Dark solitons in optical communication systems

This thesis presents experimental and theoretical work on the use of dark optical solitons as data carriers in communications systems. The background chapters provide an introduction to nonlinear optics, and to dark solitons, described as intensity dips in a bright background, with an asymmetrical phase profile. The motivation for the work is explained, considering both the superior stability of dark solitons and the need for a soliton solution suitable for the normal, rather than the anomalous (bright soliton) dispersion regime. The first chapters present two generation techniques, producing packets of dark solitons via bright pulse interaction, and generating continuous trains of dark pulses using a fibre laser. The latter were not dark solitons, but were suitable for imposition of the required phase shift by virtue of their extreme stability. The later chapters focus on the propagation and control of dark solitons. Their response to periodic loss and gain is shown to result in the exponential growth of spectral sidebands. This may be suppressed by reducing the periodicity of the loss/gain cycle or using periodic filtering. A general study of the response of dark solitons to spectral filtering is undertaken, showing dramatic differences in the behaviour of black and 99.9% grey solitons. The importance of this result is highlighted by simulations of propagation in noisy systems, where the timing jitter resulting from random noise is actually enhanced by filtering. The results of using sinusoidal phase modulation to control pulse position are presented, showing that the control is at the expense of serious modulation of the bright background. It is concluded that in almost every case, dark and bright solitons have very different properties, and to continue to make comparisons would not be so productive as to develop a deeper understanding of the interactions between the dark soliton and its bright background.

Wave chaotic behaviour generated by linear systems

It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time. © 2008 Springer Science+Business Media, LLC.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

An advanced real-time predictive maintenance framework for large scale machine systems

This thesis introduces and develops a novel real-time predictive maintenance system to estimate the machine system parameters using the motion current signature. Recently, motion current signature analysis has been addressed as an alternative to the use of sensors for monitoring internal faults of a motor. A maintenance system based upon the analysis of motion current signature avoids the need for the implementation and maintenance of expensive motion sensing technology. By developing nonlinear dynamical analysis for motion current signature, the research described in this thesis implements a novel real-time predictive maintenance system for current and future manufacturing machine systems. A crucial concept underpinning this project is that the motion current signature contains infor­mation relating to the machine system parameters and that this information can be extracted using nonlinear mapping techniques, such as neural networks. Towards this end, a proof of con­cept procedure is performed, which substantiates this concept. A simulation model, TuneLearn, is developed to simulate the large amount of training data required by the neural network ap­proach. Statistical validation and verification of the model is performed to ascertain confidence in the simulated motion current signature. Validation experiment concludes that, although, the simulation model generates a good macro-dynamical mapping of the motion current signature, it fails to accurately map the micro-dynamical structure due to the lack of knowledge regarding performance of higher order and nonlinear factors, such as backlash and compliance. Failure of the simulation model to determine the micro-dynamical structure suggests the pres­ence of nonlinearity in the motion current signature. This motivated us to perform surrogate data testing for nonlinearity in the motion current signature. Results confirm the presence of nonlinearity in the motion current signature, thereby, motivating the use of nonlinear tech­niques for further analysis. Outcomes of the experiment show that nonlinear noise reduction combined with the linear reverse algorithm offers precise machine system parameter estimation using the motion current signature for the implementation of the real-time predictive maintenance system. Finally, a linear reverse algorithm, BJEST, is developed and applied to the motion current signature to estimate the machine system parameters.

Analysis of magnetoencephaoographic data as a nonlinear dynamical system

This thesis presents the results from an investigation into the merits of analysing Magnetoencephalographic (MEG) data in the context of dynamical systems theory. MEG is the study of both the methods for the measurement of minute magnetic flux variations at the scalp, resulting from neuro-electric activity in the neocortex, as well as the techniques required to process and extract useful information from these measurements. As a result of its unique mode of action - by directly measuring neuronal activity via the resulting magnetic field fluctuations - MEG possesses a number of useful qualities which could potentially make it a powerful addition to any brain researcher's arsenal. Unfortunately, MEG research has so far failed to fulfil its early promise, being hindered in its progress by a variety of factors. Conventionally, the analysis of MEG has been dominated by the search for activity in certain spectral bands - the so-called alpha, delta, beta, etc that are commonly referred to in both academic and lay publications. Other efforts have centred upon generating optimal fits of "equivalent current dipoles" that best explain the observed field distribution. Many of these approaches carry the implicit assumption that the dynamics which result in the observed time series are linear. This is despite a variety of reasons which suggest that nonlinearity might be present in MEG recordings. By using methods that allow for nonlinear dynamics, the research described in this thesis avoids these restrictive linearity assumptions. A crucial concept underpinning this project is the belief that MEG recordings are mere observations of the evolution of the true underlying state, which is unobservable and is assumed to reflect some abstract brain cognitive state. Further, we maintain that it is unreasonable to expect these processes to be adequately described in the traditional way: as a linear sum of a large number of frequency generators. One of the main objectives of this thesis will be to prove that much more effective and powerful analysis of MEG can be achieved if one were to assume the presence of both linear and nonlinear characteristics from the outset. Our position is that the combined action of a relatively small number of these generators, coupled with external and dynamic noise sources, is more than sufficient to account for the complexity observed in the MEG recordings. Another problem that has plagued MEG researchers is the extremely low signal to noise ratios that are obtained. As the magnetic flux variations resulting from actual cortical processes can be extremely minute, the measuring devices used in MEG are, necessarily, extremely sensitive. The unfortunate side-effect of this is that even commonplace phenomena such as the earth's geomagnetic field can easily swamp signals of interest. This problem is commonly addressed by averaging over a large number of recordings. However, this has a number of notable drawbacks. In particular, it is difficult to synchronise high frequency activity which might be of interest, and often these signals will be cancelled out by the averaging process. Other problems that have been encountered are high costs and low portability of state-of-the- art multichannel machines. The result of this is that the use of MEG has, hitherto, been restricted to large institutions which are able to afford the high costs associated with the procurement and maintenance of these machines. In this project, we seek to address these issues by working almost exclusively with single channel, unaveraged MEG data. We demonstrate the applicability of a variety of methods originating from the fields of signal processing, dynamical systems, information theory and neural networks, to the analysis of MEG data. It is noteworthy that while modern signal processing tools such as independent component analysis, topographic maps and latent variable modelling have enjoyed extensive success in a variety of research areas from financial time series modelling to the analysis of sun spot activity, their use in MEG analysis has thus far been extremely limited. It is hoped that this work will help to remedy this oversight.

Numerical and statistical analysis of long-haul undersea optical communication systems

Firstly, we numerically model a practical 20 Gb/s undersea configuration employing the Return-to-Zero Differential Phase Shift Keying data format. The modelling is completed using the Split-Step Fourier Method to solve the Generalised Nonlinear Schrdinger Equation. We optimise the dispersion map and per-channel launch power of these channels and investigate how the choice of pre/post compensation can influence the performance. After obtaining these optimal configurations, we investigate the Bit Error Rate estimation of these systems and we see that estimation based on Gaussian electrical current systems is appropriate for systems of this type, indicating quasi-linear behaviour. The introduction of narrower pulses due to the deployment of quasi-linear transmission decreases the tolerance to chromatic dispersion and intra-channel nonlinearity. We used tools from Mathematical Statistics to study the behaviour of these channels in order to develop new methods to estimate Bit Error Rate. In the final section, we consider the estimation of Eye Closure Penalty, a popular measure of signal distortion. Using a numerical example and assuming the symmetry of eye closure, we see that we can simply estimate Eye Closure Penalty using Gaussian statistics. We also see that the statistics of the logical ones dominates the statistics of the logical ones dominates the statistics of signal distortion in the case of Return-to-Zero On-Off Keying configurations.

Investigation of different techniques to upgrade legacy WDM communication systems

This thesis presents experimental investigation of different effects/techniques that can be used to upgrade legacy WDM communication systems. The main issue in upgrading legacy systems is that the fundamental setup, including components settings such as EDFA gains, does not need to be altered thus the improvement must be carried out at the network terminal. A general introduction to optical fibre communications is given at the beginning, including optical communication components and system impairments. Experimental techniques for performing laboratory optical transmission experiments are presented before the experimental work of this thesis. These techniques include optical transmitter and receiver designs as well as the design and operation of the recirculating loop. The main experimental work includes three different studies. The first study involves a development of line monitoring equipment that can be reliably used to monitor the performance of optically amplified long-haul undersea systems. This equipment can provide instant finding of the fault locations along the legacy communication link which in tum enables rapid repair execution to be performed hence upgrading the legacy system. The second study investigates the effect of changing the number of transmitted 1s and Os on the performance of WDM system. This effect can, in reality, be seen in some coding systems, e.g. forward-error correction (FEC) technique, where the proportion of the 1s and Os are changed at the transmitter by adding extra bits to the original bit sequence. The final study presents transmission results after all-optical format conversion from NRZ to CSRZ and from RZ to CSRZ using semiconductor optical amplifier in nonlinear optical loop mirror (SOA-NOLM). This study is mainly based on the fact that the use of all-optical processing, including format conversion, has become attractive for the future data networks that are proposed to be all-optical. The feasibility of the SOA-NOLM device for converting single and WDM signals is described. The optical conversion bandwidth and its limitations for WDM conversion are also investigated. All studies of this thesis employ 10Gbit/s single or WDM signals being transmitted over dispersion managed fibre span in the recirculating loop. The fibre span is composed of single-mode fibres (SMF) whose losses and dispersion are compensated using erbium-doped fibre amplifiers (EDFAs) and dispersion compensating fibres (DCFs), respectively. Different configurations of the fibre span are presented in different parts.

Dissipative nonlinear structures in fiber optics

Optical fiber materials exhibit a nonlinear response to strong electric fields, such as those of optical signals confined within the small fiber core. Fiber nonlinearity is an essential component in the design of the next generation of advanced optical communication systems, but its use is often avoided by engineers because of its intractability. The application of nonlinear technologies in fiber optics offers new opportunities for the design of photonic systems and devices. In this chapter, we make an overview of recent progress in mathematical theory and practical applications of temporal dissipative solitons and self-similar nonlinear structures in optical fiber systems. The design of all-optical high-speed signal processing devices, based on nonlinear dissipative structures, is discussed.

Nonlinear pulse shaping in fibres for pulse generation and optical processing

The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science. Nonlinear phenomena occurring in optical fibres have many attractive features and great, but not yet fully explored, potential in signal processing. Here, we review recent progress on the use of fibre nonlinearities for the generation and shaping of optical pulses and on the applications of advanced pulse shapes in all-optical signal processing. Amongst other topics, we will discuss ultrahigh repetition rate pulse sources, the generation of parabolic shaped pulses in active and passive fibres, the generation of pulses with triangular temporal profiles, and coherent supercontinuum sources. The signal processing applications will span optical regeneration, linear distortion compensation, optical decision at the receiver in optical communication systems, spectral and temporal signal doubling, and frequency conversion. © Copyright 2012 Sonia Boscolo and Christophe Finot.

Localized waves in optical systems with periodic dispersion and nonlinearity management

We overview our recent developments in the theory of dispersion-managed (DM) solitons within the context of optical applications. First, we present a class of localized solutions with a period multiple to that of the standard DM soliton in the nonlinear Schrödinger equation with periodic variations of the dispersion. In the framework of a reduced ordinary differential equation-based model, we discuss the key features of these structures, such as a smaller energy compared to traditional DM solitons with the same temporal width. Next, we present new results on dissipative DM solitons, which occur in the context of mode-locked lasers. By means of numerical simulations and a reduced variational model of the complex Ginzburg-Landau equation, we analyze the influence of the different dissipative processes that take place in a laser.

Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation

We report the impact of longitudinal signal power profile on the transmission performance of coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation system after compensation of deterministic nonlinear fibre impairments. Performance improvements up to 0.6 dB (Q(eff)) are reported for a non-uniform transmission link power profile. Further investigation reveals that the evolution of the transmission performance with power profile management is fully consistent with the parametric amplification of the amplified spontaneous emission by the signal through four-wave mixing. In particular, for a non-dispersion managed system, a single-step increment of 4 dB in the amplifier gain, with respect to a uniform gain profile, at similar to 2/3(rd) of the total reach considerably improves the transmission performance for all the formats studied. In contrary a negative-step profile, emulating a failure (gain decrease or loss increase), significantly degrades the bit-error rate.

Nonlinearity compensation in multi-rate 28 Gbaud WDM systems employing optical and digital techniques under diverse link configurations

Digital back-propagation (DBP) has recently been proposed for the comprehensive compensation of channel nonlinearities in optical communication systems. While DBP is attractive for its flexibility and performance, it poses significant challenges in terms of computational complexity. Alternatively, phase conjugation or spectral inversion has previously been employed to mitigate nonlinear fibre impairments. Though spectral inversion is relatively straightforward to implement in optical or electrical domain, it requires precise positioning and symmetrised link power profile in order to avail the full benefit. In this paper, we directly compare ideal and low-precision single-channel DBP with single-channel spectral-inversion both with and without symmetry correction via dispersive chirping. We demonstrate that for all the dispersion maps studied, spectral inversion approaches the performance of ideal DBP with 40 steps per span and exceeds the performance of electronic dispersion compensation by ~3.5 dB in Q-factor, enabling up to 96% reduction in complexity in terms of required DBP stages, relative to low precision one step per span based DBP. For maps where quasi-phase matching is a significant issue, spectral inversion significantly outperforms ideal DBP by ~3 dB.

All-optical phase and amplitude regenerator for next-generation telecommunications systems

Fibre-optic communications systems have traditionally carried data using binary (on-off) encoding of the light amplitude. However, next-generation systems will use both the amplitude and phase of the optical carrier to achieve higher spectral efficiencies and thus higher overall data capacities(1,2). Although this approach requires highly complex transmitters and receivers, the increased capacity and many further practical benefits that accrue from a full knowledge of the amplitude and phase of the optical field(3) more than outweigh this additional hardware complexity and can greatly simplify optical network design. However, use of the complex optical field gives rise to a new dominant limitation to system performance-nonlinear phase noise(4,5). Developing a device to remove this noise is therefore of great technical importance. Here, we report the development of the first practical ('black-box') all-optical regenerator capable of removing both phase and amplitude noise from binary phase-encoded optical communications signals.

Design of Raman-based nonlinear loop mirror for all-optical 2R regeneration of differential phase-shift-keying transmission

We present a concept for all-optical regeneration of signals modulated in phase-sensitive modulation formats, which is based on a new design of Raman amplified nonlinear optical loop mirror (RA-NOLM). We demonstrate simultaneous amplitude-shape regeneration and phase-noise reduction in high-speed differential phase-shift-keying transmission systems by use of the RA-NOLM combined with spectral filtering.

All-optical passive quasi-regeneration in transoceanic 40 Gbit/s return-to-zero transmission systems with strong dispersion management

A method of all-optical passive quasi-regeneration in transoceanic 40 Gbit/s return-to-zero transmission systems with strong dispersion management was described. The use of in-line nonlinear optical loop mirrors (NOLM) by the method was demonstrated. The quasi-regeneration of signals performed by NOLMs was found to improve the systems's performance.