In-situ Bayesian optimization of frequency combs via limit cycle engineering

The development of frequency combs has been a boon to modern precision metrology and scientific discovery – enabling atomic and optical clocks, high-resolution spectroscopy, the generation of low-noise, coherent sources for communications. These advances were powered by optical frequency combs – created by mode-locked laser pulse trains, four-wave mixing of detuned laser sources, pumped Kerr micro-resonators, or by the electro-optic modulation of a continuous wave laser. The principal methodology behind these schemes is related to dispersion engineering. In contrast, we employ a Bayesian optimization framework that drives nonlinear self-oscillating dynamical systems toward limit cycle states with targeted frequency comb envelopes. We demonstrate the efficiency of our approach through both in-silico and in-situ implementations of the protocol using nonlinear RF self-oscillating metamolecules – comprising dynamically tunable gain, loss and nonlinear elements – that realize self-sustained stable limit cycles at various points across the multi-dimensional parameter space. Our results illuminate a pathway for nonlinear frequency synthesis by dynamically tuning a complex system without the need for a priori analytical models.