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An analysis of laser action in a periodic structure is presented. A model of two counter-running waves coupled by backward Bragg scattering is used. The resonant frequencies and threshold criteria for the modes of oscillation have been determined for both index and gain periodicities. Analytical approximations are given for both the high- and low-gain cases, and computational results for the intermediate regimes.
Kogelnik et al. (Mon,) studied this question.