The EGN model of nonlinear propagation in coherent optical transmission systems and its applications

Modeling of nonlinear interference (NLI) generated by the fiber Kerr effect is a hot topic in coherent optical transmission systems. Four years ago, the Gaussian-noise (GN) model was proposed as an approximate tool for predicting the system maximum reach performance, in realistic optical coherent transmission scenarios, over lumped-amplification dispersion uncompensated links. For this specific use, the GN model has enjoyed substantial validation, both simulative and experimental. The original GN model reference formula (GNRF) only described the simple second-order fiber dispersion. In this thesis, we first extend that formula to take the general dispersive propagation constant into account. We then make a comparison with the results of the GNRF over various types of fibers with quite different dispersions. It turns out that third-order dispersion has a very substantial effect on nonlinearity, especially near a fiber dispersion-zero. It should be mentioned that the GN model may lose accuracy for fundamental reasons when approaching a dispersion zero. These can be overcome by the enhanced-GN (EGN) model, introduced below. On the other hand, the EGN model has two contributions, one of which is the GN model, so the extension of the GN model that was the first part of this thesis provides useful results for the EGN model too. The GN model predictions, when used to obtain a detailed picture of NLI accumulation along a link rather than an estimate of the system maximum reach, may be affected by a substantial overestimation error, especially in the first few spans of the link. The error is larger for low-cardinality formats and systems with very short spans, or that use nearly-ideal distributed amplification. In this thesis, we analyze in detail the GN model errors. We discuss recently proposed formulas for correcting such errors and show that they neglect several contributions to NLI, so that they may substantially underestimate NLI in specific situations, especially over low-dispersion fibers. We derive a complete set of formulas accounting for all single-, cross-, and multi-channel effects. This set of formulas constitutes what we have called the EGN model. We extensively validate the EGN model by comparison with accurate simulations in several different system scenarios. The overall EGN model accuracy is found to be very good when assessing detailed span-by-span NLI accumulation and excellent when estimating realistic system maximum reach. The computational complexity vs. accuracy trade-offs of the various versions of the GN and EGN models, and the presence and relevance of phase noise within NLI are discussed. However, although the EGN model is theoretically rigorous, the complexity is substantially larger than that of the GN model, which makes its use difficult for real-time applications. Fortunately, we are able to derive a simple closed-form GN model correction formula based on the EGN model. The GN model, together with the correction formula, provides a low-complexity approximation to the EGN model. Such approximation has limitations, but already in its present form it effectively and rather accurately corrects for the GN model tendency to overestimate NLI, which is carefully validated over a wide range of system scenarios. The correction formula also allows to clearly identify the correction dependence on key system parameter, such as span length and loss. As a reliable model, the EGN model is then employed to evaluate NLI generation in some study-cases: 1. Dispersion pre-compensation over mixed-fiber links: The dispersion pre-compensation impact both on homogeneous links (single fiber type) and inhomogeneous links (links using a mixture of high and low dispersion fibers) is analyzed. All results demonstrate that the EGN model is capable of dealing with the dispersion pre-compensation in mixed-fiber links. 2. Determining the optimum system symbol rate: The system symbol rate impact on NLI generation is studied in detail. The EGN model is found to be quite accurate in identifying the optimum symbol rate, as well as in predicting the related performance improvement. We also derived a simple closed-form formula that very reliably predicts the optimum symbol rate for quasi-Nyquist systems with lumped amplification. 3. NLI modeling for dynamically reconfigurable networks: the variability of NLI accumulation in dynamically reconfigurable networks with re-routing, different formats and accumulated dispersion is investigated. The EGN model can take the propagation history of all channels into account, and correctly assess NLI generation with different link features. Finally, an experiment is carried out to validate the EGN model for the first time. Using a PM-QPSK Nyquist WDM transmission, we confirm the enhanced accuracy of the EGN model comparing maximum reach predictions with those of the GN model

EGN model of non-linear fiber propagation

The GN-model has been proposed as an approximate but sufficiently accurate tool for predicting uncompensated optical coherent transmission system performance, in realistic scenarios. For this specific use, the GN-model has enjoyed substantial validation, both simulative and experimental. Recently, however, it has been pointed out that its predictions, when used to obtain a detailed picture of non-linear interference (NLI) noise accumulation along a link, may be affected by a substantial NLI overestimation error, especially in the first spans of the link. In this paper we analyze in detail the GN-model errors. We discuss recently proposed formulas for correcting such errors and show that they neglect several contributions to NLI, so that they may substantially underestimate NLI in specific situations, especially over low-dispersion fibers. We derive a complete set of formulas accounting for all single, cross, and multi-channel effects, This set constitutes what we have called the enhanced GN-model (EGN-model). We extensively validate the EGN model by comparison with accurate simulations in several different system scenarios. The overall EGN model accuracy is found to be very good when assessing detailed span-by-span NLI accumulation and excellent when estimating realistic system maximum reach. The computational complexity vs. accuracy trade-offs of the various versions of the GN and EGN models are extensively discussed

The GN-Model of Fiber Non-Linear Propagation and its Applications

Several approximate non-linear fiber propagation models have been proposed over the years. Recent reconsideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-noise (GN) model. The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy versus complexity trade-off. This paper tries to gather the recent results regarding the GN-model definition, understanding, relations versus other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environmen

Alcohol Metabolizing Enzymes, Microsomal Ethanol Oxidizing System, Cytochrome P450 2E1, Catalase, and Aldehyde Dehydrogenase in Alcohol-Associated Liver Disease

Once ingested, most of the alcohol is metabolized in the liver by alcohol dehydrogenase to acetaldehyde. Two additional pathways of acetaldehyde generation are by microsomal ethanol oxidizing system (cytochrome P450 2E1) and catalase. Acetaldehyde can form adducts which can interfere with cellular function, leading to alcohol-induced liver injury. The variants of alcohol metabolizing genes encode enzymes with varied kinetic properties and result in the different rate of alcohol elimination and acetaldehyde generation. Allelic variants of these genes with higher enzymatic activity are believed to be able to modify susceptibility to alcohol-induced liver injury; however, the human studies on the association of these variants and alcohol-associated liver disease are inconclusive. In addition to acetaldehyde, the shift in the redox state during alcohol elimination may also link to other pathways resulting in activation of downstream signaling leading to liver injury

Dynamic resistance measurement in a four-tape YBCO stack with various applied field orientation

The dynamic resistance which occurs when a superconductor carrying DC current is exposed to alternating magnetic field plays an important role in HTS applications such as flux pumps and rotating machines. We report experimental results on dynamic resistance in a four-tape coated conductor stack when exposed to AC magnetic fields with different magnetic field angles (the angles between the magnetic field and normal vector component of the tape surface, θ) at 77 K. The conductors for the stack are 4-mm-wide SuperPower SC4050 wires. The field angle was varied from 0° to 120° at a resolution of 15° to study the field angle dependence of dynamic resistance on field angle as well as wire Ic (B, θ). We also varied the field frequency, the magnetic field amplitude, and the DC current level to study the dependence of dynamic resistance on these parameters. Finally, we compared the measured dynamic resistance results at perpendicular magnetic field with the analytical models for single wires. Our results show that the dynamic resistance of the stack was mainly, but not solely, determined by the perpendicular magnetic component. Ic (B, θ) influences dynamic resistance in the stack due to tilting of the crystal lattice of the superconductor layer with regard to buffer layers. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

The GN-Model of Fiber Non-Linear Propagation and its Applications

Several approximate non-linear fiber propagation models have been proposed over the years. Recent reconsideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-noise (GN) model. The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy versus complexity trade-off. This paper tries to gather the recent results regarding the GN-model definition, understanding, relations versus other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment

Few-femtosecond Electron Beam with THz-frequency Wakefield-driven Compression

We propose and demonstrate a novel method to produce few-femtosecond electron beam with relatively low timing jitter. In this method a relativistic electron beam is compressed from about 150 fs (rms) to about 7 fs (rms, upper limit) with the wakefield at THz frequency produced by a leading drive beam in a dielectric tube. By imprinting the energy chirp in a passive way, we demonstrate through laser-driven THz streaking technique that no additional timing jitter with respect to an external laser is introduced in this bunch compression process, a prominent advantage over the conventional method using radio-frequency bunchers. We expect that this passive bunching technique may enable new opportunities in many ultrashort-beam based advanced applications such as ultrafast electron diffraction and plasma wakefield acceleration.Comment: 5 pages, 4 figure

Analytical and Experimental Results on System Maximum Reach Increase Through Symbol Rate Optimization

We investigated the reach increase obtained through nonlinearity mitigation by means of transmission symbol rate optimization (SRO). First, we did this theoretically and simulatively. We showed that the nonlinearity model that properly accounts for the phenomenon is the EGN model, in its version that specifically includes four-wave mixing. We then found that for PM-QPSK systems at full C-band, the reach increase may be substantial, on the order of 10–25%, with optimum symbol rates on the order of 2–6 GBd. We show that for C-band PM-QPSK systems over SMF, the potential mitigation due to SRO is greater than that ideally granted by digital backpropagation (the latter applied over a bandwidth of a 32-GBd channel). We then set up an experiment to obtain confirmation of the theoretical and simulative predictions. It consisted of 19 PM-QPSK channels, operating at 128 Gb/s per channel, over PSCF, with span length 108 km and EDFA-only amplification. We demonstrated a reach increase of about 13.5%, when going from single-carrier per channel transmission, at 32 GBd, to eight subcarrier per channel, at 4 GBd, in line with the EGN model predictions. We also extended the theoretical investigation of SRO to PM-16QAM, where we found a qualitatively similar effect to PM-QPSK, although the potential reach increase appears to be typically only about 50% to 60% that of PM-QPSK. Further investigation is, however, in order, specifically to explore the effect on PM-16QAM SRO of the removal of long-correlated phase and polarization noise

Experimental Investigation of Nonlinear Interference Accumulation in Uncompensated Links

Noise due to nonlinear effects in uncompensated links has recently been shown to be Gaussian and additive. We experimentally investigate the law governing its accumulation. Our results suggest a mild super-linear accumulation versus number of spans, compatible with coherent accumulation model