Analysis of focal length of blue-phase liquid crystal (BPLC) cylindrical lens for the light of the various incident angles and polarisations

Horizontally non-uniform electric field along the vertical direction inside blue-phase liquid crystal (BPLC) layer induces the Gradient index (GRIN) lens effect. Dependence of lens performance on the incident angle and polarisation is investigated by calculating the spatial phase distribution and the direction of wave front for lights passing through the BPLC layer. The calculated trajectories of light rays show that the focal distance for e-wave is less affected by the incidence angle than the focal distance of the o-wave. This can be attributed to the fact that steepness of spatial distribution of the effective refractive index for e-wave decreases for the larger incident angles.