Calculation of Ray Path in Liquid Crystal Modes

In this paper, we introduce the optical approach for the calculation of optical path in arbitrary aligned birefringence media for controlling the incident light, and also calculate the ray path in representative liquid crystal (LC) modes. In calculation, we multi-dimensionally calculated the Poynting vector S and wave vector k of ordinary and extra-ordinary rays, and considered both y-axis and z-axis interfaces by using the dielectric tensor rotation method. Finally, we could achieve the exact ray path in various LC modes, and confirmed the propagating direction of the light according to azimuth angles in LC layers.