Fig. 1. （a）Schematic diagram of circular polarization holography；（b）Liquid crystal polarization grating；（c）Incidence of linearly polarized light onto the liquid crystal polarization grating that does not meet the half-wave condition；（d）Incidence of circularly polarized lights onto the liquid crystal polarization grating that perfectly meets the half-wave condition.

Fig. 2. （a）Schematic illustration of a large-aperture polarization hologram setup based on Mach-Zendel interference；（b）Practical optical path.

Fig. 3. （a）Schematic illustration of a large-aperture polarization hologram setup based on conventional double-beam interference；（b）Practical optical path.

Fig. 4. （a）Polarizing microscope image of liquid-crystal-based polarization gratings（633 nm)；（b）Polarizing microscope image of liquid-crystal-polymer-based polarization gratings（1 064 nm)；（c）Photographs of the fabricated liquid-crystal-polymer-based polarization grating（1 064 nm)；（d）Diffraction efficiency and diffraction angle test data and grating equation curves for polarization grating（1 064 nm)；（e）Flexible polarization grating；（f）White light diffraction of the sample.

Fig. 5. （a）Optical setup for fast optical beam steering；（b）Orientations of liquid crystal director with opposite polarity voltage and its corresponding mcrographs of FLC half wave plate；（c）Practical smaple；（d）Diffraction patterns；（e）Waveform of 500 Hz square wave（top）with a driving voltage of 20 V. Switching responses of -1st order（middle）and -2st order（bottom）. The scale bar is 100 μm.