Waveguide Mode Solver Avoiding Field Singularities at Corners

Computing the modes of optical waveguides is a basic and important problem in the study of integrated optics and fibre optics. Numerical methods are indispensable, since analytic solutions only exist for the simplest waveguide geometries. Many optical waveguides in integrated optics have corners where interfaces between different materials intersect. At the corners, the electric field has a weak singularity that has caused a slow convergence for existing numerical methods. This project proposes a method that avoids the field singularities at corners by hiding the corners inside sub-domains and using impedance operators for the sub-domains. The impedance operator of a sub-domain maps the magnetic field on the boundary of the sub-domain to the electric field on the boundary and it can be approximated analytically.