- Oscillation conditions for unidirectional ring resonators containing cubic photorefractive crystals are analyzed. The coupling of pump beams to intracavity modes is presumed to occur via the vectorial two-beam coupling in the crystal. It is also presumed that the intracavity field as well as the pump field are composed of two orthogonally polarized components. The solution of slowly varying envelope wave equations in the degenerate and steady-state limit is used to determine the grating action and to derive threshold conditions for both the transmission and the reflection geometry of the wave-mixing process. A number of special cases of wave-mixing coupling constants is considered. Potential applications of two-wave mixing rings in different photorefractive devices, such as optical amplifiers, switches, and logic circuits are discussed. 1995 The American Physical Society.