Theory of self-frequency detuning of oscillations by wave mixing in photorefractive crystals.

Interesting experimental findings of self-frequencydetuning effects of phase-conjugate mirrors (PCM's) were reported recently. 1-3 A dye laser in conjunction with a passive (self-pumped) phase-conjugate mirror (PPCM) caused an unexplained self-frequency scanning of the laser.1' 2 Another system of a cavity formed by two PCM's also demonstrated a nondegenerate oscillation. 3 Recently4 we presented a first theory that explains the self-frequency-shift properties of the ring PPCM and discussed its meaning as a new type of active interferometry with applications to optical sensors such as gyroscopes. In this Letter we present a general study of the frequency-detuning properties of various oscillators with photorefractive crystals. The results also suggest possible causes for detuning in the PPCM used in self-scanning experiments1' 2 but do not establish the mechanism conclusively; this will be done in further experimental work. Figures 1(a)-i(d) describe the oscillators discussed in this work. In the past5' 6 these oscillators were analyzed with the assumption of degenerate frequencies. However, the consideration of complex amplitudes with the phases of the beams in the cavity plus the crystal dictates a detuning of the mixing beams. The phase contribution of the induced moving gratings written by these beams is an essential ingredient. It is due to the detuning dependence of the complex coupling constant or of two mixing beams detuned by 6 in a photorefractive crystal 4' 5: