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Far-field coupling between moiré photonic lattices

Nature Nanotechnology volume 18, pages 514–520 (2023)Cite this article

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Abstract

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.

References

  1. Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).

    Article  CAS  Google Scholar 

  2. Andrei, E. Y. et al. The marvels of moiré materials. Nat. Rev. Mater. 6, 201–206 (2021).

    Article  CAS  Google Scholar 

  3. Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022).

    Article  CAS  Google Scholar 

  4. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    Article  CAS  Google Scholar 

  5. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    Article  CAS  Google Scholar 

  6. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    Article  CAS  Google Scholar 

  7. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

    Article  CAS  Google Scholar 

  8. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    Article  CAS  Google Scholar 

  9. Hu, G. W. et al. Topological polaritons and photonic magic angles in twisted α-MoO3 bilayers. Nature 582, 209–213 (2020).

    Article  CAS  Google Scholar 

  10. Chen, M. et al. Configurable phonon polaritons in twisted α-MoO3. Nat. Mater. 19, 1307–1311 (2020).

    Article  CAS  Google Scholar 

  11. Duan, J. et al. Twisted nano-optics: manipulating light at the nanoscale with twisted phonon polaritonic slabs. Nano Lett. 20, 5323–5329 (2020).

    Article  CAS  Google Scholar 

  12. Lubin, S. M., Zhou, W., Hryn, A. J., Huntington, M. D. & Odom, T. W. High-rotational symmetry lattices fabricated by moiré nanolithography. Nano Lett. 12, 4948–4952 (2012).

    Article  CAS  Google Scholar 

  13. Wu, Z. L. & Zheng, Y. B. Moiré metamaterials and metasurfaces. Adv. Opt. Mater. 6, 1701057 (2018).

  14. Mao, X. R., Shao, Z. K., Luan, H. Y., Wang, S. L. & Ma, R. M. Magic-angle lasers in nanostructured moiré superlattice. Nat. Nanotechnol. 16, 1099–1105 (2021).

    Article  CAS  Google Scholar 

  15. Tang, H. N. et al. Modeling the optical properties of twisted bilayer photonic crystals. Light Sci. Appl. 10, 157 (2021).

  16. Dong, K. C. et al. Flat bands in magic-angle bilayer photonic crystals at small twists. Phys. Rev. Lett. 126, 223601 (2021).

  17. Lou, B. C. et al. Theory for twisted bilayer photonic crystal slabs. Phys. Rev. Lett. 126, 136101 (2021).

  18. Hu, G., Krasnok, A., Mazor, Y., Qiu, C.-W. & Alù, A. Moiré hyperbolic metasurfaces. Nano Lett. 20, 3217–3224 (2020).

  19. Adams, M. J. An Introduction to Optical Waveguides (John Wiley & Sons, 1981).

  20. Hutter, E. & Fendler, J. H. Exploitation of localized surface plasmon resonance. Adv. Mater. 16, 1685–1706 (2004).

    Article  CAS  Google Scholar 

  21. Haes, A. J., Zou, S., Schatz, G. C. & Van Duyne, R. P. A nanoscale optical biosensor: the long-range distance dependence of the localized surface plasmon resonance of noble metal nanoparticles. J. Phys. Chem. B 108, 109–116 (2004).

    Article  CAS  Google Scholar 

  22. Wu, Z. L. & Zheng, Y. B. Moiré chiral metamaterials. Adv. Opt. Mater. 5, 1700034 (2017).

  23. Vardeny, Z. V., Nahata, A. & Agrawal, A. Optics of photonic quasicrystals. Nat. Photon. 7, 177–187 (2013).

    Article  CAS  Google Scholar 

  24. Li, Z. P., Tian, X., Qiu, C. W. & Ho, J. S. Metasurfaces for bioelectronics and healthcare. Nat. Electron. 4, 382–391 (2021).

    Article  CAS  Google Scholar 

  25. Regan, E. C. et al. Emerging exciton physics in transition metal dichalcogenide heterobilayers. Nat. Rev. Mater. 7, 778–795 (2022).

  26. Wen, J. M., Zhang, Y. & Xiao, M. The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics. Adv. Opt. Photon. 5, 83–130 (2013).

    Article  Google Scholar 

  27. Hakala, T. K. et al. Lasing in dark and bright modes of a finite-sized plasmonic lattice. Nat. Commun. 8, 13687 (2017).

    Article  CAS  Google Scholar 

  28. Rodriguez, S. R. K. et al. Coupling bright and dark plasmonic lattice resonances. Phys. Rev. X 1, 021019 (2011).

  29. Heilmann, R., Salerno, G., Cuerda, J., Hakala, T. K. & Torma, P. Quasi-BIC mode lasing in a quadrumer plasmonic lattice. ACS Photon. 9, 224–232 (2022).

    Article  CAS  Google Scholar 

  30. Guan, J. et al. Quantum dot-plasmon lasing with controlled polarization patterns. ACS Nano 14, 3426–3433 (2020).

    Article  CAS  Google Scholar 

  31. Guan, J. et al. Engineering directionality in quantum dot shell lasing using plasmonic lattices. Nano Lett. 20, 1468–1474 (2020).

    Article  CAS  Google Scholar 

  32. Watkins, N. E. et al. Surface normal lasing from CdSe nanoplatelets coupled to aluminum plasmonic nanoparticle lattices. J. Phys. Chem. C 125, 19874–19879 (2021).

    Article  CAS  Google Scholar 

  33. Tan, M. J. et al. Lasing action from quasi‐propagating modes. Adv. Mater. 34, 2203999 (2022).

  34. Winkler, J. M. et al. Dual-wavelength lasing in quantum-dot plasmonic lattice lasers. ACS Nano 14, 5223–5232 (2020).

    Article  CAS  Google Scholar 

  35. Park, J.-E. et al. Polariton dynamics in two-dimensional Ruddlesden–Popper perovskites strongly coupled with plasmonic lattices. ACS Nano 16, 3917–3925 (2022).

    Article  CAS  Google Scholar 

  36. Schokker, A. H. & Koenderink, A. F. Lasing at the band edges of plasmonic lattices. Phys. Rev. B 90, 155452 (2014).

    Article  Google Scholar 

  37. Schokker, A. H., van Riggelen, F., Hadad, Y., Alù, A. & Koenderink, A. F. Systematic study of the hybrid plasmonic-photonic band structure underlying lasing action of diffractive plasmon particle lattices. Phys. Rev. B 95, 085409 (2017).

    Article  Google Scholar 

  38. Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Cengage Learning, 2011).

  39. Schäfer, F. P. Dye Lasers (Springer Science & Business Media, 2013).

  40. Wang, D. et al. Band-edge engineering for controlled multi-modal nanolasing in plasmonic superlattices. Nat. Nanotechnol. 12, 889–894 (2017).

    Article  CAS  Google Scholar 

  41. Wang, P. et al. Localization and delocalization of light in photonic moiré lattices. Nature 577, 42–46 (2020).

    Article  CAS  Google Scholar 

  42. Guan, J. et al. Identification of Brillouin zones by in-plane lasing from light-cone surface lattice resonances. ACS Nano 15, 5567–5573 (2021).

    Article  CAS  Google Scholar 

  43. Li, R. et al. Hierarchical hybridization in plasmonic honeycomb lattices. Nano Lett. 19, 6435–6441 (2019).

  44. Juarez, X. G. et al. M-point lasing in hexagonal and honeycomb plasmonic lattices. ACS Photon. 9, 52–58 (2022).

    Article  CAS  Google Scholar 

  45. Fernandez-Bravo, A. et al. Ultralow-threshold, continuous-wave upconverting lasing from subwavelength plasmons. Nat. Mater. 18, 1172–1176 (2019).

    Article  CAS  Google Scholar 

  46. Guan, J. et al. Plasmonic nanoparticle lattice devices for white-light lasing. Adv. Mater. 2103262 (2021).

  47. Lin, Y. H. et al. Engineering symmetry-breaking nanocrescent arrays for nanolasing. Adv. Funct. Mater. 29, 1904157 (2019).

  48. Deng, S. K. et al. Ultranarrow plasmon resonances from annealed nanoparticle lattices. Proc. Natl Acad. Sci. USA 117, 23380–23384 (2020).

    Article  CAS  Google Scholar 

  49. Guo, R., Nečada, M., Hakala, T. K., Väkeväinen, A. I. & Törmä, P. Lasing at k-points of a honeycomb plasmonic lattice. Phys. Rev. Lett. 122, 013901 (2019).

  50. Daskalakis, K. S., Vakevainen, A. I., Martikainen, J. P., Hakala, T. K. & Torma, P. Ultrafast pulse generation in an organic nanoparticle-array laser. Nano Lett. 18, 2658–2665 (2018).

    Article  CAS  Google Scholar 

  51. Rekola, H. T., Hakala, T. K. & Torma, P. One-dimensional plasmonic nanoparticle chain lasers. ACS Photon. 5, 1822–1826 (2018).

    Article  CAS  Google Scholar 

  52. Guan, J. et al. Light-matter interactions in hybrid material metasurfaces. Chem. Rev. 122, 15177–15203 (2022).

    Article  CAS  Google Scholar 

  53. Henzie, J., Kwak, E. S. & Odom, T. W. Mesoscale metallic pyramids with nanoscale tips. Nano Lett. 5, 1199–1202 (2005).

    Article  CAS  Google Scholar 

  54. Gao, H., Henzie, J. & Odom, T. W. Direct evidence for surface plasmon-mediated enhanced light transmission through metallic nanohole arrays. Nano Lett. 6, 2104–2108 (2006).

    Article  CAS  Google Scholar 

  55. Lee, M. H., Huntington, M. D., Zhou, W., Yang, J.-C. & Odom, T. W. Programmable soft lithography: solvent-assisted nanoscale embossing. Nano Lett. 11, 311–315 (2011).

    Article  CAS  Google Scholar 

  56. Johnson, P. B. & Christy, R.-W. Optical constants of the noble metals. Phys. Rev. B 6, 4370 (1972).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

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

  1. Department of Chemistry, Northwestern University, Evanston, IL, USA

    Jun Guan, Jingtian Hu, Max J. H. Tan, George C. Schatz & Teri W. Odom

  2. Graduate Program in Applied Physics, Northwestern University, Evanston, IL, USA

    Yi Wang, George C. Schatz & Teri W. Odom

  3. Department of Materials Science and Engineering, Northwestern University, Evanston, IL, USA

    Teri W. Odom

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  1. Jun Guan
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Contributions

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 information

Supplementary Information

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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Source Data Fig. 3

Statistical source data.

Source Data Fig. 4

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Source Data Fig. 5

Statistical source data.

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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). https://doi.org/10.1038/s41565-023-01320-7

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