A Model for Simulating Frequency Conversion in Nonlinear Optical Media

Due to the rapid evolution of optical communications, interest in understanding nonlinear effects has grown enormously. In particular, there is an interest to characterize the frequency conversion due to the material second-order nonlinearity. In this paper we propose a time-domain model for simulating this phenomenon. The model is a nonlinear wave equation with a source term that involves the time second derivative of the square of the field. When the equation is discretized at a given time level, we get a nonlinear finite difference equation that can be written as a quadratic polynomial for the values at the next time level. Using the exact solution of the quadratic polynomial, we obtain a second-order explicit scheme. Having the total field, we can conduct Fourier analysis to characterize the harmonics.