Scattering and active acoustic control from a submerged piezoelectric-coupled orthotropic hollow cylinder

A general exact analysis for three-dimensional scattering of a time-harmonic plane-progressive sound wave obliquely incident upon an arbitrarily thick bilaminated circular hollow cylinder of infinite extent, which is composed of a cylindrically orthotropic axially polarized piezoelectric inner layer perfectly bonded to an orthotropic outer layer, is presented. An approximate laminate model in the context of the so-called state space formulation along with the classical T-matrix solution technique involving a system global transfer matrix is employed to solve for the unknown modal scattering and transmission coefficients. Numerical example is given for an air-filled and water-submerged two-layered elasto-piezoelectric hybrid (steel/PZT4) hollow cylinder insonified by an obliquely incident unit-amplitude plane sound wave. Following the acoustic resonance scattering theory (RST), the total form function amplitude together with the associated global scattering, the far-field inherent background, and the resonance scattering coefficients of the nth normal mode are computed as a function of dimensionless frequency for selected angles of incidence, piezoelectric layer thickness parameters, and electrical boundary conditions (i.e., open/closed circuit or active). Also, the electrical voltage coefficients required for partial or complete cancellation of the reflected sound field are calculated. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.     

强光场下电子与库仑势散射及多光子过程

对Schr?dinger方程引入修饰势,并将波函数展开为Floquet分波,即可实施分离变量。强光场时弱耦合法选取合适微扰量,径向波动方程可逐步近似求解。以圆极化强光场为例,计算了散射波函数、散射矩阵和截面。重要结论是:强光场下将出现多光子过程,对应m次多光子过程有相应的共振谱线族,谱线能量约为m?ω,并给出谱线强度计算公式。 关键词：     

Resonance of exchange amplitude of Compton effect in the circularly polarized laser field

We present, for general relativistic case, a theoretical study of resonance of exchange amplitude when a photon is scattered by an electron in the field of a circularly polarized wave. Resonances are related to a virtual intermediate particle that falls within the mass shell. We find conditions when resonances occur in exchange amplitude. We derive the expressions for the resonant amplitudes and the differential cross-sections when the invariant intensity parameter of the laser field is small (η≪1) and the interference of direct and exchange amplitudes is absent. It is demonstrated that the resonant cross-section of scattering may be several orders of magnitude higher than the cross-section of Compton effect in the absence of the external field.     

Radiation pressure on an inclusion with a given scattering amplitude in an arbitrary external field

A method is proposed for calculating the radiation pressure forces that act on a body characterized by a given scattering amplitude and positioned in an ideal liquid in an arbitrary acoustic field. The efficiency of the method is tested by two examples: a fluid sphere in a spherical wave and a similar sphere in the field of a traveling wave with a Gaussian amplitude distribution. The agreement with the results obtained earlier by other methods is demonstrated.     

Resonant inelastic contact scattering of X-ray photons on atoms and ions

The existence of an extended resonance structure outside the X-ray emission regions is theoretically predicted in the total double differential cross section for the scattering of linearly polarized photons on free atoms (ions). This structure is almost entirely determined by inelastic photon scattering of the contact type. The amplitude of the inelastic contact scattering probability is described using an analytical expression for a non-relativistic transition operator, which was previously obtained by the author outside the dipole and momentum approximations. The resonant inelastic contact scattering of X-ray photons on a neon atom and neonlike ions of argon, titanium, and iron has been studied. Calculations were performed in a nonrelativistic approximation for the wave functions of the scattering states, with allowance for many-body effects of the radial relaxation of one-electron orbitals in the Hartree-Fock field of a deep 1s vacancy and (for neon atom) the double excitation/ionization of the ground atomic state.     

On the problem of polarization characteristics of radio waves in a randomly inhomogeneous magnetoactive plasma

Expressions for the Stokes parameters when radio waves propagate in a turbulent magnetoactive plasma have been obtained using a refractive scattering method. The problem of the spatial coherence of polarized radiation is considered. Expressions for the correlation functions and fluctuation dispersions of the Stokes parameters are found in the case of saturated wave field fluctuation. It is shown that the fluctuation of the circular polarized component will be observed in the received radiation even if the circular polarization is absent in the radiation that is incident on the magnetoactive plasma slab. A method is proposed to define the preference orientation of the magnetic field in the inhomogeneous layer of space plasma, which is biased on the simultaneous measurement of the space correlation functions of the I, V Stokes parameter fluctuation and Faraday rotation of the radiation polarization plane from the source with known polarization characteristics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 8, pp. 1007–1013, August, 1996.This work was supported in part by the Russian Foundation for Fundamental Research under Project No. 96-02-18632.     

Propagation of terahertz waves in nonuniform plasma slab under "electromagnetic window"

The application of magnetic fields, electric fields, and the increase of the electromagnetic wave frequency are up-and-coming solutions for the blackout problem. Therefore, this study considers the influence of the external magnetic field on the electron flow and the effect of the external electric field on the electron density distribution, and uses the scattering matrix method (SMM) to perform theoretical calculations and analyze the transmission behavior of terahertz waves under different electron densities, magnetic field distributions, and collision frequencies. The results show that the external magnetic field can improve the transmission of terahertz waves at the low-frequency end. Magnetizing the plasma from the direction perpendicular to the incident path can optimize the right-hand polarized wave transmission. The external electric field can increase the transmittance to some extent, and the increase of the collision frequency can suppress the right-hand polarized wave cyclotron resonance caused by the external magnetic field. By adjusting these parameters, it is expected to alleviate the blackout phenomenon to a certain extent.     

Amplification of electromagnetic field in the course of the nonrelativistic electron scattering by ion in the presence of the field of the medium-intensity elliptically polarized light wave

The amplification factor of the electromagnetic field is theoretically studied for the scattering of nonrelativistic electrons by ions in the presence of the field of the elliptically polarized electromagnetic wave. A simple analytical formula for the gain is derived for the medium-intensity range. The formula supplements and extends the domain of applicability of the known Marcuse formula for the linear polarization in the presence of a weak field. It is demonstrated that the maximum gain is reached when the initial electron velocities belong to the polarization plane of the electromagnetic wave. In the range of optical frequencies, the amplification factor of the laser radiation can be significant for relatively high powers of electron beams.     

Relationship between cross section and matrix normalization of polarized radiation scattering

A simple relationship between the total scattering cross section and the normalizing constant of the scattering matrix for the general case of an arbitrary scattering particle and elliptically polarized incident radiation is obtained. The polarized radiation is described by the Stokes parameters I, Q, U, V. The obtained relationship is a consequence of two forms of energy conservation. The first one is in terms of the total scattering cross section. The other one involves the normalizing constant of the scattering matrix. The obtained relationship contains dimensionless integrals of the radiation scattered over all directions of scattering. The integrals depend on the elements of the first row of the scattering matrix and on the relative values of the Stokes parameters of the incident radiation. In the case of cross section, the incident radiation is assumed to be a plane wave. In the case of normalization constant, the incident radiation is assumed to be a convergent beam. The possible dependence of the scattering integrals on specificities of the particle illumination is taken into account in the obtained relationship. The relationship may be helpful in the various cases. So, the relationship allows one to determine any of the two characteristics of the scattering process under investigation, cross section or normalizing constant, via the other one. The relationship can be used for obtaining the scattering integrals and for analyzing the influence of the incident radiation polarization on cross section and normalizing constant.     

Nonresonant mechanism of scattering of electromagnetic waves by sea surface: Scattering by steep sharpened waves

We develop an asymptotic theory of nonresonant backscattering of electromagnetic waves in the X-band by the ocean surface. Small-height (5÷20 cm) breaking surface waves with sharpened edges are assumed to be the main cause of nonresonant scattering. Using the methods of physical optics and geometrical theory of diffraction, we calculate the contribution of breaking sharpened waves to the scattering cross section for two orthogonal polarizations of electromagnetic scattering. It is shown that the main contribution to the backscattering is from the mirror reflection from the leading edge of such a wave, and the sharpness of the wave edge leads to the fact that the backscattering cross section of horizontally polarized radiation can exceed that of the vertically polarized radiation. Institute for Space Research, Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 3, pp. 240–254, March 1999.     

Reduction of radiative transfer problems in semi-infinite media to linear Fredholm integral equations

Linear Fredholm integral equations are derived for the Stokes vector of polarized radiation, emergent from a scattering plane parallel semi-infinite medium, by means of the full range orthogonality and completeness properties of Case's eigensolutions. A renormalization concerning the eigenmode with the greatest discrete eigenvalue is applied, which permits us to obtain a new integral equation for the zeroth Fourier component of the radiation field. The kernel of the integral equations is given in terms of Case's eigenfunctions or of the Green's function matrix for an infinite medium. For isotropic scattering, it is shown that the integral equation can be solved by means of a very rapidly convergent Neumann series. Physical arguments lead to the conclusion that the renormalized Fredholm integral equations are well suited also for arbitrary phase matrices.     

Resonant scattering of an electron by a muon in the field of light wave

In the frame of the Born approximation we theoretically investigate resonant scattering of an electron by a muon in the field of elliptically polarized electromagnetic wave in the general relativistic case. It is studied kinematics of a scattering of an electron in resonant region. It is derived the expressions for the amplitude and the cross-section of the resonant scattering of an electron by a muon when the invariant intensity parameter of the laser field is small (η_e ≪1). It is demonstrated that the resonant cross-section of a scattering may be several orders of magnitude higher than the cross-section of a scattering in the absence of the external field.     

Motion of a particle in a static magnetic field and the field of a monochromatic electromagnetic plane wave

A solution of the equation of motion of a charged particle in an external electromagnetic field comprising a superposition of a uniform static magnetic field and the field of a monochromatic, elliptically polarized electromagnetic plane wave is obtained as the solution of a Cauchy problem. The resonance case is investigated. An analysis of the resulting solution is given. Zh. Tekh. Fiz. 69, 106–110 (May 1999)     

Polarization of photons emitted in the process of resonant coherent excitation of relativistic ions under planar channeling conditions

Owing to the recent observation of the strong anisotropy of characteristic X-ray radiation accompanying the resonant coherent excitation of relativistic Fe²⁴⁺ ions under planar channeling conditions in a silicon crystal, the resonant coherent excitation method can be considered as a candidate for a source of polarized X-ray radiation. The Stokes parameters of the radiation have been calculated using the density matrix approach. The behavior of the polarization characteristics of the radiation in various directions has been explained by considering the properties of the resonance part of the crystal field, which excites an ion and has the form of an elliptically polarized electric field.     

Approximate solution for describing polarization characteristics of radiation in a Rayleigh scattering medium

An approximate analytical solution for the 4 × 4 Green’s matrix of the problem of polarized radiation transfer in a plane-parallel layer of an absorptive Rayleigh scattering medium is proposed. It permits one to perform fast estimates of angular distributions of the Stokes parameters that are created by an incident beam with an arbitrary polarization state at different levels in a layer when the layer thickness, absorption magnitude, and albedo of the underlying surface are varied. The developed solution is compared with data obtained by the numerical doubling method. The value of the scattering coefficient for a circularly polarized radiation is shown to be somewhat smaller than that for linearly polarized radiation.     

Incoherent properties of induced radiation

The evolution of a quantized electromagnetic field in a thermally excited dispersion medium is determined by two scattering channels. The coherent channel is formed exclusively by the elastic scattering of quanta. The incoherent channel, along with elastic scattering processes, necessarily contains inelastic scattering processes, including induced radiation. Interference between the channels is absent because of the orthogonality of the wave functions of the medium in its final states, which correspond to different scattering channels. Therefore, in an excited medium, interference processes that are not described by its refractive index may arise. An interference pattern of this kind can be formed, in particular, as a result of the superposition of the resonance radiation incident on an excited medium and the radiation reflected from this medium. In this case, the conventional perturbation theory proves to be inadequate.     

Polarization characteristics of an electromagnetic wave scattered from a slightly random surface: +45° polarized incidence

Abstract

The present paper deals with the scattering of an obliquely polarized electromagnetic (EM) wave from a slightly rough surface, which is assumed to be a two-dimensional (2D), homogeneous and isotropic Gaussian random field. In contrast to the cases of TE(s) and TM(p) polarized incidence, the scattering profile for an obliquely polarized incidence is not symmetric with respect to the incident plane, despite the fact that the random surface is statistically isotropic.     

Theory of polarization phenomena in the hyper-Raman effect

This paper describes a general theory of the polarization state of hyper-Raman emission. In particular an examination is made of the azimuth and ellipticity of hyper-Raman scattered radiation relative to that of a general elliptically polarized source.

It is shown that a distinction may be made between infra-red active and inactive vibrations in the hyper-Raman effect by an analysis of the ellipticity of the scattered light. For a circularly polarized source, the scattering from infra-red inactive vibrations exhibits full reversal of circularity; infra-red active vibrations scatter with no change in circularity. In hyper-Rayleigh scattering a similar analysis is given for non-polar and polar molecules.     

Average intensity of multiply scattered waves

The methods of the theory of multiple wave scattering are applied to a calculation of the mean intensity of radiation above a jagged rough surface under conditions such that shadowing and scattering form an intricate multipath structure on the part of the scalar field. The multiple wave scattering is described in the Twersky approximation, and a relationship of the given problem to the radiative transfer problem in an infinite plane-parallel layer is indicated. Expressions are derived for the coherent and incoherent components of the intensity at interior points of the layer, and the dependence of the mean value of the total intensity on the distance, radiation wavelength, and other parameters of the problem is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 85–90, May, 1984.     

Scattering of radio waves by a two-layer medium with a weakly reflecting rough boundary

The average reflected field and the second moment of the scattered field of the main polarization are found and analyzed in the approximation of a small jump of the dielectric constant when a horizontally polarized wave is reflected by a two-layer medium with a rough upper boundary. It is shown that the oscillations due to frequency changes predicted by perturbation theory do not exist when the scattering parameter is large. Sounding at close angles of incidence and scattering is the most efficient method of layer thickness determination by the scattered radiation. Institute of Physics, State University, Rostov-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 889–903, July, 1998.