O. Frank et B. Eckhardt, EIGENVALUE DENSITY OSCILLATIONS IN SEPARABLE MICROWAVE RESONATORS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(4), 1996, pp. 4166-4175
We study periodic orbit induced oscillations in the density of states
for the electromagnetic eigenvalue problem in separable three-dimensio
nal 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 sym
metries give rise to next to leading order corrections, as is demonstr
ated in particular for cylinders with square and triangular cross sect
ions. In particular, orbits with an odd number of reflections that do
not contribute in leading order according to results of Balian and Dup
lantier [Ann. Phys. (N.Y.) 104, 300 (1977)] are shown to contribute in
next to leading order.