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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.

Steady-state thermal blooming in perfectly conductive rectangular waveguides is described by the coupling between the Helmholtz equation and the diffusion equation without convection. The fields are pinned at the walls by Dirichlet and Neumann conditions and the temperature by Dirichlet conditions. The equations are solved by Green’s functions in a perturbation scheme employing the Born approximation. The first-order solutions indicate that only about 4% of the energy is transferred from the unperturbed mode, as defined by a constant index of refraction, to all the higher-order modes for moderate absorption.

The Stokes and anti-Stokes Raman-scattering equations with pump depletion are solved for focusing in rotationally symmetric geometry using a Gauss–Laguerre decomposition. This decomposition results in a mode-coupling matrix that is an integral over products of Laguerre polynomials. In order to evaluate this matrix, we use a recursive technique. Three examples are given that show Stokes and anti-Stokes extraction for Gaussian and annular input pump beams with confocal parameters equal to 3, 5, and 8 cm focused in the center of a 25-cm cell.