An Expression for Nonlinear Noise in Optical Phase Conjugation Systems With Lumped Amplifiers

We develop an analytical formula for evaluating the impact of fiber nonlinearity in systems employing optical phase conjugation with multi-span lumped amplification, highlighting the detailed balance of effects leading to compensation when the phase conjugator is added to the middle of the link. We apply the approach to the effect of adding a pre-dispersion element to improve the symmetry, deriving the required optimum pre-dispersion. The closed form is validated through simulation and shows good matching with the results within a margin of error less than 0.2 dB.