A New Formulation of Coupled Propagation Equations in Periodic Nanophotonic Waveguides for the Treatment of Kerr-Induced Nonlinearities

Nonlinear phenomena could be used to implement important signal processing functionalities in future nanophotonic integrated optical devices. In this paper, a semi-analytical model incorporating the influence of Kerr-induced nonlinearity in the propagation of an optical signal inside a periodic nanophotonic waveguide is derived. The approach consists of a system of nonlinear coupled mode propagation equations and is applicable to both single and multimode waveguides. The influence of the mode group velocity on the value of the self-phase modulation coefficient gamma is analyzed and the impact of higher order nonlinear terms is also investigated both at the middle and edge of the guided band. The model is also applied to estimate the nonlinear coupling coefficients of a photonic crystal waveguide coupler and provides an efficient method to analyze the influence of nonlinear phenomena in periodic nanophotonic waveguide devices.