Dispersion-based short-time Fourier transform applied to dispersive wave analysis

Although time-frequency analysis is effective for characterizing dispersive wave signals, the time-frequency tilings of most conventional analysis methods do not take into account dispersion phenomena. An adaptive time-frequency analysis method is introduced whose time-frequency tiling is determined with respect to the wave dispersion characteristics. In the dispersion-based time-frequency tiling, each time-frequency atom is adaptively rotated in the time-frequency plane, depending on the local wave dispersion. Although this idea can be useful in various problems, its application to the analysis of dispersive wave signals has not been made. In this work, the adaptive time-frequency method was applied to the analysis of dispersive elastic waves measured in waveguide experiments and a theoretical investigation on its time-frequency resolution was presented. The time-frequency resolution of the proposed transform was then compared with that of the standard short-time Fourier transform to show its effectiveness in dealing with dispersive wave signals. In addition, to facilitate the adaptive time-frequency analysis of experimentally measured signals whose dispersion relations are not known, an iterative scheme for determining the relationships was developed. The validity of the present approach in dealing with dispersive waves was verified experimentally.     

Time-frequency analysis of the dispersive Rayleigh wave in stratified media

The dispersive characteristic of the Rayleigh wave propagating in a stratified media was analyzed by a time-frequency analysis method, the Reassignment of Smooth Pseudo-Wigner Ville Distribution (RSPWVD). Theoretical simulations and experiments were implemented for a homogeneous half-space and a two-layered half-space. It is indicated that the group velocity dispersion curves in different frequency ranges obtained by experimental result are all corresponding to the dominant modes in their surface displacement amplitudes. Such a mode identification of the multi-mode Rayleigh waves is required in inversing the medium parameters.     

Nonlinear Fourier analysis of localized wave fields

Summary The Fourier transform (FT) has long served as an indispensable means for analysing wave motion described by linear evlution equations. The methods are well known and include not only mathematical analysis but also the analysis of data as well. In recent years new spectral methods have been developed for analysing nonlinear evolution equations. Such methods are generalizations of the FT to specific nonlinear wave systems and are referred to as the spectral or scattering transform (ST). Herein we use numerical procedures for applying the ST directly to the analysis of localized data described by the Kortewegde Vries (KdV) equation on the infinite interval,i.e. the Cauchy problem in shallow water. In this context we emphasize the importance of the direct spectral transform (DST) as a wave number domain representation of nonlinear data. The numerical methods discussed for the KdV equation should be extendible to the large class of systems considered by Ablowitzet al., Calogero and Degasperis. We give examples of the spectral analysis of nonlinear, computer-generated data.

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Riassunto La ben nota trasformata di Fourier (FT) è di uso commune per analizzare moti ondosi descritti da equazioni di evoluzione lineari. Negli ultimi anni sono stati sviluppati nouvi metodi (detti trasformate spettrali o di scattering, ST) per l'analisi di equazioni di evoluzione non lineari basati sulla generalizzazione della FT agli specifici sistemi ondosi non lineari. Qui usiamo procedimenti numerici per applicare la ST direttamente all'analisi di dati localizzati descritti dall'equazione di Korteweg-deVries nell'intervallo infinito, cioè al problema di Cauchy in acqua bassa. In questo contesto sottolineiamo l'importanza della trasformata specttrale diretta come rappresentazione nel campo dei numeri d'onda di dati non lineari. I metodi numerici discussi, che a titolo di esempio sono qui applicati all'analisi spettrale di dati non lineari generati dal calcolatore, hanno l'interessante possibilità di essere estendibili ai problemi piú generali di propagazione ondosa.

     

THz near-field measurements of metal structures

We report on electro-optic measurements of THz electric fields in the near-field of metal structures lying on GaP electro-optic sampling crystals. With (110) oriented crystals, the x or y component of the THz electric field is measured, whereas with a (001) oriented crystal, the z-component is measured. With an estimated spatial resolution of 20 μm, the technique allows us to map the field on a scale, orders of magnitude smaller than the spatial dimensions of these structures. We illustrate the technique by showing results of measurements of the THz electric field in a plane underneath a metal sphere and a single square hole in a metal foil. The technique provides us with a wealth of information on the time-evolution of light fields near metal structures. To cite this article: A.J.L. Adam et al., C. R. Physique 9 (2008).     

等效噪声温度测量驻波分析

针对某致冷接收机系统等效噪声温度测试数据存在较为显著的疑似驻波问题,对测量数据进行了振幅谱分析和周期函数拟合。首先设计了分析方法,通过模拟数据对方法进行了有效性检验。之后分析了实测数据,并针对测量误差较大的问题,采用了事先平滑的处理方法,显著降低了拟合参数的不确定性,得到了各周期分量较为准确的特征参数,为后续链路和器件驻波的排查与处理、致冷接收机系统的调试提供了参考。     

Determination of wave fields from perturbed particle orbits

The linear problem of determining wave electric fields from measured perturbed particle distribution is considered. Previous work is extended to consider the case of arbitrary wave structure transverse to the magnetic field. The calculations are limited to electrostatic waves, although the ideas extend naturally to electromagnetic waves, and are illustrated in the one-dimensional case using data taken by laser-induced fluorescence     

超高压下冲击波速度直接测量技术

针对超高压下透明材料的高压离化机理,分析了透明材料中冲击波直接诊断技术的基本方法. 利用Drude-自由电子气模型,分析了不同冲击压力下冲击波阵面反射率的变化. 从理论上比较了不同探针光波长反射率的区别,发现探针光波长为660 nm时比探针光波长为532 nm时获得的冲击波阵面反射率要高. 对探测器"致盲"问题也进行了研究. 通过分析反射信号的时间顺序和强度大小,发现"致盲"效应是由X光对透明窗口离化引起的. 同时,发现方波驱动脉冲平台的前沿到达时刻和X光离化效应出现的时刻相同,冲击波信号到达时刻晚于X光离化时刻. 通过实验结果,得到蓝宝石中冲击波速度为35 km/s时,其波阵面的反射率约为40%. 通过理论分析和实验数据比对的方法,验证了蓝宝石中的减速曲线. 给出了加蓝宝石窗口后的测速公式. 经过和实验对比,确认了测速公式的正确性. 关键词： 冲击波 光学诊断 成像 干涉仪     

Multipole analysis of the radiation from near-field optical probes

We experimentally and theoretically analyze the radiation emitted from subwavelength-sized apertures in near-field optical probes. By decomposing the experimentally obtained radiation patterns into vector spherical waves, we describe the fields in terms of a series of multipole sources. We fit polarization-resolved angular intensity distributions, measured as far as 150 degrees from the normal, with dipole, quadrupole, and octupole radiation. We find that the magnetic and the electric dipole components are dominant but that the interference terms between dipoles and higher-order poles are not negligible. This result can be used as the basis for understanding near-field optical interactions and images.     

Direct calculation of energy streamlines in near-field thermal radiation

Accurate prediction of the energy propagation direction and the associated lateral shift is very important for the design of efficient energy conversion devices and sensors based on nanoscale thermal radiation. This paper concerns the direction of energy flow during near-field radiative transfer between two parallel plates separated by a vacuum gap. An improved formulation, fully consistent with fluctuational electrodynamics, is developed to correctly trace the energy streamlines inside the emitter, receiver, and the vacuum gap. The influence of surface waves on the direction of energy propagation as well as on the lateral shift of energy streamlines is elucidated. An important finding with the improved formulation is that the lateral shift in the emitter may exceed that in the vacuum gap. The method can be extended for tracing the energy streamlines in multilayered structures.     

Scattering in backward wave oscillators from turbulent electric fields

Relativistic electrons resonating in microwave-emitting slow-wave structures can scatter from background turbulence. We calculate the expected scattering rate from strong fields characterized by a single mean correlation length. Comparison with recent data from a backward wave oscillator, using the measured magnitude of E-fields, shows agreement with the magnitude of outward scattering. The implied correlation lengths then explain why gas ionization in the same oscillator does not proceed exponentially, as earlier work showed was expected but not observed. Plasma electrons scattered over the correlation length cannot gain the necessary energy to ionize many gas atoms. These results suggest that inadvertently produced plasmas may have a quick, decisive effect on beam geometry, ending microwave emission prematurely.     

Polynomial chaos representation of spatio-temporal random fields from experimental measurements

Two numerical techniques are proposed to construct a polynomial chaos (PC) representation of an arbitrary second-order random vector. In the first approach, a PC representation is constructed by matching a target joint probability density function (pdf) based on sequential conditioning (a sequence of conditional probability relations) in conjunction with the Rosenblatt transformation. In the second approach, the PC representation is obtained by having recourse to the Rosenblatt transformation and simultaneously matching a set of target marginal pdfs and target Spearman’s rank correlation coefficient (SRCC) matrix. Both techniques are applied to model an experimental spatio-temporal data set, exhibiting strong non-stationary and non-Gaussian features. The data consists of a set of oceanographic temperature records obtained from a shallow-water acoustics transmission experiment [1]. The measurement data, observed over a finite denumerable subset of the indexing set of the random process, is treated as a collection of observed samples of a second-order random vector that can be treated as a finite-dimensional approximation of the original random field. A set of properly ordered conditional pdfs, that uniquely characterizes the target joint pdf, in the first approach and a set of target marginal pdfs and a target SRCC matrix, in the second approach, are estimated from available experimental data. Digital realizations sampled from the constructed PC representations based on both schemes capture the observed statistical characteristics of the experimental data with sufficient accuracy. The relative advantages and disadvantages of the two proposed techniques are also highlighted.     

On wave solutions of a weakly nonlinear and weakly dispersive two-mode wave system

Abstract

In this paper, we introduce and study rigorously a Hamiltonian structure and soliton solutions for a weakly dissipative and weakly nonlinear medium that governs two Korteweg–de vries (KdV) wave modes. The bounded solution and traveling wave solution such as cnoidal wave and solitary wave are obtained. Subsequently, the equation is numerically solved by Fourier spectral method for its two-soliton solution. These solutions may be useful to explain the nonlinear dynamics of waves for an equation supporting multi-mode weakly dispersive and nonlinear wave medium. In addition, we give an explicit explanation of the mathematics behind the soliton phenomenon for a better understanding of the equation.     

Rietveld analysis for energy dispersive x-ray diffraction under high pressure with synchrotron radiation

Abstract

A new program has been developed for the conversion of energy-dispersive x-ray diffraction spectra obtained from powder samples at high pressure in a diamond anvil cell (DAC) into conventional pseudo angle-dispersive data. The program is compatible with a conventional Rietveld program. This allows the determination of the structural parameters of the samples investigated. Results of a synchrotron radiation study of polycrystalline SrFCl in the tetragonal phase at high pressure are presented.

Presented at the IUCr Workshop on ‘Synchrotron Radiation Instrumentation for High Pressure Crystallography’, Daresbury Laboratory 20-21 July 1991     

Nonlinear transformation of wave packets in weakly dispersive media

We study the propagation of nonlinear modulated waves in weakly dispersive media within the framework of the Korteveg- de Vries equation. It is shown that strong generation of overtones and mean flow by the modulated packet results in asymmetry of the wave packet envelope with respect to both horizontal and vertical axes and makes the envelope skewed. The motion of the wave packet is accompanied by the emission of low-frequency and high-frequency waves that propagate in different directions from the packet. As a result, the mean amplitude of the wave packet decreases with distance. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 4, pp. 354–358, April 1999.     

有不同附加层时Rayleigh波频散方程

首先导出了有一固体附加层时Rayleigh波的频散方程,然后对该方程进行适当的数学处理,就可把该频散方程分别过渡到附加层是固体、粘性流体和无粘性流体以及附加层是有限厚和半无限厚等各种情况下的频散方程。     

Interaction of an optical soliton with a dispersive wave

Scattering of a dispersive wave by optical solitons is studied experimentally in photonic crystal fibers in cases when the soliton and the dispersive wave have either identical or orthogonal polarization states. Observations of new resonant frequencies are reported. The experimental results are compared to numerical simulations and predictions from the recently derived wave vector matching conditions.     

一种全频散波方程的反问题

基于一种全频散波方程研究了对于谐波和波包的反问题。首先根据Mindlin理论建立了描述无耗散微结构线性固体中波传播模型一一一种全频散波方程,并讨论了其频散特性。然后基于该全频散波方程,提出了利用四种不同谐波的频率和相应波数确定波方程四个未知系数的反问题,并用严格的数学理论论证了此反问题。研究证明,通过测量同一种无耗散微结构线性固体中传播的四种不同谐波的频率和相应波数,在正常频散和反常频散情况下可唯一地确定波方程的未知系数,即材料的未知参数。     

Dynamics of dispersive photon-number QND measurements in a micromaser

A numerical analysis of dispersive quantum nondemolition measurement of the photon number of a microwave cavity field is presented. Simulations show that a key property of the dispersive atom-field interaction used in Ramsey interferometry is the extremely high sensitivity of the dynamics of atomic and field states to basic parameters of the system. When a monokinetic atomic beam is sent through a microwave cavity, a qualitative change in the field state can be caused by an uncontrollably small deviation of parameters (such as atom path length through the cavity, atom velocity, cavity mode frequency detuning, or atom-field coupling constants). The resulting cavity field can be either in a Fock state or in a super-Poissonian state (characterized by a large photon-number variance). When the atoms have a random velocity spread, the field is squeezed to a Fock state for arbitrary values of the system’s parameters. However, this makes detection of Ramsey fringes impossible, because the probability of detecting an atom in the upper or lower electronic state becomes a random quantity almost uniformly distributed over the interval between zero and unity, irrespective of the cavity photon number.