Multidimensional calculation of ray path in a twisted nematic liquid crystal cell

In general, light propagating an inhomogeneous liquid crystal (LC) cell can be modeled as bundle rays because the LC cell consists of many birefringence layers. In order to calculate the optical path of the propagating light in the inhomogeneous LC cell, we multidimensionally calculated the wavevector, k, and the Poynting vector, S, of an ordinary and an extraordinary ray at LC grid interfaces, which are isotropic to a uniaxial medium and a uniaxial-to-uniaxial medium, by using the phase matching method. Furthermore, we also investigated the transmission coefficients and transmittance of the ordinary and the extraordinary rays as a function of difference of the optical axes of the facing birefringence medium at the interface to obtain the significant rays in the LC cell. Finally, we could calculate the exact path of the significant rays in the inhomogeneous LC cell, and compared the ray path in an electrically controlled birefringence (ECB) mode and a twisted nematic (TN) LC mode.