Mathematical simulation of nonlinear waveguiding systems based on 2D photonic crystals

A mathematical model of nonlinear two-dimensional waveguiding systems based on photonic crystals was constructed using the finite-difference time-domain method (FDTD), the total field/scattered field (TF/SF) method, and the perfectly matched layer method (PML). The constructed numerical algorithm can also be used for investigation of other two-dimensional waveguiding systems. The results of simulating the elements of particular waveguiding systems are presented.