EM Eigenfrequencies in a Spheroidal Cavity Computation of eigenfrequencies in EM cavities is useful in various applicat ions. However, analytical calculation of these eigenfrequencies is severely limited by the boundary shape of these cavities. In this chapter, the interior boundary value problem in a prolate spheroidal cavity with a perfectly conducting wall and axial symmetry is solved analytically. | 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 EM Eigenfrequencies in a Spheroidal Cavity INTRODUCTION Computation of eigenfrequencies in EM cavities is useful in various applications. However analytical calculation of these eigenfrequencies is severely limited by the boundary shape of these cavities. In this chapter the interior boundary value problem in a prolate spheroidal cavity with a perfectly conducting wall and axial symmetry is solved analytically. By applying Maxwell s equations to the boundary it is possible to obtain an analytical expression of the eigenfrequency fnso using spheroidal wave functions regardless of whether the parameter c is small or large. An inspection of the plot of a series of fnSQ values confirmed in 64 indicates that variation of fnso with the coordinate parameter is of the form nsO 0 ns 0 l 5 1 2 S 2 C4 5 3 6 I when c 18 smalL BY fitting the fnso evaluated onto an equation of its derived form the first four expansion coefficients g gW and g are determined numerically using the least squares method. The method used to obtain these coefficients is direct and simple although the assumption of axial symmetry may restrict its applications to those eigenfrequencies fnsmc where mf 0. 245 246 EM EIGENFREQUENCIES IN A SPHEROIDAL CAVITY THEORY AND FORMULATION Background Theory The prolate spheroidal body under consideration is shown in Fig. . In view of the fact that Mathematica handles only vector differential operations in the prolate spheroidal coordinates in accordance with the notations used in the book by Moon and Spencer 9 pp. 28 29 a temporary change of coordinates is necessarv. The new notation used is shown in Fie. . Fig. Geometry of the spheroidal cavity. As noted by Moon and Spencer 9 the vector Helmholtz equation is more complicated than the scalar counterpart and its .
