Synchronization processes in nonlinear systems and their relation to cortical oscillatory dynamics

This thesis was focused on theoretical models of synchronization to cortical dynamics as measured by magnetoencephalography (MEG). Dynamical systems theory was used in both identifying relevant variables for brain coordination and also in devising methods for their quantification. We presented a method for studying interactions of linear and chaotic neuronal sources using MEG beamforming techniques. We showed that such sources can be accurately reconstructed in terms of their location, temporal dynamics and possible interactions. Synchronization in low-dimensional nonlinear systems was studied to explore specific correlates of functional integration and segregation. In the case of interacting dissimilar systems, relevant coordination phenomena involved generalized and phase synchronization, which were often intermittent. Spatially-extended systems were then studied. For locally-coupled dissimilar systems, as in the case of cortical columns, clustering behaviour occurred. Synchronized clusters emerged at different frequencies and their boundaries were marked through oscillation death. The macroscopic mean field revealed sharp spectral peaks at the frequencies of the clusters and broader spectral drops at their boundaries. These results question existing models of Event Related Synchronization and Desynchronization. We re-examined the concept of the steady-state evoked response following an AM stimulus. We showed that very little variability in the AM following response could be accounted by system noise. We presented a methodology for detecting local and global nonlinear interactions from MEG data in order to account for residual variability. We found crosshemispheric nonlinear interactions of ongoing cortical rhythms concurrent with the stimulus and interactions of these rhythms with the following AM responses. Finally, we hypothesized that holistic spatial stimuli would be accompanied by the emergence of clusters in primary visual cortex resulting in frequency-specific MEG oscillations. Indeed, we found different frequency distributions in induced gamma oscillations for different spatial stimuli, which was suggestive of temporal coding of these spatial stimuli. Further, we addressed the bursting character of these oscillations, which was suggestive of intermittent nonlinear dynamics. However, we did not observe the characteristic-3/2 power-law scaling in the distribution of interburst intervals. Further, this distribution was only seldom significantly different to the one obtained in surrogate data, where nonlinear structure was destroyed. In conclusion, the work presented in this thesis suggests that advances in dynamical systems theory in conjunction with developments in magnetoencephalography may facilitate a mapping between levels of description int he brain. this may potentially represent a major advancement in neuroscience.

Quasi-lossless optical links for broad-band transmission and data processing

We present the first experimental implementation of a recently designed quasi-lossless fiber span with strongly reduced signal power excursion. The resulting fiber waveguide medium can be advantageously used both in lightwave communications and in all-optical nonlinear data processing.

An investigation into the relationship between pupil and accommodation responses during near vision

A Hamamatsu Video Area Analyser has been coupled with a modified Canon IR automatic optometer. This has allowed simultaneous recording of pupil diameter and accommodation response to be made both statically and continuously, a feature not common in previous studies. Experimental work concerned pupil and accommodation responses during near vision tasks under a variety of conditions. The effects of sustained near vision tasks on accommodation have usually been demonstrated by taking post-task measures under darkroom conditions. The possibility of similar effects on pupil diameter was assessed using static and continuous recordings following a near vision task. Results showed that is luminance levels remained unchanged by using a pre-and post-task bright-empty field then, although accommodation regressed to pre-task levels,pupil diameter remained for several minutes at the contstricted level induced by the task. An investigation into the effect of a sinusoidally-modulated blur-only accommodative stimulus on pupil response demonstrated that response may be reduced or absent despite robust accommodation responses. This suggests that blur-driven acommodation alone may not be sufficient to produce a pupil near response and that the presence of other cues may be necessary. Pupil response was investigated using a looming stimulus which produced an inferred-proximity cue. It was found that a pupil response could be induced which was in synchrony with the stimulus while closed-loop accommodation response was kept constant by the constraints of optical blur. The pupil diameter of young and elderly subjects undertaking a 5 minute reading task was measured to assess the contribution of pupil constriction to near vision function in terms of depth-of-focus. Results showed that in the young subjects pupil diameter was too large to have a significant effect on depth-of-focus although it may be increased in the elderly subjects. Pupil and accommodation reponses to a temporally-modulated stimulus containing all cues present in a normal visual environment was assessed and results showed that as stimulus temporal frequency increased, pupil response showed increasing phase lag relative to closed-loop accommodation. The results of this study suggest that it may be necessary to change the accepted view of the function of pupil response as part of the near vision triad and that further study would be of benefit in particular to designers of vision aids such as, for example, bifocal contact lenses.

Incoherent fibre supercontinuum generation for all-optical random number generation

Random number generation is a central component of modern information technology, with crucial applications in ensuring communications and information security. The development of new physical mechanisms suitable to directly generate random bit sequences is thus a subject of intense current research, with particular interest in alloptical techniques suitable for the generation of data sequences with high bit rate. One such promising technique that has received much recent attention is the chaotic semiconductor laser systems producing high quality random output as a result of the intrinsic nonlinear dynamics of its architecture [1]. Here we propose a novel complementary concept of all-optical technique that might dramatically increase the generation rate of random bits by using simultaneously multiple spectral channels with uncorrelated signals - somewhat similar to use of wave-division-multiplexing in communications. We propose to exploit the intrinsic nonlinear dynamics of extreme spectral broadening and supercontinuum (SC) generation in optical fibre, a process known to be often associated with non-deterministic fluctuations [2]. In this paper, we report proof-of concept results indicating that the fluctuations in highly nonlinear fibre SC generation can potentially be used for random number generation.

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.

Application of SOA-NOLM in all-optical processing

This thesis presents experimental investigations of the use of semiconductor optical amplifiers in a nonlinear loop mirror (SOA-NOLM) and its application in all-optical processing. The techniques used are mainly experimental and are divided into three major applications. Initially the semiconductor optical amplifier, SOA, is experimentally characterised and the optimum operating condition is identified. An interferometric switch based on a Sagnac loop with the SOA as the nonlinear element is employed to realise all-optical switching. All-optical switching is a very attractive alternative to optoelectronic conversion because it avoids the conversion from the optical to the electronic domain and back again. The first major investigation involves a carrier suppressed return to zero, CSRZ, format conversion and transmission. This study is divided into single channel and four channel WDM respectively. The optical bandwidth which limits the conversion is investigated. The improvement of the nonlinear tolerance in the CSRZ transmission is shown which shows the suitability of this format for enhancing system performance. Second, a symmetrical switching window is studied in the SOA-NOLM where two similar control pulses are injected into the SOA from opposite directions. The switching window is symmetric when these two control pulses have the same power and arrive at the same time in the SOA. Finally, I study an all-optical circulating shift register with an inverter. The detailed behaviour of the blocks of zeros and ones has been analysed in terms of their transient measurement. Good agreement with a simple model of the shift register is obtained. The transient can be reduced but it will affect the extinction ratio of the pulses.

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.

Random input problem for the nonlinear Schrödinger equation

We consider the random input problem for a nonlinear system modeled by the integrable one-dimensional self-focusing nonlinear Schrödinger equation (NLSE). We concentrate on the properties obtained from the direct scattering problem associated with the NLSE. We discuss some general issues regarding soliton creation from random input. We also study the averaged spectral density of random quasilinear waves generated in the NLSE channel for two models of the disordered input field profile. The first model is symmetric complex Gaussian white noise and the second one is a real dichotomous (telegraph) process. For the former model, the closed-form expression for the averaged spectral density is obtained, while for the dichotomous real input we present the small noise perturbative expansion for the same quantity. In the case of the dichotomous input, we also obtain the distribution of minimal pulse width required for a soliton generation. The obtained results can be applied to a multitude of problems including random nonlinear Fraunhoffer diffraction, transmission properties of randomly apodized long period Fiber Bragg gratings, and the propagation of incoherent pulses in optical fibers.

Femtosecond laser micro-inscription of optical coherence tomography resolution test artifacts

Optical coherence tomography (OCT) systems are becoming more commonly used in biomedical imaging and, to enable continued uptake, a reliable method of characterizing their performance and validating their operation is required. This paper outlines the use of femtosecond laser subsurface micro-inscription techniques to fabricate an OCT test artifact for validating the resolution performance of a commercial OCT system. The key advantage of this approach is that by utilizing the nonlinear absorption a three dimensional grid of highly localized point and line defects can be written in clear fused silica substrates.

Impact of third-order fibre dispersion on the evolution of parabolic optical pulses

We develop a perturbation analysis that describes the effect of third-order dispersion on the similariton pulse solution of the nonlinear Schrodinger equation in a fibre gain medium. The theoretical model predicts with sufficient accuracy the pulse structural changes induced, which are observed through direct numerical simulations.

Generation of triangular-shaped optical pulses in normally dispersive fibre

We determine through numerical modelling the conditions for the generation of triangular-shaped optical pulses in a nonlinear, normally dispersive (ND) fibre and experimentally demonstrate triangular pulse formation in conventional ND fibre.

Effects of fourth-order fiber dispersion on ultrashort parabolic optical pulses in the normal dispersion regime

We propose a new method for the generation of both triangular-shaped optical pulses and flat-top, coherent supercontinuum spectra using the effect of fourth-order dispersion on parabolic pulses in a passive, normally dispersive highly nonlinear fiber. The pulse reshaping process is described qualitatively and is compared to numerical simulations.

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.

New developments in the study of optical parabolic pulses in normally dispersive fibers

We report two recent studies dealing with the evolution of parabolic pulses in normally dispersive fibres. On the one hand, the nonlinear reshaping from a Gaussian intensity profile towards the asymptotic parabolic shape is experimentally investigated in a Raman amplifier. On the other hand, the significant impact of the fourth order dispersion on a passive propagation is theoretically discussed: we numerically demonstrate flat-top, coherent supercontinuum generation in an all-normal dispersion-flattened photonic crystal fiber. This shape is associated to a strong reshaping of the temporal profile what becomes triangular.