A FETD Scheme and Analysis for Photonic Crystal Waveguides Comprising Third-Order Nonlinear and Linear Materials.

In this paper, we design a time-domain finite element (FETD) algorithm for solving Maxwell’s equations in third-order nonlinear media. The Cardano’s method is used to solve the nonlinear constitutive equation. At the same time, we also establish the continuous stability of the third-order nonlinear model and the numerical stability of the FETD scheme. In order to reduce the wave reflection from the truncated domain boundary, the anisotropic perfectly matched layer model is developed and solved. Extensive numerical simulations are carried out and they demonstrate that bistable transmission switches depending on the incident wave’s intensity can be obtained if a number of rods made of Kerr-type nonlinear materials are inserted around the bend of the linear bent photonic crystal waveguides.