Theory of nonlinear steady states of a parametric ring oscillator

The three-dimensional nonlinear steady states of a parametric ring SBS oscillator are determined. A classification of the oscillator scattering modes is presented, and the fundamental-mode stability is analyzed. It is demonstrated that this mode is stable near the excitation threshold. For pump beam intensities which greatly exceed the threshold value, the fundamental mode is unstable with respect to distortion of the spatial distribution of the intensity of the interacting light beams as well as with respect to the phase distortions of their wave fronts. The instability regions are found to be different for the two cases.