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We shall consider the scattering of a plane, linearly polarized monochromatic wave by a perfectly conducting prolate spheroid immersed in a homogeneous isotropic medium. Solution of the EM scattering by the oblate spheroid can be obtained by the transformations 5 --+ it and c --+ -ic. It is assumed that the surrounding medium is nonconducting and nonmagnetic. The geometry of the configuration is shown in Fig. 4.1, and the surface of the spheroid is given by | Spheroidal Wave Functions in Electromagnetic Theory Le-Wei Li Xiao-Kang Kang Mook-Seng Leong Copyright 2002 John Wiley Sons Inc. ISBNs 0-471-03170-4 Hardback 0-471-22157-0 Electronic _4 EM Scattering by a Conducting Spheroid 4.1 GEOMETRY OF THE PROBLEM We shall consider the scattering of a plane linearly polarized monochromatic wave by a perfectly conducting prolate spheroid immersed in a homogeneous isotropic medium. Solution of the EM scattering by the oblate spheroid can be obtained by the transformations and c ic. It is assumed that the surrounding medium is nonconducting and nonmagnetic. The geometry of the configuration is shown in Fig. 4.1 and the surface of the spheroid is given by c _ a _ a b 4.2 INCIDENT AND SCATTERED FIELDS Without loss of generality the direction of propagation of the linearly polarized monochromatic incident wave is assumed to be in the rr z-plane making an angle Oq with the z-axis as shown in Fig. 4.1. At an oblique incidence Oq 0 the polarized incident wave is resolved into two components the TE mode for which the electric vector of the incident wave vibrates perpendicularly to the x z-plane and the TM mode in which the electric vector lies in the x z-plane. Thus the plane-wave expressions for both modes are given by Ete ETEoye ikr 4.2a 89 90 EM SCATTERING BY A CONDUCTING SPHEROID Incident Wave 0o O X Fig. 4.1 Geometry of EM scattering by a conducting prolate spheroid. INCIDENT AND SCATTERED FIELDS 91 Etm Etmo x COS 6q z sin 0o e 4.2b where Eteo and Etmo are the amplitudes of the TE and TM fields respectively and k r fc xsin0o 4- zcos0o 4.3 with k being the wave number of the monochromatic radiation. Flammer 1 has obtained the plane-wave expansion in terms of prolate spheroidal wave functions as oo oo .n e- kr 2 52 52 Smn c cos0o SmnR l c cos in l 4.4 n mm 0 1Nmn -C where 7Vrnn c is the normalization constant given in Eq. 3.9 and em is the Neumann number 1 for m 0 and em 2 for m 0. For simplicity in what follows the .