Spectral shifts produced by scattering from rotational quasi-homogeneous anisotropic media

The scattering of the polychromatic plane light wave incident upon rotational quasi-homogeneous anisotropic media is investigated. It is different from the light wave scattered by quasi-homogeneous isotropic medium in that the spectral shift can be produced by the rotation of the anisotropic medium. We derive the analytical formula for the spectrum of the scattered field and show some numerical examples.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Scattering of scalar light wave from a Gaussianben Schell model medium

The scattering of scalar light wave from a random medium with a correlation function of Gaussian–Schell model distribution is studied. It is shown that the properties of the scattered field, i.e., the spectral density and the spectral degree of coherence of the scattered field, are closely related to the properties of the scattering medium, including the scaled effective radius and the scaled correlation length of the correlation function.     

Time reversal versus phase conjugation in a multiple scattering environment

We present experimental results on the reversibility of ultrasound in a multiple scattering medium. An ultrasonic pulsed wave is transmitted from a point source to a 128-element receiving array through 2D samples with various thickness. The samples consist of random collections of parallel steel rods immersed in water. The scattered waves are recorded, time reversed and sent back into the medium. The time-reversed waves are converging back to their source and the quality of spatial and temporal focusing on the source is related to the second-order moments of the scattered wave (correlation) in time and in space. Experimental results show that it is possible to obtain a robust estimation of the correlations on a single realisation of disorder, taking advantage of the wide frequency bandwidth. The spatial resolution of the system is only limited by the correlation length of the scattered field, and no longer by diffraction. Moreover, successful time-reversal focusing using a single element instead of an array is possible, whereas a one-channel monochromatic phase conjugation fails. The efficiency of broad-band time reversal compared to monochromatic phase conjugation lies in the number of 'information grains' in the frequency bandwidth.     

Subwavelength depth resolution in near-field microscopy

A generalized Radon transform is presented that relates, for the case of an evanescent wave that is incident upon a weakly scattering medium, the homogeneous components of the scattered field to the three-dimensional Fourier transform of the dielectric susceptibility. This relationship is used within the context of total internal reflection microscopy to reconstruct the depth structure of the dielectric susceptibility from simulated scattered field data.     

Polarization changes and beam profile deformation of light during acousto-optic interaction in isotropic media

A spatial Fourier transform approach is proposed to investigate the effects of polarization changes and beam profile deformation of light during acousto-optic (AO) interaction in isotropic media. The behaviour of the total scattered optical fields inside the AO cell can be properly described by a vector wave equation of which the permittivity is perturbed by an acoustic wave propagating inside the medium. In the Bragg regime, using a spatial Fourier transform approach, two coupled differential equations can be derived from the wave equation to depict AO interaction in the spatial frequency domain. Analytic solutions, which comprise the effects of changing polarization, beam deformation and propagating diffraction, can be found from the coupled equations. Detailed numerical simulations, including Fourier transforming the incident light profile to calculate the spectra of the scattered light beams and, hence, their profiles in space using the inverse transform, are presented.     

Stokes parameters of an electromagnetic light wave on scattering

Stokes parameters of an electromagnetic light wave on scattering have been discussed, which permit us to study the spectral degree of polarization of the far-zone scattered field. An example of scattering of a spatially coherent electromagnetic light wave from a quasi-homogeneous medium has been discussed to illustrate the changes of the Stokes parameters and the changes of the spectral degree of polarization of the far-zone scattered field.     

Magnetic line source diffraction by a conductive half-plane in an anisotropic plasma

An integral theory that is associated with the scattered fields is considered for the solution of H-polarized line source diffraction by a conductive half-plane, which is surrounded by an anisotropic plasma. As the anisotropy does not affect an E-polarized incident wave, only one polarization case is considered. The cold plasma medium is characterized by the dielectric tensor. The constant external magnetic field producing the anisotropy in a cold plasma is applied parallel to the edge of the half-plane. The total, scattered, and diffracted waves are derived in terms of the Fresnel functions. Therefore, finite magnitude values at the transition boundaries are obtained. The wave behaviours are investigated numerically for different quantities of the medium.     

Threshold fields for stimulated Brillouin scattering in spatially limited plasma

Brillouin scattering in an infinite medium is anisotropic, in this case the threshold of absolute instability is caused by attenuation of scattered waves. If the collision attenuation mechanism prevails, the minimum threshold value is observed during backward scattering. For a scattering region limited in the longitudinal direction (parallel to the direction of pumping wave propagation), the backward scattering threshold will be greater than for an infinite medium due to convective loss associated with energy removal by scattered waves. In this paper, the scattering of a wide wave beam in plasma is considered, whose dimension in the transverse direction to the pumping wave propagation substantially exceeds the dimension in the longitudinal direction. It was revealed that in this case, during angle scattering the instability threshold can be less than the threshold for backward scattering due to the increased time of radiation removal from the interaction region. This effect was not taken into account previously. In turn, the decrease of the threshold leads to increasing the radiation loss, which is important in plasma heating problems. The results can also be used for plasma diagnostics.     

Electromagnetic modelling of 3D periodic structure containing magnetized or polarized ellipsoids

Coupling matrix and coupling coefficient concepts are applied to the interaction of an incident plane wave with a regular array of small magnetized or polarized ellipsoids, placed in a homogeneous surrounding medium. In general case, the angle of incidence and polarization of the plane wave upon an array of ellipsoids can be arbitrary. In this model, it is assumed that all the ellipsoids are the same, and the direction of their magnetization is also the same. The direction of magnetization is arbitrary with respect to the direction of the propagation of the incident wave and to the boundary plane between the first medium, where the incident wave comes from, and the array material under study. Any magnetized or polarized ellipsoid is represented as a system of three orthogonal elementary magnetic radiators (EMR) and/or three orthogonal elementary electric radiators (EER). Mutual interactions of individual radiators in the array through the incident plane wave and corresponding scattered electromagnetic fields are taken into account. The electrodynamic characteristics — reflection from the surface of the semi-infinite array (in particular, containing uniaxial hexagonal ferrite resonators), transmission through the array, and absorption are analyzed.     

Localization of pulse signal in randomly layered medium

It is shown that in a medium with randomly layered inhomogeneities, a nonstationary pulse signal emitted by a plane (one-dimensional) source is localized in a closed region of space due to the interference of multiply scattered fields. A wave packet emitted by a point source in such a medium is channeled along the layers.Institute of Radio Physics and Electronics, Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, Nos. 3, 4, pp. 246–251, March–April, 1992.     

A model for the nearfield acoustics of the fish swimbladder and its relevance for directional hearing

It is a well-known fact that fish can determine the direction of an underwater sound source. For bony fish without Weberian ossicles the mechanism proposed here is the analysis of the elliptical movement of the otolith macula relative to the otolith in case a pure tone is emitted. This movement results from the superposition of the direct displacement wave and the displacement wave scattered by the swimbladder acting as a damped harmonic oscillator. A derivation of a closed analytical expression of the scattered wave is given for a prolate spheroidal air bubble (representing the swimbladder) in water. The elliptical displacement orbits of the surrounding medium were calculated. A general numerical approach is given for irregular gas bodies.     

Spectral and modal formulations for the Doppler-shifted field scattered by an object moving in a stratified medium

Spectral and normal mode formulations for the three-dimensional field scattered by an object moving in a stratified medium are derived using full-field wave theory. The derivations are based on Green's theorem for the time-domain scalar wave equation and account for Doppler effects induced by target motion as well as source and receiver motion. The formulations are valid when multiple scattering between the object and waveguide boundaries can be neglected, and the scattered field can be expressed as a linear function of the object's plane wave scattering function. The advantage of the spectral formulation is that it incorporates the entire wave number spectrum, including evanescent waves, and therefore can potentially be used at much closer ranges to the target than the modal formulation. The normal mode formulation is more computationally efficient but is limited to longer ranges. For a monochromatic source that excites N incident modes in the waveguide, there will be roughly N2 distinct harmonic components in the scattered field. The Doppler shifts in the scattered field are highly dependent upon the waveguide environment, target shape, and measurement geometry. The Doppler effects are illustrated through a number of canonical examples.     

Electromagnetic scattering from a two dimensional perfect electromagnetic conductor (PEMC) strip and PEMC strip grating simulated by circular cylinders

Electromagnetic scattering of an incident plane wave from a rectangular strip and strip grating, are presented semi-analytically. The strip and strip grating are simulated by joining parallel perfect electromagnetic conductor (PEMC) circular cylinders and are illuminated by a TM_z incident plane wave. The PEMC medium does not allow electromagnetic energy to enter. An interface of this medium serves as an ideal boundary to the electromagnetic field. The solution is based on the application of the boundary conditions on the surface of each cylinder in terms of its local coordinate system. The technique is used to predict the scattered field pattern of PEMC strip and PEMC strip grating.     

Pairs of opposite decaying evanescent waves in random media and tunneling radiative transfer

A tunneling mechanism of radiative transfer through a dielectric random medium is revealed applying technique of Dyson and Bethe-Salpeter equations for electromagnetic wave multiple scattering by medium inhomogeneities (scatterers) with near fields effects in scattered fields. The mechanism consists in existing inside of a random inhomogeneity a pair of virtually opposite decaying evanescent waves whose interference results in energy flux.     

Backscattered indicatrix from surfaces with random impedance

Intensity enhancement in the retroreflection direction is studied for waves scattered by a random interface which has a bound state (surface wave). We have found that an enhanced backscattered peak appears as the result of competition of two mechanisms: multiple scattering of a surface wave along the interface, and its leakage to upper half-space. The last one is the important distinction of surface scattering, which shifts the diffuse pole and eliminates in a natural way the divergence of second moments, which is the crucial difficulty in existing theories. New results, valid when there is no real absorption in the medium, are obtained for the diffuse scattered intensity as a function of the angles near the antispecular direction.     

On formulation of a transition matrix for electroporoelastic medium and application to analysis of scattered electroseismic wave

On the basis of Pride's theory (1994) which couples Biot's theory for poroelastic medium (1956) and Maxwell equations via flux/force transport equations, we extend Yeh et al. (2004) approach for poroelastic medium to develop a transition matrix for electroporoelastic medium. The transition matrix, which relates the coefficients of scattered waves to those of incident waves, is then derived through the application of Betti's third identity and the associated orthogonality conditions for the electroporoelastic medium. To illustrate the application, a simple case of the scattering problem of a spherical electroporoelastic inclusion, embedded within the surrounding electroporoelastic medium subjected to an incident plane compressional wave is considered.     

Scattering of phase-conjugate ultrasonic waves by microinclusions in a liquid flow

The paper presents the results of experimental and theoretical studies of processes of phase-conjugate ultrasonic wave propagation in a liquid flow containing gas microbubbles. It is shown that a signal from a phase-conjugate wave, which is recorded by a transceiving transducer, contains information on the flow velocity of scatterers and their concentration. In this case, the flow velocity is determined both in the presence and absence of moving scattering objects. A theory developed on the basis of the generalized reciprocity principle for a moving inhomogeneous medium represents the main experimentally observed features of the formation of signals from a phase-conjugate wave scattered by a disperse liquid flow.     

Multiple scattering of elliptically polarized light in two-dimensional medium with large inhomogeneities

For elliptically polarized light incident on a two-dimensional medium with large inhomogeneities, the Stokes parameters of scattered waves are calculated. Multiple scattering is assumed to be sharply anisotropic. The degree of polarization of scattered radiation is shown to be a nonmonotonic function of depth when the incident wave is circularly polarized or its polarization vector is not parallel to the symmetry axis of the inhomogeneities.     

Backscattering of electromagnetic waves by large-scale inhomogeneities in a periodically inhomogeneous medium

It is shown that backscattering of electromagnetic waves is possible in a periodically inhomogeneous medium by random inhomogeneities whose scale is greater than the wavelength. A small scattered field emerges in the case of appearance of the Bragg cavity when the periodic layer is a matching system for the incident wave. Scattering is effective even for inhomogeneities whose scale is much greater than the Fresnel radius of the inhomogeneous layer. The correlation radius of the scattered field can also be that large. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 10, pp. 1230–1240, October, 1997.