Analytically and numerically we analyze a novel nonlinear system, feedback-controlled photorefractive beam coupling. This system, being experimentally realized, keeps diffractivity of the recorded photorefractive grating near 1 or 0 within a wide range of crystal thickness and pump ratio. Inertia of the electronic feedback loop is shown to be a crucial element of the permanent operation. Typically, the feedback system has no steady state. We have found a wealth of periodic and quasi-periodic regimes (and transitions between them) for observable characteristics of the feedback-controlled beam coupling. In many respects the found behaviour is new for nonlinear systems. A good qualitative agreement between theory and experiment is obtained for LiNbO_3 crystals.
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