Numerical optimization of the performance of nematic liquid crystal optical phased arrays

In a one-dimensional liquid crystal optical phased array (LCOPA), a liquid crystal layer is electrically addressed by an array of long, narrow electrodes. A spatially periodic voltage profile can be applied to the electrodes in order to induce a sawtooth-shaped index of refraction variation in the liquid crystal layer that will steer an optical beam in a fashion analogous to that of a blazed diffraction grating. Because of non-ideal device behavior, measured phase vs. voltage data cannot be used to predict the control voltages necessary to achieve efficient steering. This paper presents a simple application of optimization to determine the appropriate voltages for every electrode in order to optimize the steering efficiency. Experimental results show that this approach can quickly determine optimal voltages for a desired far field diffraction pattern. Steering efficiency improvements of over 100 percent are obtained as compared to open loop device calibration.