Efficient high order waveguide mode solvers based on boundary integral equations

For optical waveguides with high index contrast and sharp corners, high order full-vectorial mode solvers are difficult to develop, due to the field singularities at the corners. A recently developed method (the so-called BIE-NtD method) based on boundary integral equations (BIEs) and Neumann-to-Dirichlet (NtD) maps achieves high order of accuracy for dielectric waveguides. In this paper, we develop two new BIE mode solvers, including an improved version of the BIE-NtD method and a new BIE-DtN method based on Dirichlet-to-Neumann (DtN) maps. For homogeneous domains with sharp corners, we propose better BIEs to compute the DtN and NtD maps, and new kernel-splitting techniques to discretize hypersingular operators. Numerical results indicate that the new methods are more efficient and more accurate, and work very well for metallic waveguides and waveguides with extended mode profiles.