Compensating for dispersion and nonlinear Kerr effect without phase conjugation

We propose the use of a dispersive medium with a negative nonlinear refractive-index coefficient as a way to compensate for the dispersion and the nonlinear effects resulting from pulse propagation in an optical fiber. The undoing of pulse interaction might allow for increased bit rates.

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.

All-optical nonlinear fibre signal processing

All-optical technologies for data processing and signal manipulation are expected to play a major role in future optical communications. Nonlinear phenomena occurring in optical fibre have many attractive features and great, but not yet fully exploited potential in optical signal processing. Here, we overview our recent results and advances in developing novel photonic techniques and approaches to all-optical processing based on fibre nonlinearities. Amongst other topics, we will discuss phase-preserving optical 2R regeneration, the possibility of using parabolic/flat-top pulses for optical signal processing and regeneration, and nonlinear optical pulse shaping. A method for passive nonlinear pulse shaping based on pulse pre-chirping and propagation in a normally dispersive fibre will be presented. The approach provides a simple way of generating various temporal waveforms of fundamental and practical interest. Particular emphasis will be given to the formation and characterization of pulses with a triangular intensity profile. A new technique of doubling/copying optical pulses in both the frequency and time domains using triangular-shaped pulses will be also introduced.

New fiber laser architecture with transform-limited nonlinear spectral compression

We numerically demonstrate a new fiber laser architecture supporting spectral compression of negatively chirped pulses in passive normally dispersive fiber. Such a process is beneficial for improving the energy efficiency of the cavity as it prevents narrow spectral filtering from being highly dissipative. The proposed laser design provides an elegant way of generating transform-limited picosecond pulses. © 2012 IEEE.

Dispersion-dominated nonlinear fiber-optic channel

We propose to apply a large predispersion (having the same sign as the transmission fiber) to an optical signal before the uncompensated fiber transmission in coherent communication systems. This technique is aimed at simplifica- tion of the following digital signal processing of nonlinear impairments. We derive a model describing pulse propagation in the dispersion-dominated nonlinear fiber channel. In the limit of very strong initial predispersion, the nonlinear propagation equations for each Fourier mode become local and decoupled. This paves the way for new techniques to manage fiber nonlinearity.

From rogue waves to random walks:nonlinear instabilities in supercontinuum generation

The noise properties of supercontinuum generation continue to be a subject of wide interest within both pure and applied physics. Aside from immediate applications in supercontinuum source development, detailed studies of supercontinuum noise mechanisms have attracted interdisciplinary attention because of links with extreme instabilities in other physical systems, especially the infamous and destructive oceanic rogue waves. But the instabilities inherent in supercontinuum generation can also be interpreted in terms of natural links with the general field of random processes, and this raises new possibilities for applications in areas such as random number generation. In this contribution we will describe recent work where we interpret supercontinuum intensity and phase fluctuations in this way.

New fiber laser architecture with transform-limited nonlinear spectral compression

We numerically demonstrate a new fiber laser architecture supporting spectral compression of negatively chirped pulses in passive normally dispersive fiber. Such a process is beneficial for improving the energy efficiency of the cavity as it prevents narrow spectral filtering from being highly dissipative. The proposed laser design provides an elegant way of generating transform-limited picosecond pulses. © 2012 IEEE.

Compensating for dispersion and nonlinear Kerr effect without phase conjugation

We propose the use of a dispersive medium with a negative nonlinear refractive-index coefficient as a way to compensate for the dispersion and the nonlinear effects resulting from pulse propagation in an optical fiber. The undoing of pulse interaction might allow for increased bit rates.

All-optical nonlinear fibre signal processing

All-optical technologies for data processing and signal manipulation are expected to play a major role in future optical communications. Nonlinear phenomena occurring in optical fibre have many attractive features and great, but not yet fully exploited potential in optical signal processing. Here, we overview our recent results and advances in developing novel photonic techniques and approaches to all-optical processing based on fibre nonlinearities. Amongst other topics, we will discuss phase-preserving optical 2R regeneration, the possibility of using parabolic/flat-top pulses for optical signal processing and regeneration, and nonlinear optical pulse shaping. A method for passive nonlinear pulse shaping based on pulse pre-chirping and propagation in a normally dispersive fibre will be presented. The approach provides a simple way of generating various temporal waveforms of fundamental and practical interest. Particular emphasis will be given to the formation and characterization of pulses with a triangular intensity profile. A new technique of doubling/copying optical pulses in both the frequency and time domains using triangular-shaped pulses will be also introduced.

Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers

In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear Schrödinger equation, there are nonlinear modes (nonlinear signal spectrum) that also propagate without interacting with each other and without corresponding nonlinear cross talk, effectively, in a linear manner. Here, we describe in a constructive way how to introduce such nonlinear modes for a given input signal. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. This transmission technique, combined with the appropriate distributed Raman amplification, can provide an effective eigenvalue division multiplexing with high spectral efficiency, thanks to highly suppressed channel cross talk. The proposed NIS approach can be integrated with any modulation formats. Here, we demonstrate numerically the feasibility of merging the NIS technique in a burst mode with high spectral efficiency methods, such as orthogonal frequency division multiplexing and Nyquist pulse shaping with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 4.5 dB, which is comparable to results achievable with multi-step per span digital back propagation.

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.

Periodic nonlinear Fourier transform for fiber-optic communications, Part II:eigenvalue communication

In this paper we propose the design of communication systems based on using periodic nonlinear Fourier transform (PNFT), following the introduction of the method in the Part I. We show that the famous "eigenvalue communication" idea [A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993)] can also be generalized for the PNFT application: In this case, the main spectrum attributed to the PNFT signal decomposition remains constant with the propagation down the optical fiber link. Therefore, the main PNFT spectrum can be encoded with data in the same way as soliton eigenvalues in the original proposal. The results are presented in terms of the bit-error rate (BER) values for different modulation techniques and different constellation sizes vs. the propagation distance, showing a good potential of the technique.