Electromagnetic Eigenfrequencies in a Spheroidal Cavity (Calculation By Spheroidal Eigenvectors)

Abstract

The electromagnetic eigenfrequencies f_nsm in a perfectly conducting spheroidal cavity are determined analytically. The analytical determination is possible in the case of small values of h = d/(2a), (h « 1), where d is the interfocal distance of the spheroidal cavity and 2a the length of its rotation axis. In this case exact, closed-form expressions are obtained for the expansion coefficients g⁽²⁾ _nsm and g⁽⁴⁾ _nsm in the resulting relation f_nsm(h) = f_ns (0) [1 + h²g⁽²⁾ _nsm + h⁴g⁽⁴⁾ _nsm + O(h⁶)]. Analogous expressions are obtained with the use of the parameter v = 1- a²/b² (for |v| << 1) , where 2b is the length of the other axis of the spheroidal cavity. The electromagnetic field is expressed in terms of spheroidal eigenvectors. Numerical results are given for the lower-order modes.