A spectral domain approach to modelling of EM scattering for Synthetic Aperture Radar target recognition

A Fourier-based technique for electromagnetic (EM) wave reconstruction with application to polarimetric airborne and spaceborne radar data exploitation is presented. The method is different from conventional modelling techniques for Synthetic Aperture Radar (SAR) applications as a result of the full electromagnetic treatment of field interactions with the scatterer, the possibility of introducing new and controllable feature classes for target classification, and accurate decomposition of the source impulse response function that avoids potential errors (e.g. loss of coherent information) associated with the spherical phase approximations. The capability of extracting scatterer information such as the coherent radar cross section (RCS) is explored.     

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     

Stochastic effects on the bistatic transfer function of a planar scatterer distribution

ABSTRACT

We evaluate the effects of several stochastic factors on signal transmission through a planar distribution of stationary scatterers, with non-collocated transmitter and receiver (bistatic configuration). The transmission channel is described by means of its transfer function, which –as a result of randomness in the scatterer distribution– fluctuates around its expectation value. Specifically, we consider randomness in the scatterer positions (both on the plane and in height), in their radar cross sections, and in the scattering phases. Our analytical results provide a quantitative relation between the parameters that characterize random components of each kind, and the fluctuations that alter the transfer function.     

The phase statistics of a multichannel radar interferometer

Abstract

The analysis in this paper is concerned with the problem of determining the phase statistics of the output of a multichannel coherent radar interferometer. The 2N channels of the radar consist of the outputs from N pairs of antennae. Each antenna receives a random electromagnetic wave field which has circular normal first-order statistics with an arbitrary coherence function. Each antenna in each pair receives a wave at a different time, the time difference Δt between each antenna in each pair being the same for all pairs. The signals received by each pair are independent. The signals from each pair are combined to give G(t, Δt)=Σ_k=1 ^N S_k(t) S_k*(t+Δt) where, for example, the signals from each antenna in the kth pair are S_k(t) and S_k(t+Δt).

The probability density function of the modulus and phase of G(t, Δt) is worked out. The joint density is shown to be a type of generalized K distribution, and the phase distribution is shown to be a hypergeometric function. The results show that it is possible to measure the phase of the coherence function of an electromagnetic wave field scattered from a randomly moving extended object (such as the ocean surface) using such a multichannel radar. This phase is related to asymmetry of the Doppler power spectrum. Furthermore, if this asymmetry is a result of surface currents on the ocean interacting with the surface waves which cause the electromagnetic scattering, then the surface currents may be measured in some sense.     

A monostatic inverse scattering model based on polarization utilisation

The solution of the inverse problem of electromagnetic scattering by smooth, convex shaped, perfectly conducting, 3-dimensional scatterers is analysed. Certain geometrical as well as physical-optics approximations were used to incorporate the concepts of the “Minkowski problem” of differential geometry into the space-time integral solution of electromagnetic scattering to yield the formal solution for the recovery of the surface profile of the scatterer from the scattered field data. Although various efficient solutions for target identification are available, still information contained in polarization-depolarization characteristics of the scatterer is not yet exploited to its full extent. Therefore the underlying assumption in this investigation was based on the fact that the “depolarization characteristics” of the scattered field do necessarily contain information regarding the surface profile of the scatterer.     

Multiple reflections in backscattering by a single scatterer near a perfectly reflecting surface

The scattering of a plane electromagnetic wave by a solitary scatterer randomly positioned near a perfectly reflecting surface is investigated in the dipole approximation taking into account infinite multiplicity of scattering. It is shown that the presence of multiply reflected waves increases the “effective” polarizability of the particle and adds another component of the dipole moment along the normal to the surface. As a result, the backscattering enhancement effect becomes stronger, and the angle of incidence at which amplification of the p-polarized wave vanishes becomes smaller. The influence of multiply scattered waves increases as the particle approaches the boundary in this case. Zh. Tekh. Fiz. 67, 72–75 (September 1997)     

Scattering of an electromagnetic wave from a slightly random cylindrical surface: horizontal polarization

Abstract

The scattering of an electromagnetic wave from a random cylindrical surface ir studied for a plane-wave incidence with S-(TE) polarization, by means ofthe stochastic scattering theory developed by Nakayama, Ogura. Sakati et al. The theory is based on the Wiener-Ito stochastic functional calculus combined with the group-theoretic consideration concerning the homogeneity of the random surface. The random surface is assumed to be a homogeneous Gaussian random field on the cylinder C, homogeneous with respect to the group of motiolrs on C: translations along the axis and rotations around the axis. An operator D operating on a random field on C is introduced in such a way that D keeps the homogeneous random surface invariant This gives a reprerentation of the cylbdrical group and commutes with the boundary condition and the Maxwell equation. Thus, for an injection of the mth cylindrical TE or TM wave, which is a vector eigenfunction of the D operator, the scattered random wave field is an eigenfunctiou with the same eigenvalue: it satisfies the Maxwell equation and is a stoch-tic Iunctional of the Gaussian random surface, BO that it can be expressed in a vector form of the Wiener-Ito expansion in t e m of TE and TM waves and orthogonal functional. of the Gaussian random measures associated with the random cylindrical surface. In the analysis the random surface is modelled by an approximate boundaiy condition representing a perfectly conducting cylindrical surface with a slight roughness. The boundary condition on the random cylinder is transformed into a hierarchy of equations for the Wiener kernels which can be solved approximately. The random wave field for a plane-wave injection is obtained by summing these fields over m. From the stochastic representation of the electromagnetic field so obtained, various statistical characteristics can be calculated the coherent scattering amplitude. total coherent power flow, incoherent power flow, differential sections for coherent rcatlerhig and incoherent scattering, etc. The power conservation law is cast into a stochastic electromagnetic version of the optical theorem stating that the total scatteiing cross section is given by the imaginary part of the forward coherent scattering amplitude. Numerical calculations are made for a planewave injection with S-(TE) polarization. The case of p-(TM) polarization can be treated in a similar manner.     

Analysis of tapered front‐coupling X‐ray waveguides

The coupling and propagation of electromagnetic waves through planar X‐ray waveguides (WG) with vacuum gap and Si claddings are analyzed in detail, starting from the source and ending at the detector. The general case of linearly tapered WGs (i.e. with the entrance aperture different from the exit one) is considered. Different kinds of sources, i.e. synchrotron radiation and laboratory desk‐top sources, have been considered, with the former providing a fully coherent incoming beam and the latter partially coherent beams. It is demonstrated that useful information about the parameters of the WG can be derived, comparing experimental results with computer simulation based on analytical solutions of the Helmholtz equation which take into account the amplitude and phase matching between the standing waves created in front of the WG, and the resonance modes propagating into the WG.     

Multiple Rayleigh scattering of electromagnetic waves: A partial summation

Abstract

This paper deals with the multiple scattering of electromagnetic waves by a homogeneous distribution of spherical Rayleigh scatterers. We use the Feynman diagrams symbolism and define the planar diagrams which describe the interactions with possible backscattering to a previously used scatterer (loops). Resummation over every level of overlapping loops is performed analytically. In terms of the absorption properties of the equivalent continuous medium, departure from Twersky's assumption is shown to occur only in dense media, and the first level of loops is a good approximation of the whole set. Results are compared with the scalar waves case.     

Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere

Abstract

In this paper, we study the effects of turbulent atmosphere on the degree of polarization of a partially coherent electromagnetic beam, which propagates through it. The beam is described by a 2?2 cross–spectral density matrix and is assumed to be generated by a planar, secondary, electromagnetic Gaussian Schell–model source. The analysis is based on a recently formulated unified theory of coherence and polarization and on the extended Huygens–Fresnel principle. We study the behaviour of the degree of polarization in the intermediate zone, i.e. in the region of space where coherence properties of the beam and the atmospheric turbulence are competing. We illustrate the analysis by numerical examples.     

双模非经典光场辐照下介观约瑟夫森结中超流的动力学行为

研究了直流偏置电压下介观约瑟夫森结在SU（1，1）双模相干态光场作用下超流的动力学行为、流压台阶和直流分量等特性．研究发现超流能够呈现明显的崩塌与复苏现象，对于经典电磁场和非耦合的双模相干态光场作用下的情况，超流不出现此现象，且其流压台阶结构与后两种情况也不相同． 关键词：     

The scattering of electromagnetic waves in fractal media

Abstract

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic Cosh-Gaussian pulsed beams

Based on the generalized Rayleigh–Sommerfeld diffraction integral, the analytical expression for 3×3 cross-spectral density matrix of nonparaxial spatially and spectrally partially coherent electromagnetic Cosh-Gaussian (ChG) pulsed beams propagating in free space is derived, and used to formulate the spectral density and spectral degree of polarization of electromagnetic pulsed beams at the z-plane. It is found that the parameters f and f_αα are the key parameters in determining the nonparaxiality of spatially and spectrally partially coherent electromagnetic ChG pulsed beams. And the decentered parameter, pulse duration and temporal coherence length can change the nonparaxial behavior of the electromagnetic ChG pulsed beams. The effect of decentered parameter, pulse duration and temporal coherence length on the spectral density and spectral degree of polarization of electromagnetic ChG pulsed beams is illustrated through numerical calculations. Propagation of nonparaxial spatially and spectrally partially coherent electromagnetic Gaussian Schell-model pulsed beams can be treated as a special case when the decentered parameter of electromagnetic ChG pulsed beams approaches to zero.     

Changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic J0-correlated Schell-model pulsed beams propagating in free space

Taking the stochastic electromagnetic J ₀-correlated Schell-model pulsed (JSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the analytical expressions for the cross-spectral density matrix, spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic JSMP beams propagating in free space are derived, and used to study the changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic JSMP beams. It is shown that the on-axis spectrum is blue-shifted in free-space propagation and is dependent on the pulse temporal coherence length and spatial correlation parameter. The distribution of the on-axis spectral degree of polarization depends on the frequency and spatial correlation parameter. The spectral degree of coherence increases with increasing pulse temporal coherence length. The results derived are interpreted physically.     

An effect of turbulent clustering on scattering of microwave radiation by small particles in the atmosphere

A coherent scattering of electromagnetic waves by clusters of inertial Rayleigh particles in atmospheric turbulence is considered. A preliminary estimate based on the Maxwell-Garnett theory and the Rayleigh approximation for single clusters demonstrates an importance of the coherent scattering contribution. It is confirmed by a general solution in a combination with theoretical estimates for the two-point probability density function for low-inertia spherical particles in isotropic turbulence. An approximate analytical expression for the coefficient characterizing effect of coherent scattering by the particle clusters is derived. The calculations for small Stokes numbers typical of water droplets in cumulus clouds yield an estimate of the coherent scattering effect on the microwave radar reflection. The model suggested allows solving the inverse problem to determine the pair correlation function for cloud particles. It is expected to be important for the investigations on particle–turbulence interaction in the atmosphere. The theoretical model developed is true not only in the limit of low-inertia particles and can be potentially used at arbitrary Stokes numbers in other applications.     

Radar cross sections of a random medium layer

Abstract

Analytic expressions are derived for the normalized radar cross sections (NRCS) of a random medium layer. These are calculated from the first-order solutions for diffuse intensities which are based on a multiple-scattering wave theoretical analysis. The permittivity fluctuations are assumed to be small and to obey stationary Gaussian statistics. On studying the expressions for the NRCS, some of their characteristics are pointed out. Three different correlation functions are considered and expressions for the coherent propagation constants are provided. Numerical examples are used to verify theoretical results and highlight some interesting characteristics of NRCS.     

Theory of single-mode lasing in coherent quantum cascade lasers

A theory is developed for steady-state single-mode lasing in coherent quantum-well cascade lasers. This laser model is an example of a strictly quantum mechanical problem in which approximate kinetic approaches are not used to account for dissipative scattering processes. Exact wave functions are found for the system in weak and strong electromagnetic fields, so that the output power and frequency can be determined as functions of the coherent pump current and system parameters. It is shown that for pumping by monoenergetic electrons the power has a nonlinear (root) dependence and tends to saturate in strong fields. It is predicted that the coherent pumping efficiency may be increased by adjusting the energy of the pump electrons, which will lead to a linear power dependence, a high efficiency, and low threshold currents. A population inversion is found not be a necessary condition for lasing in the coherent laser. In particular, in the high field regime the population of the lower level exceeds that of the upper, while in the optimally adjusted regime they are the same. Zh. éksp. Teor. Fiz. 112, 483–498 (August 1997)     

The T-matrix for particle with arbitrary permittivity tensor and parallelization of the computational code

Using the T-matrix approach electromagnetic scattering by a non-axisymmetric particle with an arbitrary permittivity tensor is studied. The electromagnetic fields inside the scatterer are expressed by a system of quasi-spherical vector wave functions which are derived by the use of inverse Fourier transform. Using this expansion a solution of the light scattering problem in the framework of the null-field method is obtained. The implemented T-matrix program is parallelized using both OpenMP and MPI parallel paradigms. Numerical scattering results for anisotropic ellipsoids are presented.     

New method for detection of exciton Bose condensation using stimulated two-photon emission

An investigation is reported of stimulated two-photon emission by Bose-condensed excitons accompanied by a coherent two-exciton recombination, i.e., by simultaneous recombination of two excitons with opposite momenta leaving unchanged the occupation numbers of exciton states with momenta p≠0. Raman light scattering (RLS) accompanied by a similar two-exciton recombination (or production of two excitons) is also analyzed. The processes under consideration can occur only if a system contains Bose condensate, so their detection can be used as a new method to reveal Bose condensation of excitons. The recoil momentum, which corresponds to a change in the momentum of the electromagnetic field in the processes, is transferred to phonons or impurities. If the recoil momentum is transmitted to optical phonons with frequency ω ₀ ^s , whose occupation numbers are negligible, and the incident light frequency satisfies ω<2Ω, where Ω_=Ω−ω ₀ ^s is the difference frequency and Ω is the light frequency corresponding to the recombination of an exciton with zero momentum, stimulated two-photon emission and RLS with coherent two-exciton recombination give rise to a line at 2Ω_ −ω and an anti-Stokes component at ω+2Ω_, respectively. For ω2Ω_ the RLS spectrum contains Stokes and anti-Stokes components at frequencies ω±2Ω_, whereas stimulated two-photon emission is impossible. Formulas for the cross sections at finite temperatures are obtained for the processes under consideration. Our estimates indicate that a spectral line at 2Ω_−ω, corresponding to the stimulated two-photon emission accompanied by coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu₂O. Zh. éksp. Teor. Fiz. 115, 1353–1376 (April 1999)     

Influence of the boundary of a medium on the coherent backscattering of light

The multiple scattering of light from an inhomogeneous medium occupying a half-space is investigated on the basis of the Bethe-Salpeter equation. The latter is integrated over the spatial variables to obtain an identity having the significance of the energy balance of the incident and scattered radiations. This relation is then used to derive a length parameter that plays the role of the Milne interpolation length. The use of this parameter in the method of mirror images for describing the shape of the coherent backscattering peak in isotropic single scattering yields results in almost perfect agreement with the predictions of the Milne theory. The application of the given approach for an anisotropic single-scattering diagram yields quantitative agreement of the theory with experiments on the angular dependence of coherent backscattering. The new approach is generalized to an electromagnetic (vector) field, and backscattering polarization effects are investigated. Zh. éksp. Teor. Fiz. 116, 1912–1928 (December 1999)