A collocation-based spectral element method for computing nonlinear optical waveguide

Abstract

Computation of nonlinear optical waveguide needs to solve nonlinear eigenvalue/ eigenfunction problem mathematically. However, usually the refractive index profiles in the nonlinear optical waveguide are discontinuous, which makes a solution to the nonlinear eigenvalue/eigenfunction problem not smooth enough. In this work, we mainly discuss how to use the high-order collocation-based spectral element method (SEM) to discretize such a problem and propose an iterative algorithm for computing nonlinear optical waveguide with discontinuous refractive index profiles. Starting from the linear eigenvalue/eigenfunction problem, we adopt SEM to discretize it and solve the resulting discretized system with Matlab eigen solver; for the nonlinear problem, we first change the nonlinear problem into corresponding linear problems, and then solve the linear problems by the usage of the iterative method. The proposed method has the advantage of high-order accuracy and lower-order cost. The accuracy and efficiency of the method are tested by several one-dimensional and two-dimensional linear optical waveguide structures. Numerical results for some nonlinear optical waveguides are also presented.