New method of spatial superposition of attenuated waves for ultrasound field modelling

The objective of this work is the contrary issues of ultrasonic diagnostics in medicine when modern requirements for resolution are in conflict with strict safety issues. There is only one way to make progress by starting to take into account the attenuation in biological tissues and the wave diffraction phenomena. The aim of this work is to develop the flexible ultrasound field model implemented in routine algorithms of digital signal processing. The method consists of the calculation of plane wave propagation and the calculation of an ultrasound signal field. On the basis of the spatial impulse response of an aperture for calculation of space-spread ultrasound signals and the spectrum decomposition method for modelling plane wave propagation in lossy media, the modified method of spatial superposition of attenuated waves was developed. Using the method of equidistant line calculation the time and frequency features of the ultrasound signal field caused by the geometry and dynamics of the aperture, the attenuation and velocity dispersion in the medium are determined. The method was successfully applied to the investigation of the system for intracranial media monitoring, where a new measurement channel based on the changes of attenuation and dispersion in intracranial medium has been implemented.     

波场合成与波场分析的有源房间补偿方法

波场合成是一种空间声重放技术,利用扬声器阵列在宽阔的听音区域内重建声场。为消除或者消减听音房间的反射对重建波场的影响,利用测量环绕听音区域的闭合曲线上声压和声压梯度来分析波场,推导了基于圆形阵列进行波域分解的公式,利用多通道逆滤波进行了平面波域的房间补偿,实验结果显示该算法在整个听音区域内都是有效的。与传统补偿方法相比,边界元法所需的测量传声器数目少计算复杂度低,而波域分解具有更充分的波场分析能力,因此是一种更有效的有源房间补偿方法.      

不同土壤类型的粗糙地面与其下方埋藏目标复合电磁散射研究

利用MOM研究了不同土壤类型的一维有耗介质粗糙地面与其下方二维埋藏目标的复合电磁散射问题,在数值计算中,引入了锥形入射波以减少粗糙面模拟中由于人为截断所引起的计算误差.当给定入射波频率、土壤成分及土壤温度和土壤湿度后,可以根据相关模型计算出土壤的相对介电常数.数值结果以二维无限长导体圆柱为例,利用 Monte Carlo方法统计计算了双站复合散射截面随土壤类型、土壤湿度、入射波频率及均方根高度等的变化情况,并做了详细分析及讨论.该研究结果对于探地雷达在民用、军事、工业等多领域的应用具有一定的理论指导价值. 关键词： 粗糙地面 土壤类型 相对介电常数 四成分模型     

Deeply penetrating waves in lossy media

The incidence of an inhomogeneous plane wave on the interface between two lossy media is analyzed. The analytical expressions of the incidence angle of the phase vector, for which the transmitted wave has the phase or the attenuation vector parallel to the interface, are obtained. The transmitted wave with the attenuation vector parallel to the interface is physically interpreted, finding a wave in a lossy medium without attenuation away from the interface. The same effect appears at the interface between a lossless medium and a lossy one.     

A note on Snell laws for electromagnetic plane waves in lossy media

Based on Maxwell's equations and Ohm's law, we rederived the Snell laws for reflection and transmission of harmonic inhomogeneous plane electromagnetic (EM) waves propagating through planar lossy interfaces. The present results are new, simple and exact and they recover the ordinary Snell laws in the case of lossless media. Besides, these results show that the wave propagation direction strongly depends on the polarization state of the EM wave and the lossy media can behave as a polarizing device. Moreover, we verify that in low frequency regime these traveling waves do not exhibit total internal reflection at interfaces between two adjacent lossy media.     

Scattering Analysis of Dielectric Periodic Structures by an Oblique Incidence

The scattering of dielectric periodic structures by a plane wave incident in the direction oblique to the periodic grooves is analyzed by a method which combines the multimode network theory with the rigorous mode matching method. Combining the TE and TM characteristic mode functions determined in the corresponding 2-D scattering problem resulting from a TE or TM wave incident along the principal-plane of the same structure, and using a simple mathematical transformation, the 3-D scattering problem by an oblique incidence is rigorously solved.     

二维柱几何中子输运方程的并行区域分解方法

分析不同的区域分解方法及优先级插入算法对二维柱几何下中子输运方程S_n间断有限元方程并行效率的影响,给出基于最小面体比的正方形区域分解方法及沿径向的优先级插入算法,并通过将正方形区域分解方法与径向优先级插入算法进行组合,形成新的算法.新算法更适应于二维柱几何下输运方程S_n间断有限元方法的并行计算.数值试验表明,在通信延迟较高的大型国产并行机上,新算法用数百个CPU还可以取得较好的并行效果,比已有方法具有更良好的可扩展性.     

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

In the framework of nonlinear wave optics,we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schr?dinger equation.The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method.Taking advantage of the analytical expression,we analyze the influences of various physical parameters on the breathing wave propagation,including the propagation loss and the input power on the beam width,the beam intensity,and the wavefront curvature.Also,the corresponding analytical solutions are obtained.The validity of the analysis results is verified by numerical simulation.This study provides some new insights for investigating beam propagation in lossy nonlinear media.     

Finite-difference time-domain technique as an efficient tool for calculating the regularized Green function: applications to the local-field problem in quantum optics for inhomogeneous lossy materials

The calculation of the local density of states (LDOS) in lossy materials has long been disputed due to the divergence of the homogeneous Green function with equal space arguments. For arbitrary-shaped lossy structures, such as those of interest in nanoplasmonics, this problem is particularly challenging. A nondivergent LDOS obtained in numerical methods such as the finite-difference time-domain (FDTD) technique, at first sight appears to be wrong. Here we show that FDTD is not only an ideal choice for obtaining the regularized LDOS, but it can address the local-field problem for any lossy inhomogeneous material. We exemplify the case of a finite-size photon emitter (e.g., a single quantum dot) embedded within and outside a lossy metal nanoparticle and show excellent agreement with analytical results.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

Generalized plane-wave expansion of cylindrical functions in lossy media convergent in the whole complex plane

Electromagnetic scattering by buried objects may involve a plane-wave expansion of the related fields, which depends on the objects' geometry. Furthermore, involved media in realistic cases are lossy, which requires the analytic continuation of formulae known for the lossless cases, due to the complex nature of the wave vectors. This problem has been covered in a previous paper, but the expression found still does not converge in some areas of space. In this paper, a new, convergent, expression of the spectrum of cylindrical functions in lossy media is analytically computed and its convergence limits are discussed.     

Phase imaging with rotating illumination

A modified extended-ptychographical-iterative-engine （ePIE） algorithm is proposed to overcome the dis- advantages of ePIE technique and reduce the influence of stage hysteresis or backlash error. The exit wave of a rotatable ＂screen＂ illuminated by plane wave is used as the illumination on the specimen, and the complex transmission functions of the rotatable object and specimen can be simultaneously reconstructed. Compared with the standard x - y scanning PIE algorithm, the proposed algorithm can completely avoid the influence of stage hysteresis （or backlash error）. The proposed algorithm also has higher convergence s!oeed and better accuracy than the standard PIE algorithm.     

Field generated by an anisotropic conducting plane in a half-space with chiral properties

This article inaugurates theoretical studies on a new class of composite structures that are a combination of anisotropically conducting surfaces and media possessing chiral properties. To test the mathematics, we solved the simplest model of the problem in which an in-phase electric current filament excites a plane formed by a layer of straight conductors at the interface of two isotropic media, one of which is chiral. The solution is given as a Fourier integral. As shown by analysis, one retarded wave of a discrete spectrum and three waves of a continuous spectrum are excited in the given structure. The first one exists only because of the anisotropically conducting plane and does not exist without it, while the latter three are associated with plane waves of corresponding homogeneous media, magnetodielectric and chiral.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–38, September, 1994.     

Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.     

Propagation of circularly polarized waves in one-dimensional bragg structures (magnetophotonic crystals)

A theory of electromagnetic wave propagation in structures formed by alternating magnetic and dielectric layers is proposed. Models of macroscopically thick and atomically thin layers magnetized perpendicular to their plane are considered. Transfer matrices of circularly polarized waves and characteristics of light propagation in periodic magnetic structures under normal incidence are obtained by the self-consistent electrodynamic Green’s function method in analytic form. The results obtained are employed to analyze linear-in-magnetization magneto-optical effects in the transmittance and reflectance spectra of one-dimensional magnetic Bragg structures called magnetophotonic crystals. For structures of finite thickness, Faraday rotation and other observable magneto-optical quantities are shown to vary appreciably in the spectral region of the stop bands of a magnetophotonic crystal. This is paralleled by a substantial enhancement of the magnetic-fieldinduced modulation of the reflectance of light polarized in the analyzer plane.     

Modeling of wave propagation in inhomogeneous media

We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in those points due to sources on a surface surrounding the medium. Following a predictable initial computational effort, Green's functions between arbitrary points in the medium can be computed as needed using a simple cross-correlation algorithm.     

色散负折射特异介质的1维光子晶体缺陷态

在1维光子晶体中引入色散负折射特异介质,分析了其介电常数和磁导率在微波区（1～10 GHz）与频率的关系。分别对以色散负折射介质为缺陷的正折射率介质光子晶体及以正折射率介质为缺陷的正负折射率介质光子晶体进行了数值仿真,得出了均匀平面电磁波在正入射和斜入射时的透射谱。结果表明:在介电常数和磁导率均为负值的不同禁带中,分别出现了单、双缺陷模。利用透射谱的这一特点,可实现单、双通道滤波。     

Generalized laws of reflection and refraction from real valued boundary conditions

The generalized Snell's laws are usually derived from phase-matching condition by using harmonic inhomogeneous plane waves. The inhomogeneity makes it difficult to trace curves of energy flow. Here we show that, at a lossy interface, real valued boundary conditions are valid universally. Thus a time-dependent way is developed to directly derive generalized laws of reflection and refraction from real valued boundary conditions by using harmonic homogeneous plane waves. Finally, several novel properties of transmitted wave associated with energy losses are predicted numerically, which may be applied to experimentally test our theoretical analysis.     

Plate impulse response spatial interpolation with sub-Nyquist sampling

Impulse responses of vibrating plates are classically measured on a fine spatial grid satisfying the Shannon-Nyquist spatial sampling criterion, and interpolated between measurement points. For homogeneous and isotropic plates, this study proposed a more efficient sampling and interpolation process, inspired by the recent paradigm of compressed sensing. Remarkably, this method can accommodate any star-convex shape and unspecified boundary conditions. Here, impulse responses are first decomposed as sums of damped sinusoids, using the Simultaneous Orthogonal Matching Pursuit algorithm. Finally, modes are interpolated using a plane wave decomposition. As a beneficial side effect, these algorithms can also be used to obtain the dispersion curve of the plate with a limited number of measurements. Experimental results are given for three different plates of different shapes and boundary conditions, and compared to classical Shannon interpolation.