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Far-field coupling between moiré photonic lattices


Superposing two or more periodic structures to form moiré patterns is emerging as a promising platform to confine and manipulate light. However, moiré-facilitated interactions and phenomena have been constrained to the vicinity of moiré lattices. Here we report on the observation of ultralong-range coupling between photonic lattices in bilayer and multilayer moiré architectures mediated by dark surface lattice resonances in the vertical direction. We show that two-dimensional plasmonic nanoparticle lattices enable twist-angle-controlled directional lasing emission, even when the lattices are spatially separated by distances exceeding three orders of magnitude of lattice periodicity. Our discovery of far-field interlattice coupling opens the possibility of using the out-of-plane dimension for optical manipulation on the nanoscale and microscale.

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Fig. 1: Ultralong-range coupling of plasmonic NP lattices in moiré architectures.
Fig. 2: Probing ultralong-range phase coherence of dark SLR modes.
Fig. 3: Ultralong-range phase coherence of dark SLRs is sensitive to index environment.
Fig. 4: Tunable moiré lasers from macroscale-separated NP lattices.
Fig. 5: Three-layer moiré effect from macroscale-separated NP lattices.

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Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


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This work was supported by the National Science Foundation (NSF) under DMR-1904385 (dyes as dipole sources; J.H., Y.W., M.J.H.T., G.C.S. and T.W.O.), DMR-2207215 (stacked nanoparticle lattice design; J.G., G.C.S. and T.W.O.) and CMMI-2028773 (in-plane moiré lattice model; T.W.O.). This work used the Northwestern University Micro/Nano Fabrication Facility (NUFAB), which is partially supported by Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-2025633), the Materials Research Science and Engineering Center (MRSEC) (DMR-1720139), the State of Illinois and Northwestern University. This work made use of the EPIC facilities of Northwestern University’s NUANCE Center, which received support from the SHyNE Resource (NSF ECCS-2025633); the MRSEC program (NSF DMR-1720139) at the Materials Research Center; the International Institute for Nanotechnology (IIN); the Keck Foundation; and the State of Illinois through the IIN. This research was supported in part by the Quest high-performance computing facility at Northwestern University, which is jointly supported by the Office of the Provost, the Office for Research and Northwestern University Information Technology.

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Authors and Affiliations



J.G. and T.W.O. conceived the idea of moiré photonic lattices. J.G. and J.H. designed the moiré architecture, fabricated the plasmonic NP lattices, characterized the linear optical properties of the devices and performed the FDTD numerical simulations. J.G., J.H., Y.W. and M.J.H.T. carried out the lasing measurements. Y.W. fabricated the TiO2 NP lattices. G.C.S. guided the theoretical investigations. J.G. and T.W.O. analysed the data and wrote the manuscript. All the authors commented on and revised the manuscript.

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Correspondence to Jun Guan or Teri W. Odom.

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Nature Nanotechnology thanks Fangwei Ye and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–21.

Supplementary Video 1

We demonstrated real-time tunable lasing emission over a wide angular range (θlasing = 0–45°) by rotating the first lattice relative to the second lattice (α12 = 0–30°). Increasing the twist angle α12 resulted in lasing beams emitted at higher angles.

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Guan, J., Hu, J., Wang, Y. et al. Far-field coupling between moiré photonic lattices. Nat. Nanotechnol. 18, 514–520 (2023).

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