Numerical Modeling of Frequency Combs: Functionality, Stability and Control

Abstract

Frequency comb generation has been at the scientific forefront for several decades because of its potential applications in fundamental and applied physics, including chemical sensing, optical atomic clocks and low-phase-noise microwave radiation. Still, the generation of stable frequency combs is often hand-tuned in experiments and the dynamics are sensitive to perturbations of the system. Therefore we wish to find a theoretical characterization of how the perturbations deform the frequency combs. We derive a micro-comb perturbation theory that allows one to consider the effects of higher-order terms in the microresonator for frequency comb generation, including Raman scattering, spontaneous emission noises and enforcing pump noises. To generate frequency combs at a preferable parameter regime in a semiconductor diode laser, we introduce the waveguide arrays for its temporal shaping effects to provide intensity discrimination and controllable loss by mode-coupling. The stable and efficient numerical scheme of this model is demonstrated, followed by a von-Neumann analysis. In addition, we develop a fast, reliable self-tuning controller with deep reinforcement learning to obtain the high-energy, single-pulse state in a passive mode-locked fiber laser. The self-tuning strategy allows the optical system to recognize bi-stable structures and navigate to optimally performing solutions via trajectory planning.