We investigate the effects of higher-order, ${\chi }^{\mathrm{}\left(3\right)\mathrm{}},$ nonlinearities on the process of second-harmonic generation. In the traveling-wave case we find substantive differences in the macroscopic behavior of the fields when the ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ components are present. In the intracavity case, which has been investigated before using a linearized analysis, we investigate regions where these analyses may not be valid, comparing and contrasting the full quantum simulations with previous results.

• Received 10 July 2000

DOI:https://doi.org/10.1103/PhysRevA.63.033801