Abstract
Flatbands have become a cornerstone of contemporary condensed-matter physics and photonics. In electronics, flatbands entail comparable energy bandwidth and Coulomb interaction, leading to correlated phenomena such as the fractional quantum Hall effect and recently those in magic-angle systems. In photonics, they enable properties including slow light1 and lasing2. Notably, flatbands support supercollimation—diffractionless wavepacket propagation—in both systems3,4. Despite these intense parallel efforts, flatbands have never been shown to affect the core interaction between free electrons and photons. Their interaction, pivotal for free-electron lasers5, microscopy and spectroscopy6,7, and particle accelerators8,9, is, in fact, limited by a dimensionality mismatch between localized electrons and extended photons. Here we reveal theoretically that photonic flatbands can overcome this mismatch and thus remarkably boost their interaction. We design flatband resonances in a silicon-on-insulator photonic crystal slab to control and enhance the associated free-electron radiation by tuning their trajectory and velocity. We observe signatures of flatband enhancement, recording a two-order increase from the conventional diffraction-enabled Smith–Purcell radiation. The enhancement enables polarization shaping of free-electron radiation and characterization of photonic bands through electron-beam measurements. Our results support the use of flatbands as test beds for strong light–electron interaction, particularly relevant for efficient and compact free-electron light sources and accelerators.
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Acknowledgements
We thank T. Savas for fabricating the samples; A. Massuda and J. Sloan for contributions to the building of the setup; D. Zhu and M. Lončar for sharing equipment; and C. Mao, O. D. Miller and N. Rivera for stimulating conversations. This material is based on work supported in part by the US Army Research Office through the Institute for Soldier Nanotechnologies under contract number W911NF-18-2-0048, the Air Force Office of Scientific Research under the award numbers FA9550-20-1-0115 and FA9550-21-1-0299, the US Office of Naval Research Multidisciplinary University Research Initiative grant N00014-20-1-2325 on Robust Photonic Materials with High-Order Topological Protection, and the U.S.-Israel Binational Science Foundation grant 2018288. Y.Y. acknowledges the support from the start-up fund of the University of Hong Kong and the National Natural Science Foundation of China Excellent Young Scientists Fund (HKU 12222417). C.R.-C. acknowledges funding from the MathWorks Engineering Fellowship Fund by MathWorks Inc.
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Y.Y., C.R.-C., I.K. and M.S. conceived the project. Y.Y. designed the sample. C.R.-C. and S.E.K. performed the radiation measurements. H.T. and Y.Y. performed the Fourier scattering spectroscopy. J.B. designed and fabricated the objective motorized stage with inputs from C.R.-C. and S.E.K. Y.Y. and C.R.-C. analysed the data. Y.Y. and C.R.-C. wrote the manuscript with inputs from all authors. E.M., I.K., J.D.J. and M.S. supervised the project.
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Y.Y., C.R.-C., S.E.K., I.K., J.D.J. and M.S. declare the following patent: US patent 10,505,334 (ref. 77).
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This file contains Supplementary Sections 1–15, Figs. 1–15 and References. The sections are entitled Radiation experimental setup, Band structure measurements, Beam diameter and divergence, Collection optics, Experimental analysis, Physical mechanism of enhanced interaction, Numerical methods, Distinction between sheet electrons and point electrons, Point and line degeneracies between electron surface and photonic band, Angles of enhanced radiation, Flatband-induced localization, Numerical comparisons with diffractive gratings, Experimental comparisons with diffractive gratings, Generality of the flatband scheme, and Flatband resonances for strong coupling and accelerators.
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Yang, Y., Roques-Carmes, C., Kooi, S.E. et al. Photonic flatband resonances for free-electron radiation. Nature 613, 42–47 (2023). https://doi.org/10.1038/s41586-022-05387-5
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DOI: https://doi.org/10.1038/s41586-022-05387-5
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