An Exact Solution to the Spatial Evolution of a Carrier and a Pair of Side-Bands in a Cubically Nonlinear Medium

The propagation of an amplitude modulated signal consisting of a carrier and a single side-band pair in a cubically nonlinear, nondispersive medium is solved exactly using the coupled mode approach. No approximation of undepletion is introduced. We show in the most general conditions the existence of a periodic exchange of energy between the carrier and the side-bands. Other forms of solutions are also found to exist. The steady state solution of the problem is necessarily introduced for a better understanding of the process of energy exchange