Nonorthogonality of the longitudinal eigenmodes of a laser

Abstract
Recently Siegman has discussed how the nonorthogonality of the transverse eigenmodes of an open laser resonator can lead to an excess spontaneous-emission rate [Phys. Rev. A 39, 1253 (1989); 39, 1264 (1989)]. In the present paper we show how this treatment can be extended to also incorporate the case of nonorthogonality of the longitudinal eigenmodes. This is particularly relevant for a description of the spectral properties of lasers with large outcoupling, e.g., semiconductor lasers.