Improved Full-Vectorial Meshfree Mode Solver for Step-Index Optical Waveguides With Arbitrary Dielectric Interfaces

A novel improved full-vectorial meshfree finite cloud mode solver is constructed for analysis of step-index optical waveguides with arbitrary interfaces, where the waveguide interfaces can be tilted towards the global coordinate axes or can even be curved. In order to obtain rigorous formulations capable of dealing with tilted and curved interfaces, the local coordinate transformations along with the curvilinear mapping technique are introduced to the approximation of spatial derivatives at interpolated nodes, respectively. In the improved finite cloud scheme, a simple modification to the meshfree kernel shape function is proposed to enforce the Kronecker delta property, significantly improving the computational efficiency. The computational accuracy is also greatly improved since a novel scheme is proposed to carefully treat field values in the vicinity of material interfaces. Numerical results for the fundamental and high-order modes of a rectangular rib waveguide, an equilateral triangular core waveguide, a trapezoidal rib waveguide and a circular optical fiber are presented and compared with those from the conventional mesh-based methods, which shows the validity and utility of the proposed method.