A simple numerical method has been developed to study the propagation characteristics of a nonlinear optical waveguide. The method is applicable to planar waveguides as well as fibers. In this method, second-order differential equation is converted into first-order differential equation which is solved by standard fourth-order Runge-Kutta method. Numerical results for nonlinear planar waveguide and optical fibers with power law profiles and Kerr-like nonlinearity have been presented. The results for planar waveguides match very well with the exact results. Present method can be applied to arbitrary refractive index profiles with any kind of nonlinearity.
R. K. Varshney, I. C. Goyal, and A. K. Ghatak, "A Simple and Efficient Numerical Method to Study Propagation Characteristics of Nonlinear Optical Waveguides," J. Lightwave Technol. 16, 697- (1998)