Oppositely directed running waves in a ring laser saturate themselves and one another by population depletion. In addition, as the Doppler broadening decreases, they saturate one another by scattering off induced Bragg gratings in the medium, i.e., off spatial holes burned into the population difference. This increased coupling results in bistable operation near the atomic line center for Doppler-broadened media and for any equal tuning for stationary atoms.
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Hambenne et al. (1975) studied this question.
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