Full-Vectorial Analysis of Optical Waveguide Discontinuities Using Denman–Beavers Iterative Scheme

An accurate and efficient full-vectorial numerical approach for analyzing three-dimensional optical waveguide discontinuities is proposed, where the resulting square root of the characteristic matrix from the field-based operators is approximated by the Denman-Beavers iterative scheme with a branch-cut rotation in the complex plane. Both the magnetic and electric field formulations are rigorously derived along with the robust perfectly matched layer absorbing boundary conditions. Numerical results from a typical buried waveguide, a channel waveguide, and a rib waveguide show that the present scheme is more accurate and stable than the widely used Padé approximation, while the computational load is comparative.