Full-vectorial meshfree method with an efficient iteration scheme for full anisotropic optical waveguides

A full-vectorial meshfree finite cloud mode solver is presented, for the first time, for the analysis of optical waveguides with full anisotropic permittivity tensors, where the interface can be regular or irregular. The computational window are divided along the dielectric interfaces into appropriate number of clouds with homogeneous refractive index profiles and then patched by using the continuity conditions of the longitudinal field components among clouds. Present formulations yield a nonlinear eigenvalue matrix equation, and it is solved using an efficient iterative scheme after transforming the matrix equation to a standard linear eigenvalue equation, in which the convergent solutions can be achieved after performing only four iterations. The proposed method employs an unconstrained interior node distribution scheme as well as a novel scheme for dealing with dielectric interfaces, in which two extra rows of nodes are added on either side of the interfaces, significantly improving computational accuracy and efficiency. Comparing results for a nematic liquid crystal core channel waveguide and an E7-nematic-liquid crystal waveguide in silicon V-groove with the finite-difference frequency-domain method and pseudospectral-based eigenvalue method highlight the proposed method versatility, efficiency and accuracy.