Local and global bifurcations of optically-pumped three-level lasers

Abstract

In recent years, experimental and theoretical studies of instability phenomena in active laser systems have been widely reported in the laser physics literature¹. Many theoretical studies have considered the simplest physical configurations and therefore models comprising small systems of ordinary differential equations. In general, analysis of such models has concentrated on the equilibrium solutions and their bifurcations, with particular attention to the magnitudes of instability thresholds. This latter emphasis is largely a consequence of the high instability thresholds of the Haken-Lorenz two-level laser model², which are widely considered to be physically unrealisable³. In fact, with the exception of the Haken-Lorenz model, which has been intensively studied because of its dual origin as a model of fluid flow⁴, the global bifurcation pictures of most laser models are unknown. Instead, laser physicists have focussed on dynamic features which are readily compared with experiments, such as properties of time series, power spectra, transitions to chaos and measures of chaotic attractor dimension. These observational descriptions of chaotic behaviour often appear partial and disjoint, whereas the direct study of model solutions and their global bifurcations can provide a clear and unfolded bifurcation diagram.