Scattering of a Gaussian beam by an anisotropic-coated eccentric conducting circular cylinder

2020 ◽  
Vol 12 (9) ◽  
pp. 900-905
Author(s):  
Shi-Chun Mao ◽  
Zhen-Sen Wu ◽  
Zhaohui Zhang ◽  
Jiansen Gao ◽  
Lijuan Yang
Keyword(s):  
Gaussian Beam ◽  
Plane Waves ◽  
Approximate Expression ◽  
Transverse Magnetic ◽  
Addition Theorem ◽  
Electric Polarization ◽  
Electric Conductor ◽  
Solution Convergence ◽  
Local Coordinates ◽  
Scattered Fields

AbstractA solution to the problem of Gaussian beam scattering by a circular perfect electric conductor coated with eccentrically anisotropic media is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with Taylor's series. The transmitted field in the anisotropically coated region is expressed as an infinite summation of Eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The addition theorem for cylindrical functions is applied to transfer from the local coordinates to the global ones. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting a similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the eccentric geometry comes to the concentric one.

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder

2017 ◽  
Vol 9 (10) ◽  
pp. 1925-1929 ◽  
Author(s):  
Shi-Chun Mao ◽  
Zhen-Sen Wu ◽  
Zhaohui Zhang ◽  
Jiansen Gao
Keyword(s):  
Circular Cylinder ◽  
Gaussian Beam ◽  
Approximate Expression ◽  
Wave Functions ◽  
Two Dimensional ◽  
Beam Source ◽  
Electric And Magnetic Fields ◽  
Scattered Fields ◽  
Wave Incidence ◽  
Taylor’S Series

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression with Taylor's series. The transmitted field in the homogeneous gyrotropic cylinder is expressed in terms of the series of wave functions based on the integral equation. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions of continuous tangential electric and magnetic fields. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.

scholarly journals Modified Theory of Physical Optics Approach to Diffraction by an Interface between PEMC and Absorbing Half-Planes

2021 ◽  
Vol 10 (2) ◽  
pp. 78-84
Author(s):  
Y. Z. Umul
Keyword(s):  
Plane Waves ◽  
Wave Number ◽  
Physical Optics ◽  
Magnetic Conductor ◽  
Electric Conductor ◽  
Perfect Magnetic Conductor ◽  
Scattered Fields ◽  
Electromagnetic Plane Waves ◽  
Modified Theory ◽  
Electromagnetic Plane

The scattering of electromagnetic plane waves by an interface, located between perfect electromagnetic conductor and absorbing half-planes is investigated. The perfect electromagnetic conductor half-plane is divided into perfect electric conductor and perfect magnetic conductor half-screens. The same decomposition is done for the absorbing surface. Then four separate geometries are defined according to this approach. The scattered fields by the four sub-problems are obtained with the aid of the modified theory of physical optics. The resultant scattering integrals are combined in a single expression by using key formulas, defined for the perfect electromagnetic conductor and absorbing surfaces. The scattering integral is asymptotically evaluated for large values of the wave-number and the diffracted and geometric optics fields are obtained. The behaviors of the derived field expressions are analyzed numerically.

scholarly journals Ultrasonic Scattered Field Distribution of One and Two Cylindrical Solids with Phased Array Technique

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Xiaozhou Liu ◽  
Jian Ma ◽  
Haibin Wang ◽  
Sha Gao ◽  
Yifeng Li ◽  
...  
Keyword(s):  
Plane Wave ◽  
Field Distribution ◽  
Scattered Field ◽  
Phased Array ◽  
Simulation Analysis ◽  
Plane Waves ◽  
Theoretical Solution ◽  
Steel Matrix ◽  
Field Distributions ◽  
Scattered Fields

AbstractThe scattered fields of plane waves in a solid from a cylinder or sphere are critical in determining its acoustic characteristics as well as in engineering applications. This paper investigates the scattered field distributions of different incident waves created by elastic cylinders embedded in an elastic isotropic medium. Scattered waves, including longitudinal and transverse waves both inside and outside the cylinder, are described with specific modalities under an incident plane wave. A model with a scatterer embedded in a structural steel matrix and filled with aluminum is developed for comparison with the theoretical solution. The frequency of the plane wave ranged from 235 kHz to 2348 kHz, which corresponds to scaling factors from 0.5 to 5. Scattered field distributions in matrix materials blocked by an elastic cylindrical solid have been obtained by simulation or calculated using existing parameters. The simulation results are in good agreement with the theoretical solution, which supports the correctness of the simulation analysis. Furthermore, ultrasonic phased arrays are used to study scattered fields by changing the characteristics of the incident wave. On this foundation, a partial preliminary study of the scattered field distribution of double cylinders in a solid has been carried out, and the scattered field distribution at a given distance has been found to exhibit particular behaviors at different moments. Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

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.

scholarly journals Solutions of the Relativistic Two-Body Problem. II. Quantum Mechanics

1972 ◽  
Vol 25 (2) ◽  
pp. 141 ◽  
Author(s):  
JL Cook
Keyword(s):  
Bound States ◽  
Free Particle ◽  
Plane Waves ◽  
Addition Theorem ◽  
Partial Wave Analysis ◽  
Harmonic Oscillator Potential ◽  
Two Body Problem ◽  
Probability Densities ◽  
Square Well ◽  
Potential Harmonic

This paper discusses the formulation of a quantum mechanical equivalent of the relative time classical theory proposed in Part I. The relativistic wavefunction is derived and a covariant addition theorem is put forward which allows a covariant scattering theory to be established. The free particle eigenfunctions that are given are found not to be plane waves. A covariant partial wave analysis is also given. A means is described of converting wavefunctions that yield probability densities in 4-space to ones that yield the 3-space equivalents. Bound states are considered and covariant analogues of the Coulomb potential, harmonic oscillator potential, inverse cube law of force, square well potential, and two-body fermion interactions are discussed.

Bandwidth Control of Loop Type Frequency Selective Surfaces Using Dual Elements in Various Arrangements

2021 ◽  
Author(s):  
Nickolas Littman ◽  
Steven G. O'Keefe ◽  
Amir Galehdar ◽  
Hugo G. Espinosa ◽  
David V. Thiel
Keyword(s):  
Stop Band ◽  
Transverse Magnetic ◽  
Electric Polarization ◽  
Capacitive Coupling ◽  
Electromagnetic Properties ◽  
Frequency Selective Surfaces ◽  
Simple Loop ◽  
Bandwidth Control ◽  
Frequency Selective ◽  
The Individual

Abstract Frequency-selective surfaces (FSSs) have applications across multiple disciplines due to their unique electromagnetic properties. This paper investigates the use of both rounded square loops (RSLs), and simple loop type dual elements arranged in unique patterns, to control the transmission and reflection bandwidth and resonant frequencies over KU and K frequency bands supported by equivalent circuit models (ECMs). The FSSs were fabricated using laser engraving to create conductive loop type elements on a thin, flexible and optically transparent Mylar substrate (relative permittivity of 2.7 and thickness of 65m). The frequency response of the surfaces are controlled through the element self-inductance and capacitive coupling with neighbouring elements. This work shows that different arrangements result in the formation of multiple distinct resonances. The theoretical and experimental results were in good agreement where rounded squares and dual element arrays were employed to create broadband and multiband band-stop FSSs. A polarization sensitive surface exhibited stop-bands at 12GHz and 16GHz in transverse electric polarization and a stop-band at 14.4GHz in transverse magnetic polarization. This technique can be applied to any periodic array through careful selection of the individual elements in the array, as well as their arrangement.

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

2021 ◽  
Author(s):  
Leonid I. Goray
Keyword(s):  
Plane Wave ◽  
Wave Diffraction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Transverse Magnetic ◽  
Incident Field ◽  
Boundary Integral ◽  
Cylindrical Waves ◽  
Plane Wave Diffraction

Abstract The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

FINITE ELEMENT ANALYSIS OF TE AND TM MODES IN NONLINEAR PLANAR WAVEGUIDES

1994 ◽  
Vol 03 (01) ◽  
pp. 101-116 ◽  
Author(s):  
M. ZOBOLI ◽  
S. SELLERI
Keyword(s):  
Finite Element ◽  
Refractive Index ◽  
Transverse Magnetic ◽  
Planar Waveguides ◽  
Mode Analysis ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Transverse Magnetic Mode ◽  
Solution Convergence ◽  
Index Distribution

A general approach based on the finite element method for analyzing optical waves guided by dielectric planar waveguides with arbitrary nonlinear media and with arbitrary refractive index distribution is considered. A complete transverse-electric and transverse-magnetic mode analysis is presented and TM polarization solutions are obtained without approximations on the biaxial nature of the nonlinear refractive index. Solution convergence and stability is discussed and both film-guided and surface-guided modes are presented for symmetrical and asymmetrical structures. Bistability and hysteresis phenomena have been investigated for TE as well as for TM modes.

scholarly journals UNIFORM ANALYTIC SCATTERED FIELDS OF A PEC PLATE ILLUMINATED BY A VECTOR PARAXIAL GAUSSIAN BEAM

2009 ◽  
Vol 14 ◽  
pp. 203-217 ◽  
Author(s):  
Julien Hillairet ◽  
Jérôme Sokoloff ◽  
Sylvain Bolioli
Keyword(s):  
Gaussian Beam ◽  
Scattered Fields
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