Resumen
Pairwise interactions of optical pulses lead to the creation of four-wave mixing (FWM) products in the presence of periodic damping and amplification. In this manuscript, we examine how these FWM products grow in the presence of small to moderate random dispersion. Namely, we show that (i) the growth of the FWM products in the presence of white noise is inversely proportional to the noise strength $\bar{D}$, confirmed by both analytical and numerical results; (ii) the FWM products as a function of $\bar{D}$ obey a gamma-type probability distribution function; and (iii) the presence of either white or Ornstein–Uhlenbeck (OU) noise has a similar influence on the growth of these FWM products. This work shows that small random dispersion can effectively mitigate the deleterious effects of FWM in wavelength-division–multiplexed optical communications systems for either sech-type or Gaussian-type input pulses.