4.7 Article

Modelling the Delayed Nonlinear Fiber Response in Coherent Optical Communications

期刊

JOURNAL OF LIGHTWAVE TECHNOLOGY
卷 39, 期 7, 页码 1937-1952

出版社

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JLT.2020.3046998

关键词

Mathematical model; Analytical models; Optical imaging; Nonlinear optics; Optical distortion; Optical scattering; Numerical models; C plus L band transmission; delayed nonlinear response; first-order perturbation; Gaussian noise model; Kramers– Kronig relations; nonlinear distortion; nonlinear interference; optical fiber communications; Raman spectrum; stimulated raman scattering

资金

  1. U.K. EPSRC Programme TRANSNET [EP/R035342/1]
  2. EPSRC [EP/R035342/1] Funding Source: UKRI

向作者/读者索取更多资源

The research reveals that the direct implications of the real part of the Raman spectrum on nonlinear distortions in optical fibers have not been extensively explored. A theory is proposed in this work to quantitatively assess the impact of the real Raman spectrum on nonlinear interference power (NLI), offering a new perspective on understanding and modeling nonlinear signal distortion.
Fiber nonlinearities, that lead to nonlinear signal distortion, are normally considered to be the result of an instantaneous material response with respect to the optical field. However, in addition to an instantaneous part, the nonlinear fiber response includes a delayed contribution, referred to as the Raman response. The imaginary part of its Fourier transform, referred to as the Raman gain spectrum, leads to inter-channel stimulated Raman scattering (ISRS). ISRS is a nonlinear effect that redistributes optical power from high to lower frequencies during propagation. However, as the nonlinear fiber response is causal, the Raman spectrum obeys the Kramers-Kronig relations resulting in the real part of the complex valued Raman spectrum. While the impact of the imaginary part (i.e. ISRS) is well studied, the direct implications of its associated real part on the nonlinear distortions are unexplored. In this work, a theory is proposed to analytically quantify the impact of the real Raman spectrum on the nonlinear interference power (NLI), which models nonlinear distortion as noise in optical transmission. Starting from a generalized Manakov equation, an extension of the ISRS Gaussian Noise (GN) model is derived to include the real part of the Raman spectrum and, thus, to account for the complete nonlinear Raman response. Accurate integral expressions are derived and approximations in closed-form are proposed. Different formulations for the case of single -and dual polarized signals are derived and novel analytical approximations of the real Raman spectrum are proposed. Moreover, it is shown that the impact of the real Raman spectrum can be considered as a multiplicative factor to the instantaneous nonlinear distortions depending on the frequency separation of the interacting frequencies. A simple functional form is derived to assess the multiplicative impact of the real Raman spectrum on the NLI. The proposed theory is validated by numerical simulations over C-and C+L band, using experimentally measured fiber data.

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