruling machine, ion etching technology as well as laser interference lithography. While the old ZEISS ruling machine GTM-6 allows ruling for a grating length up to 170 mm, the new GTM-24 will have the capacity for 600 mm (24 inch) gratings with groove densities between 50 lines mm -1 and 1200 lines mm -1 . A new ion etching machine with a scanning radiofrequency excited ion beam (HF) source allows gratings to be etched into substrates of up to 500 mm length. For a final at-wavelength characterization, a new reflectometer at a new Optics beamline at the BESSY-II storage ring is under operation. This paper reports on the status of the grating fabrication, the measured quality of fabricated items by ex situ and in situ metrology, and future development goals.

Spherical grating spectrometers

NASA Astrophysics Data System (ADS)

O'Donoghue, Darragh; Clemens, J. Christopher

2014-07-01

We describe designs for spectrometers employing convex dispersers. The Offner spectrometer was the first such instrument; it has almost exclusively been employed on satellite platforms, and has had little impact on ground-based instruments. We have learned how to fabricate curved Volume Phase Holographic (VPH) gratings and, in contrast to the planar gratings of traditional spectrometers, describe how such devices can be used in optical/infrared spectrometers designed specifically for curved diffraction gratings. Volume Phase Holographic gratings are highly efficient compared to conventional surface relief gratings; they have become the disperser of choice in optical / NIR spectrometers. The advantage of spectrometers with curved VPH dispersers is the very small number of optical elements used (the simplest comprising a grating and a spherical mirror), as well as illumination of mirrors off axis, resulting in greater efficiency and reduction in size. We describe a "Half Offner" spectrometer, an even simpler version of the Offner spectrometer. We present an entirely novel design, the Spherical Transmission Grating Spectrometer (STGS), and discuss exemplary applications, including a design for a double-beam spectrometer without any requirement for a dichroic. This paradigm change in spectrometer design offers an alternative to all-refractive astronomical spectrometer designs, using expensive, fragile lens elements fabricated from CaF2 or even more exotic materials. The unobscured mirror layout avoids a major drawback of the previous generation of catadioptric spectrometer designs. We describe laboratory measurements of the efficiency and image quality of a curved VPH grating in a STGS design, demonstrating, simultaneously, efficiency comparable to planar VPH gratings along with good image quality. The stage is now set for construction of a prototype instrument with impressive performance.

Choice of Grating Orientation for Evaluation of Peripheral Vision

PubMed Central

Venkataraman, Abinaya Priya; Winter, Simon; Rosén, Robert; Lundström, Linda

2016-01-01

ABSTRACT Purpose Peripheral resolution acuity depends on the orientation of the stimuli. However, it is uncertain if such a meridional effect also exists for peripheral detection tasks because they are affected by optical errors. Knowledge of the quantitative differences in acuity for different grating orientations is crucial for choosing the appropriate stimuli for evaluations of peripheral resolution and detection tasks. We assessed resolution and detection thresholds for different grating orientations in the peripheral visual field. Methods Resolution and detection thresholds were evaluated for gratings of four different orientations in eight different visual field meridians in the 20-deg visual field in white light. Detection measurements in monochromatic light (543 nm; bandwidth, 10 nm) were also performed to evaluate the effects of chromatic aberration on the meridional effect. A combination of trial lenses and adaptive optics system was used to correct the monochromatic lower- and higher-order aberrations. Results For both resolution and detection tasks, gratings parallel to the visual field meridian had better threshold compared with the perpendicular gratings, whereas the two oblique gratings had similar thresholds. The parallel and perpendicular grating acuity differences for resolution and detection tasks were 0.16 logMAR and 0.11 logMAD, respectively. Elimination of chromatic errors did not affect the meridional preference in detection acuity. Conclusions Similar to peripheral resolution, detection also shows a meridional effect that appears to have a neural origin. The threshold difference seen for parallel and perpendicular gratings suggests the use of two oblique gratings as stimuli in alternative forced-choice procedures for peripheral vision evaluation to reduce measurement variation. PMID:26889822

Choice of Grating Orientation for Evaluation of Peripheral Vision.

PubMed

Venkataraman, Abinaya Priya; Winter, Simon; Rosén, Robert; Lundström, Linda

2016-06-01

Peripheral resolution acuity depends on the orientation of the stimuli. However, it is uncertain if such a meridional effect also exists for peripheral detection tasks because they are affected by optical errors. Knowledge of the quantitative differences in acuity for different grating orientations is crucial for choosing the appropriate stimuli for evaluations of peripheral resolution and detection tasks. We assessed resolution and detection thresholds for different grating orientations in the peripheral visual field. Resolution and detection thresholds were evaluated for gratings of four different orientations in eight different visual field meridians in the 20-deg visual field in white light. Detection measurements in monochromatic light (543 nm; bandwidth, 10 nm) were also performed to evaluate the effects of chromatic aberration on the meridional effect. A combination of trial lenses and adaptive optics system was used to correct the monochromatic lower- and higher-order aberrations. For both resolution and detection tasks, gratings parallel to the visual field meridian had better threshold compared with the perpendicular gratings, whereas the two oblique gratings had similar thresholds. The parallel and perpendicular grating acuity differences for resolution and detection tasks were 0.16 logMAR and 0.11 logMAD, respectively. Elimination of chromatic errors did not affect the meridional preference in detection acuity. Similar to peripheral resolution, detection also shows a meridional effect that appears to have a neural origin. The threshold difference seen for parallel and perpendicular gratings suggests the use of two oblique gratings as stimuli in alternative forced-choice procedures for peripheral vision evaluation to reduce measurement variation.

High-power, surface-emitting quantum cascade laser operating in a symmetric grating mode

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

Boyle, C.; Sigler, C.; Kirch, J. D.

2016-03-21

Grating-coupled surface-emitting (GCSE) lasers generally operate with a double-lobed far-field beam pattern along the cavity-length direction, which is a result of lasing being favored in the antisymmetric grating mode. We experimentally demonstrate a GCSE quantum-cascade laser design allowing high-power, nearly single-lobed surface emission parallel to the longitudinal cavity. A 2nd-order Au-semiconductor distributed-feedback (DFB)/distributed-Bragg-reflector (DBR) grating is used for feedback and out-coupling. The DFB and DBR grating regions are 2.55 mm- and 1.28 mm-long, respectively, for a total grating length of 5.1 mm. The lasers are designed to operate in a symmetric (longitudinal) grating mode by causing resonant coupling of the guided optical modemore » to the antisymmetric surface-plasmon modes of the 2nd-order metal/semiconductor grating. Then, the antisymmetric modes are strongly absorbed by the metal in the grating, causing the symmetric mode to be favored to lase, which, in turn, produces a single-lobed beam over a range of grating duty-cycle values of 36%–41%. Simulations indicate that the symmetric mode is always favored to lase, independent of the random phase of reflections from the device's cleaved ends. Peak pulsed output powers of ∼0.4 W were measured with nearly single-lobe beam-pattern (in the longitudinal direction), single-spatial-mode operation near 4.75 μm wavelength. Far-field measurements confirm a diffraction-limited beam pattern, in agreement with simulations, for a source-to-detector separation of 2 m.« less

Design of compressors for FEL pulses using deformable gratings

NASA Astrophysics Data System (ADS)

Bonora, Stefano; Fabris, Nicola; Frassetto, Fabio; Giovine, Ennio; Miotti, Paolo; Quintavalla, Martino; Poletto, Luca

2017-06-01

We present the optical layout of soft X-rays compressors using reflective grating specifically designed to give both positive or negative group-delay dispersion (GDD). They are tailored for chirped-pulse-amplification experiments with FEL sources. The optical design originates from an existing compressor with plane gratings already realized and tested at FERMI, that has been demonstrated capable to introduce tunable negative GDD. Here, we discuss two novel designs for compressors using deformable gratings capable to give both negative and positive GDD. Two novel designs are discussed: 1) a design with two deformable gratings and an intermediate focus between the twos, that is demonstrated capable to introduce positive GDD; 2) a design with one deformable grating giving an intermediate focus, followed by a concave mirror and a plane grating, that is capable to give both positive and negative GDD depending on the distance between the second mirror and the second grating. Both the designs are tunable in wavelength and GDD, by acting on the deformable gratings, that are rotated to tune the wavelength and the GDD and deformed to introduce the radius required to keep the spectral focus. The deformable gratings have a laminar profile and are ruled on a thin silicon plane substrate. A piezoelectric actuator is glued on the back of the substrate and is actuated to give a radius of curvature that is varying from infinite (plane) to few meters. The ruling procedure, the piezoelectric actuator and the efficiency measurements in the soft X-rays will be presented. Some test cases are discussed for wavelengths shorter than 12 nm.

Reflection Properties of Metallic Gratings on ZnO Films over GaAs Substrates

NASA Technical Reports Server (NTRS)

Hickernell, Fred S.; Kim, Yoonkee; Hunt, William D.

1994-01-01

A potential application for piezoelectric film deposited on GaAs substrates is the monolithic integration of surface acoustic wave (SAW) devices with GaAs electronics. Metallic gratings are basic elements required for the construction of such devices, and analyzing the reflectivity and the velocity change due to metallic gratings is often a critical design parameter. In this article, Datta and Hunsinger technique is extended to the case of a multilayered structure, and the developed technique is applied to analyze shorted and open gratings on ZnO films sputtered over (001)-cut (110)-propagating GaAs substrates. The analysis shows that zero reflectivity of shorted gratings can be obtained by a combination of the ZnO film and the metal thickness and the metalization ratio of the grating. Experiments are performed on shorted and an open gratings (with the center frequency of about 180 MHz) for three different metal thicknesses over ZnO films which are 0.8 and 2.6 micrometers thick. From the experiments, zero reflectivity at the resonant frequency of the grating is observed for a reasonable thickness (h/Alpha = 0.5%) of aluminum metalization. The velocity shift between the shorted and the open grating is also measured to be 0.18 MHz and 0.25 MHz for 0.8 and 1.6 micrometers respectively. The measured data show relatively good agreement with theoretical predictions.

Large-area full field x-ray differential phase-contrast imaging using 2D tiled gratings

NASA Astrophysics Data System (ADS)

Schröter, Tobias J.; Koch, Frieder J.; Kunka, Danays; Meyer, Pascal; Tietze, Sabrina; Engelhardt, Sabine; Zuber, Marcus; Baumbach, Tilo; Willer, Konstantin; Birnbacher, Lorenz; Prade, Friedrich; Pfeiffer, Franz; Reichert, Klaus-Martin; Hofmann, Andreas; Mohr, Jürgen

2017-06-01

Grating-based x-ray differential phase-contrast imaging (DPCI) is capable of acquiring information based on phase-shift and dark-field signal, in addition to conventional x-ray absorption-contrast. Thus DPCI gives an advantage to investigate composite materials with component wise similar absorption properties like soft tissues. Due to technological challenges in fabricating high quality gratings over a large extent, the field of view (FoV) of the imaging systems is limited to a grating area of a couple of square centimeters. For many imaging applications (e.g. in medicine), however, a FoV that ranges over several ten centimeters is needed. In this manuscript we propose to create large area gratings of theoretically any extent by assembling a number of individual grating tiles. We discuss the precision needed for alignment of each microstructure tile in order to reduce image artifacts and to preserve minimum 90% of the sensitivity obtainable with a monolithic grating. To achieve a reliable high precision alignment a semiautomatic assembly system consisting of a laser autocollimator, a digital microscope and a force sensor together with positioning devices was built. The setup was used to tile a first four times four analyzer grating with a size of 200 mm  ×  200 mm together with a two times two phase grating. First imaging results prove the applicability and quality of the tiling concept.

The Time-Dependent Sensitivity of the MAMA and CCD Long-Slit Gratings

NASA Astrophysics Data System (ADS)

Holland, Stephen T.; Aloisi, Alessandra; Bostroem, Azalee; Oliveria, Cristina; Proffitt, Charles

2014-12-01

We present the results of observing flux standard stars used to determine trends in the sensitivities of the five STIS low-resolution, long-slit gratings between 1997 and 2013. Also, the assumption that the sensitivity trends for the medium-resolution and echelle gratings are the same as those for the corresponding low-resolution gratings is tested.

Diffraction gratings used as identifying markers

DOEpatents

Deason, Vance A.; Ward, Michael B.

1991-01-01

A finely detailed defraction grating is applied to an object as an identifier or tag which is unambiguous, difficult to duplicate, or remove and transfer to another item, and can be read and compared with prior readings with relative ease. The exact pattern of the defraction grating is mapped by diffraction moire techniques and recorded for comparison with future readings of the same grating.

Suppressing Ghost Diffraction in E-Beam-Written Gratings

NASA Technical Reports Server (NTRS)

Wilson, Daniel; Backlund, Johan

2009-01-01

A modified scheme for electron-beam (E-beam) writing used in the fabrication of convex or concave diffraction gratings makes it possible to suppress the ghost diffraction heretofore exhibited by such gratings. Ghost diffraction is a spurious component of diffraction caused by a spurious component of grating periodicity as described below. The ghost diffraction orders appear between the main diffraction orders and are typically more intense than is the diffuse scattering from the grating. At such high intensity, ghost diffraction is the dominant source of degradation of grating performance. The pattern of a convex or concave grating is established by electron-beam writing in a resist material coating a substrate that has the desired convex or concave shape. Unfortunately, as a result of the characteristics of electrostatic deflectors used to control the electron beam, it is possible to expose only a small field - typically between 0.5 and 1.0 mm wide - at a given fixed position of the electron gun relative to the substrate. To make a grating larger than the field size, it is necessary to move the substrate to make it possible to write fields centered at different positions, so that the larger area is synthesized by "stitching" the exposed fields.

Research and design on orthogonal diffraction grating-based 3D nanometer displacement sensor

NASA Astrophysics Data System (ADS)

Liu, Baoshuai; Yuan, Yibao; Yin, Zhehao

2017-10-01

This study concerns an orthogonal diffraction grating-based nanometer displacement sensor. In this study, we performed calculation of displacements in the XYZ directions. In the optical measured path part, we used a two-dimensional orthogonal motion grating and a two-dimensional orthogonal reference grating with the pitch of 0.5um to measure the displacement of XYZ in three directions by detecting ±1st diffraction fringes. The self-collimated structure of the grating greatly extended the Z-axis range. We also simulated the optical path of the sensor with ZEMAX software and verified the feasibility of the scheme. For signal subdivision and processing, we combined large number counting (completed grating line) with small number counting (digital subdivision), realizing high multiples of subdivision of grating interference signals. We used PC to process the interference fringes and greatly improved the processing speed. In the scheme, the theoretical multiples of subdivision could reach 1024 with 10-bit AD conversion, but the actual multiples of subdivision was limited by the quality of the grating interference signals. So we introduced an orthogonal compensation circuit and a filter circuit to improve the signal quality.

A low cost method for hard x-ray grating interferometry.

PubMed

Du, Yang; Lei, Yaohu; Liu, Xin; Huang, Jianheng; Zhao, Zhigang; Guo, Jinchuan; Li, Ji; Niu, Hanben

2016-12-07

Grating interferometry is advantageous over conventional x-ray absorption imaging because it enables the detection of samples constituted by low atomic number elements (low-Z materials). Therefore, it has a potential application in biological science and medical diagnostics. The grating interferometry has some critical optics components such as absorption gratings which are conventionally manufactured by the lithography, electroplating, and molding (LIGA) technique and employing gold as the absorbent material in it. However, great challenge lies in its implementations for practical applications because of the cost and difficulty to achieve high aspect ratio absorbing grating devices. In this paper, we present a low-cost approach that involves using the micro-casting technique with bismuth (Bi) as the absorber in source grating and as well as filling cesium iodide thallium(CsI:Tl) in a periodically structured scintillator. No costly facilities as synchrotron radiation are required and cheap material is used in our approach. Our experiment using these components shows high quality complementary images can be obtained with contrast of absorption, phase and visibility. This alternative method conquers the limitation of costly grating devices for a long time and stands an important step towards the further practical application of grating interferometry.

Narrow groove plasmonic nano-gratings for surface plasmon resonance sensing

PubMed Central

Dhawan, Anuj; Canva, Michael; Vo-Dinh, Tuan

2011-01-01

We present a novel surface plasmon resonance (SPR) configuration based on narrow groove (sub-15 nm) plasmonic nano-gratings such that normally incident radiation can be coupled into surface plasmons without the use of prism-coupling based total internal reflection, as in the classical Kretschmann configuration. This eliminates the angular dependence requirements of SPR-based sensing and allows development of robust miniaturized SPR sensors. Simulations based on Rigorous Coupled Wave Analysis (RCWA) were carried out to numerically calculate the reflectance - from different gold and silver nano-grating structures - as a function of the localized refractive index of the media around the SPR nano-gratings as well as the incident radiation wavelength and angle of incidence. Our calculations indicate substantially higher differential reflectance signals, on localized change of refractive index in the narrow groove plasmonic gratings, as compared to those obtained from conventional SPR-based sensing systems. Furthermore, these calculations allow determination of the optimal nano-grating geometric parameters - i. e. nanoline periodicity, spacing between the nanolines, as well as the height of the nanolines in the nano-grating - for highest sensitivity to localized change of refractive index, as would occur due to binding of a biomolecule target to a functionalized nano-grating surface. PMID:21263620

Enhancement of Light Absorption in Silicon Nanowire Photovoltaic Devices with Dielectric and Metallic Grating Structures.

PubMed

Park, Jin-Sung; Kim, Kyoung-Ho; Hwang, Min-Soo; Zhang, Xing; Lee, Jung Min; Kim, Jungkil; Song, Kyung-Deok; No, You-Shin; Jeong, Kwang-Yong; Cahoon, James F; Kim, Sun-Kyung; Park, Hong-Gyu

2017-12-13

We report the enhancement of light absorption in Si nanowire photovoltaic devices with one-dimensional dielectric or metallic gratings that are fabricated by a damage-free, precisely aligning, polymer-assisted transfer method. Incorporation of a Si 3 N 4 grating with a Si nanowire effectively enhances the photocurrents for transverse-electric polarized light. The wavelength at which a maximum photocurrent is generated is readily tuned by adjusting the grating pitch. Moreover, the electrical properties of the nanowire devices are preserved before and after transferring the Si 3 N 4 gratings onto Si nanowires, ensuring that the quality of pristine nanowires is not degraded during the transfer. Furthermore, we demonstrate Si nanowire photovoltaic devices with Ag gratings using the same transfer method. Measurements on the fabricated devices reveal approximately 27.1% enhancement in light absorption compared to that of the same devices without the Ag gratings without any degradation of electrical properties. We believe that our polymer-assisted transfer method is not limited to the fabrication of grating-incorporated nanowire photovoltaic devices but can also be generically applied for the implementation of complex nanoscale structures toward the development of multifunctional optoelectronic devices.

Accurate Estimation of Solvation Free Energy Using Polynomial Fitting Techniques

PubMed Central

Shyu, Conrad; Ytreberg, F. Marty

2010-01-01

This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem 30: 2297–2304, 2009). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and non-equidistant λ values, the solvation free energy can be estimated with high accuracy without using soft-core scaling and separate simulations for Lennard-Jones and partial charges. The results from our study suggest these polynomial techniques, especially with use of non-equidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software. PMID:20623657

Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials

PubMed Central

Corteel, Sylvie; Williams, Lauren K.

2010-01-01

We introduce some combinatorial objects called staircase tableaux, which have cardinality 4nn !, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities α and γ, and they may exit and enter at the right with probabilities β and δ. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials. PMID:20348417

Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials.

PubMed

Corteel, Sylvie; Williams, Lauren K

2010-04-13

We introduce some combinatorial objects called staircase tableaux, which have cardinality 4(n)n!, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities alpha and gamma, and they may exit and enter at the right with probabilities beta and delta. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials.

Realization of back-side heterogeneous hybrid III-V/Si DBR lasers for silicon photonics

NASA Astrophysics Data System (ADS)

Durel, Jocelyn; Ferrotti, Thomas; Chantre, Alain; Cremer, Sébastien; Harduin, Julie; Bernabé, Stéphane; Kopp, Christophe; Boeuf, Frédéric; Ben Bakir, Badhise; Broquin, Jean-Emmanuel

2016-02-01

In this paper, the simulation, design and fabrication of a back-side coupling (BSC) concept for silicon photonics, which targets heterogeneous hybrid III-V/Si laser integration is presented. Though various demonstrations of a complete SOI integration of passive and active photonic devices have been made, they all feature multi-level planar metal interconnects, and a lack of integrated light sources. This is mainly due to the conflict between the need of planar surfaces for III-V/Si bonding and multiple levels of metallization. The proposed BSC solution to this topographical problem consists in fabricating lasers on the back-side of the Si waveguides using a new process sequence. The devices are based on a hybrid structure composed of an InGaAsP MQW active area and a Si-based DBR cavity. The emitted light wavelength is accordable within a range of 20 nm around 1.31μm thanks to thermal heaters and the laser output is fiber coupled through a Grating Coupler (GC). From a manufacturing point of view, the BSC approach provides not only the advantages of allowing the use of a thin-BOX SOI instead of a thick one; but it also shifts the laser processing steps and their materials unfriendly to CMOS process to the far back-end areas of fabrication lines. Moreover, aside from solving technological integration issues, the BSC concept offers several new design opportunities for active and passive devices (heat sink, Bragg gratings, grating couplers enhanced with integrated metallic mirrors, tapers…). These building boxes are explored here theoretically and experimentally.

Experimental observation of acoustic sub-harmonic diffraction by a grating

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

Liu, Jingfei, E-mail: benjamin.jf.liu@gatech.edu; Declercq, Nico F., E-mail: declercqdepatin@gatech.edu

2014-06-28

A diffraction grating is a spatial filter causing sound waves or optical waves to reflect in directions determined by the frequency of the waves and the period of the grating. The classical grating equation is the governing principle that has successfully described the diffraction phenomena caused by gratings. However, in this work, we show experimental observation of the so-called sub-harmonic diffraction in acoustics that cannot be explained by the classical grating equation. Experiments indicate two physical phenomena causing the effect: internal scattering effects within the corrugation causing a phase shift and nonlinear acoustic effects generating new frequencies. This discovery expandsmore » our current understanding of the diffraction phenomenon, and it also makes it possible to better design spatial diffraction spectra, such as a rainbow effect in optics with a more complicated color spectrum than a traditional rainbow. The discovery reveals also a possibly new technique to study nonlinear acoustics by exploitation of the natural spatial filtering effect inherent to an acoustic diffraction grating.« less

Apodized grating coupler using fully-etched nanostructures

NASA Astrophysics Data System (ADS)

Wu, Hua; Li, Chong; Li, Zhi-Yong; Guo, Xia

2016-08-01

A two-dimensional apodized grating coupler for interfacing between single-mode fiber and photonic circuit is demonstrated in order to bridge the mode gap between the grating coupler and optical fiber. The grating grooves of the grating couplers are realized by columns of fully etched nanostructures, which are utilized to digitally tailor the effective refractive index of each groove in order to obtain the Gaussian-like output diffractive mode and then enhance the coupling efficiency. Compared with that of the uniform grating coupler, the coupling efficiency of the apodized grating coupler is increased by 4.3% and 5.7%, respectively, for the nanoholes and nanorectangles as refractive index tunes layer. Project supported by the National Natural Science Foundation of China (Grant Nos. 61222501, 61335004, and 61505003), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20111103110019), the Postdoctoral Science Foundation of Beijing Funded Project, China (Grant No. Q6002012201502), and the Science and Technology Research Project of Jiangxi Provincial Education Department, China (Grant No. GJJ150998).

MEMS-based tunable gratings and their applications

NASA Astrophysics Data System (ADS)

Yu, Yiting; Yuan, Weizheng; Qiao, Dayong

2015-03-01

The marriage of optics and MEMS has resulted in a new category of optical devices and systems that have unprecedented advantages compared with their traditional counterparts. As an important spatial light modulating technology, diffractive optical MEMS obtains a wide variety of successful commercial applications, e.g. projection displays, optical communication and spectral analysis, due to its features of highly compact, low-cost, IC-compatible, excellent performance, and providing possibilities for developing totally new, yet smart devices and systems. Three most successful MEMS diffraction gratings (GLVs, Polychromator and DMDs) are briefly introduced and their potential applications are analyzed. Then, three different MEMS tunable gratings developed by our group, named as micro programmable blazed gratings (μPBGs) and micro pitch-tunable gratings (μPTGs) working in either digital or analog mode, are demonstrated. The strategies to largely enhance the maximum blazed angle and grating period are described. Some preliminary application explorations based on the developed grating devices are also shown. For our ongoing research focus, we will further improve the device performance to meet the engineering application requirements.

Quantitative x-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size.

PubMed

Morgan, Kaye S; Paganin, David M; Siu, Karen K W

2011-01-01

The ability to quantitatively retrieve transverse phase maps during imaging by using coherent x rays often requires a precise grating or analyzer-crystal-based setup. Imaging of live animals presents further challenges when these methods require multiple exposures for image reconstruction. We present a simple method of single-exposure, single-grating quantitative phase contrast for a regime in which the grating period is much greater than the effective pixel size. A grating is used to create a high-visibility reference pattern incident on the sample, which is distorted according to the complex refractive index and thickness of the sample. The resolution, along a line parallel to the grating, is not restricted by the grating spacing, and the detector resolution becomes the primary determinant of the spatial resolution. We present a method of analysis that maps the displacement of interrogation windows in order to retrieve a quantitative phase map. Application of this analysis to the imaging of known phantoms shows excellent correspondence.

Fabrication of Extremely Short Length Fiber Bragg Gratings for Sensor Applications

NASA Technical Reports Server (NTRS)

Wu, Meng-Chou; Rogowski, Robert S.; Tedjojuwono, Ken K.

2002-01-01

A new technique and a physical model for writing extremely short length Bragg gratings in optical fibers have been developed. The model describes the effects of diffraction on the spatial spectra and therefore, the wavelength spectra of the Bragg gratings. Using an interferometric technique and a variable aperture, short gratings of various lengths and center wavelengths were written in optical fibers. By selecting the related parameters, the Bragg gratings with typical length of several hundred microns and bandwidth of several nanometers can be obtained. These short gratings can be apodized with selected diffraction patterns and hence their broadband spectra have a well-defined bell shape. They are suitable for use as miniaturized distributed strain sensors, which have broad applications to aerospace research and industry as well.

SU8 inverted-rib waveguide Bragg grating filter.

PubMed

Huang, Cheng-Sheng; Wang, Wei-Chih

2013-08-01

A polymeric SU8 inverted-rib waveguide Bragg grating filter fabricated using reactive ion etching (RIE) and solvent assisted microcontact molding (SAMIM) is presented. SAMIM is one kind of soft lithography. The technique is unique in that a composite hard-polydimethysiloxane/polydimethysiloxane stamp is used to transfer the grating pattern onto an inverted SU8 rib waveguide system. The composite grating stamp can be used repeatedly several times without degradation. Using this stamp and inverter-rib waveguide structure, the Bragg grating filter fabrication can be significantly simplified. The experiment result shows an attenuation dip in the transmission spectra, with a value of -7 dBm at 1550 nm for a grating with a period of 0.492 μm on an inverted-rib waveguide with 6.6 μm width and 4 μm height.

Bragg gratings inscription in step-index PMMA optical fiber by femtosecond laser pulses at 400 nm

NASA Astrophysics Data System (ADS)

Hu, X.; Kinet, D.; Chah, K.; Mégret, P.; Caucheteur, C.

2016-05-01

In this paper, we report photo-inscription of uniform Bragg gratings in trans-4-stilbenemethanol-doped photosensitive step-index polymer optical fiber. Gratings were produced at ~1575 nm by the phase mask technique with a femtosecond laser emitting at 400 nm with different average optical powers (8 mW, 13 mW and 20 mW). The grating growth dynamics in transmission were monitored during the manufacturing process, showing that the grating grows faster with higher power. Using 20 mW laser beam power, the reflectivity reaches 94 % (8 dB transmission loss) in 70 seconds. Finally, the gratings were characterized in temperature in the range 20 - 45 °C. The thermal sensitivity has been computed equal to - 86.6 pm/°C.

Phase plate technology for laser marking of magnetic discs

DOEpatents

Neuman, B.; Honig, J.; Hackel, L.; Dane, C.B.; Dixit, S.

1998-10-27

An advanced design for a phase plate enables the distribution of spots in arbitrarily shaped patterns with very high uniformity and with a continuously or near-continuously varying phase pattern. A continuous phase pattern eliminates large phase jumps typically expected in a grating that provides arbitrary shapes. Large phase jumps increase scattered light outside of the desired pattern, reduce efficiency and can make the grating difficult to manufacture. When manufacturing capabilities preclude producing a fully continuous grating, the present design can be easily adapted to minimize manufacturing errors and maintain high efficiencies. This continuous grating is significantly more efficient than previously described Dammann gratings, offers much more flexibility in generating spot patterns and is easier to manufacture and replicate than a multi-level phase grating. 3 figs.

Ultra-broad gain quantum cascade lasers tunable from 6.5 to 10.4 μm.

PubMed

Xie, Feng; Caneau, C; Leblanc, H; Ho, M-T; Zah, C

2015-09-01

We present a quantum cascade laser structure with an ultra-broad gain profile that covers the wavelength range from 6.5 to 10.4 μm. In a grating-tuned external cavity, we demonstrated continuous tuning from 1027  cm(-1) to 1492  cm(-1) with this broad gain laser chip. We also fabricated distributed feedback quantum cascade laser arrays with this active region design and varied grating periods. We demonstrated single wavelength lasing from 962 (10.4) to 1542  cm(-1) (6.5 μm). The frequency coverage (580  cm(-1)) is about 46% of center frequency.

Wilson-Racah quantum system

NASA Astrophysics Data System (ADS)

Alhaidari, A. D.; Taiwo, T. J.

2017-02-01

Using a recent formulation of quantum mechanics without a potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.

On the Waring problem for polynomial rings

PubMed Central

Fröberg, Ralf; Ottaviani, Giorgio; Shapiro, Boris

2012-01-01

In this note we discuss an analog of the classical Waring problem for . Namely, we show that a general homogeneous polynomial of degree divisible by k≥2 can be represented as a sum of at most kn k-th powers of homogeneous polynomials in . Noticeably, kn coincides with the number obtained by naive dimension count. PMID:22460787

A DDDAS Framework for Volcanic Ash Propagation and Hazard Analysis

DTIC Science & Technology

2012-01-01

probability distribution for the input variables (for example, Hermite polynomials for normally distributed parameters, or Legendre for uniformly...parameters and windfields will drive our simulations. We will use uncertainty quantification methodology – polynomial chaos quadrature in combination...quantification methodology ? polynomial chaos quadrature in combination with data integration to complete the DDDAS loop. 15. SUBJECT TERMS 16. SECURITY

On computation of Gröbner bases for linear difference systems

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.

2006-04-01

In this paper, we present an algorithm for computing Gröbner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The algorithm is an adaptation to difference ideals of our polynomial algorithm based on Janet-like reductions.

A modal analysis of lamellar diffraction gratings in conical mountings

NASA Technical Reports Server (NTRS)

Li, Lifeng

1992-01-01

A rigorous modal analysis of lamellar grating, i.e., gratings having rectangular grooves, in conical mountings is presented. It is an extension of the analysis of Botten et al. which considered non-conical mountings. A key step in the extension is a decomposition of the electromagnetic field in the grating region into two orthogonal components. A computer program implementing this extended modal analysis is capable of dealing with plane wave diffraction by dielectric and metallic gratings with deep grooves, at arbitrary angles of incidence, and having arbitrary incident polarizations. Some numerical examples are included.

An update on X-ray reflection gratings developed for future missions

NASA Astrophysics Data System (ADS)

Miles, Drew

2018-01-01

X-ray reflection gratings are a key technology being studied for future X-ray spectroscopy missions, including the Lynx X-ray mission under consideration for the 2020 Decadal Survey. We present an update on the status of X-ray reflection gratings being developed at Penn State University, including current fabrication techniques and mass-replication processes and the latest diffraction efficiency results and resolving power measurements. Individual off-plane X-ray reflection gratings have exceeded the current Lynx requirements for both effective area and resolving power. Finally, we discuss internal projects that will advance the technology readiness level of these gratings.

Polarization Measurements on SUMI's TVLS Gratings

NASA Technical Reports Server (NTRS)

Kobayashi, K.; West, E. A.; Davis, J. M.; Gary, G. A.

2007-01-01

We present measurements of toroidal variable-line-space (TVLS) gratings for the Solar Ultraviolet Magnetograph Investigation (SUMI), currently being developed at the National Space Science and Technology Center (NSSTC). SUMI is a spectro-polarimeter designed to measure magnetic fields in the solar chromosphere by observing two UV emission lines sensitive to magnetic fields, the CIY line at 155nm and the MgII line at 280nm. The instrument uses a pair of TVLS gratings, to observe both linear polarizations simultaneously. Efficiency measurements were done on bare aluminum gratings and aluminum/MgF2 coated gratings, at both linear polarizations.

Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings

PubMed Central

Gan, Qiaoqiang; Gao, Yongkang; Wagner, Kyle; Vezenov, Dmitri; Ding, Yujie J.; Bartoli, Filbert J.

2011-01-01

We report the experimental observation of a trapped rainbow in adiabatically graded metallic gratings, designed to validate theoretical predictions for this unique plasmonic structure. One-dimensional graded nanogratings were fabricated and their surface dispersion properties tailored by varying the grating groove depth, whose dimensions were confirmed by atomic force microscopy. Tunable plasmonic bandgaps were observed experimentally, and direct optical measurements on graded grating structures show that light of different wavelengths in the 500–700-nm region is “trapped” at different positions along the grating, consistent with computer simulations, thus verifying the “rainbow” trapping effect. PMID:21402936

Propagating bound states in the continuum in dielectric gratings

NASA Astrophysics Data System (ADS)

Bulgakov, E. N.; Maksimov, D. N.; Semina, P. N.; Skorobogatov, S. A.

2018-06-01

We consider propagating bound states in the continuum in dielectric gratings. The gratings consist of a slab with ridges periodically arranged ether on top or on the both sides of the slab. Based on the Fourier modal approach we recover the leaky zones above the line of light to identify the geometries of the gratings supporting Bloch bound states propagating in the direction perpendicular to the ridges. Most importantly, it is demonstrated that if a two-side grating possesses either mirror or glide symmetry the Bloch bound states are stable to variation of parameters as far as the above symmetries are preserved.

Gelator-doped liquid-crystal phase grating with multistable and dynamic modes

NASA Astrophysics Data System (ADS)

Lin, Hui-Chi; Yang, Meng-Ru; Tsai, Sheng-Feng; Yan, Shih-Chiang

2014-01-01

We demonstrate a gelator-doped nematic liquid-crystal (LC) phase grating, which can be operated in both the multistable mode and the dynamic mode. Thermoreversible association and dissociation of the gelator molecules can vary and fix the multistable diffraction efficiencies of the gratings. A voltage (V) can also be applied to modulate dynamically the diffraction efficiencies of the grating, which behaves as a conventional LC grating. Experimental results show that the variations of the diffraction efficiencies in the multistable and dynamic modes are similar. The maximum diffraction efficiency is approximately 30% at V = 2 V.