Oblique incidence effect on steering efficiency of liquid crystal polarization gratings used for optical phased array beam steering amplification

A liquid crystal polarization grating (LCPG) is proposed that amplifies the steering angle of a liquid crystal optical phased array for non-mechanical beam steering, taking advantage of its high steering efficiency under normal incidence. However, oblique incidence may play an important role in the overall steering efficiency. The effect of oblique incidence on steering efficiency of a LCPG was analyzed by numerically solving the extended Jones matrix and considering propagation crosstalk. The results indicate that the outgoing laser beam is amplitude-modulated under the effect of oblique incidence and behaves as a sinusoidal-modulated amplitude grating, which diffracts certain energies to non-blazed orders. Over-oblique incidence may even eliminate the steering effect of the incident beam. The modulation depth of the induced amplitude grating was found to be proportional to the product of sinusoidal value of oblique incidence angle and the LC layer thickness, and inversely proportional to the periodic pitch length of the LCPG. Both in-plane incidence and out-of-plane incidence behave similarly to influence the steering efficiency. Finally, the overall steering efficiency for cascaded LCPGs was analyzed and a difference of up to 11 % steering efficiency can be induced between different LCPG configurations, even without considering the over-oblique incidence effect. Both the modulation depth and final steering efficiency can be optimized by varying the LC birefringence and layer thickness.