All optical networking beyond 10 Gbits/s OTDM networks based on electro-optic modulators and fibre ring lasers

This thesis examines options for high capacity all optical networks. Specifically optical time division multiplexed (OTDM) networks based on electro-optic modulators are investigated experimentally, whilst comparisons with alternative approaches are carried out. It is intended that the thesis will form the basis of comparison between optical time division multiplexed networks and the more mature approach of wavelength division multiplexed networks. Following an introduction to optical networking concepts, the required component technologies are discussed. In particular various optical pulse sources are described with the demanding restrictions of optical multiplexing in mind. This is followed by a discussion of the construction of multiplexers and demultiplexers, including favoured techniques for high speed clock recovery. Theoretical treatments of the performance of Mach Zehnder and electroabsorption modulators support the design criteria that are established for the construction of simple optical time division multiplexed systems. Having established appropriate end terminals for an optical network, the thesis examines transmission issues associated with high speed RZ data signals. Propagation of RZ signals over both installed (standard fibre) and newly commissioned fibre routes are considered in turn. In the case of standard fibre systems, the use of dispersion compensation is summarised, and the application of mid span spectral inversion experimentally investigated. For green field sites, soliton like propagation of high speed data signals is demonstrated. In this case the particular restrictions of high speed soliton systems are discussed and experimentally investigated, namely the increasing impact of timing jitter and the downward pressure on repeater spacings due to the constraint of the average soliton model. These issues are each addressed through investigations of active soliton control for OTDM systems and through investigations of novel fibre types respectively. Finally the particularly remarkable networking potential of optical time division multiplexed systems is established, and infinite node cascadability using soliton control is demonstrated. A final comparison of the various technologies for optical multiplexing is presented in the conclusions, where the relative merits of the technologies for optical networking emerges as the key differentiator between technologies.

The use of loop mirrors and chirped fibre Bragg gratings in actively-modelocked fibre lasers

The development of an all-optical communications infrastructure requires appropriate optical switching devices and supporting hardware. This thesis presents several novel fibre lasers which are useful pulse sources for high speed optical data processing and communications. They share several attributes in common: flexibility, stability and low-jitter output. They all produce short (picosecond) and are suitable as sources for soliton systems. The lasers are all-fibre systems using erbium-doped fibre for gain, and are actively-modelocked using a dual-wavelength nonlinear optical loop mirror (NOLM) as a modulator. Control over the operating wavelength and intra-cavity dispersion is obtained using a chirped in-fibre Bragg grating.Systems operating both at 76MHz and gigahertz frequencies are presented, the latter using a semiconductor laser amplifier to enhance nonlinear action in the loop mirror. A novel dual-wavelength system in which two linear cavities share a common modulator is presented with results which show that the jitter between the two wavelengths is low enough for use in switching experiments with data rates of up to 130Gbit/s.

Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

Direct real-time cavity mode assessment and optimization technique for fiber lasers

A simple technique for direct real-time assessment of a fiber laser cavity-mode condition during operation is demonstrated. Mode stabilization and optimization with this cavity-mode monitoring and conditioning feedback scheme shows significant improvements to the output performance.

On the robustness of random Boolean formulae

Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models. © 2010 IOP Publishing Ltd.

Statnote 9: The one-way analysis of variance (random effects model)

There is an alternative model of the 1-way ANOVA called the 'random effects' model or ‘nested’ design in which the objective is not to test specific effects but to estimate the degree of variation of a particular measurement and to compare different sources of variation that influence the measurement in space and/or time. The most important statistics from a random effects model are the components of variance which estimate the variance associated with each of the sources of variation influencing a measurement. The nested design is particularly useful in preliminary experiments designed to estimate different sources of variation and in the planning of appropriate sampling strategies.

Soliton dynamics in transmission through ultralong lasers

We have studied the dynamics and stability of solitonic pulses (including soliton interaction) across URFL transmission links, as well as the dependence of these dynamics on cavity design (length, symmetry, reflectivity) and input pulse characteristics. The first experimental demonstration of long-distance ldquotruerdquo soliton propagation through optical fibre. The results conclude that even relatively long links of the order of 50 km show excellent nonlinear resilience and are capable of providing virtually transparent transmission under a broad range of input pulse characteristics.

Ultra-long raman laser with a feedback based on the Rayleigh scattering

This paper reports the Rayleigh scattering effects in ultra-long Raman fibre laser. It has been found that in a long fibre cavity (-100 km) the distributed feedback due to Rayleigh back scattering at propagation of light between fibre Bragg grating reflectors may be comparable with the lumped feedback provided by the FBG itself. As a result, Raman lasing in the fibre span limited by lumped (FBG) reflector at one side only appears possible due to significant reflection from the RS-based "random" distributed mirror at the other side. Thus, it concludes that a distributed Rayleigh scattering "random" mirror can form a cavity together with a single FBG spliced to the opposite cavity end.

Optical communications applications of ultra-long Raman fiber lasers

Recent work on ultra-long Raman fiber lasers has shown that it is possible to create quasi-lossless transmission conditions in fiber spans long enough to be considered for high speed optical communications. This paper reviews how quasi-lossless transmission conditions are reached and presents experimental results of 40Gb/s transmission in a quasi lossless system. The performance is compared with a conventional EDFA based system.

Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback

We present experimental demonstration of a 200-km-long, dual-wavelength Raman laser utilizing two slightly different-wavelength fiber Bragg gratings, one on each side of the fiber span. The obtained results clearly prove the generation of two independent Raman lasers with a distributed “random” Rayleigh scattering mirror forming a cavity together with each of the individual fiber Bragg grating reflectors.

Appearance of bound states in random potentials with applications to soliton theory

We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg–de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.

Simultaneous spatial and spectral transparency in ultralong fiber lasers

We demonstrate that ultralong Raman lasers can be used to generate a transmission medium with simultaneous transparency over the spatial and the spectral domains. Numerical calculations show this cross-domain transparency to be preserved when the medium is used for transmitting high-intensity signals, which makes ultralong lasers an ideal experimental test bed for the study of multifrequency nonlinear interactions in optical fiber waveguides. Full spatiospectral transparency is experimentally obtained over a 20 nm x 20 km window.

Advanced fibre gratings fabricated in standard and infrared glass fibres by ultraviolet and near-infrared-femtosecond lasers

In this thesis, I describe studies on fabrication, spectral characteristics and applications of tilted fibre gratings (TFGs) with small, large and 45° tilted structures and novel developments in fabrication of fibre Bragg gratings (FBGs) and long period gratings (LPGs) in normal silica and mid-infrared (mid-IR) glass fibres using near-IR femtosecond laser. One of the major contributions presented in this thesis is the systematic investigation of structures, inscription methods and spectral, polarisation dependent loss (PDL) and thermal characteristics of TFGs with small (<45°), large (>45°) and 45° tilted structures. I have experimentally characterised TFGs, obtaining relationships between the radiation angle, central wavelength of the radiation profile, Bragg resonance and the tilt angle, which are consistent with theoretical simulation based on the mode-coupling theory. Furthermore, thermal responses have been measured for these three types of TFGs, showing the transmission spectra of large and 45° TFGs are insensitive to the temperature change, unlike the normal and small angle tilted FBGs. Based on the distinctive optical properties, TFGs have been developed into interrogation system and sensors, which form the other significant contributions of the work presented in this thesis. The 10°-TFG based 800nm WDM interrogation system can function not just as an in-fibre spectrum analyser but also possess refractive index sensing capability. By utilising the unique polarisation properties, the 81 °-TFG based sensors are capable of sensing the transverse loading and twisting with sensitivities of 2.04pW/(kg/m) and 145.90pW/rad, repectively. The final but the most important contribution from the research work presented in this thesis is the development of novel grating inscription techniques using near-IR femtosecond laser. A number of LPGs and FBGs were successfully fabricated in normal silica and mid-IR glass fibres using point-by-point and phase-mask techniques. LPGs and 1st and 2nd order FBGs have been fabricated in these mid-IR glass fibres showing resonances covering the wavelength range from 1200 to 1700nm with the strengths up to 13dB. In addition, the thermal and strain sensitivities of these gratings have been systematically investigated. All the results from these initial but systematic works will provide useful function characteristics information for future fibre grating based devices and applications in mid-IR range.

Contrast sensitivity for complex and random gratings

This thesis studied the effect of (i) the number of grating components and (ii) parameter randomisation on root-mean-square (r.m.s.) contrast sensitivity and spatial integration. The effectiveness of spatial integration without external spatial noise depended on the number of equally spaced orientation components in the sum of gratings. The critical area marking the saturation of spatial integration was found to decrease when the number of components increased from 1 to 5-6 but increased again at 8-16 components. The critical area behaved similarly as a function of the number of grating components when stimuli consisted of 3, 6 or 16 components with different orientations and/or phases embedded in spatial noise. Spatial integration seemed to depend on the global Fourier structure of the stimulus. Spatial integration was similar for sums of two vertical cosine or sine gratings with various Michelson contrasts in noise. The critical area for a grating sum was found to be a sum of logarithmic critical areas for the component gratings weighted by their relative Michelson contrasts. The human visual system was modelled as a simple image processor where the visual stimuli is first low-pass filtered by the optical modulation transfer function of the human eye and secondly high-pass filtered, up to the spatial cut-off frequency determined by the lowest neural sampling density, by the neural modulation transfer function of the visual pathways. The internal noise is then added before signal interpretation occurs in the brain. The detection is mediated by a local spatially windowed matched filter. The model was extended to include complex stimuli and its applicability to the data was found to be successful. The shape of spatial integration function was similar for non-randomised and randomised simple and complex gratings. However, orientation and/or phase randomised reduced r.m.s contrast sensitivity by a factor of 2. The effect of parameter randomisation on spatial integration was modelled under the assumption that human observers change the observer strategy from cross-correlation (i.e., a matched filter) to auto-correlation detection when uncertainty is introduced to the task. The model described the data accurately.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.