Passive nonlinear pulse shaping in normally dispersive fiber systems

We propose a novel approach to characterize the parabolically-shaped pulses that can be generated from more conventional pulses via nonlinear propagation in cascaded sections of commercially available normally dispersive (ND) fibers. The impact of the initial pulse chirp on the passive pulse reshaping is examined. We furthermore demonstrate that the combination of pulse pre-chirping and propagation in a single ND fiber yields a simple, passive method for generating various temporal waveforms of practical interest.

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.

Nonlinear spectral shaping and optical rogue events in fiber-based systems

We provide an overview of our recent work on the shaping and stability of optical continua in the long pulse regime. Fibers with normal group-velocity dispersion at all-wavelengths are shown to allow for highly coherent continua that can be nonlinearly shaped using appropriate initial conditions. In contrast, supercontinua generated in the anomalous dispersion regime are shown to exhibit large fluctuations in the temporal and spectral domains that can be controlled using a carefully chosen seed. A particular example of this is the first experimental observation of the Peregrine soliton which constitutes a prototype of optical rogue-waves.

Dissipative nonlinear structures in optical fiber systems I : dissipative dispersion managed solitons in mode-locked lasers

In this first talk on dissipative structures in fiber applications, we extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths leading to the generation of stable, short pulses with high energy. Two types of intra-map pulse evolutions are observed depending on the net cavity dispersion. These are characterized by a reduced model and semi-analytical solutions are obtained.

Dissipative nonlinear structures in optical fiber systems II : self-similar parabolic pulses in active fibers

In this second talk on dissipative structures in fiber applications, we overview theoretical aspects of the generation, evolution and characterization of self-similar parabolic-shaped pulses in fiber amplifier media. In particular, we present a perturbation analysis that describes the structural changes induced by third-order fiber dispersion on the parabolic pulse solution of the nonlinear Schrödinger equation with gain. Promising applications of parabolic pulses in optical signal post-processing and regeneration in communication systems are also discussed.

Dissipative nonlinear structures in optical fiber systems III : dissipative solitons via nonlinear mapping

In the third and final talk on dissipative structures in fiber applications, we discuss mathematical techniques that can be used to characterize modern laser systems that consist of several discrete elements. In particular, we use a nonlinear mapping technique to evaluate high power laser systems where significant changes in the pulse evolution per cavity round trip is observed. We demonstrate that dissipative soliton solutions might be effectively described using this Poincaré mapping approach.

Auto-solitons guided by in-line nonlinear optical loop mirrors in dispersion-managed communication systems

Summary form only given. Both dispersion management and the use of a nonlinear optical loop mirror (NOLM) as a saturable absorber can improve the performance of a soliton-based communication system. Dispersion management gives the benefits of low average dispersion while allowing pulses with higher powers to propagate, which helps to suppress Gordon-Haus timing jitter without sacrificing the signal-to-noise ratio. The NOLM suppresses the buildup of amplifier spontaneous emission noise and background dispersive radiation which, if allowed to interact with the soliton, can lead to its breakup. We examine optical pulse propagation in dispersion-managed (DM) transmission system with periodically inserted in-line NOLMs. To describe basic features of the signal transmission in such lines, we develop a simple theory based on a variational approach involving Gaussian trial functions. It, has already been proved that the variational method is an extremely effective tool for description of DM solitons. In the work we manage to include in the variational description the point action of the NOLM on pulse parameters, assuming that the Gaussian pulse shape is inherently preserved by propagation through the NOLM. The obtained results are verified by direct numerical simulations

Nonlinear spectral shaping and optical rogue events in fiber-based systems

We provide an overview of our recent work on the shaping and stability of optical continua in the long pulse regime. Fibers with normal group-velocity dispersion at all-wavelengths are shown to allow for highly coherent continua that can be nonlinearly shaped using appropriate initial conditions. In contrast, supercontinua generated in the anomalous dispersion regime are shown to exhibit large fluctuations in the temporal and spectral domains that can be controlled using a carefully chosen seed. A particular example of this is the first experimental observation of the Peregrine soliton which constitutes a prototype of optical rogue-waves. © 2012 Elsevier Inc. All rights reserved.

Dissipative nonlinear structures in optical fiber systems I:dissipative dispersion managed solitons in mode-locked lasers

In this first talk on dissipative structures in fiber applications, we extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths leading to the generation of stable, short pulses with high energy. Two types of intra-map pulse evolutions are observed depending on the net cavity dispersion. These are characterized by a reduced model and semi-analytical solutions are obtained.

Dissipative nonlinear structures in optical fiber systems II:self-similar parabolic pulses in active fibers

In this second talk on dissipative structures in fiber applications, we overview theoretical aspects of the generation, evolution and characterization of self-similar parabolic-shaped pulses in fiber amplifier media. In particular, we present a perturbation analysis that describes the structural changes induced by third-order fiber dispersion on the parabolic pulse solution of the nonlinear Schrödinger equation with gain. Promising applications of parabolic pulses in optical signal post-processing and regeneration in communication systems are also discussed.