Effective and compact active optical elements such as lenses with variable focus distance and beam steering devices are highly required for many photonic applications. Liquid crystals (LCs) are especially attractive due to their property to be controlled with an external electrical field. The main idea is based on the fact that an external non-uniform electrical field and/or particular alignment features enable one to achieve a desired spatial distribution of the LC molecules (director). Non-uniformity of the LC medium leads to internal refraction that, in turn, affects the trajectory of the light passed. In other words, the light trajectory is steered by the electrical field.
Functional abilities of LC optical elements are restricted by refractive index changes, poor control over index profiles, and thickness of the LC layer. In order to increase the steering angle and the lens aperture, the LC light steering elements are built on principles of diffractive optics, i.e. Fresnel’s lenses and switchable diffraction gratings are used. The present work concentrates on investigation of the potential of diffraction gratings and Fresnel’s lenses based on liquid crystals. Specificity of formation of a desired spatial distribution of the LC director, as well as the correspondent restrictions, is studied. The aim is to clarify the relationship between the width of the fly-back zone, the LC thickness, the principal physical constants of the LC material, and factors that can cause a sharp profile in the LC director distribution, i.e. external field and non-uniform alignment [1,2].
V. G. Chigrinov, Liquid crystal devices: physics and applications (Artech House, Norwood, MA, 1999)
I. W. Stewart, The static and dynamic continuum theory of liquid crystals (Taylor & Francis, 2004).