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.

Observations of diffraction and self diffraction effects during two wave mixing in a nematic liquid crystal

We report observations of the diffraction pattern resulting when a nematic liquid crystal is illuminated with two equal power, high intensity beams of light from an Ar+ laser. The time evolution of the pattern is followed from the initial production of higher diffraction orders to a final striking display arising as a result of the self-diffraction of the two incident beams. The experimental results are described with good approximation by a model assuming a phase distribution at the output plane of the liquid crystal in the form of the sum of a gaussian and a sinusoid.

The application of fibre Bragg grating networks as strain sensors and as phased array antenna true time delay elements

The fabrication of in-fibre Bragg gratings, and the application of arrays of such gratings as strain sensors and as true time delay elements for the control of phased array antennas is reported. Chirped period Bragg gratings were produced using the fibre deformation fabrication technique, with chirps of between 2.9nm and 17.3nm achieved. Arrays of 5mm and 2mm long uniform period Bragg gratings were fabricated using the inscription method, for use as true time delay elements,dissimilar wavefronts and their spectral characteristics recorded. The uniform period grating arrays were used to create minimum time delays of 9.09ps, 19.02ps and 31ps; making them suitable for controlling phased array antennas operating at RF frequencies of up to 3GHz, with 10° phase resolution. Four 4mm long chirped gratings were produced using the dissimilar wavefronts fabrication method, having chirps of 7nm, 12nm, 20nm and 30nm, and were used to create time delays of between 0.3ps and 59ps. Hence they are suitable for controlling phased array antennas at RF frequencies of up to 48GHz. The application of in fibre Bragg gratings as strain sensors within smart structure materials was investigated, with their sensitivity to applied strain and compression measured for both embedded and surface mounted uniform period and fibre Fabry-Perot filter gratings. A fibre Bragg grating sensor demultiplexing scheme based on a liquid crystal filled Fabry-Perot etalon tuneable transmission filter was proposed, successfully constructed and fully characterised. Three characteristics of the LCFP etalon were found to pose operational limitations to its application in a Bragg grating sensor system; most significantly, the resonance peak wavelength was highly (-2,77nm/°C) temperature dependent. Several methods for minimising this temperature sensitivity were investigated, but enjoyed only limited success. It was therefore concluded that this type (E7 filled) of LCFP etalon is unsuitable for use as a Bragg grating sensor demultiplexing element.

Strong spectral filtering for a mode-locked similariton fiber laser

We propose a novel mode-locked fiber laser design that relies on attracting similariton solutions in fiber amplifiers with normal group-velocity dispersion and strong spectral filtering to compensate increased pulse duration and bandwidth. Stable high-energy, large-bandwidth pulses are obtained that can be linearly compressed, resulting in ultrashort pulses.

Amplifier similariton fiber laser with nonlinear spectral compression

We propose a new concept of a fiber laser architecture supporting self-similar pulse evolution in the amplifier and nonlinear spectral pulse compression in the passive fiber. The latter process allows for transform-limited picosecond pulse generation, and improves the laser’s power efficiency by preventing strong spectral filtering from being highly dissipative. Aside from laser technology, the proposed scheme opens new possibilities for studying nonlinear dynamical processes. As an example, we demonstrate a clear period-doubling route to chaos in such a nonlinear laser system.

Towards a practical implementation of coherent WDM:analytical, numerical, and experimental studies

Future optical networks will require the implementation of very high capacity (and therefore spectral efficient) technologies. Multi-carrier systems, such as Orthogonal Frequency Division Multiplexing (OFDM) and Coherent WDM (CoWDM), are promising candidates. In this paper, we present analytical, numerical, and experimental investigations of the impact of the relative phases between optical subcarriers of CoWDM systems, as well as the effect that the number of independently modulated subcarriers can have on the performance. We numerically demonstrate a five-subcarrier and three-subcarrier 10-GBd CoWDM system with direct detected amplitude shift keying (ASK) and differentially/coherently detected (D) phase shift keying (PSK). The simulation results are compared with experimental measurements of a 32-Gbit/s DPSK CoWDM system in two configurations. The first configuration was a practical 3-modulator array where all three subcarriers were independently modulated, the second configuration being a traditional 2-modulator odd/even configuration, where only odd and even subcarriers were independently modulated. Simulation and experimental results both indicate that the independent modulation implementation has a greater dependency on the relative phases between subcarriers, with a stronger penalty for the center subcarrier than the odd/even modulation scheme.

Enhanced spectral sensitivity of fibre long period gratings to refractive index of aqueous solutions utilising copper patterned coatings

A set of long period grating devices have been fabricated in photosensitive single mode fibre coated with a series of copper rings (period of 380μm, 50% duty cycle and length of 4cm). The long period gratings were inscribed with a uniform UV-laser exposure across the entire length of the copper ring patterned coating. The devices ranged in copper thickness from 0.5μm to 1.5μm. In addition, a control long period grating was fabricated in the same type of fibre with the same period for comparison. The refractive index and temperature spectral sensitivity of these devices were investigated and it was found that the index and temperature sensitivity is a function of the thickness of the copper rings, as supported by theoretical modelling. Furthermore, the index sensitivity of these devices in the 1.333 index region is greater than the control long period grating. The patterned 0.5μm coated long period grating gave a sensitivity of Δλ/Δn = -74 nm leading to a resolution of 1.4×10-3 compared to the control which had a sensitivity of Δλ/Δn = -32 nm with a resolution of 3.2×10-3 in the index region of 1.320 to 1.380 (aqueous solution regime). This demonstrates a two fold increase in the sensitivity. This novel fibre long period grating device shows potential for increasing the resolution of measurements of the index of aqueous solutions.

Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.

A near real-time water surface detection method based on HSV transformation of MODIS multi-Spectral time series data

In the face of global population growth and the uneven distribution of water supply, a better knowledge of the spatial and temporal distribution of surface water resources is critical. Remote sensing provides a synoptic view of ongoing processes, which addresses the intricate nature of water surfaces and allows an assessment of the pressures placed on aquatic ecosystems. However, the main challenge in identifying water surfaces from remotely sensed data is the high variability of spectral signatures, both in space and time. In the last 10 years only a few operational methods have been proposed to map or monitor surface water at continental or global scale, and each of them show limitations. The objective of this study is to develop and demonstrate the adequacy of a generic multi-temporal and multi-spectral image analysis method to detect water surfaces automatically, and to monitor them in near-real-time. The proposed approach, based on a transformation of the RGB color space into HSV, provides dynamic information at the continental scale. The validation of the algorithm showed very few omission errors and no commission errors. It demonstrates the ability of the proposed algorithm to perform as effectively as human interpretation of the images. The validation of the permanent water surface product with an independent dataset derived from high resolution imagery, showed an accuracy of 91.5% and few commission errors. Potential applications of the proposed method have been identified and discussed. The methodology that has been developed 27 is generic: it can be applied to sensors with similar bands with good reliability, and minimal effort. Moreover, this experiment at continental scale showed that the methodology is efficient for a large range of environmental conditions. Additional preliminary tests over other continents indicate that the proposed methodology could also be applied at the global scale without too many difficulties

Observations of diffraction and self diffraction effects during two wave mixing in a nematic liquid crystal

We report observations of the diffraction pattern resulting when a nematic liquid crystal is illuminated with two equal power, high intensity beams of light from an Ar+ laser. The time evolution of the pattern is followed from the initial production of higher diffraction orders to a final striking display arising as a result of the self-diffraction of the two incident beams. The experimental results are described with good approximation by a model assuming a phase distribution at the output plane of the liquid crystal in the form of the sum of a gaussian and a sinusoid.

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.

Intensity dynamics and statistical properties of random distributed feedback fiber laser

We present first experimental investigation of fast-intensity dynamics of random distributed feedback (DFB) fiber lasers. We found that the laser dynamics are stochastic on a short time scale and exhibit pronounced fluctuations including generation of extreme events. We also experimentally characterize statistical properties of radiation of random DFB fiber lasers. We found that statistical properties deviate from Gaussian and depend on the pump power.

Control of the in-cavity dynamics in mode-locked fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral intensity profile, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this talk, we review our recent progress on the realisation of different regimes of pulse generation in passively mode-locked fibre lasers through control of the in-cavity propagation dynamics. We report on the possibility to achieve both parabolic self-similar and triangular pulse shaping in a mode-locked fibre laser via adjustment of the net normal dispersion and integrated gain of the cavity [1]. We also show that careful control of the gain/loss parameters of a net-normal dispersion laser cavity provides the means of achieving switching among Gaussian pulse, dissipative soliton and similariton pulse solutions in the cavity [2,3]. Furthermore, we report on our recent theoretical and experimental studies of pulse shaping by inclusion of an amplitude and phase spectral filter into the cavity of a laser. We numerically demonstrate that a mode-locked fibre laser can operate in dif- ferent pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [4]. An application of technique using a flat-top spectral filter is demonstrated to achieve the direct generation of sinc-shaped optical Nyquist pulses of high quality and of a widely tuneable bandwidth from the laser [5]. We also report on a recently-developed versa- tile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soli- ton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [6]. References: 1. S. Boscolo and S. K. Turitsyn, Phys. Rev. A 85, 043811 (2012). 2. J. Peng et al., Phys. Rev. A 86, 033808 (2012). 3. J. Peng, Opt. Express 24, 3046-3054 (2016). 4. S. Boscolo, C. Finot, H. Karakuzu, and P. Petropoulos, Opt. Lett. 39, 438-441 (2014). 5. S. Boscolo, C. Finot, and S. K. Turitsyn, IEEE Photon. J. 7, 7802008 (2015). 6. J. Peng and S. Boscolo, Sci. Rep. 6, 25995 (2016).

In-cavity pulse shaping and dissipative parametric instability mode-locking in fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral shape, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this work, we review our recent progress on the realisation of pulse shaping in passively- mode-locked fibre lasers by inclusion of an amplitude and phase spectral filter into the laser cavity. We present a fibre laser design in which pulse shaping occurs through filtering of a spectrally nonlinearly broadened pulse in the cavity. This strategy of pulse shaping is illustrated through the numerical demonstration of the laser operation in different pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [1]. As an application of this general approach, we show that the use of an in-cavity flat-top spectral filter makes it possible to directly generate sinc-shaped Nyquist pulses of high quality and of a widely tunable bandwidth from the laser [2]. We also report on a recently-developed versatile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soliton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [3]. Further, we report on our recent results on the passive mode locking of a Raman fibre laser by a recently predicted new type of parametric instability – the dissipative Faraday instability [4], where spatially periodic zig-zag modulation of spectrally dependent losses can lead to pattern formation in the temporal domain. High-order harmonic mode locking is achieved in a very simple experimental configuration, with the laser cavity including an optical fibre and two chirped fibre Bragg gratings, and no additional mode-locking elements. The results not only open up new possibilities for the design of mode-locked lasers, but extend beyond fibre optics to other fields of physics and engineering. References [1] S. Boscolo, C. Finot, H. Karakuzu, P. Petropoulos, “Pulse shaping in mode-locked fiber laser by in-cavity spectral filter,” Opt. Lett., vol. 39, pp. 438–441, 2014. [2] S. Boscolo, C. Finot, S. K. Turitsyn, “Bandwidth programmable optical Nyquist pulse generation in passively mode-locked fiber laser,” IEEE Photon. J., vol. 7, 7802008(8), 2015. [3] J. Peng, S. Boscolo, “Filter-based dispersion-managed versatile ultrafast fibre laser,” Sci. Rep., 2016, In press. [4] A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett., vol. 116, 028701, 2016.

An autoregressive conditional filtering process to remove intraday seasonal volatility and its application to testing the noisy rational expectations model

We develop a new autoregressive conditional process to capture both the changes and the persistency of the intraday seasonal (U-shape) pattern of volatility in essay 1. Unlike other procedures, this approach allows for the intraday volatility pattern to change over time without the filtering process injecting a spurious pattern of noise into the filtered series. We show that prior deterministic filtering procedures are special cases of the autoregressive conditional filtering process presented here. Lagrange multiplier tests prove that the stochastic seasonal variance component is statistically significant. Specification tests using the correlogram and cross-spectral analyses prove the reliability of the autoregressive conditional filtering process. In essay 2 we develop a new methodology to decompose return variance in order to examine the informativeness embedded in the return series. The variance is decomposed into the information arrival component and the noise factor component. This decomposition methodology differs from previous studies in that both the informational variance and the noise variance are time-varying. Furthermore, the covariance of the informational component and the noisy component is no longer restricted to be zero. The resultant measure of price informativeness is defined as the informational variance divided by the total variance of the returns. The noisy rational expectations model predicts that uninformed traders react to price changes more than informed traders, since uninformed traders cannot distinguish between price changes caused by information arrivals and price changes caused by noise. This hypothesis is tested in essay 3 using intraday data with the intraday seasonal volatility component removed, as based on the procedure in the first essay. The resultant seasonally adjusted variance series is decomposed into components caused by unexpected information arrivals and by noise in order to examine informativeness.