Electromagnetic plane wave excitation of an open-ended conducting frustum
TL;DR: In this paper, a Chebyshev-Galerkin solution of the electric field integral equation for the surface current induced on a conducting frustum by an incident plane wave is presented.
Abstract: A Chebyshev-Galerkin solution of the electric field integral equation for the surface current induced on a conducting frustum by an incident plane wave is presented. The physically motivated mathematics takes proper account of the static singularity in the kernel function and of the edge conditions at both apertures, to yield complete and convergent current expansions. Coupling of the electromagnetic field into the tapered interior of the open scatterer can be substantial, even in electrically narrow cross sections, due to the focusing action of the conical transmission line. >
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TL;DR: In this article, an analytical regularization technique for rigorous solution of dual series equations in diffraction theory for structures, which consist of coaxial perfect (perfectly conducting, rigid or soft) conical sections, is proposed.
Abstract: [1] The analytical regularisation technique for rigorous solution of dual series equations in diffraction theory for structures, which consist of coaxial perfect (perfectly conducting, rigid or soft) conical sections, is proposed. The conical sections do not form biconical regions and the continuation of their generatrices has a single crossing point. The proposed approach is based on the mode matching technique as well as on establishing of the rule for correct transition to the infinite systems of linear algebraic equations and on receiving the solutions, which provide the fulfilment of all the necessary conditions for all the boundary value problems considered here: Neumann, Dirichlet, scalar electromagnetic problem. These systems are proved to be regularized by a pair of operators, which consist of the convolution type operator and the corresponding inverse one. The elements of the inverted operator are founded analytically using the factorization procedure for kernel functions for each boundary value problem. The peculiarities of the far field formation by one- and two-section cones in the case of their axially symmetric excitation by TM- electromagnetic wave are analyzed numerically.
16 citations
Cites methods from "Electromagnetic plane wave excitati..."
...[3] Some of the conical scatterers have been analyzed thus so far using a variety of different analytical asymptotical and numerical methods by Ufimtsev [1962], Northover [1965a, 1965b], Pridmore-Brown [1968], Senior and Uslenghi [1971], Bevensee [1973], Syed [1981], Eremin and Sveshnikov [1987], Goshin [1987], and Davis and Scharstein [1994] ....
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TL;DR: In this article, a Galerkin procedure using a Chebyshev polynomial basis with built-in edge condition behavior is used to construct a periodic array of finite-length conducting cylinders.
Abstract: Source-free and forced solutions for the electromagnetic fields in and around a periodic array of finite-length conducting cylinders are assembled from a Galerkin procedure using a Chebyshev polynomial basis with built-in edge-condition behavior. A localized source excites slow surface-waves under certain conditions on the electrical circumference and spacing of the tubular structure. These eigenmodes are the solutions to the homogeneous boundary value problem. A numerical search for the axial propagation constant that minimizes the smallest singular value of the governing Galerkin matrix provides the required dispersion relation.
5 citations
Cites background or methods from "Electromagnetic plane wave excitati..."
...Edgecondition behavior is anticipated by the Chebyshev polynomial expansions [3], for...
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...The mathematical statement and solution of the boundary value problem for the periodic arrangement of tubes is a modification of the method used in [3] for a single tube: The Fourier integral (in ) for the aperiodic geometry is replaced by a Fourier series of Floquet modes in the infinite array problem....
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17 Oct 2011
TL;DR: In this paper, a perfectly electrically conducting hollow cylindrical strip under horizontally and vertically polarized plane wave incidences is formulated by an electric field integro-differential mixed potential equation in order to apply corresponding analytical regularization.
Abstract: Electromagnetic diffraction by a perfectly electrically conducting hollow cylindrical strip under horizontally and vertically polarized plane wave incidences is formulated by an electric field integro-differential mixed potential equation in order to apply corresponding Analytical Regularization. This reduces the considered problem to solving a linear algebraic system of the second kind which provides the solution with arbitrary pre-determined accuracy limited by the available finite precision of the computer, owing it to the bounded condition numbers of mentioned systems in space l2.
Cites background from "Electromagnetic plane wave excitati..."
...1 INTRODUCTION A perfectly electrically conductive (PEC) hollow cylindrical strip S as in Figure 1, is a rather canonical geometry that electromagnetic (EM) wave diffraction from it has been subject to elaboration either by analytical approaches as in [1] and [2] or direct numerical ones as in [3]....
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References
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46,339 citations
9,185 citations
Book•
01 Jun 1961
TL;DR: In this paper, a revised version of the Revised edition of the book has been published, with a new introduction to the concept of plane wave functions and spherical wave functions, as well as a detailed discussion of the properties of these functions.
Abstract: Foreword to the Revised Edition. Preface. Fundamental Concepts. Introduction to Waves. Some Theorems and Concepts. Plane Wave Functions. Cylindrical Wave Functions. Spherical Wave Functions. Perturbational and Variational Techniques. Microwave Networks. Appendix A: Vector Analysis. Appendix B: Complex Permittivities. Appendix C: Fourier Series and Integrals. Appendix D: Bessel Functions. Appendix E: Legendre Functions. Bibliography. Index.
5,655 citations
Book•
01 Dec 1990
TL;DR: In this article, the fundamental field equations of wave propagation in homogeneous and layered media waveguides and cavities have been studied, including the effects of a dipole on the conducting earth, inverse scattering radiometry, and interferometry numerical techniques.
Abstract: Fundamental field equations waves in homogeneous and layered media waveguides and cavities Green's functions radiation from apertures and beam waves periodic structures and coupled mode theory dispersion and anisotropic media antennas, apertures and arrays scattering of waves by conducting and di-electric objects waves in cylindrical structures, spheres and wedges scattering of complex objects geometric theory of diffraction and low fequency techniques planar layers, strip lines, patches and apertures radiation from a dipole on the conducting earth, inverse scattering radiometry, noise temperature and interferometry numerical techniques.
1,050 citations