Theory of polariton parametric oscillator

A theory is developed of the steady-state emission of light due to the stimulated Raman scattering by polaritons in a plane-parallel optical resonator. The emission occurs at the Stokes frequency in the presence of traveling pump and polariton waves. Linear losses at the pump and Stokes wave frequencies are not restricted in any way; a strong absorption is assumed in the polariton region. It is also assumed that one longitudinal Stokes mode with a homogeneous transverse structure is excited. Expressions are obtained for the description of the stimulated radiation field and for the fall of the intensity of the pump wave in the course of its propagation in the resonator. Formulas are also obtained for the power of the Stokes radiation emerging from the resonator. The resonator parameters (reflection coefficients of the mirrors) are optimized so as to achieve the maximum stimulated emission power from a resonator of fixed length and a nonlinear crystal of fixed parameters. It is shown that the eigenfrequency spectrum of steady-state emission differs from the spectrum of an empty resonator and this difference increases with the wave mismatch and with linear losses. The analytic formulas are illustrated by numerical calculations.