Electromagnetic eigenfrequencies in a spheroidal cavity (calculation by spheroidal eigenvectors)

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 much less than 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(nsm)((2)) and g(nsm)((4)) in the resulting relation f(nsm)(h) = f(ns)(0) [1 + h(2) g(nsm)((2)) +h(4) g(nsm)((4)) + O(h(6))]. Analogous expressions are obtained with the use of the parameter v = 1 - a(2)/b(2) (for \v\ much less than 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.