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.     

Interference effects in wave propagation in periodically inhomogeneous media

Radiophysics Scientific-Research Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1144–1151, September, 1989.     

Waveguide propagation of intense electromagnetic radiation in slightly inhomogeneous nonlinear media

The propagation of self-localizing beams of electromagnetic waves in the form of nonlinear waveguides in a slightly inhomogeneous medium is studied analytically and numerically. The trajectories of the axial ray are studied as a function of its direction and the field strength at the initial point on the basis of a nonlinear scalar Helmholtz equation. Analytic expressions are derived. The longitudinal refractive index, the field intensity, and the waveguide radius are plotted as functions of the instantaneous position of the point on the axial ray. Deep penetration of the beam into the opaque region and the position of the screening surface are studied as functions of the parameters of the beam and the medium. A steady-state 3D problem is analyzed for a power-law nonlinearity with an arbitrary power. A 2D problem is analyzed for the case of a ponderomotive nonlinearity with saturation.     

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735. This article was translated by the authors.     

Relativistic effects on electromagnetic wave propagation in a cold inhomogeneous electron plasma

We construct a method which permits to investigate the propagation of a travelling wave in different cases. We present the results we obtained in the case of an inhomogeneous plasma taking into account relativistic effects.     

Experimental study of electromagnetic wave propagation in dense random media

Controlled experiments have been conducted to measure the propagation of synthetically generated pulses in dense random media. The dense media were prepared by embedding spherical dielectric scatterers in a homogeneous background medium: the size and volume fraction of the scatterers were the controlled parameters. A network analyser-based system operating in the frequency domain was used to measure the electric field reflected and transmitted by slab-shaped samples of dense media as the source signal was swept from 26.5 to 40 GHz. An inverse Fourier transform was used to convert the frequency domain response into time domain pulse waveforms. The time domain response was then used to obtain pulse propagation velocity and attenuation in the controlled samples. The experimental results are shown to be in general agreement with dense medium theories.     

Fast volumetric integral-equation solver for acoustic wave propagation through inhomogeneous media

Elements are described of a volumetric integral-equation-based algorithm applicable to accurate large-scale simulations of scattering and propagation of sound waves through inhomogeneous media. The considered algorithm makes possible simulations involving realistic geometries characterized by highly subwavelength details, large density contrasts, and described in terms of several million unknowns. The algorithm achieves its competitive performance, characterized by O(N log N) solution complexity and O(N) memory requirements, where N is the number of unknowns, through a fast and nonlossy fast Fourier transform based matrix compression technique, the adaptive integral method, previously developed for solving large-scale electromagnetic problems. Because of its ability of handling large problems with complex geometries, the developed solver may constitute an efficient and high fidelity numerical simulation tool for calculating acoustic field distributions in anatomically realistic models, e.g., in investigating acoustic energy transfer to the inner ear via nonairborne pathways in the human head. Examples of calculations of acoustic field distribution in a human head, which require solving linear systems of equations involving several million unknowns, are presented.     

Correlated coherent states and the problem of wave propagation in randomly inhomogeneous media

Radiophysics and Quantum Electronics -     

Seismic wave propagation in laterally inhomogeneous geological region via a new hybrid approach

2D seismic wave propagation in a local multilayered geological region rested in an inhomogeneous half-space with a seismic source is studied. Plane strain state is suggested. The vertical variation of the soil properties in the half-space is modelled by a set of horizontal flat isotropic, elastic and homogeneous layers. The finite local region is with non-parallel layers and free surface relief. Efficient hybrid wavenumber integration-boundary integral equation method (WNI-BIEM) is proposed, validated and applied for synthesis of seismic signals in the finite soil stratum. The numerical simulation reveals that the developed hybrid method is able to demonstrate the sensitivity of the obtained synthetic signals to the seismic source properties, to the heterogeneous character of the wave path and to the relief peculiarities of the local stratified geological deposit. The advantages and disadvantages of the proposed method are discussed.     

Numerical analysis of propagation characteristics of electromagnetic wave in lossy left-handed material media

The propagation characteristics of electromagnetic wave in lossy left-handed materials (LHM) are studied using finite-difference time-domain (FDTD) method base on auxiliary differential equation (ADE) technology. The LHM medium is realized with lossy Drude models for both the negative electric permittivity and the negative magnetic permeability. The discretized ADE-FDTD equations are derived in detail. The incident wave used in the simulation is a multiple cycle m-n-m pulses source. The term of Poynting's vector E_xH_y was calculated. These numerical results demonstrate conclusively that the phase velocity direction of electromagnetic wave propagation and the direction of the Poynting vectors are anti-parallel in LHM. The amplitude of electric field is reduced with the enhancive distance of LHM slab. It is also demonstrated that the energy of electromagnetic wave in the LHM slab is obviously attenuated, and the attenuation of energy becomes stronger with the angular plasma frequency ω_p increasing. These results indicate that LHM stealth is effective in theory, and reasonable selection of the large negative index of refraction can greatly enhance its effectiveness.     

Exact solutions for electromagnetic waves in inhomogeneous media

Exact solutions of the wave equation for the propagation of electromagnetic waves in some inhomogeneous media are found. The first solution corresponds to the barometric model of the atmosphere, whose index of refraction can be expressed by the formulaN ²(z)=1+(N ₀ ² -1) exp (–z/z ₀). The other cases correspond toN ²(z)=1+(N ₀ ² -1) ch^–2(z) andN ²(z)=a-b. [1+exp(z/L)]^–1.Dedicated to Academician Vladimír Hajko on the occasion of his 65th birthday.     

Sound wave propagation in a vertically inhomogeneous ocean

Propagation of sound waves generated by a time dependent acoustic source in a vertically inhomogeneous ocean is considered. The effect of the solid bottom is included so that both the longitudinal and shear waves can be excited inside the bottom. The possibility of exciting a lateral shear wave by the acoustic source is also discussed. Although the results presented here are formal and general, physical interpretations have been offered whenever possible.     

Pseudo-Hermiticity and electromagnetic wave propagation: The case of anisotropic and lossy media

Pseudo-Hermitian operators can be used in modeling electromagnetic wave propagation in stationary lossless media. We extend this method to a class of non-dispersive anisotropic media that may display loss or gain. We explore three concrete models to demonstrate the utility of our general results and reveal the physical meaning of pseudo-Hermiticity and quasi-Hermiticity of the relevant wave operator. In particular, we consider a uniaxial model where this operator is not diagonalizable. This implies left-handedness of the medium in the sense that only clockwise circularly polarized plane-wave solutions are bounded functions of time.     

不均匀等离子体中电磁波与Langmuir波的相互作用

通过理论研究与数值计算,不均匀等离子体中Langmuir波与电磁波的相互作用及其线性模式转换规律得到了充分的展示.导出了不均匀等离子体中的电磁色散关系,研究了入射电磁波或Langmuir波在通过不均匀等离子体的过程中发生转换的物理过程,以及波的传播矢量随空间坐标变化的关系,并对电磁波与Langmuir波相互作用的机理进行了讨论.研究结果对密度梯度所驱动的等离子体波产生电磁辐射的研究具有重要意义. 关键词： 电磁波 Langmuir波 不均匀等离子体 线性模式转换     

Transient acoustic wave propagation in rigid porous media: a time-domain approach

Wave propagation of acoustic waves in porous media is considered. The medium is assumed to have a rigid frame, so that the propagation takes place in the air which fills the material. The Euler equation and the constitutive relation are generalized to take into account the dispersive nature of these media. It is shown that the connection between the fractional calculus and the behavior of materials with memory allows time-domain wave equations, the coefficients of which are no longer frequency dependent, to be worked out. These equations are suited for direct and inverse scattering problems, and lead to the complete determination of the porous medium parameters.