Reflection of Rayleigh waves from a mechanical resonator grating

The problem of Rayleigh wave scattering from a set of N chains of closely spaced identical mechanical resonators is considered. The distance between the chains is identical to the half-wavelength of Rayleigh waves at the frequency ω taken to be identical or close to the natural frequency of the chain of resonators with allowance for the associated elasticity. The coefficient of reflection of Rayleigh waves from the diffraction grating specified above is calculated.     

Laser excitation of flexural waves and their scattering by fractal inhomogeneities in a thin plate

The excitation of flexural waves in a thin plate (film) by harmonically modulated laser radiation and their scattering by small fractal inhomogeneities are considered. An expression for the mean fluctuation intensity for the scattered wave field is obtained. A relationship between the intensity, parameters of the laser radiation and the plate, and the fractal dimension of inhomogeneities is found. The expected frequency dependence of the flexural wave attenuation in the plate due to their scattering by fractal inhomogeneities is discussed.     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Scattering of a Rayleigh wave by monopole-dipole resonators

The problem of scattering of a Rayleigh wave by a chain of identical closely spaced monopole-dipole resonators with friction is considered. The values of resonator parameters that provide the rejection of the Rayleigh wave are found. The conditions under which the Rayleigh wave is much more efficiently reflected by the dipole resonators than by the monopole ones are determined.     

Comparison of light scattering from self assembled array of nanoparticle chains with cylinders

We use a magnetic field to generate array of linear chains of magnetic nanoparticles in a magnetically polarizable nanofluid. The scattered patterns by these chains are described by electromagnetic wave scattering from an infinite cylinder. Comparison of the incident angle dependent scattered patterns from the linear chains of nanoparticles and macroscopic cylinders show a striking similarity. But, unlike the diffraction fringes of different orders observed on the cone of scattered light from macroscopic cylinder, the observed scattered cone from the field induced nanostructures is diffused. The observed optical patterns for micron sized cylinder are a simultaneous manifestation of both scattering and diffraction due to the interaction of light with cylindrical surfaces, whereas for nanoparticle chains it is mainly due to scattering. The diameters of the cylinders are precisely calculated from the best fit on the experimental diffraction intensity pattern. These results are important for better understanding of self assembled nanostructures for applications.     

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.     

Acoustic scattering by multiple elliptical cylinders using collocation multipole method

This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.     

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.     

Corrections to the Thomson cross section caused by relativistic effects and by the presence of the drift velocity of a classical charged particle in the field of a monochromatic plane wave

An approach to the solution of the relativistic problem of the motion of a classical charged particle in the field of a monochromatic plane wave with an arbitrary polarization (linear, circular, or elliptic) is proposed. It is based on the analysis of the 4-vector equation of motion of the charged particle together with the 4-vector and tensor equations for the components of the electromagnetic field tensor of a monochromatic plane wave. This approach provides analytical expressions for the time-averaged square of the 4-acceleration of the charge, as well as for the averaged values of any quantities periodic in the time of the reference frame. Expressions for the integral power of scattered radiation, which is proportional to the time-averaged square of the 4-acceleration of the charge, and for the integral scattering cross section, which is the ratio of the power of scattered radiation to the intensity of incident radiation, are obtained for an arbitrary inertial reference frame. An expression for the scattering cross section, which coincides with the known results at the circular and linear polarizations of the incident waves and describes the case of elliptic polarization of the incident wave, is obtained for the reference frame where the charged particle is on average at rest. An expression for the scattering cross section including relativistic effects and the nonzero drift velocity of a particle in this system is obtained for the laboratory reference frame, where the initial velocity of the charged particle is zero. In the case of the circular polarization of the incident wave, the scattering cross section in the laboratory frame is equal to the Thompson cross section.     

Light scattering by a 2D electron system with spin-orbit interaction in a strong magnetic field

We theoretically investigate light scattering by electrons of a 2D system in a strong magnetic field perpendicular to the plane of the system (the filling factor is smaller than two, i.e., only the states of the zeroth Landau level are filled). Analysis is carried out in the resonance approximation, in which the frequencies of the incident and scattered light are close to the effective separation between the conduction band and one of the branches of the valence band of the semiconductor. Spin splitting of the Landau level in the conduction band associated with Zeeman and the spin-orbit interactions is taken into account. The dynamic screening effects are considered in the random phase approximation (RPA).     

Reflection of lamb waves in a solid layer by a grating formed by mechanical resonators

The scattering of the mth Lamb mode by a grating formed by P chains of closely spaced identical mechanical resonators (springs with loads) attached to the boundaries of a solid layer is considered. The distance between the chains is identical to the half-wavelength of the given mode at a frequency ω identical to or close to the natural frequency of the resonator chain with allowance for the interaction of neighboring chains through inhomogeneous modes. The coefficient of reflection of the mth Lamb mode from the aforementioned diffraction grating is calculated.     

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.     

High-efficiency frequency-modulation non-redundant scanning of a light beam in a half space

It is shown that a large fraction of the energy of the impinging light beam on a parallel plate grating can be injected into only one transmitted order, which is not the zeroth transmitted order, when the incident angle of the beam and the refractive indices of the lossless dielectric bounding media satisfy the condition of total reflection. This signififies that non-redundant scanning of the radiation transmitted through the grafting can be obtained by varying the frequency of the incident radiation with little of the incident energy being scattered into the reflected orders.     

The scattering of flexural waves by random fractal inhomogeneities in a thin plate

The scattering of flexural waves by small statistical fractal inhomogeneities in a thin plate is considered. An expression for the average intensity of the fluctuations of the scattered wave field is obtained. A relation of the intensity to the plate parameters and to the fractal dimension of the inhomogeneities is determined. An expected frequency dependence of the attenuation of flexural waves in a plate due to the scattering by fractal inhomogeneities is discussed.     

Specular propagation over rough surfaces: numerical assessment of Uscinski and Stanek's mean Green's function technique

The purpose of this paper is to numerically evaluate the effectiveness and accuracy of Uscinski and Stanek's mean Green's function technique for computing the mean field of a wave scattered by a rough surface. We present here a direct comparison of this technique with a rigorous numerical method, the forward scattering integral equation method, and another analytical method, the first-order smoothing approximation. Furthermore, we compare the roughness generated equivalent admittance using the three methods. Numerical computations reveal that the scattered field calculated by this technique is not accurate particularly for the equivalent admittance at low grazing angles, even though the mean surface current density is recovered when the wave has traversed several correlation lengths on the surface.     

Truncating cylindrical wave modes in two-dimensional multiple scattering

When analyzing the two-dimensional multiple scattering of electromagnetic waves by cylinders, the incident, scattered, and transmitted fields need to be represented by infinite sums of cylindrical wave modes. These infinite sums need to be truncated to a finite limit in order to calculate the scattering matrix. The accuracy of the scattered field representation and the stability of the matrix inversion are both critically dependent on the truncation limit. The parameters involved in the scattering are analyzed to determine their effect on the upper and lower bounds of an appropriate modal truncation.     

Appearance of extrema in the frequency shift produced by scattering from a rotational anisotropic particle

We investigate the analytical expression of the spectrum that is produced by scattering of a polychromatic plane light wave incident upon a rotational anisotropic particle. It is found that the appearance of extrema in the frequency shift of the scattered field can be exactly predicted by our derived equations of the rotation angle. Numerical examples are presented to illustrate the theoretical results and also to show the impact of the effective radius of the scattering potential on the frequency shift.     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

Abstract

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Frequency shifts of spectral lines induced by scattering from a rotational anisotropic particle

We investigate the scattering of a polychromatic plane light wave incident upon an anisotropic particle. It is different from light wave scattered by an isotropic particle that the frequency shifts of spectral lines will be induced by the rotation of the anisotropic particle. The analytical expression for the spectrum of the scattered field is derived and numerical examples are also illustrated. We suggest an application that the angular speed of rotation of the anisotropic scatterer can be scaled by measurement of the spectrum of the scattered field.     

A new boundary method for electromagnetic scattering from inhomogeneous bodies

A new numerical method for scattering from inhomogeneous bodies is presented. In particular, the 2D case of a TM-polarizated incident wave scattered by an infinite cylinder is considered. The scattered field is sought in two different domains. The first one is a bounded region inside the scattering body with an inhomogeneous permittivity ε(x,y). The second one is an unbounded homogeneous region outside the scatterer. An approximate solution for the scattered field inside the scatterer is sought by applying the QTSM technique. The method of discrete sources is used to approximate the scattered field in the unbounded region outside the scattering body. A comparison of the numerical solution with an analytic solution is performed.