Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> The ISRS GN model in integral-form <s> An exact analytical solution for the evolution of stimulated Raman crosstalk in a singlemode WDM fiber system is presented utilizing the triangular approximation to the Raman gain spectrum. This approach provides a rigorous expression for crosstalk impairment. In the limit of small interchannel power exchange, our result reduces to Chraplyvy's previous estimate. Our formulation can be employed to predict the Raman penalty in future multiwavelength fiber communication systems. <s> BIB001 </s> Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> The ISRS GN model in integral-form <s> A Gaussian noise (GN) model is presented that properly accounts for an arbitrary frequency dependent signal power profile along the link. This enables the evaluation of the impact of inter-channel stimulated Raman scattering (ISRS) on the optical Kerr nonlinearity. Additionally, the frequency dependent fiber attenuation can be taken into account and transmission systems that use hybrid amplification schemes can be modeled, where distributed Raman amplification is partly applied over the optical spectrum. To include the latter two cases, a set of coupled ordinary differential equations must be numerically solved in order to obtain the signal power profile yielding a semi-analytical model. However for lumped amplification and negligible variation in fiber attenuation, a less complex and fully analytical model is presented which is referred to as the ISRS GN model. The derived model is exact to first-order for Gaussian modulated signals and extensively validated by numerical split-step simulations. A maximum deviation of $0.1$~dB in nonlinear interference power between simulations and the ISRS GN model is found. The model is applied to a transmission system that occupies an optical bandwidth of $10$~THz, representing the entire C+L band. At optimum launch power, changes of up to $2$~dB in nonlinear interference power due to ISRS are reported. Furthermore, comparable models published in the literature are benchmarked against the ISRS GN model. <s> BIB002 </s> Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> The ISRS GN model in integral-form <s> An analytical model to estimate nonlinear performance in ultra-wideband optical transmission networks is presented. The model accurately accounts for inter-channel stimulated Raman scattering, variably loaded fibre spans and is validated through C+L band simulations for uniform and probabilistically shaped 64-QAM. <s> BIB003
In order, to precisely account for arbitrary ISRS power transfers, as well as for distributed amplification, the GN model has been rederived to account for an arbitrary signal power profile [4]- BIB002 as being the power spectral density (PSD) of the signal at the transmitter and B i is the channel bandwidth. Eq. (2) can be used for multiple spans by interpreting ρ (ζ, f ) as the signal power profile of the entire link. Eq. (2) is exact to first-order for arbitrary power profiles, enabling the modelling of strong ISRS transfers and distributed amplification scenarios. The computational complexity is higher than the effective attenuation approach 2.1, due to an additional integration dimension over distance ζ. Moreover, the Raman equations must be solved manually for every span along the transmission link and substituted in BIB001 . For lumped amplification and optical bandwidths of up to 15 THz, the ISRS GN model can be written in analytical form, avoiding the necessity of solving the Raman equations, easing implementation and providing more insight into the underlying parameter dependencies. This is enabled by an approximate solution of the Raman equations BIB001 . This dramatically simplifies the description of ISRS which can then be parametrised by only a single parameter C r , which is a linear regression of the Raman gain spectrum. The NLI coefficient can then be written as BIB002 , BIB003  (3) where G k andP k are the signal PSD and total power launched into span k,L k is the accumulated distance of span k, L eff = 1−exp(−αζ) . Eq. (3) can be conveniently used to model the NLI in point-to-point transmission with different launch power distributions per span due to non-ideal gain equalisation as well as for complex ultra-wideband network scenarios BIB003 . The computational complexity of (3) is comparable to that of (2).