Dynamic band structure measurement in the synthetic space

Band structure theory plays an essential role in exploring physics in both solid-state systems and photonics. Here, we demonstrate a direct experimental measurement of the dynamic band structure in a synthetic space including the frequency axis of light, realized in a ring resonator under near-resonant dynamic modulation. This synthetic lattice exhibits the physical picture of the evolution of the wave vector reciprocal to the frequency axis in the band structure, analogous to a one-dimensional lattice under an external force. We experimentally measure the trajectories of the dynamic band structure by selectively exciting the band with a continuous wave source with its frequency scanning across the entire energy regime of the band. Our results not only provide a new perspective for exploring the dynamics in fundamental physics of solid-state and photonic systems with the concept of the synthetic dimension but also enable great capability in band structure engineering in photonics.