Finite-element mode-solver for nonlinear periodic optical waveguides and its application to photonic crystal circuits

A finite-element method (FEM) is newly formulated for the modal analysis of nonlinear periodic optical waveguides. In order to treat periodicity in the propagation direction, periodic boundary conditions are imposed on the envelope of electromagnetic fields. The validity of this method is verified by way of numerical examples of a PC waveguide composed of nonlinear dielectric pillars placed on square array in the cladding region. Furthermore, the present method is applied to various nonlinear photonic crystal waveguide structures for exploring appropriate structures to enhance the nonlinearity and their nonlinear modal properties are presented, including coupled-resonator optical waveguides.