Pattern formation in a liquid-crystal light valve with feedback, including polarization, saturation, and internal threshold effects

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Abstract
The use of liquid-crystal light valves (LCLV’s) as nonlinear elements in diffractive optical systems with feedback leads to the formation of a variety of optical patterns. The spectrum of possible spatial instabilities is shown to be even richer when the LCLV’s capability for polarization modulation is utilized and internal threshold and saturation effects are considered. We derive a model for the feedback system based on a realistic description of the LCLV’s internal function and coupling to a polarizer. Thresholds of pattern formation are compared to the common Kerr-type approximation and show transitions involving rolls, squares, hexagons, and tiled patterns. Numerical and experimental results confirm our theoretical predictions and unveil how patterns and their typical length scales can be easily controlled by changes of the parameters.