Nonlinear dynamics and spatiotemporal instabilities in semiconductor laser arrays.

Abstract

By coupling several semiconductor lasers to form a laser array, a compact high power source of coherent radiation can be obtained. In addition to their technological importance, these devices also serve as useful paradigms for the study of spatiotemporal complexity in coupled nonlinear oscillators. In this thesis, we investigate the nature and origin of dynamical instabilities in semiconductor laser arrays and present practical models for their analysis. For a two-emitter array, we use a coupled-mode approach to determine the conditions under which the system can attain a (stable) phase-locked state. We show that with complex coupling, the array is stable over a wider range of coupling strengths $\eta$ than it is with real coupling. The antiguiding parameter plays a critical role in the dynamical stability. We also present results pertaining to the stability of larger arrays of identical or dissimilar emitters. For a three-emitter array and for some values of $\eta$, we predict the existence of a remarkable state of synchronized chaos where a subset of emitters in the array synchronize with each other even though the array evolution is chaotic. For other values of $\eta$, the system displays spatiotemporal chaos. We characterize these phenomena using a variety of measures. The coupled-mode approach is normally valid for strongly index-guided lasers. To explore the dynamics of a wider class of laser arrays, we present a propagation model that treats the array as a single waveguiding structure. The model is exact to all orders of $\eta$. We use this model to simulate the dynamics of single-, two- and three-emitter laser arrays and discuss a variety of dynamical instabilities in them. We show that carrier diffusion leads to enhanced stability of a two-emitter laser array while rendering a three-emitter array unstable for almost all $\eta$. Based on the propagation model, we develop an improved coupled-mode theory for a weakly index-guided array. It includes the effects of carrier diffusion and carrier-induced antiguiding. The theory considerably simplifies the analysis of stability and complex behavior in laser arrays. We compare the results obtained from this theory to those obtained from the propagation model and find excellent qualitative and quantitative agreement.