Novel frequency domain finite element formulation for optical circuits in nonlinear photonic crystals

An efficient technique based on the finite element method in the frequency domain for the analysis of nonlinear photonic crystals based optical circuits is here presented. The solution of the nonlinear Helmholtz equation is obtained by an iterative process involving linear problem solutions. The present approach uses isoparametric curvilinear elements for the spatial discretization and perfectly matched layers to truncate the computational domain. Numerical examples are presented in order to validate the efficiency of the present method.