Electromagnetic eigenfrequencies in a spheroidal cavity

The electromagnetic eigenfrequencies f(nsm) in a perfectly conducting spheroidal cavity are determined analytically, by a shape perturbation method. The analytical determination is possible in the case of small values of the quantity v = 1 - a(2)/b(2), (\v\ <much less than 1), where 2a and 2b are the lengths of the rotation axis and the other axis of the spheroidal cavity, respectively. In this case, exact, closed-form expressions are obtained for the expansion coefficients ((1)(gnsm)) and ((2)(gnsm)) in the resulting relation f(nsm)(v) = f(ns)(0)[1 + vg(nsm)((1)) + v(gnsm)(2)((2)) + O(v(3))]. There is no need for using any spheroidal eigenvectors in our solution. The electromagnetic field is expressed in a series of spherical eigenvectors, while the equation of the spheroidal boundary is given in terms of the spherical coordinates. Numerical results are given for the eigenfrequencies of the lower-order magnetic and electric modes.