Special features of calculation for processes of scattering by contrast and strongly absorbing two- and three-dimensional inhomogeneities

A direct problem of scattering for refractive-absorbing scatterers of different shapes and strengths is considered. A rigorous solution for two- and three-dimensional problems and its numerical implementation are obtained on the basis of equations of the Lippmann-Schwinger type in the coordinate space and in the space of special frequencies that is Fourier-conjugate to it. Attention is given to selection of parameters for problem sampling that are fundamentally important for providing adequacy of numerical simulation. Techniques for restricting the Green’s function support and introducing a reserve band are used. The results of numerical calculation for wave fields and secondary sources are given for different scatterers. The major laws connected with the effects of sound wave rescattering are illustrated and discussed.     

Direct Solution of the Inverse Problem for Rough Surface Scattering

We consider the inverse scattering problem for a scalar wave field incident on a perfectly conducting one-dimensional rough surface. The Dirichlet Green function for the upper half-plane is introduced, in place of the free-space Green function, as the fundamental solution to the Helmholtz equation. Based on this half-plane Green function, two reasonable approximate operations are performed, and an integral equation is formulated to approximate the total field in the two-dimensional space, then to determine the profile of the rough surface as a minimum of the total field. Reconstructions of sinusoidal, non-sinusoidal and random rough surface are performed using numerical techniques. Good agreement of these results demonstrates that the inverse scattering method is reliable.     

The physical optics integral on the scatterer's unlit surface

The scattering integrals of the modified theory of physical optics are redefined according to the illuminated and unlit surfaces of the scattering object. With this aim the canonical problem of wedge diffraction is taken into account. It is shown that the new scattering integral contain two geometrical optics and diffracted fields. One of the geometrical optics waves is the reflected field component that propagates in the real space. The other one transmits to an imaginary space through the scattering surface and does not have any influence in the real space. The diffracted waves exist in the real space and satisfy the related boundary condition on the scattering surfaces. The resultant field expressions are compared with the exact series solution of the problem numerically.     

An Iterative Two-Grid Method of a Finite Element PML Approximation for the Two Dimensional Maxwell Problem

In this paper, we propose an iterative two-grid method for the edge finite element discretizations (a saddle-point system) of Perfectly Matched Layer (PML) equations to the Maxwell scattering problem in two dimensions. Firstly, we use a fine space to solve a discrete saddle-point system of $H(grad)$ variational problems, denoted by auxiliary system 1. Secondly, we use a coarse space to solve the original saddle-point system. Then, we use a fine space again to solve a discrete$\boldsymbol{H}(curl)$-elliptic variational problems, denoted by auxiliary system 2. Furthermore, we develop a regularization diagonal block preconditioner for auxiliary system 1 and use $H$-$X$ preconditioner for auxiliary system 2. Hence we essentially transform the original problem in a fine space to a corresponding (but much smaller) problem on a coarse space, due to the fact that the above two preconditioners are efficient and stable. Compared with some existing iterative methods for solving saddle-point systems, such as PMinres, numerical experiments show the competitive performance of our iterative two-grid method.     

A novel method for solving the three-body scattering problem

A numerical scheme for solving a three-body scattering problem within the framework of the configuration space Faddeev equations in three-dimension, i.e., without resort to explicit partial wave expansion, is presented. The method is applied to calculate the low-energy n-d observables.     

Method for solving the problems of multiple scattering by several bodies in a homogeneous unbounded medium

A method is developed for solving problems of multiple scattering by an aggregate of bodies in a homogeneous unbounded medium. For this purpose, the problem on the multiple scattering produced by two bodies in the field of a plane wave is first considered under the assumption that the initial unperturbed scattering amplitudes of both scatterers are known. The solution is constructed by considering plane waves multiply rescattered by the scatterers. Integral equations are obtained that allow one to calculate the resulting scattering amplitude of each scatterer and the combined scattering amplitude of the system of two scatterers. It is shown that knowledge of the solution to this problem is sufficient to solve the problem on the scattering field of a system consisting of an arbitrary number of scatterers. Expressions for the scattering amplitude in the case of an arbitrary primary field are presented. The relationship between the integral equations describing the multiple scattering in a homogeneous space and the multiple scattering by a single scatterer located near an interface is demonstrated. Approximate expressions are given for calculating the scattering amplitude in the case of multiple scattering.     

Bragg scattering of cooper pairs in an ultracold Fermi gas

We present a theoretical treatment of Bragg scattering of a degenerate Fermi gas in the weakly interacting BCS regime. Our numerical calculations predict correlated scattering of Cooper pairs into a spherical shell in momentum space. The scattered shell of correlated atoms is centered at half the usual Bragg momentum transfer, and can be clearly distinguished from atoms scattered by the usual single-particle Bragg mechanism. We develop an analytic model that explains key features of the correlated-pair Bragg scattering, and determine the dependence of that scattering on the initial pair correlations in the gas.     

Electromagnetic Modelling of Fine Features in Photonic Applications

Straightforward application of numerical modelling approaches to Photonic Band-Gap structures demands the use of fine meshes, notably finer that the size of a single scattering element, in order that high accuracy is achieved. However simulations employing sufficiently fine meshing to correctly represent the geometry of the scatterers lead to very long computational run-times and huge memory consumption. Such direct numerical approaches to PBG characterisation are only suited to the analysis of single unit cells or for benchmarking. In practice, the computational overheads significantly increase when one deals with an array of cells or when modelling the global behaviour of a large number of devices integrated on a single substrate. Therefore in order to model the macroscopic response of PBG structures the possibility of employing meshes of much larger size than the individual scattering elements has been explored. A suitable approach, initially developed for Electromagnetic Compatibility predictions, has been modified to permit modelling of Photonic Crystal Waveguides. The method provides second order accuracy and leaves a designer with the flexibility to discretise the entire problem space with an arbitrary number of scatterers per mesh cell. Results are first presented for small clusters of scatterers and subsequently for complete photonic structures.     

The phenomenon of simplified scattering from rough surfaces to reflection in fractional space

In this paper, the scattering of incident plane waves from rough surfaces has been modeled in a fractional space. It is shown how wave scattering from a rough surface could correspond to a simple reflection problem in a fractional space. In an integer dimensional space, fluctuations of the surface result in wave scattering, while in the fractional space, these fluctuations are compensated by the geometry of space. In the fractional space, reflection is equivalent to scattering from the integer dimensional space. Comparing scattered wave functions from different self-affine rough surfaces in the framework of the Kirchhoff theory with the results from the fractional space, we see good agreement between them.     

楔形理想波导中球体散射的镜像方法

应用镜像原理和球波函数加法公式,把楔形理想波导中球体的散射声场等效为无界空间中多球体散射声场,镜像解析解与边界元数值结果相同,可以作为边界随水平距离变化波导中目标散射数值方法的标准解。比较无界空间和楔形理想波导中球体散射声场空间分布特征,结果表明:楔形理想波导中球体的散射声场在水平和倾斜边界反射;散射声场沿楔形理想波导下坡方向的衰减在相同的水平距离下小于无界空间的情况,散射声场在楔形理想波导上坡的空间分布受到限制。     

Radiation and scattering of sound waves in oceanic waveguides

The applicability conditions for the concept of a directivity pattern (a scattering amplitude) in the problems of waveguide propagation are formulated. The consideration is based on the solution of the Sturm-Liouville problem. The results of the comparison between these conditions and the analogous conditions obtained earlier in the ray approximation are discussed. The expression for the scattering matrix of waveguide modes is modified on the basis of the suggested conditions in such a way that it involves only the quantities determined from the solution of the Schrödinger equation. This makes it possible to perform numerical calculations by using the results of numerous studies of the propagation in inhomogeneous waveguides and the diffraction by complex-structured bodies in free space.     

Operation of the Faddeev Kernel in Configuration Space

We present a practical method to solve Faddeev three-body equations at energies above the three-body breakup threshold as integral equations in coordinate space. This is an extension of a previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions.     

浅海波导中目标散射的简正波-Kirchhoff近似混合方法

提出了计算浅海波导中复杂目标散射的数值方法:简正波-Kirchhoff近似混合方法。通过把目标散射的Kirchhoff近似方法和简正波声传播模型相结合,可对大尺寸复杂目标在浅海波导中的散射声场进行计算。以浅海波导中刚性球体散射的解析解为标准解验证了本方法,说明简正波-Kirchhoff近似混合方法是有一定计算精度的工程预报方法。数值计算Pekeris浅海波导中球体目标散射声场在深度-频率平面和距离-频率平面上的二维干涉结构及其与自由空间中的差异。进而通过FFT获得目标时域回波随深度的分布图,分析浅海波导中目标姿态、声速剖面对Benchmark潜艇目标散射的影响。      

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

The discrete ordinates method for anisotropic scattering in the neutron transport theory: The critical sphere problem

The spherical harmonics method for anisotropic scattering in the neutron transport theory related to the critical sphere problem was investigated by Yildiz [The spherical harmonics method for anisotropic scattering in neutron transport theory: the critical sphere problem. JQSRT 2001;71:25-37]. Some numerical results and figures that they provided are incorrect. The correct numerical results for the critical radius are obtained and tabulated for different scattering parameters by using the discrete ordinates method.     

Faddeev approach to the three-body problem in total-angular-momentum representation

For a system of three charged particles the Faddeev equations are derived in the total-angular-momentum representation. They have the form of coupled sets of partial differential equations in three-dimensional space and can be used to develop new efficient numerical procedures to tackle the three-body Coulomb problem. The asymptotic conditions at large distances corresponding both to binary scattering and bound-state problems are presented. The behaviour of the Faddeev components near the triple and double collision points is studied.     

A method to solve an acoustic inverse scattering problem involving smart obstacles

A time-harmonic acoustic inverse scattering problem involving smart obstacles is formulated and a method to solve it is proposed. A smart obstacle is an obstacle that, when hit by an incoming acoustic wave, tries to pursue a given goal circulating a suitable pressure current on its boundary. A pressure current is a quantity whose physical dimension is pressure divided by time. The goals pursued by the smart obstacles that we have considered are the following ones: to be undetectable or to appear with a shape and/or acoustic boundary impedance different from its actual ones eventually in a location in space different from the actual location. The following time-harmonic inverse scattering problem is considered: from the knowledge of several far fields generated by the smart obstacle when hit by known time-harmonic waves, the knowledge of the goal pursued by the smart obstacle and of its acoustic boundary impedance reconstruct the boundary of the obstacle. A method to solve this inverse problem that generalizes the so-called Herglotz function method is proposed. Some numerical experiments that validate the method proposed are presented. The website http://www.econ.univpm.it/recchioni/w13 contains some auxiliary material that helps the understanding of the current paper.     

Coherent nuclear resonant scattering of X-rays: Time and space picture

Hyperfine Interactions - The problem of coherent resonant scattering of X-rays by an ensemble of nuclei is solved directly in time and space. In a first step the problem with a single coherently...     

Rigorous solutions for electromagnetic scattering from rough surfaces

Abstract

First, the rough surface scattering problem is formulated from a statistical point of view. Then, different numerical schemes that permit one to solve Maxwell equations without approximation are presented for the three-dimensional scattering problem. Particular attention is paid to boundary integral methods and to the numerical techniques developed to handle large linear systems when short-range interactions dominate. Lastly, several important connected issues that require further numerical and theoretical improvements are discussed.