Time-domain beam propagation method for nonlinear optical propagation analysis and its application to photonic crystal circuits

A time-domain beam propagation method (BPM) based on a finite-element scheme is newly formulated for nonlinear optical propagation analysis. In order to obtain steady-state solutions, a way of continuous-wave (CW) excitation is also described. The validity of this method is verified by numerical examples: self-focusing guiding phenomena and nonlinear gratings. Furthermore, this approach is also applied to characterizing nonlinear photonic crystal circuits. Specifically, a grating structure designed to modify the characteristics of light propagating within a photonic crystal waveguide and a stub-like structure including nonlinear rods are proposed, and the potential for use as optical limiting and switching devices is investigated.