A Closed-Form Expression for the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering Extended for Arbitrary Loss and Fibre Length

Abstract

A closed-form formula for the nonlinear interference (NLI) estimation using the Gaussian noise (GN) model in the presence of inter-channel stimulated Raman scattering (ISRS) is derived. The formula enables accurate estimation of the NLI evolution along any portion of the fibre span together with arbitrary values of optical fibre losses. The formula also accounts for wavelength-dependent fibre parameters, variable modulation formats and launch power profiles. The formula is suitable for ultra-wideband (UWB) optical transmission systems and its accuracy is assessed for a system with 20 THz optical bandwidth over the entire S-, C-, and L-band through comparison with numerical integration of the ISRS GN model and split-step Fourier method (SSFM) simulations in point-to-point transmission and inline NLI estimation scenarios.

A Closed-Form Expression for the Gaussian Noise Model in the Presence of Raman Amplification

“…The remaining launch power can be recovered, for instance, with lumped amplification. An example of fully recovered launch power using RA can be found in [30]. For all scenarios, the pumps' allocation with non-zero power found by the described algorithm is shown in Table I.…”

“…We also include a complete discussion on the semi-analytical approach used to obtain an accurate estimation of the fibre signal profile evolution along the fibre distance. This work together with [30] represents the first closed-form expression of the GN model supporting FW-RA and BW-RA in the presence of ISRS.…”

“…Of interest for UWB transmission systems are closed-form expressions for the GN model in the presence of ISRS effect [18], namely ISRS GN model. Closedform expressions of this model were derived in [20]- [28].…”

“…The closed-form expression presented in this work was first published in [30]. In this work, we extensively discuss its validation and present all the mathematical derivations used to obtain it.…”

Multi-Band Transmission Over E-, S-, C- and L-Band With a Hybrid Raman Amplifier

“…Together with experimental designs and demonstrations using Raman amplifiers, real-time nonlinear modelling of MBT is an essential tool to introduce intelligence, achieve the best resource allocation and maximise system throughput in the optical networks [30], [31]. For Raman amplified links, one way of achieving that goal is using analytical expressions of the Gaussian noise (GN) model in the presence of Raman amplification [32], [33]. Such real-time prediction enables an efficient and fast design of the Raman pumps, achieving the desired amplification gain dynamically in the network [34], [35].…”