High Order Vectorial Analysis of Waveguides With Curved Dielectric Interfaces

This letter introduces a novel full vectorial higher order finite difference method for the modal analysis of optical waveguides with smoothly curved dielectric interfaces. Based on a simple Cartesian grid, a new matched interface and boundary formulation is derived to enforce the interface conditions so that the staircasing error can be eliminated. Benchmark problems are employed to validate the proposed method. A fourth order convergence is numerically confirmed irrespective of the presence of the step-index interfaces.