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.

Design of a flat-top fiber Bragg filter via quasi-random modulation of the refractive index

The statistics of the reflection spectrum of a short-correlated disordered fiber Bragg grating are studied. The averaged spectrum appears to be flat inside the bandgap and has significantly suppressed sidelobes compared to the uniform grating of the same bandwidth. This is due to the Anderson localization of the modes of a disordered grating. This observation prompts a new algorithm for designing passband reflection gratings. Using the stochastic invariant imbedding approach it is possible to obtain the probability distribution function for the random reflection coefficient inside the bandgap and obtain both the variance of the averaged reflectivity as well as the distribution of the time delay of the grating.

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.

Long-distance soliton transmission through ultralong fiber lasers

We present the first experimental demonstration (to our knowledge) of long-distance unperturbed fundamental optical soliton transmission in conventional single-mode optical fiber. The virtual transparency in the fiber required for soliton transmission, over 15 complete periods, was achieved by using an ultralong Raman fiber laser amplification scheme. Optical soliton pulse duration, pulse bandwidth, and peak intensity are shown to remain constant along the transmission length. Frequency-resolved optical gating spectrograms and numerical simulations confirm the observed optical soliton dynamics.

Persistence in a random bond ising model of socio-econo dynamics

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a nite temperature on hypercubic lattices in dimensions up to ve. The model includes a \social" local eld which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We nd no evidence of \blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic elds. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in dierent scenarios.

Carbon nanotube-polycarbonate composites for ultrafast lasers

Carbon nanotube polycarbonate composites with controlled nanotube-bundle size are prepared by dispersion with conjugated polymers followed by blending with polycarbonate. The composite has uniform sub-micrometer nanotube bundles in high concentration, shows strong nonlinear optical absorption, and generates 193 fs pulses when used as passive mode-locker in a fiber laser.

Dissipative dispersion-managed solitons in mode-locked lasers

We extend the theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fiber lasers. Dissipative structures exist at high map strengths, leading to the generation of stable, short pulses with high energy. Two types of intramap pulse evolution are observed depending on the net cavity dispersion. These are characterized by a reduced model, and semianalytical solutions are obtained.

Intracavity dynamics in high-power mode-locked fiber lasers

A theoretical model is developed which characterizes the intracavity pulse evolutions in high-power fiber lasers. It is shown that experimentally observed dynamics of the key pulse parameters can be described by a reduced model of ordinary differential equations. Critical in driving the intracavity dynamics is the amplitude and phase modulations generated by the discrete elements in the laser. The theory gives a simple geometrical description of the intracavity dynamics and possible operation modes of the laser cavity. Furthermore, it provides a simple and efficient method for optimizing the performance of complex multiparametric laser systems.

Dispersion and nonlinearity-management in mode-locked fibre lasers

In this work we extend theory of dispersion-managed (DM) solitons to dissipative systems with the main focus on applications in mode-locked lasers. In general, pulses in mode-locked fibre lasers experience both nonlinear and dispersion management per cavity round trip. In stretched-pulse lasers, this concept was utilized to obtain high energy pulses. Here we model the pulse propagation in a mode-locked fibre laser with a distributed nonlinear and DM Ginzburg-Landau type equation. We extend existing results on DM solitons and investigate the impact on soliton properties of dissipative perturbations that occur due to the effects of gain amplification, saturable absorption, and loss. In conclusion, in contrast to standard DM solitons in Hamiltonian systems, dissipative DM solitons do exist at high map strengths, thus opening a way for the generation of stable, short pulses with high energy.

Pulse shaping in mode-locked ring-cavity fibre lasers

By means of extensive numerical modelling we have demonstrated the possibility of nonlinear pulse shaping in a mode-locked fibre laser using control of the intra-cavity propagation dynamics by adjustment of the normal net dispersion and integrated gain. Beside self-similar mode-locking, the existence of a novel type of pulse shaping regime that produces pulses with a triangular temporal intensity profile and a linear frequency chirp has been observed.