Einstein relations for gain-guided semiconductor lasers

The Einstein equations which relate the transition rates for stimulated emission, spontaneous emission and stimulated absorption in a laser active medium are re-examined for the special case of a semiconductor laser with complex wave-guiding. It is shown that, owing to the nonorthogonality of the gain-guided laser modes, the Einstein relations have to be modified. In particular, the spontaneous emission rate per laser mode no longer equals the stimulated emission rate per laser photon.