A new phase-matching factor is derived for four-wave mixing (FWM) that includes the effects of self-phase and cross-phase modulation in optical fibers. Theoretical results predict that the wavelength of peak FWM efficiency shifts away from the fiber zero-dispersion wavelength and indicate that the conventional phase-matching factor may induce significant errors in FWM calculations. Experiments are presented to verify the new phase-matching factor and the related theoretical results. The measured results agree well with those predicted by the new phase-matching factor.
Shuxian Song, Christopher T. Allen, Kenneth R. Demarest, and Rongqing Hui, "Intensity-Dependent Phase-Matching Effects on Four-Wave Mixing in Optical Fibers," J. Lightwave Technol. 17, 2285- (1999)