Inter-channel Stimulated Raman Scattering Research Articles

Virtual Network Embedding Over Multi-Band Elastic Optical Network Based on Cross-Matching Mechanism and Hypergraph Theory

The commercialization of 5G and the explosive emergence of new applications stimulate the exponential growth of network traffic and diversification of services. It is promising to integrate multi-band elastic optical network (MBEON) and network virtualization for large volume traffic transmission and highly diverse services. However, performing virtual network embedding (VNE) for network virtualization over MBEON faces the challenge of severe inter-channel stimulated Raman scattering (ISRS) effect, which complicates the underlying physical layer effect in the substrate network. In this paper, we investigate the ISRS-aware VNE over MBEON, where a cross-matching mechanism is proposed for virtual node mapping (VNM) and a hypergraph is introduced for parallel virtual link mapping (VLM). A lightpath-level integer linear programming model is first formulated. To integrate the cost and availability of VLM, which significantly affect the performance of the VNE under the ISRS effect, into the VNM process, the “virtual node-substrate node” mapping pairs are specifically evaluated through the cross-matching mechanism. Moreover, to tackle the couplings among multiple lightpaths induced by the wide spectrum ISRS effect, hypergraphs are used to model the ISRS effect-aware quality of transmission (QoT) constraints among multiple lightpaths. A hypergraph maximal weight independent set heuristic is presented for lightpath selection, which guarantees the obedience of basic constraints and generates near-optimal solutions. Experimental results show that the proposed methods decrease blocking ratio by more than 30% compared with the benchmarks with similar computational complexity.

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

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.

Performance Analysis and Power Tilt Mitigation of Ultra-Wideband WDM Transmission Systems

Ultra-wideband (UWB) wavelength division multiplexing (WDM) transmission, which utilizes low-loss spectral windows of single-mode fiber for data transmission, is a highly promising method for increasing the capacity of optical communication. In this paper, we investigate the performance of a UWB WDM transmission system that covers the widely used C+L band as well as the additional O-, E-, and S-bands. We establish the transmission system for UWB and discuss the effects of the channel, including Kerr nonlinearity and inter-channel interference from inter-channel stimulated Raman scattering (ISRS) between O-, E-, S-, C-, and L-bands. Moreover, we demonstrate an optimization scheme for compensating the spectral power tilt caused by SRS in the S+C+L band system, which utilizes the Raman amplifier and the partition particle swarm optimization (PPSO) algorithm. The results show that the power tilt value of the algorithm is reduced from 18 to 2.93 dB, and the iteration speed is improved by 10% compared with the normal particle swarm algorithm. The scheme provides an efficient way to improve the generalized mutual information (GMI) performance of UWB WDM systems.

Impairment- and fragmentation-aware dynamic routing, modulation and spectrum allocation in C+L band elastic optical networks using Q-learning

The paper presents a Q-learning based dynamic routing algorithm for C+L band elastic optical networks (EONs) considering fiber impairments such as cross-phase modulation (XPM), self-phase modulation (SPM), amplified spontaneous emission (ASE), and inter-channel stimulated Raman scattering (ISRS). The effect of fragmentation is considered in the Q-learning process in addition to considering constraints related to spectrum continuity, contiguity, and non-overlapping. Three classical spectrum allocation strategies, first-fit, last-fit, and exact-fit are used after the Q-learning routing algorithm. The proposed routing, modulation, and spectrum allocation (RMSA) approach is shown to have a lower blocking probability compared with using K-shortest path routing combined with the three classical spectrum allocation strategies.

On the impact of launch power optimization and transceiver noise on the performance of ultra-wideband transmission systems [Invited

Ultra-wideband transmission is a promising, cost-effective solution to meet the increasing demand for data traffic in optical fiber systems. However, system performance and quality of transmission (QoT) are limited by fiber nonlinearity, in particular, interchannel stimulated Raman scattering (ISRS), leading to a power transfer from short to long wavelengths. As the result, per-channel launch power optimization is required to maximize the system throughput. In this paper, we investigate how the transceiver noise and launch power optimization impact the total throughput and the per-channel QoT for transmission bandwidths of up to 20 THz, using the S-, C-, and L-bands. To measure the gains through the optimum launch power profile, a spectrally uniform launch power is used as a baseline. Through experimental analysis and theoretical modeling, the main limitations constraining the achieved data throughput of 178 Tb/s over a continuous bandwidth of 16.83 THz and 40 km were investigated. The impact of the launch power optimization and the transceiver constrained signal-to-noise ratio (SNR) are analyzed and compared, and the approaches to overcome data throughput limitations are considered. An extensive theoretical investigation for different system configurations is described, demonstrating the trade-off between ISRS impact and transceiver noise. The former degrades the QoT and increases the gains in performance obtained by optimizing the launch power, while the latter reduces these gains and the SNR variation across the bandwidth, with a major impact over short distances.

Optimization strategy of power control for C+L+S band transmission using a simulated annealing algorithm.

To increase the transmission capacity, ultra-wideband wavelength-division multiplexing (UWB WDM) has been exploited to enlarge the spectral range. However, inter-channel stimulated Raman scattering (ISRS) results in power transition from high-frequency channels to low-frequency channels in wideband scenarios, which degrades the Q-factor of signals. Hence, we modify the optimization method of power control by applying the simulated annealing (SA) algorithm to search for the optimal power slopes and offsets of three bands to construct an optimum distribution of launch powers over channels. High transmission capacity can be reached by carrying 384 channels (96+96+192) in the C+L+S band with the consideration of dynamic Raman gain and channel-dependent parameters. We show that compared to using brute-force searching (BFS), a comparable and even higher transmission capacity can be achieved by the SA algorithm. Meanwhile, the searching speed of the SA algorithm is much faster. Also, different optimizing strategies can be selected to balance the trade-off between capacity and spectral flatness. This method can be used for designing arbitrary optical fiber UWB WDM systems before practical testing.

Multi-Band Elastic Optical Networks: Inter-Channel Stimulated Raman Scattering-Aware Routing, Modulation Level and Spectrum Assignment

Recently, multi-band elastic optical networks (MB-EONs) have been introduced to increase the transmission capacity of optical networks by expanding the transmission frequency range beyond the conventional C-band (e.g., O-, E-, S-, and L-band). Thus, by utilizing the idle frequency bands of the existing standard single mode fibers (SMFs), the capacity improvement in MB-EONs is achieved with lower capital expenditure compared to other techniques, such as space division multiplexing (SDM) in multi-core fibers (MCFs). The routing, modulation level and spectrum assignment (RMLSA) problem in MB-EONs is more challenging than that of the conventional single band EONs, and the inter-channel stimulated Raman scattering (ISRS) process should be considered in signal-to-noise ratio (SNR) analysis. In this article, ISRS-aware RMLSA problem in MB-EONs is studied. We obtain the optimal solution of this problem by formulating a path-based integer linear programming (ILP) model. Since the number of slots and demands are too large in a multi-band system, the ILP problem is too complex to be solved in polynomial time. Therefore, we propose heuristic algorithms to solve the ISRS-aware RMLSA problem. Then, performance of the proposed schemes is evaluated through exhaustive simulations. The results reveal that among all the proposed heuristic algorithms, the algorithm named as enhanced in-process estimation (EIPE) has the best performance in saving more frequency slots for future demands, while achieving higher spectral efficiency and SNR estimation accuracy. Moreover, for a special case of small-scale scenario, the performance of EIPE is close to the results of ILP formulation. Finally, our results indicate that by ignoring ISRS process in the SNR estimation, outage occurs for some of lightpaths, where the outage percentage depends on the launch power.

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 to the optical field. However, in addition to an instantaneous part, the nonlinear fiber response consists of 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 NLI are unexplored. In this work, a theory is proposed to analytically quantify the impact of the real Raman spectrum on the nonlinear interference power. Starting from a generalized Manakov equation, an extension of the ISRS Gaussian Noise (GN) model is derived to include the real 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 analytically shown that the real Raman spectrum scales the strength of the instantaneous nonlinear distortions depending on the frequency separation of the interacting frequencies. A simple functional form is derived to assess the scaling of the NLI strength. The proposed theory is validated by numerical simulations over C-and C+L band, using experimentally measured fiber data.

Modeling and mitigation of fiber nonlinearity in wideband optical signal transmission [Invited

The adoption of open optical networks (OONs) requires the development of open and effective network planning tools, enabling the use of multi-vendor or white-box transport solutions. Such tools for studying and planning optical networks must be able to take into account the physical layer impairments, including fiber nonlinearity. The use of wideband wavelength division multiplexing in OONs, with channel frequencies extending across the short, conventional, and long bands and beyond, offers a pathway to increasing data rates through the installed fiber infrastructure. However, achievable information rates are limited by the resulting signal distortion due to fiber nonlinearity as signal bandwidths are increased, in particular, inter-channel stimulated Raman scattering (ISRS). In this paper, we describe the nonlinear effects observed in wideband transmission systems, and review recently developed analytical tools, based on the Gaussian noise (GN) model of nonlinear interference with the inclusion of ISRS. Using the ISRS GN model, we assess the impact of fiber nonlinearity on the achievable information rates in transmission systems with bandwidths of up to 12 THz. We demonstrate the use of the model in the optimization of launch power spectral profiles for a variety of dynamic gain equalizer arrangements in a 1000 km standard single-mode fiber link, using particle swarm optimization and the steepest descent algorithm. Such nonlinear models and optimization methods could be applied in OON planning tools, for example, in optical link emulators to estimate quality-of-transmission and data throughput, and in impairment-aware software-defined network control and management.

Corrections to “A Modulation Format Correction Formula for the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering”

This document corrects a misprint in the printed version of this paper, published in vol 37, issue 19, pp. 5122–5131, Oct. 2019. The results, figures and conclusion are unchanged, and the error only appears in the print version of the manuscript.

Effect of Channel Launch Power on Fill Margin in C+L Band Elastic Optical Networks

Increasing traffic in the optical backbone network has made it incumbent upon operators to extend the use of optical spectrum beyond the C-band. In this work we estimate network performance over the C+L band using a physical layer model for estimating the optical signal to noise ratio (OSNR) for lightpaths operating over the C+L band optical spectrum. The model considers nonlinear interference (NLI) due to inter-channel stimulated Raman scattering (ISRS) and the impact of ISRS gain on amplified spontaneous emission (ASE) noise generated by in-line amplifiers while estimating the OSNR. This model is used to account for the capacity benefits associated with OSNR estimation while considering current state of spectral occupancy to account for NLI as compared to the fully-filled, worst-case NLI assumption. OSNR estimation based on current state of spectral occupancy provide higher capacity benefits for smaller networks like the BT-UK while for larger networks like the USA NSFNET the capacity benefit is significantly reduced. Further network capacity benefits of operating over C+L band as compared to C band have been reported. For BT-UK the capacity benefit is more than 100% while for larger networks like USA NSFNET the maximum capacity benefit is 73% with 37.5 GHz of bandwidth until 10% of demands are blocked.

A Modulation Format Correction Formula for the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

A closed-form formula is derived, which corrects for the modulation format dependence of the Gaussian Noise (GN) model in the presence of inter-channel stimulated Raman scattering (ISRS). The analytical result enables a rapid estimate of the nonlinear interference (NLI) for arbitrary modulation formats and avoids the need for complex integral evaluations and split-step simulations. It is shown that the modulation format dependent NLI can be approximated by two contributions, one originating from a single span and one asymptotic contribution for a large number of spans. The asymptotic contribution is solved in closed-form for an arbitrary link function, making the result applicable for generic fiber systems using lumped, distributed or hybrid amplification schemes. The methodology is applied to the ISRS GN model and a modulation format correction formula in closed-form is derived which accounts for an arbitrary number of spans, inter-channel stimulated Raman scattering, arbitrary launch power distributions and wavelength dependent dispersion and attenuation. The proposed formula is validated by numerical simulations over the entire C+L band for multiple fiber types.

A Closed-Form Approximation of the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

An accurate, closed-form expression evaluating the nonlinear interference (NLI) power in coherent optical transmission systems in the presence of inter-channel stimulated Raman scattering (ISRS) is derived. The analytical result enables a rapid estimate of the signal-to-noise ratio (SNR) and avoids the need for integral evaluations and split-step simulations. The formula also provides new insight into the underlying parameter dependence of ISRS on the NLI. The proposed result is applicable for dispersion unmanaged, ultra-wideband transmission systems that use optical bandwidths of up to 15 THz. The accuracy of the closed-form expression is compared to numerical integration of the ISRS Gaussian Noise model and split-step simulations in a point-to-point transmission, as well as in a mesh optical network scenario.

The Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

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.