Scholarly record
SCATTERING OF ELECTROMAGNETIC WAVES AND PREDICTION REMARKS REGARDING MINING
Abstract
A number of scattering and diffraction problems concerning semi infinite wave guides have been solved by many authors and for many years. Theoretical analysis of electromagnetic wave scattering and diffraction problems has been investigated extensively with regard to a number of scatterers which have physical and geometrical discontinuities. As is well-known, Sommerfeld introduced the exact solutions to the diffraction by a wedge by defining the idea of multiple-valued functions. His method is known as the Sommerfeld theory of diffraction which is commonly defined for diffraction by Wedge- Shaped obstacles. Wiener-Hopf showed that a certain singular integral equation could be solved exactly using the theory of Complex Fourier transforms and functions of a complex variable. This method of solution is known as the Wiener-Hopf technique. Multiple diffraction of electromagnetic waves due to physical and geometrical discontinuity is creating surface waves which are still dominant in communication phenomena. Surface waves and related currents are analyzed by using Wiener-Hopf technique in detail.
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References11
A.Sommerfeld, "Mathematische Theorie der Diffraction", Math. Ann., 47,1986,317-374.
N.Wiener and R.E. Paley, Fourier Transforms in the Complex Domain, American Mathematical Society, NY, 1934, 49-58.
W.Magnus, "Über die Beugung electromagnetische Wellen an einer Halbebene", ZPhys., Vol.117, 1941,168-179.
J.F. Carlson and A.E. Heins, "The reflection of an electromagnetic plane wave by an infinite set of plates, I", Quart. Appi. Math.,4, 1947, 313-329.
H.Levine and J. Schwinger, " On the radiation of sound from an unflanged circular pipe", Phys.Rev., 73, 1948, 338-406.
P.C.Clemmow, " A method for the exact solution of a class of two-dimensional diffraction problems", Proc.Roy.Soclondon, Ser. A, 205, 1951,286-308.
D.C. Jones, "A simplifying technique in the solution of a class of diffraction problems", Quart.J.Math.Oxford(2),3, 1952,189-196.
R.A. Hurd, "The Wiener-Hopf-Hilbert method for diffraction problems", CanJ.Phys., 54, 1976, 775-780.
E.Lüneburg and R.A.Hurd, "Diffraction by an infinite set of hard and soft parallel half planes", Can.J.Phys.,60, 1982,1-9, 1982.
M. idemen, "A new method to obtain exact solutions of vector Wiener-Hopf equations", ZAngew. Math.Mech., 59, 1979,656-658.
A.D. Rawlins and W.E. Williams, "Matrix Wiener-Hopf factorization", Quart J.Mech.Appl.Math., 34, 1981,1-8.
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