等离子体覆盖立方散射体目标雷达散射截面的时域有限差分法分析

采用分段线性电流密度递归卷积时域有限差分（PLJERC-FDTD）算法计算了均匀非磁化等离子体覆盖三维立方体目标的散射特性.分析了等离子体厚度、密度和碰撞频率对雷达散射截面（RCS）的影响.计算结果表明：等离子体包层能有效地减小雷达目标的RCS，当等离子体频率比入射电磁波频率小得多时，主要靠增大等离子体的厚度使立方散射体目标的RCS值减小，增大等离子体碰撞频率对立方散射体目标的RCS值影响不大；当等离子体频率约为入射电磁波频率的一半时，增大等离子体厚度和碰撞频率都对立方散射体目标的RCS值减小有影响；当等 关键词： FDTD算法 电磁波 等离子体隐身 雷达散射截面     

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.     

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.     

Polarized light propagation through tissue phantoms containing densely packed scatterers

We demonstrate that polarized light is maintained differently in densely packed versus dilute suspensions of polystyrene microspheres. The degrees of linear and circular polarization were measured versus scatterer concentration in aqueous suspensions of 0.48-, 0.99-, 2.092-, and 9.14-mum-diameter polystyrene microspheres. The results indicate that, for dilute suspensions of microspheres where independent scattering is assumed, the degrees of linear and circular polarization decrease as the scatterer concentration increases. For dense suspensions, however, the degree of polarization begins to increase as the scatterer concentration increases. The preferential propagation of linear over circular polarization states in dense suspensions is similar to results seen in biological tissue.     

Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.     

Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

Abstract

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.     

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.     

One-Dimensional Inverse Scattering Problem in Acoustics

We are concerned with the inverse scattering problem (ISP) in acoustics within the Marchenko inversion scheme. The quantum ISP is first discussed and applied in order to exhibit certain characteristics and application prospects of the method which could be useful in extending it to classical systems. We then consider the ISP in acoustics by assuming plane waves propagating in an elastic, isotropic, and linear medium. The wave equation is first transformed into a Schrödinger-like equation which can be brought into the Marchenko integral equation for the associated nonlocal kernel the solution of which provides us the full information of the underlying reflective profile. We apply the method in several model problems where the reflection coefficient of the multi-layer reflective medium is used as input to the ISP and in all cases we obtain excellent reproduction of the original structure of the scatterer. We then applied the inverse scattering scheme to construct profiles with certain predetermined reflection and transmission characteristics.     

Analysis of the time-reversal operator for scatterers of finite size

Recently, it was shown that the time-reversal operator for a single, small spherical scatterer could have up to four distinguishable eigenstates [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (2001)]. In this paper, that analysis is generalized for scatterers of arbitrary shape and larger size. It is shown that the time-reversal operator may have an indefinitely large number of distinguishable eigenstates, with the exact number depending on the nature of the scatterer and the geometry of the time-reversal mirror. In addition, the case of a multiple number of well-separated scatterers is investigated, with the result that the total spectrum is the direct combination of the eigenstates associated with each scatterer. As an example, the singular value spectrum of the time-reversal operator for a linear array is calculated explicitly for bubbles and hard rubber spheres of finite size. Both resonance peaks and apparent crossing points can be observed in the spectrum as the size of the scatterer increases.     

The integrated extinction for broadband scattering of acoustic waves

In this paper, physical bounds on scattering of acoustic waves over a frequency interval are discussed based on the holomorphic properties of the scattering amplitude in the forward direction. The result is given by a dispersion relation for the extinction cross section which yields an upper bound on the product of the extinction cross section and the associated bandwidth of any frequency interval. The upper bound is shown to depend only on the geometry and the material properties of the scatterer in the static or low-frequency limit. The results are exemplified by permeable and impermeable scatterers with homogeneous and isotropic material properties.     

Scattering of a Gaussian Beam by a Sphere Using a Bromwich Formulation: Case of an arbitrary location

A complete theory of Gaussian beam scattering by a sphere is exposed. It is a generalization of the Lorenz-Mie Theory to the case of Gaussian beam illumination. The spherical, isotropic and homogeneous scatterer may be located anywhere with respect to the beam. The Bromwich Scalar Potentials are used to solve the scattering problem and expressions are obtained for the scattered field (both in the near field and far field regions), the scattered intensities and the phase angle. In the limit of special cases the expressions agree with previous works restricted to more particular problems.     

An approach for obtaining the intensity of the radiation transmitted through a scatterer

Monte Carlo simulation was applied to the investigation of intensity of the radiation transmitted through a scatterer. Simulations consisted of a pencil beam of monoenergetic photons with energies from 50 keV to 10 meV incident on water, aluminium, iron, copper, tin and lead slabs. We determined the scattered radiation and the scatter fractions recorded in the detector plane. An empirical formula, which is a function of the physical parameters scatterer thickness, the linear attenuation coefficient, and the atomic number was obtained for intensity of radiation transmitted through a scatterer. This work was supported by the Scientific and Technical Research Council of Turkey (TUBITAK) [TBAG-2032 (101T053)].     

Acoustic Pulse Diffraction by a Sphere in a Planar Layered Waveguide with a Gradient Layer

Consideration of the vertical sound velocity profile is highly important for solving problems of sound propagation in waveguides and scattering problems. A pulsed echo signal reflected from a spherical scatterer in a waveguide is modeled for the case of a waveguide characterized by sound velocity increasing with depth. The simplest model of the medium is considered in which the scatterer, the source, and the receiver are positioned in a layer with constant sound velocity. Below this layer, the sound velocity increases with depth so that the square of refractive index varies according to linear law. The scattering coefficients for the sphere are calculated using the normal wave method. The number of normal waves forming the echo signal is determined by the preset directionality of the source. Modeling is performed in a frequency band of 70?90 kHz for distances between the scatterer and the transmitter-receiver within 500?1000 m. The transmitted signal has the form of a pulse with cosine envelope and central frequency of 80 kHz.     

On the possibility of using the maximum entropy method in ultrasonic nondestructive testing for scatterer visualization from a set of echo signals

We have studied the possibility of solving the inverse scattering problem in the Born approximation, i.e., the reconstruction of scatterer images from the measured set of echo signals. We have considered generalization of the classical combined SAFT (C-SAFT) algorithm to the case of multiple reflections from uneven boundaries of the tested object taking into account the transformation of the wave type for several positions of the antenna grid, which makes it possible to obtain high-quality scatterer images. Representation of the direct problem in matrix form makes it possible to switch to solving the inverse problem, which can be solved using the Tikhonov regularization procedure, because it is an ill-posed. We have considered the possibility of using the entropy of the image estimate as the stabilizing functional that forms the essence of the maximum entropy method (MEM). The advantage of the MEM over the conventionally used linear C-SAFT method has been shown. The ray model taking into account reflections of rays from the boundaries of the tested object with uneven boundaries has been used for constructing the function estimate. We have demonstrated the ability of the MEM to obtain the scatterer images with superresolution and to suppress the “side lobes” of the function of the point scattering on the collapsed set of echo signals. The use of echo signals reflected from the boundaries of the tested object makes it possible to reconstruct the scatterer shape more exactly. Examples of images reconstructed by the MEM on echo signals obtained in the numerical and model experiments have been presented.     

Missing spots in low energy electron diffraction

Recent attempts to justify the use, after appropriate data averaging, of kinematical theory in surface structure determination by LEED, make it important to be able to distinguish truly kinematical features from those which can also be predicted from entirely general symmetry arguments. Such arguments are therefore developed formally into a set of rules determining the consequences of symmetry for LEED patterns. In particular the conditions for missing spots due to the presence of glide planes are given. It is pointed out that in some circumstances the isotropic scatterer model leads to spurious selection rules, that will not be satisfied in general.     

Detection of interaction-induced nonlocal effects using perfectly transmitting nanostructures

We consider one-dimensional transport through an interacting region in series with a point-like one-body scatterer. When the conductance of the interacting region is perfect, independently of the interaction strength, a nonlocal interaction effect yields a total conductance of the composed system that depends on the interaction strength and is lower than the transmission of the one-body scatterer. This qualitative nonlocal effect allows to probe the dressing cloud of an interacting system in ideal noninteracting leads. The conductance correction increases with the strength of the interaction and the reflection of the one-body scatterer (attaining relative changes >50%), and decreases with the distance between the interacting region and the one-body scatterer. Scaling laws are obtained and possible experimental realizations are suggested.     

Method of improved scatterer size estimation and application to parametric imaging using ultrasound

The frequency dependence of RF signals backscattered from random media (tissues) has been used to describe the microstructure of the media. The frequency dependence of the backscattered RF signal is seen in the power spectrum. Estimates of scatterer properties (average scatterer size) from an interrogated medium are made by minimizing the average squared deviation (MASD) between the measured power spectrum and a theoretical power spectrum over an analysis bandwidth. Estimates of the scatterer properties become increasingly inaccurate as the average signal to noise ratio (SNR) over the analysis bandwidth becomes smaller. Some frequency components in the analysis bandwidth of the measured power spectrum will have smaller SNR than other frequency components. The accuracy of estimates can be improved by weighting the frequency components that have the smallest SNR less than the frequencies with the largest SNR in the MASD. A weighting function is devised that minimizes the noise effects on the estimates of the average scatterer sizes. Simulations and phantom experiments are conducted that show the weighting function gives improved estimates in an attenuating medium. The weighting function is applied to parametric images using scatterer size estimates of a rat that had developed a spontaneous mammary tumor.     

Cancellation of simple optical anisotropies without use of a Faraday mirror

We first derive the round-trip Jones matrix for double passage through a reciprocal optical medium by means of reflection off a plane mirror that could be optically anisotropic. We then show that if a medium with only linear birefringence and linear dichroism is placed between a pair of orthogonal quarter-wave plates with principal axes at 45 degrees to that of the medium and the sandwich is placed in front of an isotropic mirror it behaves, under double passage, like an isotropic medium. We describe a simple liquid crystal device that behaves, in reflection, as an isotropic medium whose refractive index can be varied by application of an electric field, thus acting as a phase only modulator for light in any polarization state.     

The DORT solution in acoustic inverse scattering problem of a small elastic scatterer

The DORT (French acronym for Décomposition de l’Opérateur de Retournement Temporel) method is a novel approach for active detection and focusing of acoustic waves on the targets in the scattering medium. This technique involves the determination of the invariant of the time-reversal operator obtained by measurement of the scattering data in a pulse-echo mode. In this paper, a proposed approach based on the DORT method is developed to solve the acoustic inverse scattering problem of a small metallic scatterer. The proposed approach not only estimates the position of the scatterer, but also determines the physical properties of an unknown metallic scatterer such as the shape (cylinder or sphere), the material (density), and the size (radius) in an anisotropic scattering case. Theoretical and numerical simulation results are also studied and investigated to show that the proposed approach can simultaneously characterize all those properties of an unknown metallic scatterer. Moreover, the advantage of the proposed approach is to avoid the complex iterative scheme in solving the direct scattering problem and results in smaller computational load and faster implementation.