Q parameter estimation using numerical simulations for linear and nonlinear transmission systems

We compare the Q parameter obtained from scalar, semi-analytical and full vector models for realistic transmission systems. One set of systems is operated in the linear regime, while another is using solitons at high peak power. We report in detail on the different results obtained for the same system using different models. Polarisation mode dispersion is also taken into account and a novel method to average Q parameters over several independent simulation runs is described. © 2006 Elsevier B.V. All rights reserved.

Semi-analytical Q parameter estimate in linear and nonlinear transmission systems

We compare the Q parameter obtained from the semi-analytical model with scalar and vector models for two realistic transmission systems. First a linear system with a compensated dispersion map and second a soliton transmission system.

Expressions for the nonlinear transmission performance of multi-mode optical fiber

We develop an analytical theory which allows us to identify the information spectral density limits of multimode optical fiber transmission systems. Our approach takes into account the Kerr-effect induced interactions of the propagating spatial modes and derives closed-form expressions for the spectral density of the corresponding nonlinear distortion. Experimental characterization results have confirmed the accuracy of the proposed models. Application of our theory in different FMF transmission scenarios has predicted a ~10% variation in total system throughput due to changes associated with inter-mode nonlinear interactions, in agreement with an observed 3dB increase in nonlinear noise power spectral density for a graded index four LP mode fiber. © 2013 Optical Society of America.

Non-periodic quasi-stable nonlinear optical carrier pulses with sliding chirp-free points for transmission at 40 Gbit/s rate

In this paper, we demonstrate the possibility of reaching a quasi-stable nonlinear transmission regime with carrier pulses of 12.5 ps width in multi-channel 40 Gbit/s systems. The quasi-stable pulses that are presented in this work for the first time are not dispersion-managed solitons, and are indeed supported by a large normal span average dispersion and misbalanced optical amplification, and representing a new type of nonlinear carrier.

Capacity in nonlinear fiber transmission systems

We review the nonlinear channel capacity of optical fiber communication systems using both linear and nonlinear amplifiers. We show that the capacity of a nonlinear transmission system employing linear optical amplifiers can be enhanced by over 300% by using all optical regeneration. © OSA 2013.

How should pathogen transmission be modelled?

Host-pathogen models are essential for designing strategies for managing disease threats to humans, wild animals and domestic animals. The behaviour of these models is greatly affected by the way in which transmission between infected and susceptible hosts is modelled. Since host-pathogen models were first developed at the beginning of the 20th century, the 'mass action' assumption has almost always been used for transmission. Recently, however, it has been suggested that mass action has often been modelled wrongly. Alternative models of transmission are beginning to appear, as are empirical tests of transmission dynamics.

Nonlinear spectral management:linearization of the lossless fiber channel

Using the integrable nonlinear Schrodinger equation (NLSE) as a channel model, we describe the application of nonlinear spectral management for effective mitigation of all nonlinear distortions induced by the fiber Kerr effect. Our approach is a modification and substantial development of the so-called eigenvalue communication idea first presented in A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993). The key feature of the nonlinear Fourier transform (inverse scattering transform) method is that for the NLSE, any input signal can be decomposed into the so-called scattering data (nonlinear spectrum), which evolve in a trivial manner, similar to the evolution of Fourier components in linear equations. We consider here a practically important weakly nonlinear transmission regime and propose a general method of the effective encoding/modulation of the nonlinear spectrum: The machinery of our approach is based on the recursive Fourier-type integration of the input profile and, thus, can be considered for electronic or all-optical implementations. We also present a novel concept of nonlinear spectral pre-compensation, or in other terms, an effective nonlinear spectral pre-equalization. The proposed general technique is then illustrated through particular analytical results available for the transmission of a segment of the orthogonal frequency division multiplexing (OFDM) formatted pattern, and through WDM input based on Gaussian pulses. Finally, the robustness of the method against the amplifier spontaneous emission is demonstrated, and the general numerical complexity of the nonlinear spectrum usage is discussed. © 2013 Optical Society of America.

High spectral efficiency transmission emulation for non-linear transmission performance estimation for high order modulation formats

We demonstrate a simple method to experimentally evaluate nonlinear transmission performance of high order modulation formats using a low number of channels and channel-like ASE. We verify it's behaviour is consistent with the AWGN model of transmission.

Eigenvalue communications in nonlinear fiber channels

Continuous progress in optical communication technology and corresponding increasing data rates in core fiber communication systems are stimulated by the evergrowing capacity demand due to constantly emerging new bandwidth-hungry services like cloud computing, ultra-high-definition video streams, etc. This demand is pushing the required capacity of optical communication lines close to the theoretical limit of a standard single-mode fiber, which is imposed by Kerr nonlinearity [1–4]. In recent years, there have been extensive efforts in mitigating the detrimental impact of fiber nonlinearity on signal transmission, through various compensation techniques. However, there are still many challenges in applying these methods, because a majority of technologies utilized in the inherently nonlinear fiber communication systems had been originally developed for linear communication channels. Thereby, the application of ”linear techniques” in a fiber communication systems is inevitably limited by the nonlinear properties of the fiber medium. The quest for the optimal design of a nonlinear transmission channels, development of nonlinear communication technqiues and the usage of nonlinearity in a“constructive” way have occupied researchers for quite a long time.

PMD tolerant nonlinear compensation using in-line phase conjugation

In this paper, we numerically investigate the impact of polarisation mode dispersion on the efficiency of compensation of nonlinear transmission penalties for systems employing one of more inline phase conjugation devices. We will show that reducing the spacing between phase conjugations allows for significantly improved performance in the presence polarisation mode dispersion or a significant relaxation in the acceptable level of polarization mode dispersion. We show that these results are consistent with previously presented full statistical analysis of nonlinear transmission appropriately adjusted for the reduced section length undergoing compensation.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Nichtüberlappende Gebietszerlegungsmethoden für lineare und quasilineare (monotone und nichtmonotone) Probleme

In dieser Arbeit werden nichtüberlappende Gebietszerlegungsmethoden einerseits hinsichtlich der zu lösenden Problemklassen verallgemeinert und andererseits in bisher nicht untersuchten Kontexten betrachtet. Dabei stehen funktionalanalytische Untersuchungen zur Wohldefiniertheit, eindeutigen Lösbarkeit und Konvergenz im Vordergrund. Im ersten Teil werden lineare elliptische Dirichlet-Randwertprobleme behandelt, wobei neben Problemen mit dominantem Hauptteil auch solche mit singulärer Störung desselben, wie konvektions- oder reaktionsdominante Probleme zugelassen sind. Der zweite Teil befasst sich mit (gleichmäßig) monotonen koerziven quasilinearen elliptischen Dirichlet-Randwertproblemen. In beiden Fällen wird das Lipschitz-Gebiet in endlich viele Lipschitz-Teilgebiete zerlegt, wobei insbesondere Kreuzungspunkte und Teilgebiete ohne Außenrand zugelassen sind. Anschließend werden Transmissionsprobleme mit frei wählbaren $L^{\infty}$-Parameterfunktionen hergeleitet, wobei die Konormalenableitungen als Funktionale auf geeigneten Funktionenräumen über den Teilrändern ($H_{00}^{1/2}(\Gamma)$) interpretiert werden. Die iterative Lösung dieser Transmissionsprobleme mit einem Ansatz von Deng führt auf eine Substrukturierungsmethode mit Robin-artigen Transmissionsbedingungen, bei der eine Auswertung der Konormalenableitungen aufgrund einer geschickten Aufdatierung der Robin-Daten nicht notwendig ist (insbesondere ist die bekannte Robin-Robin-Methode von Lions als Spezialfall enthalten). Die Konvergenz bezüglich einer partitionierten $H^1$-Norm wird für beide Problemklassen gezeigt. Dabei werden keine über $H^1$ hinausgehende Regularitätsforderungen an die Lösungen gestellt und die Gebiete müssen keine zusätzlichen Glattheitsvoraussetzungen erfüllen. Im letzten Kapitel werden nichtmonotone koerzive quasilineare Probleme untersucht, wobei das Zugrunde liegende Gebiet nur in zwei Lipschitz-Teilgebiete zerlegt sein soll. Das zugehörige nichtlineare Transmissionsproblem wird durch Kirchhoff-Transformation in lineare Teilprobleme mit nichtlinearen Kopplungsbedingungen überführt. Ein optimierungsbasierter Lösungsansatz, welcher einen geeigneten Abstand der rücktransformierten Dirichlet-Daten der linearen Teilprobleme auf den Teilrändern minimiert, führt auf ein optimales Kontrollproblem. Die dabei entstehenden regularisierten freien Minimierungsprobleme werden mit Hilfe eines Gradientenverfahrens unter minimalen Glattheitsforderungen an die Nichtlinearitäten gelöst. Unter zusätzlichen Glattheitsvoraussetzungen an die Nichtlinearitäten und weiteren technischen Voraussetzungen an die Lösung des quasilinearen Ausgangsproblems, kann zudem die quadratische Konvergenz des Newton-Verfahrens gesichert werden.

Self-phase modulation dependent dispersion mitigation in high power SSB and DSB + dispersion compensated modulated radio-over-fiber links

The joint effect of fiber chromatic dispersion and fiber nonlinearity onto single-sideband and double-sideband modulated radio-over-fiber links is investigated. Experimental and simulated results show that modulation suppression caused by the chromatic dispersion in radio-over-fiber links can be successfully eliminated in both schemes only when the system is in the linear regime. Under nonlinear transmission the received microwave carrier power depends on the optical incident power.

Optical communications : past, present and future trends

In this talk we will review some of the key enabling technologies of optical communications and potential future bottlenecks. Single mode fibre (SMF) has long been the preferred waveguide for long distance communication. This is largely due to low loss, low cost and relative linearity over a wide bandwidth. As capacity demands have grown SMF has largely been able to keep pace with demand. Several groups have been identifying the possibility of exhausting the bandwidth provided by SMF [1,2,3]. This so called “capacity-crunch” has potentially vast economic and social consequences and will be discussed in detail. As demand grows optical power launched into the fibre has the potential to cause nonlinearities that can be detrimental to transmission. There has been considerable work done on identifying this nonlinear limit [4, 5] with a strong re- search interest currently on the topic of nonlinear compensation [6, 7]. Embracing and compensating for nonlinear transmission is one potential solution that may extend the lifetime of the current waveguide technology. However, at sufficiently high powers the waveguide will fail due to heat-induced mechanical failure. Moving forward it be- comes necessary to address the waveguide itself with several promising contenders discussed, including few-mode fibre and multi-core fibre.