Optimizing liquid crystal cell thickness in electro-optical Fresnel lenses through theoretical calculations and experimental validation.

Tunable liquid crystal (LC) lenses have gained significant attention in recent decades due to their lightweight, low cost, and versatility in applications such as augmented reality, ophthalmic devices, and astronomy. Although various structures have been proposed to improve the performance of LC lenses, the thickness of the LC cell is a critical design parameter that is often reported without sufficient justification. While increasing the cell thickness can lead to a shorter focal length, it also results in higher material response times and light scattering. To address this issue, the Fresnel structure has been introduced as a solution to achieve a higher focal length dynamic range without increasing the cell thickness. In this study, we numerically investigate, for the first time (to our knowledge) the relationship between the number of phase resets and the minimum required cell thickness to achieve a Fresnel phase profile. Our findings reveal that the diffraction efficiency (DE) of a Fresnel lens also depends on the cell thickness. Specifically, to achieve a fast response Fresnel-structured-based LC lens with high optical transmission and over 90% DE using E7 as the LC material, the cell thickness should fall within the range of 13 to 23 µm.