AXISYMMETRICAL SPHERICAL-CAVITY RESONATOR .1. NORMAL-MODES

The problem of the normal modes of electromagnetic oscillations in a spherical-cavity resonator with axisymmetric interior and ideally conducting walls is solved. The method involves the construction of a complete set of solutions of the axisymmetric wave equation in spherical coordinates, a coordinate system in which the equation is not separable. Fitting the boundary conditions at the surface of the sphere results in an equation for the normal modes in the form of the roots of an infinite-dimensional determinant. The determinant is evaluated by the method of successive truncations. Numerical results are presented for the normal modes as a function of the dielectric asymmetry. The field lines for some of the lowest modes and selected choices of parameters are drawn.