Cấu trúc sóng chức năng trong điện lý thuyết P5

EM Scattering by a Coated Dielectric Spheroid5.1 GEOMETRY OF THE PROBLEM In this chapter we consider the scattering of a linearly polarized plane monochromatic wave by a homogeneous lossy/lossless dielectric spheroid with a confocal lossy/lossless dielectric coating immersed in a homogeneous isotropic medium. It is assumed that the surrounding medium is nonconducting and nonmagnetic
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Cấu trúc sóng chức năng trong điện lý thuyết P5 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) 5 EM Scattering by a Coated Dielectric Spheroid5.1 GEOMETRY OF THE PROBLEMIn this chapter we consider the scattering of a linearly polarized plane mono-chromatic wave by a homogeneous lossy/lossless dielectric spheroid with aconfocal lossy/lossless dielectric coating immersed in a homogeneous isotropicmedium. It is assumed that the surrounding medium is nonconducting andnonmagnetic. Results are presented only for the prolate spheroids, as the re-sults for the oblate cases can be obtained by the transformations < --+ i116 EM SCATTERING BY A COATED DIELECTRIC SPHEROID Incident Wave $2 Wave Fig. 5.1 Scattering geometry of a coated spheroid. INCIDENT, TRANSMITTED AND SCATTERED FIELDS 117 62 c2 = -co* (5.lc) lr CO5.2 INCIDENT, TRANSMITTED AND SCATTERED FIELDSUnlike the case of the perfectly conducting spheroid, the existence of fieldsinside the dielectric spheroid makes the problem more complicated, and it isnecessary to use the magnetic fields in the boundary conditions. The magneticfield of a propagating wave is related to the electric field via H - &VxE, - (5 .2)where k is the wave number and 2 is the characteristic impedance of themedium. The incident electric fields for TE and TM polarizations are thesame as those of the conductor case, and the corresponding magnetic fieldsare 00 HTE = jETE0 MO coseo n=m x m=O (5.3a) HTM = (5.3b) n=m m=O The scattered fields are also derived in the same way as in the conductorcase, but a slight change in the notation of the scattering coefficients is nowmade: (5.4a) (5*4b) Ifor the TE case; and aM M+t4) &TM = mn *,m+l,ntCO) + PmM+l,n+l M$Z+l,n+l 00 M- M-c4) +>: Qcln oln CcO), (5.5a) n=l aM mn M- N-c4) (5.5b) %n oln (‘0)118 EM SCATTERUVG BY A COATED DIELECTRIC SPHEROIDfor the TM case. The transmitted fields inside the core (t < &) can be expressed as (5.6a)for the TE case, and E2t,TM = ...