Dynamics of a Q-switched all-fibre laser

Abstract

This thesis considers a series of experimental and numerical investigations of self-pulsing in fibre lasers with a gain section and an absorber section via a mechanism known as Q-switching. In the context of an all-fibre laser, experimentally, we consider a Fabry-Perot resonator with sectional gain and absorption and their interaction while, numerically, we investigate in detail at the Yamada ordinary differential equation model for the laser describing its intensity, gain, and absorption. We first consider the interactions between an Erbium doped fibre as the gain section and several lengths of Thulium doped absorber section, which has a relatively faster relaxation time. Through comprehensive experiments and numerical computations we demonstrate two distinct ways in which Q-switched pulses are born, with a subsequent path from regular to irregular pulsing. The observed dynamics are interpreted in terms of bifurcations of equilibria and periodic orbits. Specifically, we examine the coefficient of absorption of the Thulium doped fibre and study how the efficiency of its saturation depends on the physical length of the absorber section that initiates the Q-switching process. We find that the length of the absorber section has a significant effect on its saturation and, as a consequence, the mechanism of the onset of Q-switched pulses. Additionally, we report observed hysteresis and multi-stable dynamics for a range of absorber lengths for which the laser evolves along two different operational paths during up-scans and down-scans over ranges of the input pump. This bistable region is close to the switch between the two mechanisms for the onset of Q-switched pulse. We also investigate all the cases of gain and absorber decaying on different time scales. An overall bifurcation structure is presented by showing how the two-parameter bifurcation diagram in the plane of pump strength versus decay rate of the gain changes with the ratio between the two decay rates. In total, there are ten cases BI to BX of qualitatively different two-parameter bifurcation diagrams, which we present with an explanation of the transitions between them. Moreover, we show for each of the associated eleven cases of structurally stable phase portraits (in open regions of the parameter space) a three-dimensional representation of the organisation of phase space by the two-dimensional manifolds of saddle equilibria and saddle periodic orbits. The overall bifurcation structure constitutes a comprehensive picture of the exact nature of the observable dynamics, including multi-stability and excitability, which we expect to be of relevance for recent and future experimental work on Q-switching lasers with different kinds of saturable absorbers. Finally, we demonstrate experimentally for the first time excitability in an all-fibre laser with saturable absorber experimentally; this is supported by careful numerical considerations. Experiments and numerical investigations are carried out to characterise the influence of properties of pulse perturbations on the generation of the excitatory responses of our Q-switched all fibre laser.