Phase retardation vs. pretilt angle in liquid crystal cells with homogeneous and inhomogeneous LC director configuration

Phase retardation of both extraordinary and ordinary polarized rays passing through a liquid crystal (LC) cell with homogeneous and inhomogeneous LC director distribution is calculated as a function of the LC pretilt angle θ₀ on the cell substrates in the range 0 ≤ θ₀ ≤ 90°. The LC pretilt on both substrates can have the same or opposite direction, thereby forming homogeneous, splay, or bend director configurations. At the same pretilt angle value, the largest phase retardation ΔΦ is observed in splay LC cells, whereas the smallest phase retardation is observed in bend cells. For the θ₀ values close to 0, 45°, and 90°, analytical approximations are derived, showing that phase retardation depends on LC birefringence variation.