Plane-wave theory of nondegenerate oscillation in the linear photorefractive passive phase-conjugate mirror.

The observation of frequency-shifted phase-conjugate reflection in photorefractive passive (self-pumped) phase-conjugate mirrors1' 2 (PPCM's) has given rise to considerable efforts for its theoretical explanation. In this Letter we give a plane-wave theory of oscillation in the linear PPCM,3 compare it with the previously developed theory of detuning in the ring PPCM,2 and discuss the circumstances in which the plane-wave theory indicates the possibility of nondegenerate oscillation in these devices and in the cat PPCM.4 The linear PPCM consists of a photorefractive crystal enclosed by a linear oscillation cavity (Fig. 1). The signal beam, beam 4, passes through this crystal and pumps oscillation beams 1 and 2 between the cavity mirrors Ml and M2. These self-induced oscillation beams then pump the crystal as a phase-conjugate mirror (PCM) for beam 4 and produce beam 3, the phase-conjugate reflection. To examine the possibility of nondegenerate oscillation, we analyze the roundtrip phase sum requirements of oscillation in a linear resonator. The coupled-wave equations describing photorefractive four-wave mixing in the slowly varying field approximation for the transmission grating without linear absorption are