Simulation of guiding-centre soliton transmission system stability in the presence of polarisation mode dispersion

Results of full numerical simulations of a guiding-centre soliton system with randomly birefringent SMF fibre are shown and analysed. It emerges that the soliton system becomes unstable even for small amounts of PMD.

Q parameter estimation using numerical simulations for linear and nonlinear transmission systems

We compare the Q parameter obtained from scalar, semi-analytical and full vector models for realistic transmission systems. One set of systems is operated in the linear regime, while another is using solitons at high peak power. We report in detail on the different results obtained for the same system using different models. Polarisation mode dispersion is also taken into account and a novel method to average Q parameters over several independent simulation runs is described. © 2006 Elsevier B.V. All rights reserved.

Semi-analytical Q parameter estimate in linear and nonlinear transmission systems

We compare the Q parameter obtained from the semi-analytical model with scalar and vector models for two realistic transmission systems. First a linear system with a compensated dispersion map and second a soliton transmission system.

Simultaneous clock recovery and data regeneration using a nonlinear optical loop mirror as an all-optical mixer

High-speed optical clock recovery, demultiplexing and data regeneration will be integral parts of any future photonic network based on high bit-rate OTDM. Much research has been conducted on devices that perform these functions, however to date each process has been demonstrated independently. A very promising method of all-optical switching is that of a semiconductor optical amplifier-based nonlinear optical loop mirror (SOA-NOLM). This has various advantages compared with the standard fiber NOLM, most notably low switching power, compact size and stability. We use the SOA-NOLM as an all-optical mixer in a classical phase-locked loop arrangement to achieve optical clock recovery, while at the same time achieving data regeneration in a single compact device

Soliton transmission through a disordered system

An exact formula for the transmission time in a disordered nonlinear soliton-bearing classical one-dimensional system is obtained.

Identification of nonlinear systems by correlation using pseudorandom signals

This thesis is concerned with the measurement of the characteristics of nonlinear systems by crosscorrelation, using pseudorandom input signals based on m sequences. The systems are characterised by Volterra series, and analytical expressions relating the rth order Volterra kernel to r-dimensional crosscorrelation measurements are derived. It is shown that the two-dimensional crosscorrelation measurements are related to the corresponding second order kernel values by a set of equations which may be structured into a number of independent subsets. The m sequence properties determine how the maximum order of the subsets for off-diagonal values is related to the upper bound of the arguments for nonzero kernel values. The upper bound of the arguments is used as a performance index, and the performance of antisymmetric pseudorandom binary, ternary and quinary signals is investigated. The performance indices obtained above are small in relation to the periods of the corresponding signals. To achieve higher performance with ternary signals, a method is proposed for combining the estimates of the second order kernel values so that the effects of some of the undesirable nonzero values in the fourth order autocorrelation function of the input signal are removed. The identification of the dynamics of two-input, single-output systems with multiplicative nonlinearity is investigated. It is shown that the characteristics of such a system may be determined by crosscorrelation experiments using phase-shifted versions of a common signal as inputs. The effects of nonlinearities on the estimates of system weighting functions obtained by crosscorrelation are also investigated. Results obtained by correlation testing of an industrial process are presented, and the differences between theoretical and experimental results discussed for this case;

Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

Optical phase conjugation for dispersion and nonlinearity compensation in a 1600km, 42 Gb/s quasi-lossless system

We experimentally investigate a long-distance, high-bit-rate transmission system which combines optical-phase-conjugation with quasi-lossless amplification. Comparison with a conventional system configuration demonstrates the possibility of obtaining both dispersion compensation and improved nonlinear tolerance using proposed scheme.

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Autosoliton propagation at 80 Gbit/s using concatenated nonlinear loop switches in standard fibre

Experimental observation of autosoliton propagation in a nonlinear switch-guided, dispersion-managed system operating at 80 Gbit/s is reported for the first time. The system is based on a strong dispersion map and supports autosoliton propagation over 3000 km.

Transmission of non-uniform OTDM channels in nonlinearly-guided dispersion-managed fibre system

The effects of channel inequality on nonlinear signal switching in a nonlinear optical fiber loop mirror (NOLM) were investigated. It was found that the channel-to-channel amplitude differences in optical time division multiplexing (OTDM) have strong impact on swiching behavior of individual channels in a 2R regenerator. The optical pulses in different channels face either suppression of the amplitude noise or increase in noise, depending on the inter-channel amplitude difference. It was stated that appropriate control of the channel uniformity in the OTDM transmitters is required to support stable long-haul transmission in 2R regenerated systems.

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.

The development and stability analysis of a nonlinear growth model for microorganisms

A nonlinear dynamic model of microbial growth is established based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. Except for the two traditional variables, i.e. the density of bacteria and the concentration of attractant, the pH value, a crucial influencing factor to the microbial growth, is also considered in this model. The pH effect on the microbial growth is taken as a Gaussian function G0e-(f- fc)2/G1, where G0, G1 and fc are constants, f represents the pH value and fc represents the critical pH value that best fits for microbial growth. To study the effects of the reproduction rate of the bacteria and the pH value on the stability of the system, three parameters a, G0 and G1 are studied in detail, where a denotes the reproduction rate of the bacteria, G0 denotes the impacting intensity of the pH value to microbial growth and G1 denotes the bacterial adaptability to the pH value. When the effect of the pH value of the solution which microorganisms live in is ignored in the governing equations of the model, the microbial system is more stable with larger a. When the effect of the bacterial chemotaxis is ignored, the microbial system is more stable with the larger G1 and more unstable with the larger G0 for f0 > fc. However, the stability of the microbial system is almost unaffected by the variation G0 and G1 and it is always stable for f0 < fc under the assumed conditions in this paper. In the whole system model, it is more unstable with larger G1 and more stable with larger G0 for f0 < fc. The system is more stable with larger G1 and more unstable with larger G0 for f0 > fc. However, the system is more unstable with larger a for f0 < fc and the stability of the system is almost unaffected by a for f0 > fc. The results obtained in this study provide a biophysical insight into the understanding of the growth and stability behavior of microorganisms.

Intermediate asymptotics in nonlinear optical systems

Using a fiber laser system as a specific illustrative example, we introduce the concept of intermediate asymptotic states in finite nonlinear optical systems. We show that intermediate asymptotics of nonlinear equations (e.g., coherent structures with a finite lifetime or distance) can be used in applications similar to those of truly stable asymptotic solutions, such as, e.g., solitons and dissipative nonlinear waves. Applying this general idea to a particular, albeit practically important, physical system, we demonstrate a novel type of nonlinear pulse-shaping regime in a mode-locked fiber laser leading to the generation of linearly chirped pulses with a triangular distribution of the intensity.

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.