Numerical study of transmissive liquid crystal Pancharatnam–Berry gratings with small periods

Abstract

Advances in patterning molecular orientations in liquid crystals have made possible the fabrications of various high-quality flat optical elements, ranging from gratings to beam shaping devices. These devices are based on modulating the Pancharatnam–Berry (PB) phase. It is well known that the diffraction efficiency for liquid crystal PB optical elements decreases for large diffraction angles. Here we study this issue using numerical simulations based on finite-difference time-domain algorithms and show that the optical efficiency formula commonly used for liquid crystal gratings deviates significantly from numerical results and is inaccurate for small grating periods because of its assumption that light beams do not diffract inside the liquid crystal films. We show that, for large diffraction angles, the polarization of the diffracted beam is generally elliptically polarized, and we further show that, by using liquid crystal materials with larger birefringence Δ n ∼ 0.4 , the diffraction efficiency for a grating period of 0.8 µm can go above 90%, which can be used for various flat optical elements with numerical aperture   ∼ 0.7 .