Full-Vectorial Finite Difference Mode Solver for Leaky Optical Waveguides

Abstract
Due to its simplicity and efficiency, a full-vectorial mode solver based on a finite difference scheme is applied to investigate the propagation characteristics of optical waveguides. Since uniform meshes are used in the numerical implementation, it is very easy to divide the computational window of any arbitrary cross-sectional geometries of the waveguides. An index averaging technique is employed to deal with curved dielectric interfaces for stabilizing the numerical calculation and accelerating convergence. In addition, for solving leaky-mode problems, such as the investigation of waveguide confinement loss, the perfectly matched layer (PML) absorbing boundary condition is incorporated into our finite difference formulations. The influence of the index averaging technique on the leaky-mode analysis is also discussed. We employ the shift inverse power method (SIPM) for solving the formulated eigenvalue problems. In this work, both one-dimensional and two-dimensional problems are considered, including the slab waveguide, the antiresonant reflecting optical waveguide (ARROW), the step-index optical fiber, the rectangular channel waveguide, the anisotropic embedded-channel LiNbO3 integrated optical waveguide, and microstructured optical fibers (MOFs). Comparsion of our calculation with other methods is discussed.