Universal dynamics and microwave control of programmable cavity electro-optic frequency combs

Electro-optic (EO) frequency combs are foundational for metrology and spectroscopy. Specifically, microresonator-based cavity EO combs are distinguished by efficient sideband generation, precisely controlled by microwave signals, enabling high-performance integrated frequency references and pulse sources. However, the apparent simplicity of these devices, often described by the EO modulation-induced coupling of nearest-neighbor cavity modes, has limited investigations of their fundamental physics, thereby restricting their full potential. Here, we uncover the universal dynamics and complete frequency lattice connectivity underpinning cavity EO microcombs, as well as characterize the full space of nonlinear optical states, controlled by modulation depth and optical detuning, using the thin-film lithium niobate photonic platform. Leveraging this understanding, we design complex long-range couplings between cavity modes to realize programmable spectro-temporal shaping of the generated combs and pulses. We achieve three technological advances, including repetition-rate flexibility, substantial comb bandwidth extension beyond traditional scaling laws, and resonantly-enhanced flat-top spectrum. Our results provide physical insights for synchronously driven cavity-based EO systems, broadly defined, paving the way for electrically controlled and electrically enhanced comb generators for next-generation photonic applications.