We present a complete analysis of the amplification process occurring in a nonlinear fiber, either driven with one or two pumps. After determining the solution for the signal and idler fields resulting from this amplification, we analyze the physical transformations undergone by these fields. To this aim, we use a Bloch–Messiah decomposition for the symplectic transformation governing the fields’ evolution. This analysis is shown to be particularly simple and permits us not only to gather results already present in other approaches [Opt. Express 21, 1374 (2013)], but also to predict original features of parametric amplification in fibers. In particular, we present a study of the correlations of the signal-idler fields at the amplifier output, and we clarify the impact these correlations have on the amplifier noise figure. Finally, we address the effect of losses. We determine whether it is advantageous to consider a link consisting in an amplifying nonlinear fiber, followed by a standard fiber-based lossy transmission line or whether the two elements should be reversed by comparing the respective noise figures.
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