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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. [ABSTRACT FROM AUTHOR]

A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method (3D-FV-BPM) formulation along the longitudinal direction. The cross-coupling terms (CCTs) are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply-and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides. [ABSTRACT FROM AUTHOR]

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin’s method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach. [ABSTRACT FROM AUTHOR]