Precision closed-loop control of optical beam steering

Unlike in the microwave domain, where open loop phase control is adequate, a phased array antenna working at optical frequencies will require precise closed loop control of each element pixel to realize a well defined high brightness far-field antenna pattern. We describe and present experimental data for a design that permits precision, to < (lambda) /100, phase control with a high bandwidth that compensates for temperature, mechanical effects, delay times of each phase shift element, and non- linear response. Experimentally, the output of a phase measurement system is used in an electronic feedback loop to dynamically linearize an inherently non-linear liquid crystal. The experiment consisted of a spatial heterodyne, temporal homodyne, fiber optic Mach-Zehnder interferometer to recover phase of a single nematic liquid crystal element. The resulting phase measurement, represented as an analog voltage, is used in a feedback loop to correct for the non- linear drive voltage-to-phase retardance response of the liquid crystal. A demonstration of this technique using several periodic drive waveforms at frequencies of 10-100 Hz was performed. Data are presented showing a phase retardance resolution of < 1 nm which enabled a significant improvement in the linearity of the liquid crystal response.