Vector analysis of bending waveguides by using a modified finite-difference method in a local cylindrical coordinate system

A vector mode solver for bending waveguides by using a modified finite-difference (FD) method is developed in a local cylindrical coordinate system, where the perfectly matched layer absorbing boundary conditions are incorporated. Utilizing Taylor series expansion technique and continuity condition of the longitudinal field components, a standard matrix eigenvalue equation without the averaged index approximation approach for dealing with the discrete points neighboring the dielectric interfaces is obtained. Complex effective indexes and field distributions of leaky modes for a typical rib bending waveguide and a silicon wire bend are presented, and solutions accord well with those from the film mode matching method, which shows the validity and utility of the established method. (C) 2012 Optical Society of America