Abstract

Second harmonic generation is traditionally analyzed by assuming a quadratically nonlinear medium which may or may not be dispersive. In the former case, the second harmonic asymptotically builds up during propagation, while the fundamental monotonically decreases. In the latter case, however, there is a periodic exchange of energy between the fundamental and second harmonic. In our analysis, we first assume a medium with quadratic and cubic nonlinearities without dispersion (i.e., assuming perfect phase matching). Results from the initial value problem for harmonic generation indicate asymptotic behavior for low values of the cubic nonlinearity and periodic behavior for higher values. In other words, the role of dispersion (phase mismatch) in the traditional treatment is served by an adequate amount of the cubic nonlinearity. The same problem is also solved for the more general case when dispersion may be present. Finally, subharmonic generation in a quadratically and cubically nonlinear medium is also studied for the nondispersive and dispersive cases.

© 1988 Optical Society of America