Grazing-angle scattering of waves in infinitely wide periodic gratings

The approximate method of analysis of grazing-angle scattering (GAS), based on allowance for the diffractional divergence of the scattered wave, is justified and extended to GAS in infinitely wide, slanted, periodic gratings. The analysis has revealed an unusual and strong dependence of the pattern of GAS on small variations of mean structural parameters at the grating boundary. Several times increase of already resonantly large scattered wave amplitudes can be achieved in this case. Sharp resonance-like maximums on the angular dependence of the scattered wave amplitude are predicted inside the grating. The theory is extended to the case of GAS of optical modes guided by a slab with a semi-infinite periodic groove array. Physical interpretation of the obtained results is presented.     

浅海波导中目标散射的边界元方法

提出了一种计算三维散射体在声速剖面随深度变化、距离无关浅海波导中散射声场的数值方法波导边界元方法。当散射体不十分靠近波导界面因而边界多次散射可以忽略时,在边界元计算中可以用自由场格林函数近似波导格林函数。应用镜像法和球波函数加法定理推导了理想波导中球体散射声场的解析解,用来验证波导边界元方法的计算精度,证明该数值方法是准确的。对浅海波导中水下潜器散射声场数值模拟的结果表明,浅海波导海面、海底界面反射、声速剖面等对目标散射声场的幅值和方向性都有很大的影响。     

A high-frequency warm shallow water acoustic communications channel model and measurements

Underwater acoustic communication is a core enabling technology with applications in ocean monitoring using remote sensors and autonomous underwater vehicles. One of the more challenging underwater acoustic communication channels is the medium-range very shallow warm-water channel, common in tropical coastal regions. This channel exhibits two key features-extensive time-varying multipath and high levels of non-Gaussian ambient noise due to snapping shrimp-both of which limit the performance of traditional communication techniques. A good understanding of the communications channel is key to the design of communication systems. It aids in the development of signal processing techniques as well as in the testing of the techniques via simulation. In this article, a physics-based channel model for the very shallow warm-water acoustic channel at high frequencies is developed, which are of interest to medium-range communication system developers. The model is based on ray acoustics and includes time-varying statistical effects as well as non-Gaussian ambient noise statistics observed during channel studies. The model is calibrated and its accuracy validated using measurements made at sea.     

An experimental study of acoustic scattering from thermocline in shallow sea

I.IntroductionThetemperature,salinityandstaticprcssureofscawaterchangewithdepth,whichformsthcsoundvelocityvertica1distributioninthesea.Duringsummcrscason,thercaren0n-uniformthermoclinelaycrsinthedepths0fshallowseaal0ngChinacoast.Wearenowabletodeducctheimpedanccproflle(pc)byechoesofacousticwavesfr0mvarioustherm0c1ine1ayers.Thewaterdcnsityvaricsonlyslight1y,hencetheac0usticve1ocityde-Pendsmainlyonthetemperatureofseawatcr,andthercfore,itispossiblctorecordthcdepthofthermoclinelaycrsbyusingacoust…     

On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders

The aim of this paper is to propose a numerical strategy for computing the solution of two-dimensional time-harmonic acoustic multiple scattering problems at high-frequency. The scatterers are assumed to be circular, leading therefore to semi-analytical representation formulae of the scattered field through the solution of a large linear system of equations. Taking advantage of the special block Toeplitz structure of the matrix of the linear system, a fast iterative and preconditioned numerical method yielding large memory savings is proposed. Several numerical experiments for general configurations are presented to show the efficiency of the numerical method.     

On propagation characteristics of SH-type surface acoustic waves in periodic metal gratings by variational principle

Based on D.P. Chen and Haus＇ theory, a theoretical method was presented to analyze dispersion characteristics of SH-type surface acoustic waves （SAWs） propagating on periodic metallic grating structures with a variational principle and coupling-of-modes equation. Without using complicated Green＇s function, the calculating results of the method agree well with those of Hashimoto＇s theory. On the other hand, Hashimoto＇s method is helpless for calculating the dispersion relation of short-circuited gratings on ST-90°X quartz etc. However, the method developed in this paper can successfully calculate it.     

Inverse scattering problem for gratings with deep modulation

The similarity between one-dimensional Schrödinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrödinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qualitatively predict some properties of the reflection spectrum.     

High-overtone self-focusing acoustic transducers for high-frequency ultrasonic Doppler

This work reports the potential use of high-overtone self-focusing acoustic transducers for high-frequency ultrasonic Doppler. By using harmonic frequencies of a thick bulk Lead Zirconate Titanate (PZT) transducer with a novel air-reflector Fresnel lens, we obtained strong ultrasound signals at 60 MHz (3rd harmonic) and 100 MHz (5th harmonic). Both experimental and theoretical analysis has demonstrated that the transducers can be applied to Doppler systems with high frequencies up to 100 MHz.     

Variations in the ionospheric wave perturbation spectrum during periodic heating of the plasma by high-power high-frequency radio waves

We present the results of spectral analysis of temporal variations in the Doppler frequency shift of the ionosphere-reflected signals from a high-frequency vertical ionospheric sounding radar located near the city of Kharkov in the days of exposure of the ionospheric plasma to the high-power radio emission of the Sura facility (Nizhny Novgorod) and in the reference day in the absence of such an exposure. It was established that the spectral characteristics of quasiperiodic variations in the Doppler frequency shift in the range of periods 10–60 min in the days of work of the facility and in the reference day differed significantly. This is considered as evidence in favor of the generation (amplification) of acoustic–gravity waves propagating at the ionospheric altitudes by high-power periodic high-frequency radiation of the Sura facility.     

A fast directional algorithm for high-frequency electromagnetic scattering

This paper is concerned with the fast solution of high-frequency electromagnetic scattering problems using the boundary integral formulation. We extend the O(N log N) directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case. We also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm. When combined with a standard iterative method, this results in an almost linear complexity solver for the combined field integral equations. In addition, the butterfly algorithm is utilized to compute the far field pattern and radar cross section with O(N log N) complexity.     

Stretched backgrounds for acoustic scattering models

For the computational solution of the acoustic scattering problem, new domain integral equations are proposed. These domain integral equations describe the acoustic wave propagation in some chosen inhomogeneous background, whereas the influence of the scattering object is viewed as a superposition of contrast sources. A stretching procedure of the inhomogeneous background to a homogeneous one leads to a domain integral equation in a stretched space, where the Green function has the same simple functionality as the one of the non-stretched homogeneous background. This leads to improved efficiency in the computation of the scattering problem at hand.     

Crystal electrons in magnetic fields: Second-order perturbation for general periodic potentials

Summary The diamagnetic band structure is derived up to second order in the periodic potential. This is done for arbitrary crystal potentials and rational magnetic fields. Our perturbative treatment should give the correct energy spectrum in the Landau regime including the condition for magnetic breakdown. We also present an exact effective Hamiltonian which is reduced to 2 space dimensions for a general crystal potential.

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Riassunto Si deduce la struttura di banda diamagnetica fino al second'ordine nel potenziale periodico. Ciò è fatto per potenziali di cristallo arbitrari e campi magnetici razionali. Il nostro procedimento perturbativo dovrebbe dare il corretto spettro di energia nel regime di Landau che include la condizione di caduta magnetica. Si presenta anche un'hamiltoniana efficace esatta che è ridotta a due dimensioni spaziali per un potenziale cristallino generale.

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Резюме Определяется диамагнитная зонная структура с точностью до второго порядка по периодическому потенциалу. Вычисления проводятся для произвольных кристаллических потенциалов и рациональных магнитных полей. Наш пертурбационный подход должен давать правильный энергетический спектр В режиме Ландау, включая условие для магнитного нарушения. Мы также приводим точный эффективный Гамильтониан, который сводится к двум пространственным измерениям для общего кристаллического потенциала.

     

Dalgarno–Lewis perturbation theory for scattering states

We apply the method of Dalgarno and Lewis to scattering states and discuss the choice of the unperturbed model in order to have a convergent perturbation series for the phase shift. We show that a recently proposed approach is a particular case of the method of Dalgarno and Lewis.     

采用连续/不连续单元边界元法的声学灵敏度分析

采用连续单元与不连续单元混合离散建模的方法,将源点与场点分别划分为连续单元与不连续单元,由于两种网格节点互不重合,从而可以有效避免边界元法中奇异积分的问题。该方法简单易执行,利于工程应用。将该边界元公式应用于声学灵敏度分析中,所得的公式可以用来计算设计参数的改变而导致的场点声压改变量,为验证这一方法的正确性,以脉动球为例进行声灵敏度计算,并与常单元方法比较,证实了该方法的准确性。     

Speaker compensation for local perturbation of fricative acoustic feedback

Feedback perturbation studies of speech acoustics have revealed a great deal about how speakers monitor and control their productions of segmental (e.g., formant frequencies) and non-segmental (e.g., pitch) linguistic elements. The majority of previous work, however, overlooks the role of acoustic feedback in consonant production and makes use of acoustic manipulations that effect either entire utterances or the entire acoustic signal, rather than more temporally and phonetically restricted alterations. This study, therefore, seeks to expand the feedback perturbation literature by examining perturbation of consonant acoustics that is applied in a time-restricted and phonetically specific manner. The spectral center of the alveopalatal fricative [∫] produced in vowel-fricative-vowel nonwords was incrementally raised until it reached the potential for [s]-like frequencies, but the characteristics of high-frequency energy outside the target fricative remained unaltered. An "offline," more widely accessible signal processing method was developed to perform this manipulation. The local feedback perturbation resulted in changes to speakers' fricative production that were more variable, idiosyncratic, and restricted than the compensation seen in more global acoustic manipulations reported in the literature. Implications and interpretations of the results, as well as future directions for research based on the findings, are discussed.     

Boundary effects in the diffraction of light by volume gratings: II. Phase transmission gratings

The two-wave approximation of the method of characteristics modes is used to analyze theoretically the diffraction of light by volume phase transmission gratings for arbitrary proportions between the average refractive index of the grating and the refractive indices of the ambient media. Simple expressions are derived for calculating the amplitudes of the diffracted waves in the case where the angle of incidence of the primary wave coincides with the Bragg angle. The roles of the front and back boundaries of the grating are discussed separately, and a new method for separating the contribution of the boundary diffraction, which is due to the periodic inhomogeneity of the grating boundaries, is proposed. The experimental possibility of selecting partial Bloch waves in the measurements of the diffraction efficiency of gratings that have high reflection coefficients of both boundaries is demonstrated.     

Accurate summation of the perturbation series for periodic eigenvalue problems

We show that algebraic approximants prove suitable for the summation of the perturbation series for the eigenvalues of periodic problems. Appropriate algebraic approximants constructed from the perturbation series for a given eigenvalue provide information about other eigenvalues connected with the chosen one by branch points in the complex plane. Such approximants also give those branch points with remarkable accuracy. We choose Mathieu's equation as illustrative example. Received 6 December 2000     

New methods of fabricating gratings for deformation measurements: A review

Gratings have been widely accepted as practical and effective deformation carriers/sensors and are commonly used in many deformation measurement methods. Since the deformation measurement sensitivity is directly proportional to the grating frequency, and the measurement accuracy is strongly affected by the grating quality. Thus, it is crucial to prepare an appropriate grating on the specimen surface that is to be measured. Over the past few decades, an increasing number of grating fabrication methods have been developed, including holographic photolithography, electron beam lithography, focused ion beam etching, nanoimprinting, soft lithography, and others. Although substantial literature regarding grating fabrication can be found, a comprehensive review is still necessary to promote the application of these methods. This review introduces the technical details and characteristics of recently developed grating fabrication methods and provides suggestions of which grating fabrication methods to use in correspondence with different deformation measurement methods. Emphasis is placed on the introduction of grating fabrication processes and the quality and applicability of the resulting gratings.     

Boundary condition model for diffractive elastic scattering

Diffractive elastic scattering is studied by a boundary condition model that does not utilize a potential model.S-matrix elements are calculated and compared to those found from an optical potential model calculation. The unitarity of the model is related to the boundary condition imposed. A radially ingoing boundary condition is imposed on the wave function at one angle only, at a scattering angle of 180 °. This condition is required to hold in the vicinity of the nuclear radius, but not for all radii. Elastic scattering peaks at forward and backward angles are reproduced and discussed. The model is applied to composite particle scattering above the Coulomb barrier.     

A boundary perturbation method for circularly periodic plates with a core

Fundamental frequencies of vibrating circularly periodic plates with a circular core have been determined analytically. A boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem. The method is then applied to wavy and polygonal plates with clamped and simply supported outer boundary conditions. Clamped, simply supported, and free circular cores are considered. Approximate analytical formulations of the fundamental frequency for such plates with core are obtained.