Abstract
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.
Highlights
Dielectric waveguides are essential building blocks of diverse photonic integrated circuits such as polarizers, switches, filters, rotators, and modulators
Only horizontal and vertical interfaces are considered because the aim of this study is to develop an efficient waveguide mode solver for anisotropic waveguides with arbitrary permittivity tensors
The proposed scheme was formulated as an eigenvalue matrix equation by applying only the transverse magnetic field components with 2N unknowns, where N is the number of unknowns
Summary
Dielectric waveguides are essential building blocks of diverse photonic integrated circuits such as polarizers, switches, filters, rotators, and modulators. The required computational effort is relatively low These BPM-based schemes [3,4,9,16,17] can study field profiles along the longitudinally variant waveguides but they need to consider the extra convergence conditions involving the step size of propagation, the two-point recurrence scheme, and the reference refractive index while solving the mode problems. To formulate a standard eigenvalue matrix equation in the FDFD [10], the authors adopted 4N unknowns including two transverse electric field and two transverse magnetic field components to study LC waveguides with arbitrary molecular director orientations.
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