Recently, moiré lattices induce extensive research interest in solid-state physics for the exotic phenomena exhibited in twisted double-layer graphene. Meanwhile, the moiré lattice’s structures in two-dimensional space are extended to optics domain to explore novel method of flexibly modulating optical field. Since the concept of one-dimensional(1D) analogs of moiré lattice was introduced, it shows the ability of studying physics associated with the moiré lattice in simpler geometry. When combined with synthetic dimension, not only the possible difficulty of experimental condition to study moiré will be reduced for the cut down of geometry dimension, but also interaction between multilayer optical synthetic lattice can be realized by the coupling between ring resonators, which provides insight into optical simulation in synthetic frequency dimension.

The research group studied a 1D analog of a “moiré” lattice along the frequency dimension in two coupled ring resonators with different lengths under resonant modulations. Two sublattices with different lattice period are formed, with their relative lattice period ratio playing the role of the twist angle. Together with the coupling between two rings, the coupled model constructs a synthetic 1D moiré lattice in the frequency dimension (Fig. 1). The coupling strength between two rings control nonflat to flat band transition, which realized a controllable transition between localization and delocalization along frequency axis of light. Moreover, when the coupling strength reaches a threshold, every band of this synthetic structure is flat, where one flat band corresponds to one localized frequency mode.

The work explored a moiré lattice in 1D frequency dimension, enriched optical simulation in synthetic frequency dimension, and expanded the means of optical field modulation. In the Future, the strongly correlated phases and Floquet engineering of topological phase in the 1D moiré lattice can be further studied.

Fig. 1. Moiré in one-dimensional frequency dimension

The research was published in “Danying Yu, Guangzhen Li, Luojia Wang, Daniel Leykam, Luqi Yuan, and Xianfeng Chen, Moiré Lattice in One-Dimensional Synthetic Frequency Dimension, Physical Review Letters 130, 143801 (2023)”.

Link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.143801