Eigenvalue density oscillations in separable microwave resonators

We study periodic orbit induced oscillations in the density of states for the electromagnetic eigenvalue problem in separable three-dimensional resonator geometries. The periodic orbit theory of Berry and Tabor [J. Phys. A 10, 371 (1977)] is adapted to the eigenvalue problem for the transverse electric and magnetic modes, respectively. Discrete symmetries give rise to next to leading order corrections, as is demonstrated in particular for cylinders with square and triangular cross sections. In particular, orbits with an odd number of reflections that do not contribute in leading order according to results of Balian and Duplantier [Ann. Phys. (N.Y.) 104, 300 (1977)] are shown to contribute in next to leading order.