Mr. Belic et al., SPATIOTEMPORAL EFFECTS IN DOUBLE-PHASE CONJUGATION, Journal of the Optical Society of America. B, Optical physics, 12(9), 1995, pp. 1602-1616
Spatial and temporal effects arising in photorefractive crystals durin
g the process of double phase conjugation are analyzed numerically wit
h a novel beam-propagation method. Slowly varying envelope wave equati
ons in the paraxial approximation are solved under the appropriate bou
ndary conditions. Our analysis includes dynamical effects caused by th
e buildup of diffraction gratings in the crystal and the turn-on of ph
ase-conjugate beams as well as spatial effects caused by the finite tr
ansverse spread of beams and by the propagation directions of the beam
s. Various phenomena are observed, such as self-bending of phase-conju
gate beams, convective flow of energy out of the interaction region, m
ode oscillations, critical slowing down at the oscillation threshold,
and irregular spatial pattern formation. For a real beam-coupling cons
tant and constructive interaction of interference fringes in the cryst
al we find steady or periodic behavior. For a complex coupling constan
t and/or induced phase mismatch in the grating a transition to spatiot
emporal chaos is observed. We believe that under stable operating cond
itions the transverse double phase-conjugate mirror in the paraxial ap
proximation is a convective oscillator, rather than an amplifier. Impr
oved agreement with experimental results is obtained.