Isolated Photonic Flatband with the Effective Magnetic Flux in A Synthetic Space including the Frequency Dimension.

The exploration of flatband in photonics is fundamentally important, aiming to control the localization of light for potential applications in optical communications. We study the flatband physics in a synthetic space including the frequency axis of light. A ring-resonator array is used to construct a synthetic Lieb-type lattice, where the modulation phase distribution supports a locally non-zero effective magnetic flux pointing into the synthetic space. We find that the flatband is isolated from other dispersive bands and the light can still be localized even with the perturbation from the group velocity dispersion of the waveguide. Our work points out a route towards manipulating the localization performance of a wavepacket of light along both the spatial dimension and the frequency dimension, which holds the potential implication for controlling the storage of optical information in dispersive materials.