Classical theory of cylindrical nonlinear optics: Second-harmonic generation

The second-harmonic generation of cylindrical electromagnetic waves in a nonlinear nondispersive medium is investigated two separate ways. One method uses the exact solutions of the Maxwell equations, which describe propagation of cylindrical electromagnetic waves, and the other method uses the traditional coupled-wave equations, which are derived from the interaction between cylindrical electromagnetic waves and a nonlinear nondispersive medium. The results obtained by these two methods are concordant with each other. We also show that both methods are useful in dealing with the problem of cylindrical second-harmonic generation and each of them has particular advantages in several aspects. The method of using the exact solution can solve problems of second-harmonic generation under initial-value and boundary-value conditions and the approach of using coupled-wave equations can be directly extended to describe other nonlinear phenomena such as sum-frequency and four-wave mixing.