Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses

This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium

Optimisation and statistical analysis of 21.4 Gb/s RZ-DPSK WDM non-slope matched transmission

Considering a numerical example, we analyse the performance of Return-to-Zero (RZ) Differential Phase Shift Keyed (DPSK) transmission when deployed in a large scale transmission system. It is shown that at high distances, RZ-DPSK performs well whilst being limited by nonlinear effects. We also show that when nonlinear effects become dominant, we can still estimate channel statistics to reasonable accuracy

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

Control of the properties of micro-structured waveguides in lithium niobate crystal

We study numerically depressed-cladding, buried waveguides that can be formed in a lithium niobate crystal by femtosecond laser writing. We demonstrate that the guiding properties can be controlled by the waveguide structural characteristics

All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses

We propose a new all-optical, all-fibre scheme for conversion of time-division multiplexed to wavelength-division multiplexed signals using cross-phase modulation with triangular pulses. Partial signal regeneration using this technique is also demonstrated

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations

Autosoliton propagation and mapping problem in optical fiber lines with lumped nonlinear devices

A theoretical model is developed to describe the propagation of ultrashort optical pulses in fiber transmission systems in the quasilinear regime, with periodically inserted in-line nonlinear optical devices

Breathing Solitons in a Passively Harmonic Mode-Locked Fibre Laser

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