A finite-difference scheme for accurately analyzing step-index dielectric waveguides with angled and curved dielectric interfaces has been proposed by Chiang Here, this formulation is generalized to take into account a possible curvature of the entire waveguide along the propagation direction, and it is shown how Perfectly Matched Layers can be incorporated in order to accurately compute the bending or curvature loss of dielectric waveguides with step-index profiles of arbitrary shape. Furthermore, the formulation of the interface equations that relate the fields and their derivatives on both sides of a dielectric interface has been simplified, so that their implementation no longer requires any further explicit conversions between coordinate systems.
© 2011 IEEE
Michael Krause, "Finite-Difference Mode Solver for Curved Waveguides With Angled and Curved Dielectric Interfaces," J. Lightwave Technol. 29, 691-699 (2011)