Quantitative analysis on self-focusing properties of H-PDLC flexible curved radius gratings.

In general, the shape of traditional holographic grating is fixed and immutable, the period will not change after fabrication, this means that the modulation effect on the light field is unalterable. However, traditional grating cannot satisfy all requirements of current optical systems. In order to increase the versatility of holographic grating, a flexible curved radius grating (FCRG) which consists of holographic polymer-dispersed liquid crystal (H-PDLC) was proposed. The FCRG has an important self-focusing property that it can be adjusted the focal length by changing its own radius of curvature correspondingly. In this paper, we use the scalar diffraction theory to analysis the interference and diffraction processes for FCRG under different conditions, then a relationship equation has been deduced to express quantitatively about FCRG between its radius and focal length. According to the relationship, a tunable holographic element is achieved for the function of mechanically-controlled self-focusing effect. Experiments show that the FCRG has two conjugated focusing effects on the positive first-order and negative first-order, both two effects can achieve focus-adjusted ability by changing their radius of curvature. The FCRG provides a way for the coupler of curved waveguide display system for augmented reality in the future.