Designing one-pump fiber optical parametric amplifiers for an insensitive amplification to dispersion fluctuations

Small-signal gain spectrum of one-pump fiber optical parametric amplifiers (1-P FOPAs) is investigated in the presence of dispersion fluctuations. By assuming the dispersion fluctuations along the fiber as a stochastic process and using the matrix approach, the full gain spectrum of 1-P FOPAs is simulated. We have examined the gain spectrum of 1-P FOPAs for a wide range of fluctuation parameters, and it is shown for the first time that there are two specific wavelengths at which the dispersion fluctuations play no role. Analytical formulas are also presented to design 1-P FOPAs for amplifying signals with a gain insensitive to dispersion fluctuations.