  A new set of vector solutions to Maxwell's equations based on solutions to
the wave equation in spheroidal coordinates allows laser beams to be described
beyond the paraxial approximation. Using these solutions allows us to calculate
the complete first-order corrections in the short-wavelength limit to
eigenmodes and eigenfrequencies in a Fabry-Perot resonator with perfectly
conducting mirrors. Experimentally relevant effects are predicted. Modes which
are degenerate according to the paraxial approximation are split according to
their total angular momentum. This includes a splitting due to coupling between
orbital angular momentum and spin angular momentum.
