Multiple scattering by a linear array of conducting spheres

1990 ◽  
Vol 68 (10) ◽  
pp. 1157-1165 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Multiple Scattering ◽  
Cross Sections ◽  
Linear Array ◽  
Plane Electromagnetic Wave ◽  
Spherical Wave ◽  
Approximate Solutions ◽  
Addition Theorem ◽  
Wave Functions ◽  
Coordinate Systems ◽  
Conducting Spheres

The problem of multiple scattering of a plane electromagnetic wave incident on N closely spaced perfectly conducting spheres is solved analytically by expanding the incident and scattering fields in terms of an appropriate set of vector spherical wave functions. To impose the boundary conditions, the scattered field from one sphere is expressed in coordinate systems attached to the others by using the translation addition theorem. An approximate solution is obtained to solve for the scattering by N small spheres. Numerical results for the normalized backscattering and bistatic cross sections for systems of spheres show that the agreement between the analytic and approximate solutions is better for larger electrical distances between neighbouring spheres.

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

The Scattering Waves by Two Spheres in Solid

2013 ◽  
Vol 423-426 ◽  
pp. 1640-1643
Author(s):  
Yan Ru Zhang ◽  
Pei Jun Wei
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Spherical Wave ◽  
Addition Theorem ◽  
Wave Functions ◽  
Interface Condition ◽  
Elastic Sphere ◽  
Numerical Examples ◽  
Transmitted Waves ◽  
Expansion Coefficients

The scattering waves by two elastic spheres in solid are studied. The incident wave, the scattering waves in the host and the transmitted waves in the elastic spheres are all expanded in the series form of spherical wave functions. The total waves are obtained by addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the solid host. The scattering cross section is computed as numerical examples.

scholarly journals SCALAR WAVES IN A WORMHOLE TOPOLOGY

2006 ◽  
Vol 15 (05) ◽  
pp. 669-693 ◽  
Author(s):  
NECMI BUĞDAYCI
Keyword(s):  
Wave Equation ◽  
Multiple Scattering ◽  
Infinite Series ◽  
Spherical Wave ◽  
Wave Functions ◽  
Scattering Method ◽  
Explicit Solutions ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Multiple Scattering Method

Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions (2+1) and (3+1). The solutions are in the form of infinite series involving cylindrical and spherical wave functions, and they are elucidated by the multiple scattering method. Explicit solutions for some limiting cases are illustrated as well. The results presented in this work constitute instances of solutions of the scalar wave equation in a space–time admitting closed time-like curves.

An addition theorem for spherical wave functions

1982 ◽  
Vol 35 (11) ◽  
pp. 353-357
Author(s):  
L. Ronchi ◽  
S. Barbarino ◽  
P. Grasso ◽  
G. Guerriera ◽  
F. Musumeci ◽  
...  
Keyword(s):  
Spherical Wave ◽  
Addition Theorem ◽  
Wave Functions

Electromagnetic scattering by an arbitrary configuration of dielectric spheres

1990 ◽  
Vol 68 (12) ◽  
pp. 1419-1428 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Cross Sections ◽  
Electromagnetic Scattering ◽  
Plane Electromagnetic Wave ◽  
Linear Equations ◽  
Spherical Wave ◽  
Expansion Method ◽  
Multipole Expansion ◽  
Arbitrary Configuration ◽  
Multipole Expansion Method ◽  
Dielectric Spheres

An analytic solution is obtained for the problem of plane electromagnetic-wave scattering by an arbitrary configuration of N dielectric spheres. The multipole expansion method is employed, and the boundary condition is imposed using the translational addition theorem for vector spherical wave functions. A system of simultaneous linear equations is given in matrix form for the scattering coefficients. An approximate solution, which has been developed and employed by the authors for the scattering by N conducting spheres, is extended to the dielectric spheres case. Plots for the normalized backscattering, bistatic, and forward-scattering cross sections are presented over wide ranges of permittivity, size, and electrical separations between the neighbouring spheres. The results show a reduction in the normalized backscattering and bistatic cross sections for certain choices of permittivity relative to conducting arrays of spheres of the same dimensions and separations.

scholarly journals Two-Dimensional Scattering by a Homogeneous Gyrotropic-Type Elliptic Cylinder

2016 ◽  
Vol 5 (3) ◽  
pp. 106
Author(s):  
A. K. Hamid ◽  
F. Cooray
Keyword(s):  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Separation Of Variables ◽  
Elliptic Cylinder ◽  
Wave Functions ◽  
Two Dimensional ◽  
Vector Wave ◽  
Expansion Coefficients ◽  
Scattering Cross Sections ◽  
Uniform Plane

The separation of variables procedure has been employed for solving the problem of scattering from an infinite homogeneous gyrotropic-type (G-type) elliptic cylinder, when a uniform plane electromagnetic wave perpendicular to its axis, illuminates it. The formulation of the problem involves expanding each electric and magnetic field using appropriate elliptic vector wave functions and expansion coefficients. Imposing suitable boundary conditions at the surface of the elliptic cylinder yields the unknown expansion coefficients related to the scattered and the transmitted fields. To demonstrate how the various G-type materials and the size of the cylinder affects scattering from it, plots of scattering cross sections are given for cylinders having different permittivity/permeability tensors and sizes.

Diffraction of a plane electromagnetic wave by a parallel plate grating with dielectric loading: the case of transverse magnetic incidence

1985 ◽  
Vol 63 (4) ◽  
pp. 453-465 ◽  
Author(s):  
Kazuya Kobayashi
Keyword(s):  
Cross Sections ◽  
Parallel Plate ◽  
Plane Electromagnetic Wave ◽  
Approximate Solutions ◽  
Transverse Magnetic ◽  
Transform Domain ◽  
Wave Scattering And Diffraction ◽  
Decomposition Procedure ◽  
Dielectric Loading ◽  
The Fourier Transform

Wave scattering and diffraction problems concerning objects with complex cross sections have been widely investigated so far with the advance of electronic computers. In this paper, a periodically placed parallel plate grating with dielectric loading is considered, and the problem of diffraction of a TM polarized plane wave is analyzed with the aid of the Wiener–Hopf technique. Introducing the Fourier transform pair for the unknown scattered field and applying boundary conditions in the transform domain, one can formulate this problem as the single Wiener–Hopf equation. This functional equation is then solved by a decomposition procedure and a rigorous solution is obtained. Furthermore, approximate solutions are derived by applying the modified residue calculus technique. Based on the above analysis, several numerical examples are given and the characteristics of this grating are discussed.

Analysis of STEM micrographs of thick objects

1978 ◽  
Vol 36 (2) ◽  
pp. 106-107
Author(s):  
S. Golladay
Keyword(s):  
Inelastic Scattering ◽  
Multiple Scattering ◽  
Mass Distribution ◽  
Cross Sections ◽  
Phase Contrast ◽  
Image Point ◽  
Contrast Effects ◽  
Total Cross Sections ◽  
Elastic And Inelastic Scattering

The theory of multiple scattering has been worked out by Groves and comparisons have been made between predicted and observed signals for thick specimens observed in a STEM under conditions where phase contrast effects are unimportant. Independent measurements of the collection efficiencies of the two STEM detectors, calculations of the ratio σe/σi = R, where σe, σi are the total cross sections for elastic and inelastic scattering respectively, and a model of the unknown mass distribution are needed for these comparisons. In this paper an extension of this work will be described which allows the determination of the required efficiencies, R, and the unknown mass distribution from the data without additional measurements or models. Essential to the analysis is the fact that in a STEM two or more signal measurements can be made simultaneously at each image point.

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