Stability in a Raman ring resonator is studied by using the adiabatic approximation. The analysis is based on far-off resonance Raman scattering in hydrogen. A medium-power approximation is employed, which is good for intensities less than 30 MW/cm2. The resulting differential equations retain their standard low-power Raman gain dependance in addition to an intensity-dependent phase. The steady-state intensity input–output behavior, as well as the linear stability analysis, is accomplished analytically without invoking the mean-field approximation. Feedback is applied to the Stokes beam, a gain situation, or to the depleted pump beam. The Stokes frequency is assumed to be perfectly tuned to the atomic and cavity resonances. It is shown that both situations are multistable and that the power-dependent phase largely determines the stability characteristics. Furthermore, we show that the negative slope branches can be stable when feedback is applied to the pump if the output pump intensity is decreasing with increasing input pump intensity.
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