Herarchically slaved multi-pulsing mode-lock dynamics

Abstract

Passive mode-locking is the self-assembly of optical energy in a laser cavity to-wards narrow pulses. Often, the energy available in the cavity goes into multiple coexisting pulses with little control on their number, their energies, or their tem-poral positions. This phenomenon is vaguely known as pulse energy quantization and has been anecdotally linked to pulse splitting induced by optical nonlinear-ity. Research has focussed mainly on avoiding pulse energy quantization and any complex behavior associated with it while driving the pulses to higher and higher energies. The complex multi-pulsing behavior is often regarded as an output of a black box filled with complex nonlinear dynamics with little hope to control it. There’s a want for a clear and workable understanding of these dynamics. The central point of this thesis is that standard, few-dimensional, nearly de-terministic nonlinear dynamics offers this understanding; while mode-locking is indeed the result of noisy interactions of thousands of optical modes shaping the optical pulses, due to fast pulse-shaping processes involved in mode-locking, the pulse shapes tend to be slaved to one or few order parameters, mainly the pulse energy. Then, the complex behavior is understood as the result of a much simpler nonlinear dynamical system. This understanding is supported by our experiments on a multi-pulsing Mamyshev oscillator, and in return, it guides us towards re-liably controlling it. With this control, multiple pulsation, which has been little more than a scientific curiosity, becomes technologically valuable for applications such as ablation-cooled material removal and frequency metrology. First, we address the issue of multiple pulsation. We define an energy map which describes the evolution of each pulse. Using the energy map, we show that stable coexistence of multiple pulses is permitted despite their competition on the gain if the growth of a pulse is self-limiting, i.e., if the energy map features a stable fixed point even at a constant gain. The energy map similarly explains the intimately related phenomena of period-doubling, non-identical pulses, and response to perturbations. The physical processes leading to these phenomena in our laser and others are discussed in parallel, and analogies to other systems are drawn. Many attractors are permitted by the energy map, highlighting the effect of bifurcations, hysteresis, and kinetics of pulse formation. Accordingly, we present guidelines for the control of multi-pulsing lasers and a procedure to control the number of pulses in a Mamyshev oscillator. Having controlled the number of pulses, we turn our attention to the temporal organization they take. Pulses coexisting in a laser cavity tend to evolve towards stable patterns due to long-range interactions between them. Several interaction mechanisms have been proposed in the literature, but the pulse interactions are still poorly understood. This is due partially to the multitude of possible inter-action mechanisms and partially to the focus of their discussion on the physical processes that allow the pulses to interact without analyzing the dynamics that result from these interactions. We argue that the temporal organization dynamics is slaved and present the form of the dynamical system for all long-ranged inter-action mechanisms and use it to derive for the first time the stability criterion for harmonic mode-locking. A comparison between the interaction mechanisms sug-gests the dominance of acoustically mediated interactions in our oscillator. We show theoretically that the acoustic effect is coupled to the single-pulse evolution dynamics and influences the individual pulse energies, which in turn, slave their speeds. This is a distinguishing feature of pulse interactions in our oscillator. We show experimentally that these interactions permit multiple stable fixed points for a given number of pulses and demonstrate noise-induced transitions as well as bifurcation based on parameters of single-pulse mode-lock dynamics, confirm-ing our interaction theory. Lastly, we demonstrate drastic manipulation of the acoustic interactions using a novel secondary loop, allowing richer pulse patterns, and further supporting our interactions theory.