Scattering Of Plane Wave Research Articles

Scattering of an arbitrary plane wave by a dielectric wedge: Integral equations and fields near the edge

The behavior of the field components near the edge has been shown to be that of the static fields, which is derived here without rigor for an infinite wedge. Fields scattered by a finite dielectric wedge illuminated by an arbitrary plane monochromatic wave are computed using either singular or hypersingular integral equations (SIEs or HIEs), derived by the single integral equation method. Field components are then computed near the edge of a finite wedge. Longitudinal components of the fields behave like constants, other components of the electric field behave like those in the transverse magnetic mode, and other components of the magnetic field behave like those in the transverse electric mode. Exceptions occur when approaching the wedge along the bisector. Boundary functions and transverse field components computed with SIEs rise more sharply than predicted approaching the edge after a range in which the agreement with those computed with HIEs is good.

Calculation of periodic metal nanostructures via the method of approximate boundary conditions

Scattering of an H-polarized optical plane wave by a periodic grating of metal strips located on an interface between two dielectrics is analyzed. The scattering problem is solved under the assumption that the material of the strips is characterized by a complex permittivity, which is typical of metals in the optical band. Approximate boundary conditions are used. The results are compared to the data obtained by means of alternative methods.

Scattering of TE Plane Wave from Periodic Grating with Single Defect

Scattering of TE Plane Wave from Periodic Grating with Single Defect

Scattering of a TM Plane Wave from a Periodic Surface with Finite Extent: Perturbation Solution

This paper studies the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent by the small perturbation method. We obtain the first and second order perturbed solutions explicitly, in terms of which the differential scattering cross section and the total scattering cross section per unit surface are calculated and are illustrated in figures. By comparison with results by a numerical method, it is concluded that the perturbed solution is reasonable even for a critical angle of incidence if the surface is small in roughness and gentle in slope and if the corrugation width is less than certain value. A brief discussion is given on multiple scattering effects.

Scattering of TM plane wave from a finite periodic surface

AbstractScattering of a TM plane wave from a finite periodic surface is studied by the spectral formalism. First, the diffraction beam, the optical theorem, the total scattering cross section and the relative power of diffraction beam are defined. By use of the principle of reflection, it is shown that the spectrum of the scattered wave can be written by the boundary value only on the corrugated part of the surface. Expanding such boundary value into a Fourier series, the integral equation determining the boundary value is transformed into a matrix equation of the Fourier coefficients, which is solved numerically. Then the total power of scattering and the relative power of diffraction beam are calculated against the angle of incidence. Wood's anomaly, the beam width of a diffraction beam, and the singularity of the spectrum of the scattered wave are discussed. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 89(3): 10–19, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20217

Plane Wave Scattering From Three Dimensional Multiple Objects Using the Iterative Multiregion Technique Based on the FDFD Method

An iterative approach using the finite difference frequency domain method is presented in this paper in order to solve the problem of scattering from large three-dimensional electromagnetic scatterers. The idea of iterative multiregion technique is introduced to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory has been achieved.

TM Plane-Wave Scattering From Finite Rectangular Grooves in a Conducting Plane Using Overlapping T-Block Method

Transverse magnetic plane-wave scattering from finite rectangular grooves in a conducting plane is systematically analyzed with the overlapping T-block method. Multiple rectangular grooves are divided into several overlapping T-blocks to obtain the fast CPU time, simple applicability, and wide versatility. The field representations within T-blocks are expressed using the Green's function relation and mode-matching method. The scattered fields are obtained in simple closed forms including a fast-convergent integral.

Scattering of electromagnetic plane waves by a spheroid uniformly moving in free space

We investigate the scattering process, generated by a plane electromagnetic field that is incident upon a moving perfectly conducting spheroid. An accurate treatment of the electromagnetic waves interaction with scatterers in uniform motion is based on the special relativity principle. In the object's frame the incident wave is assumed to have a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low-frequency approximation method is applicable to the scattering problem. For the near electromagnetic field we obtain the zeroth-order low-frequency coefficients, while in the far field we calculate the leading terms for the scattering amplitude and scattering cross-section. Finally, using the inverse Lorentz transform, we obtain the same approximations in the observer's frame. Copyright © 2006 John Wiley & Sons, Ltd.

Improvements to the Hybrid MoM-PO Technique for Scattering of Plane Wave by an Infinite Wedge

The combined method of moments (MoM)-physical optics (PO) approach proposed by Bilow fails in some cases. Based on the geometrical theory of diffraction (GTD), the uniform theory of diffraction (UTD) and the fundamental theory of electromagnetism, Bilow's diffracted current basis function is modified both within and outside the transition regions. The improved MoM-PO technique is validated by comparison with exact solutions for a right-angled perfectly conducting wedge at normal incidence. The analysis of an impedance wedge also yields accurate results that are in good agreement with available UTD results.

Scattering of Plane Waves by a Rigid Sphere in an Acoustic Quarterspace

The acoustic scattering by a submerged spherical rigid obstacle near an acoustically hard concave corner, which is insonified by plane waves at arbitrary angles of incidence, is studied. The formulation utilizes the appropriate wave-harmonic field expansions and the classical method of images in combination with the translational addition theorems for spherical wave functions to develop a closed-form solution in form of infinite series. The analytical results are illustrated by numerical examples where the spherical object is located near the rigid boundary of a fluid-filled quarterspace and is insonified by plane waves at oblique angles of incidence. Subsequently, the basic acoustic field quantities such as the form function amplitude, the scattered far-field pressure, and the scattered acoustic intensity are evaluated for representative values of the parameters characterizing the system. The limiting case involving a spherical object submerged in an acoustic halfspace is considered and good agreement with a well-known solution is established.

Scattering of Plane Waves at the Junction of Two Corrugated Half-Planes

In this paper, the boundary conditions given by Weinstein (1969) are employed to simulate two corrugated half-planes with the same slot height but different slot width. The scattering mechanism at the junction of these half-planes is investigated via the Fourier transform technique, which leads to two coupled Wiener–Hopf equations. The solution of the Wiener–Hopf system is obtained by the Daniele–Khrapkov method and some numerical results are presented about the analysis of the scattered field.

Scattering of plane waves by the junction of transmissive and soft-hard half-planes

A uniform asymptotic high frequency solution is developed for the diffraction of plane waves by the junction of two half-planes. One of the half-planes is assumed to be characterized by “Senior’s resistive-type” partially transmissive boundary conditions and the other is soft at the top and hard at the bottom. The related boundary-value problem is formulated as a matrix Wiener-Hopf equation which is solved explicitly through the Daniele-Khrapkov method. Some graphical results are also presented.

An Analytical Method of Auxiliary Sources Solution For Plane Wave Scattering By Impedance Cylinders — a Reference Solution For The Numerical Method of Auxiliary Sources

To facilitate the validation of the numerical Method of Auxiliary Sources an analytical Method of Auxiliary Sources solution is derived in this paper. The analytical solution is valid for transverse magnetic, and electric, plane wave scattering by circular impedance cylinders, and it is derived by transformation of the exact eigenfunction series solution. The transformation employs the Hankel function wave transformation to express the eigenfunction series of higher-order Hankel functions, with their singularities at the coordinate system origin, as a superposition of zero-order Hankel functions with their singularities at different positions away from the origin. The transformation necessitates a truncation of the wave transformation but the inaccuracy introduced hereby is shown to be negligible. The analytical Method of Auxiliary Sources solution is employed as a reference to investigate the accuracy of the numerical Method of Auxiliary Sources for a range of scattering configurations.

Scattering of plane wave from moving body underwater with finite impedance surface

An acoustic analogy model and numerical approach to predict propeller aircraft sound field have been developed to predict the scattering of incident plane wave by moving body with the surface of finite impedance. The scale rule of Mach number and Helmholtz number in the model was derived and demonstrated in the numerical experiments. Two types of check in numerical experiments illustrate the validity of the present model and the numerical approach developed in present paper. The effect of Helmholtz number and movement velocity has been discussed finally.

Scattering of electromagnetic plane waves by a buried vertical dike

The complete and exact solution of the scattering of a TE mode frequency domain electromagnetic plane wave by a vertical dike under a conductive overburden has been established. An integral representation composed of one-sided Fourier transforms describes the scattered electric field components in each one of the five media: air, overburden, dike, and the country rocks on both sides of the dike. The determination of the terms of the series that represents the spectral components of the Fourier integrals requires the numerical inversion of a sparse matrix, and the method of successive approaches. The zero-order term of the series representation for the spectral components of the overburden, for given values of the electrical and geometrical parameters of the model, has been computed. This result allowed to determine an approximate value of the variation of the electric field on the top of the overburden in the direction perpendicular to the strike of the dike. The results demonstrate the efficiency of this forward electromagnetic modeling, and are fundamental for the interpretation of VLF and Magnetotelluric data.

Scattering of plane wave by a 3D smooth convex impedance surface using physical theory of diffraction with transition currents

AbstractThis paper discusses a method of calculation that uses physical optics with transition currents for the scattering field produced when a plane wave illuminates a 3D smooth convex impedance surface. The high‐frequency technique is necessary for evaluating RCS of large objects with respect to wavelength, such as automobiles, and physical optics is a powerful approximation method. However, the evaluation of electromagnetic current is based on geometric optics and there has been a need to improve accuracy in diffraction areas in directions other than mirror reflection. The method proposed in this paper estimates electromagnetic current in a transition region from canonical problems. It is seen that calculation accuracy is greatly improved by considering the transition currents in a small area. This paper evaluates the transition current by using the Fock‐type current as the canonical problem for a smooth convex impedance surface and recognizes the effectiveness of this method of calculation through numerical calculation of these 2D or 3D convex objects. © 2001 Scripta Technica, Electron Comm Jpn Pt 1, 85(2): 30–40, 2002

Plane Wave Scattering By an Achiral Multilayered Sphere in an Infinitely Extended Chiral Host Medium - Abstract

An analytic solution to the problem of plane wave scattering by an achiral multilayered sphere in a host chiral medium is obtained in this paper. By applying the radiation-to-scattering transform, the scattering problem can be considered as the specific radiation problems where the radiated source equivalent to the electromagnetic plane wave is located at infinity. The volumetric currents which generate right circular polarization (RCP) and left circular polarization (LCP) plane waves, respectively, are found. An integral equation consisting the volumetric current distributions and the dyadic Green's functions is formulated to obtain both the equivalent incident wave fields and the scattered fields. Two-layered lossless and lossy dielectric spheres and a conducting sphere with a dielectric coated layer buried in an infinitely extended host chiral medium are considered and the expressions for the scattered fields in far-zone are found in explicit analytic form. The characteristics of scattered fields are illustrated and discussed in terms of the circular polarization degree and linear polarization degree against different chiral admittances and sizes.

Plane Wave Scattering by an Achiral Multilayered Sphere in an Infinitely Extended Chiral Host Medium

Plane Wave Scattering by an Achiral Multilayered Sphere in an Infinitely Extended Chiral Host Medium

Extinction theorem for object scattering in a stratified medium

A simple relation for the rate at which energy is extinguished from the incident wave of a far field point source by an obstacle of arbitrary size and shape in a stratified medium is derived from wave theory. This relation generalizes the classical extinction theorem, or optical theorem, that was originally derived for plane wave scattering in free space and greatly facilitates extinction calculations by eliminating the need to integrate energy flux about the obstacle. The total extinction is shown to be a linear sum of the extinction of each wave guide mode. Each modal extinction involves a sum over all incident modes that are scattered into the extinguished mode and is expressed in terms of the object’s plane wave scatter function in the forward azimuth and equivalent plane wave amplitudes of the modes. The only assumptions are that multiple scattering between the object and wave guide boundaries is negligible, and the object lies within a constant sound speed layer. Modal extinction cross sections of an object for the extinction of the individual modes of a wave guide are then defined. Calculations for a shallow water wave guide show that, after correcting for absorption loss in the medium, the modal cross section of an object for mode 1 in a typical ocean wave guide is very nearly equal to its free space cross section. This new extinction theorem may be applied to estimate the cross section of an object submerged in a wave guide from a measurement of its forward scattered field.

Extinction theorem for object scattering in a stratified medium

A simple relation for the rate at which energy is extinguished from the incident wave of a far-field point source by an obstacle of arbitrary size and shape in a stratified medium is derived from wave theory. This relation generalizes the classical extinction theorem, or optical theorem, that was originally derived for plane wave scattering in free space and greatly facilitates extinction calculations by eliminating the need to integrate energy flux about the obstacle. The total extinction is shown to be a linear sum of the extinction of each waveguide mode. Each modal extinction involves a sum over all incident modes that are scattered into the extinguished mode and is expressed in terms of the object’s plane wave scatter function in the forward azimuth and equivalent plane wave amplitudes of the modes. The only assumptions are that multiple scattering between the object and waveguide boundaries is negligible, and the object lies within a constant sound-speed layer. Calculations for a shallow-water waveguide show that the extinction cross section is highly dependent on measurement geometry, and medium stratification, as well as the scattering properties of the object and may be significantly modified by the presence of absorption in the medium.