Solving the full anisotropic liquid crystal waveguides by using an iterative pseudospectral-based eigenvalue method

This study develops an efficient mode solver based on pseudospectral eigenvalue algorithm to analyze liquid crystal waveguides with full 3 × 3 anisotropic permittivity tensors. Present formulation yields a cubic eigenvalue matrix equation with an eigenvalue of the propagation constant, and they are solved using an iterative approach following the transformation of the matrix equation to a standard linear eigenvalue equation. The proposed scheme significantly reduces the memory storage and computational time by using only transverse magnetic field components. Although the proposed scheme requires an iterative procedure, the convergent eigenvalues are achieved after performing only four iterations. Therefore, for this scheme, computational efforts remain greatly lower than those for other reported schemes that used at least three field components. For solving the modes of nematic liquid crystal waveguides, the numerical results obtained by the proposed scheme are in good agreement with those calculated by using the finite-element and the finite-difference frequency-domain schemes, thus verifying the applicability of the proposed approach. Furthermore, the mode patterns of liquid crystal waveguides under arbitrary molecular orientations are also characterized in detail.