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Modelling the delayed nonlinear fiber response in coherent optical communications

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Document pages: 17 pages

Abstract: Fiber nonlinearities, that lead to nonlinear signal interference (NLI), aretypically regarded as an instantaneous material response with respect to theoptical field. However, in addition to an instantaneous part, the nonlinearfiber response consists of a delayed contribution, referred to as the Ramanresponse. The imaginary part of its Fourier transform, referred to as the Ramangain spectrum, leads to inter-channel stimulated Raman scattering (ISRS). ISRSis a nonlinear effect that redistributes optical power from high to lowerfrequencies during propagation. However, as the nonlinear fiber response iscausal, the Raman spectrum obeys the Kramers-Kronig relations resulting in thereal part of the complex valued Raman spectrum. While the impact of theimaginary part (i.e. ISRS) is well studied, the direct implications of itsassociated real part on the NLI are unexplored.In this work, a theory is proposed to analytically quantify the impact of thereal Raman spectrum on the nonlinear interference power. Starting from ageneralized Manakov equation, an extension of the ISRS Gaussian Noise (GN)model is derived to include the real Raman spectrum and, thus, to account forthe complete nonlinear Raman response. Accurate integral expressions arederived and approximations in closed-form are proposed. Different formulationsfor the case of single -and dual polarized signals are derived and novelanalytical approximations of the real Raman spectrum are proposed. Moreover, itis analytically shown that the real Raman spectrum scales the strength of theinstantaneous nonlinear distortions depending on the frequency separation ofthe interacting frequencies. A simple functional form is derived to assess thescaling of the NLI strength. The proposed theory is validated by numericalsimulations over C-and C+L band, using experimentally measured fiber data.

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