A general relation considering an interface condition between a sampled point and its nearby points in the finite-difference analysis of optical waveguides is derived. Our formulation is a full-vectorial one, and the interface can be oblique to the global coordinate axes or even can be with curvature. Using the derived formulation, optical waveguide structures with arbitrary step-index profiles can be dealt with. The validity of the proposed method is examined by comparing the numerical calculation with the analytical solution of a step-index optical fiber. The method is also applied to the analysis of fused fiber-optic couplers and compared with prior analysis using the surface integral equation method.
Yen-Chung Chiang, Yih-Peng Chiou, and Hung-Chun Chang, "Improved Full-Vectorial Finite-Difference Mode Solver for Optical Waveguides With Step-Index Profiles," J. Lightwave Technol. 20, 1609- (2002)