A numerical technique for the determination of the propagation characteristics of nonlinear planar optical waveguides

A numerical method is proposed and implemented into computer code for the analysis of propagation characteristics of nonlinear optical waveguides. This technique follows the concept of the shooting method, and the fourth-order Runge-Kutta method is adapted to integrate the differential wave equation from one side to the other. An error function is defined to estimate the discrepancy between the computed and expected boundary values. A secant method is then used to evaluate the sign and magnitude of the correction term for the initial guesses of effective index. This procedure is performed in an iterative manner until the error reduces to a specified range. Experiments show that very accurate results can be obtained through this method, and only six to seven iterations are needed for solutions to converge. With this method we analyze nonlinear waveguides with varying guide parameters for realization of their behavior. All the findings and results can be used in further investigations of optical devices composed of waveguide structures