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Numerical solution of a non-linear Maxwell problem for the characterization of nematic liquid crystals

This work reports on the implementation of an an iterative procedure to solve the non-linear problem of wave propagation in homeotropic Nematic Liquid Crystals (N-LC). The nematic structure of the crystal molecules is strongly dependent on the applied external electromagnetic field. In our case, a monochromatic plane wave is normally incident on the liquid crystal, which is sandwiched between two glass layers. The orientation of these molecules, called the directors, determine the dielectric tensor properties of the medium. A Mode-Matching Technique (MMT) was used to accurately solve for the governing fields in each of the subdivided layers composing the crystal, whereas an explicit finite-difference scheme with relaxation was implemented to solve for the directors' orientation. The non-linear problem was also solved using a more efficient implicit finite difference scheme characterized by a faster convergence rate. Obtained computational results were compared to published data indicating good agreement.