Dynamics of feedback controlled photorefractive beam coupling

Abstract

We investigate theoretically and experimentally the operation of a nonlinear system, feedback controlled photorefractive beam coupling. It is shown that the feedback equations used earlier $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ phase shift between the diffracted and transmitted beam components) are satisfactory only during a relatively short initial stage of development. We have generalized these equations by taking into account the inertia inherent in any real feedback loop. The inertial feedback equations ensure the permanent operation of the nonlinear system and lead to a variety of periodic and quasiperiodic regimes. We investigate the distinctive features of these regimes and transitions between them for moderately thick crystals. Good qualitative agreement between theory and experimental data is obtained for ${\mathrm{LiNbO}}_{3}$ crystals.