“…Only the small-signal approximation limit is considered where the pump pulse intensities remain constant. Neglecting optical absorption, the collinear parametric four-photon amplification in the slowly varying amplitude approximation is described by Equations 1 and 2 [1,10,12,14,15] where E s , 2s x , E x and E 2 are the amplitudes of the electrical field strengths at the angular frequencies u; s (signal), UJX (idler), UJX and UJ2 (pump pulses); c 0 is the light velocity in vacuum; z is the propagation direction; and Ak z = k Sz + k Xz -k x z -k 2z -k$ + k\ -k x -k 2 is the wavevector mismatch. The wavevectors k t (i = 1,2, S, I) are given by k t = HiUii/cQ = lirriii/i/cQ = lirriii/i == Inni/Xi, where the n t are the refractive indices at the angular frequencies uj i9 frequencies v i9 wavenumbers v t or wavelengths A;.…”