A Heuristic Fast Method to Solve the Nonlinear Schrödinger Equation in Fiber Bragg Gratings with Arbitrary Shape Input Pulse

Abstract

Using a combination of Runge‐Kutta and Jacobi iterative method, we could solve the nonlinear Schrödinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge‐Kutta method.