Nonlinear and Dynamical Processes in Complex Lasers

Abstract

The goal of this thesis is to study the impact of optical nonlinearities on emission characteristics of complex laser systems. Nonlinearities in lasers give rise to spatial hole-burning, or regions of high inversion depletion that result from complex modal interactions that saturate the gain medium. These interactions can result in sub-optimal utilization of the laser gain medium and they can also affect the spectral characteristics of the laser, as studied in the past in simple lasers. Recent advancements in semiconductor technology have made it possible to fabricate microcavity-based lasers with complex geometries that have been studied using the Steady-state Ab Initio Laser Theory (SALT), a modern steady-state reformulation of the Maxwell-Bloch equations. SALT has successfully explained emission properties of various modern lasers but a systematic study of the consequences of spatial hole-burning interactions in complex lasers has not been carried out. Here, we report that spatial hole-burning interactions generally reduce the output power efficiency and that they can be gainfully controlled using spatially selective pumping to reduce the lasing threshold, improve laser spectral characteristics, and enhance output power efficiency, in some cases by orders of magnitude. In addition to this steady-state study of spatial hole-burning nonlinearities, we also study four-wave mixing nonlinearities that manifest in the dynamical regime. SALT fundamentally neglects dynamical effects, a limitation we overcome by developing the Constant Flux Time Domain (CFTD) method, an efficient solver of the Maxwell-Bloch equations that can simulate time-dependent behavior in open laser systems. Using CFTD, we study mode synchronization and frequency comb generation, quantifying the role of the inversion relaxation rate γ∥ and the cavity free spectral range ∆, on dynamical effects. In the steady-state, correspondence between SALT and CFTD is shown and their divergence in the dynamical regime is explained through the parameter γ∥/∆. In the highly multi-modal regime, we simulate the emergence of frequency combs in a parameter regime applicable to quantum cascade lasers (QCLs), recovering the hysteresis seen in experiments, and we predict sudden frequency-comb formation from within plateaus of chaotic behavior.