Statistics of Wavelength Division Multiplexed Channels in Fiber-Optical Parametric Amplification

The amplification of wavelength division multiplexed (WDM) data in fiber-optical parametric amplifiers give rise to cross-gain saturation and four-wave mixing crosstalk. This crosstalk affects the data quality, especially at higher input powers. The statistics in this regime are nontrivial to obtain and we present, for the first time, a model based on a combination of theory and numerics that gives accurate statistics at a highly reduced computational cost. This model is obtained from an exact solution of WDM data being amplified in the strictly nonlinear regime which is derived in this paper. Using this model, predictions of the bit-error rate (BER) can be obtained even at very low rates impossible to reach by numerical methods alone. We show that there exists no trivial relationship between the BER and the commonly used quality measure, the Q-value. We also study how different amplifier parameters affect the statistics and suggest design rules to reduce channel crosstalk.