  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.
