An improved wide-angle FD-BPM for nonlinear and nonreciprocal waveguides

An improved wide-angle finite-difference beam-propagation method for the simulation of multifunction optical waveguides employing simultaneously nonlinear and nonreciprocal materials is introduced in this paper. This formalism can be applied to nonlinear Kerr-type materials exhibiting any kind of nonlinearity mechanisms. The nonreciprocal behavior is based on the difference between forward and backward propagation constants for TM modes. The z derivatives of the inverse permittivity are also taken into account so that longitudinal varying structures can be more accurately simulated.