Analysis of the rotation of the polarisation direction in a cylindrical liquid crystal lens where the direction of the incident linear polarisation is not parallel to the axis of the cylindrical lens

A liquid crystal (LC) lens is used to change the propagating direction of the incident light at the lens-shaped boundary of two different media and shows strong dependence on the polarisation direction of the incident light. The performance of the cylindrical LC lens is investigated in the situation that the directions of the incident linear polarisation and the axis of the cylindrical lens are not parallel. Two LC cell configurations were considered where LC directors aligned twisted or homogeneously. In case of the twisted LC configuration, the polarisation direction of the propagating light follows the twist of the LC directors if the directions of the incident linear polarisation and the LC alignment on the side of the lower substrate are parallel. For these two configurations, the LC lens can control the propagating light in the LENS-ON state. In case of homogeneously aligned LC configuration, polar angle distributions of LC directors are not uniform due to the lens-shaped boundary. So in the LENS-OFF state where LC directors rotate under the driving voltage, a LC domain boundary may occur in some cases.