Strong-coupling and high-bandwidth cavity electro-optic modulation for advanced pulse-comb synthesis.

Cavity electro-optic (EO) modulation plays a pivotal role in optical pulse and frequency comb synthesis, supporting a wide range of applications including communication, computing, ranging, and quantum information. The ever-growing demand for these applications has driven efforts in enhancing modulation coupling strength and bandwidth towards advanced pulse-comb synthesis. However, the effects of strong-coupling and high-bandwidth cavity EO modulation remain underexplored, due to the lack of a general, unified model that captures this extreme condition. In this work, we present a universal framework for pulse-comb synthesis under cavity EO modulation, where coupling strength and modulation bandwidth far exceed the cavity's free spectral range (FSR). We show that, under such intense and ultrafast driving conditions, EO-driven frequency combs and pulses exhibit rich higher-order nonlinear dynamics, including temporal pulse compression and comb generation with arbitrary pump detuning. Leveraging this framework, we reveal a direct link between the higher-order dynamics of EO pulse-comb generation and the band structure of synthetic dimension. Furthermore, we demonstrate arbitrary comb shaping via machine-learning-based inverse microwave drive design, achieving a tenfold enhancement in cavity EO comb flatness by exploring the synergistic effects of high-bandwidth driving and detuning-induced frequency boundaries. Our findings push cavity EO modulation into a new frontier, unlocking significant potential for universal and machine-learning-programmable EO frequency combs, topological photonics, as well as photonic quantum computing in the strong-coupling and high-bandwidth regimes.