Recently, diverse twisting structures have been discovered to be a potential approach to design liquid crystal polarization gratings and lenses (LCPGs and LCPLs) with a high diffraction efficiency, broad bandwidth, wide view, and large diffraction angle. In this review, we divide these twisting structures into two main types, namely, multi-layer twisting structures with phase compensation and twisting structures forming Bragg diffraction. We found that multi-layer twisting structure LCPGs and LCPLs presented a broader bandwidth and a wider view angle by phase compensation. While for transmissive or reflective Bragg LCPGs, a large diffraction angle with high diffraction efficiency could be achieved. Based on the theoretical analysis in the review, potential research directions on novel twisting structures were prospected.

We introduce and demonstrate a switchable novel linear polarization grating (LPG) consisting of a circular polarization grating (CPG) and a special cycloidal diffractive quarter waveplate (CQWP). The CQWP is developed that marvelously matches the polarization-state of beams passing through the CPG. Such an LPG is so polarization-sensitive that it can split an incident linear polarized beam into two proportionally controllable left- or right-handed circularly polarized lights. We establish rigorous simulation model based on finite element method to investigate near-field polarization-state distribution of CPGs. Furthermore, LPGs are demonstrated and the diffraction properties are obtained with simulation and Jones Matrix analysis. The combination of CPGs and CQWPs is achieved with polymerizable liquid crystal. The experimental results of deflection angle and polarization selectivity of LPGs are consistent with those of simulation.

Sub-aperture coherence (SAC) is a classical phase control method for high-precision beam steering using liquid crystal optical phased arrays (LCOPA). On this basis, radial sub-aperture coherence (RSAC) and symmetrical radial sub-aperture coherence (SRSAC) were proposed, which guarantee the stability of steering angles when the beam aperture and incident position fluctuate. In this article, the pre-existing one-dimensional SRSAC was firstly extended to a more universal 2D phase generation algorithm. Meanwhile, for the intractable problem of local precision defects caused by the basic two-dimensional variable period grating (2D-VPG) algorithm, we tracked their locations accurately and designed a targeted elimination method carefully. So these remarkable error peaks could be thoroughly removed by using 2D-SRSAC optimized by the local precision defect elimination method. Since then, all the excellent performance of 1D-SRSAC can be perfectly transplanted to 2D, which makes the non-mechanical beam steering technology using LCOPA more mature and competitive in the applications required ultra-high precision.

We introduce and demonstrate a new structure of polarisation grating which can substantially enlarge the deflection angle. We derive the polarisation state of a beam passing through the reflective composite polarisation grating by Jones matrix and build a rigorous simulation about the deflection angle of reflective composite polarisation grating using finite-element analysis. The theoretical diffraction efficiency of the reflective composite polarisation grating can reach up to 90%. The experimental result of deflection angle of the reflective composite polarisation grating is consistent with that of simulation. The reflective composite polarisation grating could be expected to be applied in augment reality system, spectroscopy, optical telecommunications, non-mechanical beam steering and so on. Graphical abstract

The incidence angle of a beam entering a liquid crystal variable retarder (LCVR) and the liquid crystal polarization grating (LCPG) is greater when the LCPG is utilized in the quadrature cascade, which reduces the diffraction efficiency. Therefore, this study investigates the best method for controlling a cascaded LCPG. By optimizing the control coefficient and the method for controlling the voltage of the LCVR, this study reduces the angle between the incident LCVR and the polarization grating, and increases the diffraction efficiency of the grating. It was confirmed that this strategy can increase the diffraction effectiveness of the quadrature cascaded LCPG through the design of the experimental setup.

Based on the fundamental of traditional Sub-aperture coherence (SAC) algorithm, Radial Sub-aperture coherence (RSAC) and Symmetrical Radial Sub-aperture coherence (SRSAC) have been designed to achieve non-mechanical beam steering with ultra-high precision and stability by utilising two-dimensional Liquid Crystal Optical Phased Array (LCOPA). Both of them inherit the original advantages, that is, to eliminate the local pointing accuracy defects and greatly improve the angular resolution of the beam steering system. Meanwhile, the steering angle error caused by the aperture variation and the alignment error can be also effectively restricted by SRSAC. In this paper, the essential mathematical framework of SRSAC and its affiliated local error elimination method was established to supplement the theoretical support of these phase generation algorithms. By dissecting the generation mechanism of each pointing error branch, the theoretical formulae with great universality are finally proposed, which provide visualised and necessary references for the specific application in other beam control situations.