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High order vectorial analysis of waveguides with curved dielectric interfaces

By Shan Zhao


Abstract—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. Index Terms—Eigenvalues and eigenfunctions, finite difference methods, nonhomogeneous media, waveguide theory. I

Year: 2010
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