Global Bifurcation Analysis in Laser Systems

Abstract

Nonlinear dynamics of lasers has been a lively theoretical and experimental field since the invention of the laser in 1960. Its focus in the last two decades have been instabilities in widely used semiconductor lasers. Nonlinear studies of laser systems contributed to the field of dynamical systems with general phenomena including chaos, (chaotic) synchronization of coupled oscillators, competition, excitability, delay-induced instabilities, unfolding of high-codimension bifurcations, bifurcation cascades, and spatial patterns; see [1, 28, 30, 36, 51, 63] for general reading and further references. These studies also deepened the understanding of nonlinear phenomena that are important for technological applications, e.g. external-modulation response of semiconductor lasers for faster Internet connections [57]. Furthermore, nonlinear analysis of laser systems stimulated and helped to validate the feasibility of novel, chaos-based applications including secure communication schemes [4, 50], chaotic radars [34], and instability-based laser sensors [56]. Much of the recent progress in the field of laser dynamics is owing to the application of numerical continuation techniques. The study of lasers with tools from bifurcation theory started already in 1987 with the work of Maloney and coworkers on the nonlinear dynamics of three-level molecular lasers [37]. By now, there are over one hundred publications where tools from bifurcation theory are used to investigate dynamics of various laser systems. To explain the strong impact that numerical continuation techniques had and are still having on the field of nonlinear laser dynamics we mention here four key properties that we found to be very influential in our research. Namely, numerical continuation techniques: