Nonlinear detuning of three-wave interactions

The parametric decay and sum-frequency generation of intense optical radiation, in a medium with both second- and third-order nonlinearities, is considered. In steady state, nonlinear wave-number shifts usually detune these interactions before a complete exchange of energy between the pump and product waves can be achieved. Fortunately, however, it is possible to compensate for this nonlinear detuning by imposing a linear wave-number mismatch on each type of interaction. Simple criteria are given for the conditions under which a complete exchange of energy is possible, and a simple expression is obtained for the required medium length. Some exact solutions of the three-wave equations are used to illustrate the underlying wave physics, and some useful approximate solutions are described. As an application of the general theory, Type II frequency doubling in a KDP crystal is discussed briefly.