Liquid crystalʼs photoalignment for formation of phase profiles via geometric phase distribution

Basic understandings on the concept of geometric phase, also known as Pancharatnam – Berry phase, and its application to creation of photonic liquid crystal devices as thin-films of photoaligned nematic liquid crystals are presented. The significance of the strong azimuthal anchoring energy and the role of birefringence in liquid crystal photoalignment layer for formation of geometric phase gradients are shown. The dependence of phase retardation of circular polarised light passing through the half-wave phase plate on the azimuthal angle of the plate orientation is explained in details, as it gives ground to formation of geometric phase distribution of optical liquid crystal devices, working in circular polarised light. The effective refractive index is introduced for characterisation of the optical properties of linear periodic liquid crystal’s structure that forms profile of geometric phase surface. The successful implementations of photonic liquid crystal devices (polarisation diffraction grating, annular diffraction grating, q-plate, q-plate with a phase core) are analysed in terms of geometric phase distributions and the corresponding equations of profile of the phase surfaces that ensure functioning of the devices are presented.