When electric field diverges at corners of optical waveguides, conventional numerical techniques such as the finite-difference method cannot be used for discretization of the wave equations. We have developed an algorithm for modal analysis such that singularity points at corner regions are handled properly. Calculation results are also shown to illustrate the effectiveness of this method.
Wayne W. Lui, C.-L. Xu, Wei-Ping Huang, Kiyoyuki Yokoyama, and S. Seki, "Full-Vectorial Mode Analysis with Considerations of Field Singularities at Corners of Optical Waveguides," J. Lightwave Technol. 17, 1509- (1999)