The effect of higher order harmonics on second order nonlinear phenomena

A new method which is a combination of the harmonic balance and finite difference techniques (HBFD) is proposed for complete time-harmonic solution of the nonlinear wave equation. All interactions between different harmonics up to an arbitrary order can be incorporated. The effect of higher order harmonics on two important nonlinear optical phenomena, namely, the second harmonic generation (SHG) and frequency mixing is investigated by this method and the results are compared with well-known analytical solutions. The method is quite general and can be used to study wave propagation in all nonlinear media.