Modelling the Delayed Nonlinear Fiber Response in Coherent Optical Communications

Fiber nonlinearities, that lead to nonlinear signal interference (NLI), are typically regarded as an instantaneous material response with respect the optical field. However, in addition part, fiber consists of a delayed contribution, referred Raman response. The imaginary part its Fourier transform, gain spectrum, leads inter-channel stimulated scattering (ISRS). ISRS is effect redistributes power from high lower frequencies during propagation. causal, spectrum obeys Kramers-Kronig relations resulting real complex valued spectrum. While impact (i.e. ISRS) well studied, direct implications associated on NLI unexplored. In this work, theory proposed analytically quantify power. Starting generalized Manakov equation, extension Gaussian Noise (GN) model derived include and, thus, account for complete Accurate integral expressions and approximations closed-form proposed. Different formulations case single -and dual polarized signals novel analytical Moreover, it shown scales strength distortions depending frequency separation interacting frequencies. A simple functional form assess scaling strength. validated by numerical simulations over C-and C+L band, using experimentally measured data.