The theory of the quantum walk comb laser.

The development of on-chip optical frequency comb devices paves the way for novel applications in environmental tracking, fast ranging and smart communication solutions. Recently, a new type of frequency comb device, based on a modulated ring quantum cascade laser, was introduced and demonstrated. Here we present a rigorous theoretical study of this type of device, also known as the quantum walk comb laser. We show that resonant phase modulation of a fast gain laser with a dispersive circular cavity is sufficient to support a broadband comb. This method requires the gain to have a sufficiently fast recovery time to support quasi-instantaneous suppression of intensity fluctuations. When this condition is met, the modulation leads to quantum walk dynamics, and then to stabilization onto a stable and controllable frequency comb. We show this type of dynamics through simulations using realistic parameters and reveal the impact of higher-order contributions from gain and dispersion. We also study the resilience of this type of mode-locked laser to noise injection and show its superiority to that of active mode-locking. We believe that this work will allow the development of comb devices with high wall-plug efficiency, arbitrary output spectral shaping and increased stability properties.