Effects of higher order nonlinearities on second-order frequency mixing

Equations are presented here which describe second-order nonlinear frequency mixing under conditions where third-order non-linearities significantly alter the phase-matching relations. The coupled amplitude and phase equations illustrate that additional phase mismatch of the second-order process can be expected due to third-order nonlinearities. These nonlinearities include refractive index changes for a wave at one frequency due to waves at other frequencies. Growth of off-axis weak waves (small scale self-focusing) is described in terms of four-wave mixing in the presence of the second-order frequency mixing. It is shown that in at least some cases growth of off-axis waves is enhanced by second-order frequency mixing.