A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals

In this paper, we present a computationally efficient and highly accurate numerical method for the analysis of electromagnetic wave propagation in nematic liquid crystal (N-LC) cells. An iterative procedure is employed where the mode-matching technique (MMT) is used to solve the time-harmonic Maxwell equations inside the N-LC cell, whereas a finite-difference method (FDM) with relaxation is utilized to treat the nonlinear stationary Ginzburg-Landau equation for the director field. The angular distortion of the directors in the N-LC cell depends on the applied electric field which, in turn, affects the anisotropic dielectric properties of the medium. Numerical results are obtained for various values of the governing parameters. These simulations provide further insight into the Fréedericksz transition with special emphasis on resonances, bi-stability, hysteresis, phase shift between ordinary and extraordinary waves (birefringence), and soft anchoring effects. Obtained results are compared and validated against measurements and data published in the literature.