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Incorporation of the field singularity behaviors at edges into the finite-difference solution of waveguide modes

A drawback of the finite difference (FD) method in solving waveguide eigenmodes exists in the difficulty to accurately describe the field singularities at sharp edges. In this paper, we incorporate the boundary conditions proposed previously into the FD method to solve this problem. An alternative form of the boundary condition at the edge of a wedge with external angle 2/spl pi/ is also derived, which is more flexible for field eigenvalue problems. Numerical results show the validity and accuracy of the proposed treatments. Compared with the traditional treatment, our methods are more accurate and numerically more stable, especially for the computation of field distributions near edges.