Nonlinear Dynamics in Photonic Systems: Generic models for semiconductor ring lasers & dissipative solitons

Photonic systems display a wealth of dynamical phenomena and as such they are ideal testbeds to study ideas from nonlinear dynamics, both theoretically and experimentally. On the one hand, assuming that the spatial structure of the light ?eld does not change in time, one can study the temporal dynamics of nonlinear optical systems. For example, periodic or chaotic spike sequences have been observed in the output of lasers. On the other hand, during the last decades the study of spontaneously appearing patterns in photonic systems has also evolved into an effervescent ?eld. A wealth of spatial patterns has been found e.g. in broad-area lasers or in cells ?lled with sodium vapor. Most of these spatio-temporal phenomena encountered in optical systems can also be observed in a variety of other disciplines such as hydrodynamics, electrical discharges, chemical and biological systems, etc... because they essentially share the same mathematical formalism referring to universal concepts. In this work, we address both temporal and spatial dynamics in optical systems, employing tools from bifurcation theory, nonlinear dynamics and stochastic processes. In the first part, as an example of purely temporal dynamics, we study the dynamical behavior of semiconductor ring lasers, recently recognized to be promising sources in photonic integrated circuits. In particular, the bistability between the two counter-propagating modes allows to encode digital information in the emission direction of ring lasers. For such applications, an understanding of the nonlinear dynamical behaviour is essential. Studying the underlying phase space structure, in combination with deter-ministic and stochastic processes, leads us to an improved understanding of the bistable (in fact, multistable) regime and of the switching behavior of semiconductor ring lasers. Our theoretical predictions have been successfully compared to experimental results. The second part of this thesis deals with a couple of selected topics in the field of spatially localized structures in extended photonic systems, also referred to as dissi-pative solitons. Here, the presence of a local or nonlocal spatial interaction between each part and its immediate surroundings has important consequences on the dynamical behavior. In this work, we unravel several fundamental principles and present a study of the bifurcation structure of dissipative solitons.