Turing patterns in a fiber laser with a nested microresonator : Robust and controllable microcomb generation

Microcombs based on Turing patterns have been extensively studied in configurations that can be modeled by the Lugiato-Lefever equation. Typically, such schemes are implemented experimentally by resonant coupling of a continuous wave laser to a Kerr microcavity in order to generate highly coherent and robust waves. Here, we study the formation of such patterns in a system composed of a microresonator nested in an amplifying laser cavity, a scheme recently used to demonstrate laser cavity solitons with high optical efficiency and easy repetition rate control. Utilizing this concept, we study different regimes of Turing patterns, unveiling their formation dynamics and demonstrating their controllability and robustness. By conducting a comprehensive modulational instability study with a mean-field model of the system, we explain the pattern formation in terms of its evolution from background noise, paving the way towards complete self-starting operation. Our theoretical and experimental paper provides a clear pathway for repetition rate control of these waves over both fine (Megahertz) and large (Gigahertz) scales, featuring a fractional frequency nonuniformity better than 7×10⁻¹⁴ with a 100-ms time gate and without the need for active stabilization.