Pulse Collision Picture of Inter-Channel Nonlinear Interference in Fiber-Optic Communications

We model the build-up of inter-channel nonlinear interference noise (NLIN) that is generated by cross-phase-modulation in wavelength division multiplexed systems by considering the pulse collision dynamics in the time domain. The fundamental interactions can be classified as two-pulse, three-pulse, or four-pulse collisions, and they can be either complete, or incomplete. Each type of collision is shown to have its unique signature and the overall nature of NLIN is determined by the relative importance of the various classes of pulse collisions in a given wavelength division multiplexed (WDM) system. The pulse-collision picture provides qualitative and quantitative insight into the character of NLIN, offering a simple and intuitive explanation to all of the reported and previously unexplained phenomena. In particular, we show that the most important contributions to NLIN follow from two-pulse and four-pulse collisions. While the contribution of two-pulse collisions is in the form of phase-noise and polarization-state-rotation with strong dependence on modulation format, four-pulse collisions generate complex circular noise whose variance is independent of modulation format. In addition, two-pulse collisions are strongest when the collision is complete, whereas four-pulse collisions are strongest when the collision is incomplete. We show that two-pulse collisions dominate the formation of NLIN in short links with lumped amplification, or in links with distributed amplification extending over arbitrary length. In long links using lumped amplification, the relative significance of four-pulse collisions increases, emphasizing the circularity of the NLIN while reducing its dependence on modulation format.