Transverse modes of active hollow waveguide resonators

The effect of an active medium on the mode structure of a hollow waveguide resonator is investigated. A coupled-mode approach is employed. The field propagation through the resonator is described by a propagation matrix; thus, the solution is found by solving the generally nonlinear eigenvalue problem of the matrix for complete resonator round-trip. This has been performed numerically using an appropriate iteration procedure. The method was applied to duel-case I resonators. It was found that thermally induced refractive index profiles and, in the case of larger guide cross sections, the gain properties can also alter the mode structure significantly. These alterations influence the power gain coefficient as well as the conditions for single-transverse-mode operation