Theory of phase-conjugate oscillator applied to a phase-conjugate resonator

Abstract

Optical resonators containing a phaseconjugate mirror (PCM) have been a subject of great interest, especially for cases in which the PCM is employed as an end mirror of a resonator cavity for intracavity aberration correction.1 Recent theoretical analysis indicates that the insertion of a PCM inside a ring-laser cavity results in a reduction of the lock-in threshold and reduces the imbalance between the amplitudes of the oppositely directed travelling waves.2 We have developed a general theory for nondegenerate oscillations in a phase-conjugate oscillator (PCO) that consists of a Fabry-Perot cavity with a PCM as an intracavity element. The PCM is a nonlinear transparent medium pumped by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation with gain is possible for an injected signal of a slightly different frequency by nearly degenerate four-wave mixing (NDFWM). The linear absorption/gain in the medium is also taken into account. In this presentation, we apply the results of the general theory to a phase-conjugate resonator by equating the reflectivity of one of the conventional mirrors to zero. Analytic expressions are obtained for the two reflection coefficients and the two transmission coefficients of the injected signal, and the condition for oscillation is derived. A novel approach yields the mode spacing of such a phase-conjugate resonator.