Plane Wave Model Research Articles

Quantitative method for measurement of the Goos-Hanchen effect based on source divergence considerations

In this paper we report on a method for quantitative measurement and characterization of the Goos-Hanchen effect based upon the real world performance of optical sources. A numerical model of a nonideal plane wave is developed in terms of uniform divergence properties. This model is applied to the Goos-Hanchen shift equations to determine beam shift displacement characteristics, which provides quantitative estimates of finite shifts near critical angle. As a potential technique for carrying out a meaningful comparison with experiments, a classical method of edge detection is discussed. To this end a line spread Green's function is defined which can be used to determine the effective transfer function of the near critical angle behavior of divergent plane waves. The process yields a distributed (blurred) output with a line spread function characteristic of the inverse square root nature of the Goos-Hanchen shift equation. A parameter of interest for measurement is given by the edge shift function. Modern imaging and image processing methods provide suitable techniques for exploiting the edge shift phenomena to attain refractive index sensitivities of the order of ${10}^{\ensuremath{-}6}$, comparable with the recent results reported in the literature.

Spatial Gradient Analysis for Linear Seismic Arrays

I incorporate the spatial gradient of the wave field recorded from one- dimensional arrays into a processing method that yields the horizontal-wave slowness and the change of geometrical spreading with distance. In general, the model for seismic-wave propagation is enough to be appropriate for body and surface waves propagating from nearby seismic sources but can be simplified into a plane-wave model. Although computation of the spatial gradient requires that array elements be closer than 10% of the horizontal wavelength, seismic-array apertures, in the usual sense, may extend over many horizontal wavelengths and illuminate changes within the wave field. Array images of horizontal slowness and the relative geometrical- spreading changes of seismic waves are derived using filter theory and used to interpret observed array wave fields. Errors in computing finite-difference spatial gradients from array nodes are explicitly considered to avoid spatial aliasing in the estimates. I apply the method to interpret waves in strong ground motion and small- scale refraction data sets. Use of the wave spatial gradient accentuates spatial differences in the wave field that can be theoretically exploited in fine-scale tomographic studies of structure and is complementary to frequency/wavenumber or beam- forming array-processing techniques.

27Al and 23Na NMR spectroscopy and structural modeling of aluminofluoride minerals

Simulations of high-resolution 19F-decoupled 27Al and 23Na magic-angle spinning nuclear magnetic resonance (MAS NMR) spectra of the aluminofluoride minerals, cryolite, cryolithionite, thomsenolite, weberite, chiolite, prosopite, and ralstonite combined with theoretical modeling have given accurate values of chemical shift (δiso), and quadrupolar interaction parameters (Cq and η), thereby eliminating ambiguities incurred by the complex nuclear interactions. These NMR data have been correlated with local electronic environments in the minerals, which were calculated using Full Potential Linearized Augmented Plane Wave (FP LAPW) modeling based on the structures from X-ray diffraction (XRD) data. This combination of NMR, XRD, and modeling techniques allowed the analysis and optimization of the crystal structures.

Complex Permittivity of Planar Building Materials Measured With an Ultra-Wideband Free-Field Antenna Measurement System.

Building materials are often incorporated into complex, multilayer macrostructures that are simply not amenable to measurements using coax or waveguide sample holders. In response to this, we developed an ultra-wideband (UWB) free-field measurement system. This measurement system uses a ground-plane-based system and two TEM half-horn antennas to transmit and receive the RF signal. The material samples are placed between the antennas, and reflection and transmission measurements made. Digital signal processing techniques are then applied to minimize environmental and systematic effects. The processed data are compared to a plane-wave model to extract the material properties with optimization software based on genetic algorithms.

Instantons, supersymmetric vacua, and emergent geometries

We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on $R\times S^2$ with sixteen supercharges. We get the superpotential in the weak coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.

DFT-Based Characterization of the Multiple Adsorption Modes of Nitrogen Oxides on Pt(111)

Pt is the most common catalyst for NO oxidation to NO2, a key reaction in NOx remediation chemistry. In this work, density functional theory calculations and plane-wave supercell models are used to calculate the energies, charge distributions, and vibrational spectra of the stable and metastable states of adsorbed NO, NO2, and NO3 on Pt(111), the most likely active metal face for this catalytic oxidation. NO, NO2, and NO3 are all strong electron acceptors and bind to the Pt(111) surface via charge donation from the surface. NO and NO2, in particular, exhibit a variety of adsorption geometries, the most favorable at low coverage being those that maximize surface−adsorbate charge transfer through binding to multiple surface Pt. At low coverage, the order of binding energies is NO > NO3> NO2, and the oxidation of adsorbed NO to NO2 is endothermic by 0.78 eV. Higher surface coverages favor migration of NO and NO2 to lower-coordination surface sites due to competition for metal d charge density. These changes in surface binding configurations, along with the general decrease in surface−adsorbate bond energies associated with higher surface coverages, both tend to energetically promote NO conversion to NO2 and are important in describing this catalytic chemistry.

Noise suppression using the coherent onion peeler

An innovative noise suppression algorithm, called the coherent onion peeler (COP) (patent detained) is derived by minimizing the error in the coherent subtraction of the data from a single plane wave model. The COP solution "collapses" for all beamforming algorithms to the same solution at the complex hydrophone FFT level. Thus, any beamformer can be applied to the residual FFTs after the COP has been applied. The COP is applied to the strongest interferer first and the residual FFTs represent the acoustic field with this interferer coherently "peeled back" like the outer skin of an onion. This procedure can be repeated any number of times to coherently suppress the noise from all interferers present. A new nonadaptive beamformer is developed that "blends" together the best beam pattern properties of conventional beamforming (CBF) near array design frequency and the generalized fourier integral method (GFIM) at very low frequencies (VLF). In between these frequency extremes, the GFIM-CBF Blend (patent pending) (G-C Blend) is a frequency-dependent weighted average of both individual beamformers. COP and G-C Blend are applied to the broadband noise emitted by the tow ship, which severely degrades the performance of the towed array; COP reduced this broadband noise by over 19 dB in a single pass.

Fivebranes from gauge theory

We study theories with 16 supercharges and a discrete energy spectrum. One class of theories has symmetry group $SU(2|4)$. They arise as truncations of $\mathcal{N}=4$ super Yang-Mills theory. They include the plane-wave matrix model, $2+1$ super Yang-Mills theory on $R\ifmmode\times\else\texttimes\fi{}{S}^{2}$ and $\mathcal{N}=4$ super Yang-Mills theory on $R\ifmmode\times\else\texttimes\fi{}{S}^{3}/{Z}_{k}$. We explain how to obtain their gravity duals in a unified way. We explore the regions of the geometry that are relevant for the study of some $1/2$ BPS and near BPS states. This leads to a class of two dimensional (4,4) supersymmetric sigma models with nonzero $H$ flux, including a massive deformed WZW model. We show how to match some features of the string spectrum with the Yang-Mills theory. The other class of theories are also connected to $\mathcal{N}=4$ super Yang-Mills theory and arise by making some of the transverse scalars compact. Their vacua are characterized by a 2D Yang-Mills theory or 3D Chern-Simons theory. These theories realize peculiar super-Poincar\'e symmetry algebras in $2+1$ or $1+1$ dimensions with ``noncentral'' charges. We finally discuss gravity duals of $\mathcal{N}=4$ super Yang-Mills theory on ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$.

Model Equation for Acoustic Nonlinear Measurement ofDispersive Specimens at High Frequency

We present a theoretical model for acoustic nonlinearity measurement ofdispersive specimens at high frequency. The nonlinearKhokhlov–Zabolotskaya–Kuznetsov (KZK) equation governs the nonlinearpropagation in the SiO2/specimen/SiO2 multi-layer medium.The dispersion effect is considered in a special manner by introducingthe frequency-dependant sound velocity in the KZK equation. Simpleanalytic solutions are derived by applying the superposition techniqueof Gaussian beams. The solutions are used to correct the diffractionand dispersion effects in the measurement of acoustic nonlinearity ofcottonseed oil in the frequency range of 33–96 MHz. Regarding twodifferent ultrasonic devices, the accuracies of the measurements areimproved to ±2.0% and ±1.3% in comparison with ±9.8%and ±2.9% obtained from the previous plane wave model.

Bit-error rate for free-space optical communication with tip–tilt compensation

In this paper, a new kind of method is developed to analyse the bit-error rate for a free-space optical communication system, which is based on the three most important parameters of scintillation statistics, i.e. fraction of time of fade and surge, mean frequency of level crossings, and mean duration of fade and surge. By using this method, the relationship between the bit-error rate and scintillation is clearly identified. The tip–tilt error deteriorates the performance of a free-space optical communication system. Fine tracking ability of adaptive optics (through tip–tilt compensation) can overcome this difficulty. The fade and surge statistical parameters with tip–tilt compensation are evaluated for the plane wave model. The bit-error rate as a function of the scintillation statistical parameters (with tip–tilt compensation) is developed. The results show that the bit-error rate is reduced notably through tip–tilt compensation for free-space optical communication.

Ultrasonic interferometric sensor for rheological changes of fluids

An ultrasonic interferometric sensor has been introduced for the measurement of subtle changes in the physical properties of fluids such as density, viscosity, and bulk modulus. Tone burst ultrasonic waves are generated using a single peizocrystal bonded in between two solid delay line media of slightly different lengths. One side is in contact with a reference fluid (with known properties) and the other with a fluid whose properties are to be measured. The ultrasonic waves reflect from the two solid-fluid boundaries and are received back by the peizocrystal where the interference effects are measured. The longitudinal waves were used to measure the longitudinal impedance, while shear waves were used to measure the shear impedance. Glycerin-water mixtures were used as the test material. A simple plane wave model was shown to provide satisfactory comparison with experiments. Various parameters that influence the measurement were studied.

Dynamical aspects of the plane-wave matrix model at finite temperature

We study dynamical aspects of the plane-wave matrix model at finite temperature. One-loop calculation around general classical vacua is performed using the background field method, and the integration over the gauge field moduli is carried out both analytically and numerically. In addition to the trivial vacuum, which corresponds to a single M5-brane at zero temperature, we consider general static fuzzy-sphere type configurations. They are all 1/2 BPS, and hence degenerate at zero temperature due to supersymmetry. This degeneracy is resolved, however, at finite temperature, and we identify the configuration that gives the smallest free energy at each temperature. The Hagedorn transition in each vacuum is studied by using the eigenvalue density method for the gauge field moduli, and the free energy as well as the Polyakov line is obtained analytically near the critical point. This reveals the existence of fuzzy sphere phases, which may correspond to the plasma-ball phases in N=4 SU(\infty) SYM on S^1 X S^3. We also perform Monte Carlo simulation to integrate over the gauge field moduli. While this confirms the validity of the analytic results near the critical point, it also shows that the trivial vacuum gives the smallest free energy throughout the high temperature regime.

Point-like graviton scattering in plane-wave matrix model

In a plane-wave matrix model we discuss a two-body scattering of gravitons in the SO(3) symmetric space. In this case the graviton solutions are point-like in contrast to the scattering in the SO(6) symmetric space where spherical membranes are interpreted as gravitons. We concentrate on a configuration in the 1-2 plane where a graviton rotates with a constant radius and the other one elliptically rotates. Then the one-loop effective action is computed by using the background field method. As the result, we obtain the 1/r^7-type interaction potential, which strongly suggests that the scattering in the matrix model would be closely related to that in the light-front eleven-dimensional supergravity.

Computational study of cation substitutions in apatites

Density-functional theory plane-wave modeling of fluor- and hydroxyapatites has been performed, where one or two calcium ions per unit cell were replaced with cadmium or zinc cations. It was found that cadmium ions favor Ca(1) positions in fluorapatites and Ca(2) positions in hydroxyapatites, in agreement with experiment. A similar pattern is predicted for zinc substitutions. In the doubly substituted cases, where only hydroxyapatites were modeled, a preference for the substituting ions to be located in Ca(2) position was also observed. Displacement of the hydroxide ions from their symmetrical positions on the hexagonal axis can be used to explain the preferred configurations of substituting ions around the axis.

Slow light and chromatic temporal dispersion in photonic crystal waveguides using femtosecond time of flight

We report time-of-flight experiments on photonic-crystal waveguide structures using optical Kerr gating of a femtosecond white-light supercontinuum. These photonic-crystal structures, based on engineered silicon-nitride slab waveguides, possess broadband low-loss guiding properties, allowing the group velocity dispersion of optical pulses to be directly tracked as a function of wavelength. This dispersion is shown to be radically disrupted by the spectral band gaps associated with the photonic-crystal periodicity. Increased time-of-flight effects, or "slowed light," are clearly observed at the edges of band gaps in agreement with two-dimensional plane-wave theoretical models of group velocity dispersion. A universal model for slow light in such photonic crystals is proposed, which shows that slow light is controlled predominantly by the detuning from, and the size of, the photonic band gaps. Slowed light observed up to time delays of approximately 1 ps, corresponds to anomalous dispersion of approximately 3.5 ps/nm per mm of the photonic crystal structure. From the decreasing intensity of time-gated slow light as a function of time delay, we estimate the characteristic losses of modes which are guided in the spectral proximity of the photonic band gaps.

Dynamical generation of a single M5-brane in plane-wave matrix model at finite temperature(Fundamental Problems and Applications of Quantum Field Theory)

Dynamical generation of a single M5-brane in plane-wave matrix model at finite temperature(Fundamental Problems and Applications of Quantum Field Theory)

Analyzing powers for exclusive1s1/2proton knockout from light nuclei

Analyzing power data are reported for exclusive proton-induced proton knockout from the $1{s}_{1/2}$ states of 10 target nuclei ranging from $^{2}\mathrm{H}$ to $^{19}\mathrm{F}$ for an incident energy of 392 MeV. Compared to free proton-proton scattering, the data are significantly suppressed, the amount of suppression increasing monotonically as a function of increasing separation energies for the knocked-out protons. It is also possible to consider that this suppression increases monotonically as a function of the increasing effective mean density for most of the target nuclei, but data for $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ targets clearly deviate from such systematic change. The data are compared to model predictions based on the nonrelativistic and relativistic distorted-wave impulse approximation. Both relativistic plane wave model and a nonrelativistic distorted-wave model incorporating a relativistic correction associated with an effective nucleon mass predict a significant suppression of the analyzing power, but the magnitude of the suppression is not sufficient to explain the experimental data. However, a relativistic distorted wave model predicts values that are closer to the data, but the result is inconclusive in this work since recoil corrections are neglected.

Site Amplification, Scattering, and Intrinsic Attenuation in the Mississippi Embayment from Coda Waves

We estimate site amplification, intrinsic Q ( Q I ) and scattering Q ( Q S ) values from three-component coda of broadband data recorded by Cooperative New Madrid Sesimic Network stations for center frequencies 0.2, 0.5, 1.0, 2.0, and 5.0 Hz. Near 0.5 and 1.0 Hz, site amplification factors for the transverse component recorded by stations in the Mississippi embayment are between 1.7 and 18, compared with stations outside the embayment. The amplification factor becomes smaller at frequencies lower than 0.5 Hz and higher at those greater than 1.0 Hz. The radial component shows a similar amplification; however, the vertical component shows relatively less amplification. Q I and Q S are estimated from coda using an energy flux model for two time windows after the direct S wave and at 0.5 and 1.0 Hz center frequencies. The two time windows include coda up to and after twice the S -wave travel time at each station. Coda parameters change with the time window and are attributed to a mixture of incoherent coda with coherent S-wave reverberations directly after the S wave. Q I and Q S inferred from stations outside of the embayment have higher values than those from stations within the embayment. A plane wave model qualitatively explains the lack of coda amplification at high frequencies compared with a low frequency without recourse to anelastic attenuation arguments. However, the plane wave model cannot explain the very large observed coda amplifications at 1 and 0.5 Hz seen in the data, suggesting that other wave-scattering effects must be occurring in the embayment velocity structure. This is consistent with the relatively low Q S values inferred from the energy flux model for stations within the embayment. In addition to coda amplification, we performed a synoptic noise study that revealed that pre-event ambient background noise behaves in a similar manner to the coda for stations within and outside of the embayment. The presence of large lateral velocity heterogeneities in the embayment may cause Q S values to be low there.

Transverse effects in the four-wave-mixing: The influence of the Gauss–Laguerre functions

A well known nonlinear device is the four-wave-mixing. The interaction of these three beams inside the nonlinear medium leads to the generation of a fourth beam, the signal beam intensity. In taking into account the transverse spatial structure of the signal beam, an improvement of the model is obtained. In this aim, we can write the electric field as spatial modes. The Gauss–Laguerre function U n l , solution of the paraxial propagation equation, may be used in this idea. This device is used to the study of two cases: the probe is a spatial mode of empty space and we can study the measure of the susceptibility and make a comparison between the Gauss–Laguerre model and the plane-wave model. Or the probe is a spatial mode of the Raman nonlinear propagation and we observe an enhancement of the fundamental Raman mode according to the other Raman modes.

A new type photonic crystal fiber with high birefringence

In this paper, a new type of photonic crystal fiber with high birefringence is proposed and analyzed with a full-vector model based on the super-lattice and the plane-wave expansion model. Due to the two different sizes of the holes introduced into the cladding of the PCF, the fiber is two-fold rotational symmetry and appears to be with high birefringence. Numerical results demonstrate that a modal birefringence at wavelength 1.31 μm is 1.8×10−3 in the PCF with Λ=2.55 μm,d 1/Λ=0.3 andd 2/Λ=0.833. A near 200 nm SPSM region within the wavelength range from 1.4 μm to 1.6 μm is obtained.