| Summary: | 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.
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