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Maximal spontaneous photon emission and energy loss from free electrons

Nature Physics volume 14, pages 894–899 (2018)Cite this article

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A Publisher Correction to this article was published on 23 July 2018

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Abstract

Free-electron radiation such as Cerenkov1, Smith–Purcell2 and transition radiation3,4 can be greatly affected by structured optical environments, as has been demonstrated in a variety of polaritonic5,6, photonic-crystal7 and metamaterial8,9,10 systems. However, the amount of radiation that can ultimately be extracted from free electrons near an arbitrary material structure has remained elusive. Here we derive a fundamental upper limit to the spontaneous photon emission and energy loss of free electrons, regardless of geometry, which illuminates the effects of material properties and electron velocities. We obtain experimental evidence for our theory with quantitative measurements of Smith–Purcell radiation. Our framework allows us to make two predictions. One is a new regime of radiation operation—at subwavelength separations, slower (non-relativistic) electrons can achieve stronger radiation than fast (relativistic) electrons. The other is a divergence of the emission probability in the limit of lossless materials. We further reveal that such divergences can be approached by coupling free electrons to photonic bound states in the continuum11,12,13. Our findings suggest that compact and efficient free-electron radiation sources from microwaves to the soft X-ray regime may be achievable without requiring ultrahigh accelerating voltages.

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Fig. 1: Theoretical framework and predictions.
Fig. 2: Optimal electron velocities for maximal Smith–Purcell radiation.
Fig. 3: Experimental probing of the upper limit.
Fig. 4: Strong enhancement of Smith–Purcell radiation via high-Q resonances near a photonic BIC.

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Change history

  • 23 July 2018

    In the version of this Letter originally published, an older version of the Supplementary Information was uploaded by mistake, in which the notation did not match the main text. This has been corrected.

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Acknowledgements

The authors acknowledge fruitful discussions with K. Berggren, S. Yang, C. Peng, A. Gover, B. Zhen, L. J. Wong, X. Lin, D. Zhu, Yu. Yang, T. Dubcek and N. Rivera. We thank P. Rebusco for critical reading and editing of the manuscript. This work was performed in part at the Harvard University Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure Network (NNCI), which is supported by the National Science Foundation under NSF ECCS award no. 1541959. This work was partly supported by the Army Research Office through the Institute for Soldier Nanotechnologies under contract nos W911NF-18-2-0048 and W911NF-13-D-0001. Y.Y. was partly supported by the MRSEC Program of the National Science Foundation under grant no. DMR-1419807. T.C. was supported by the Danish Council for Independent Research (grant no. DFFC6108-00667). O.D.M. was supported by the Air Force Office of Scientific Research under award no. FA9550-17-1-0093. I.K. was partially supported by the Azrieli foundation and the Seventh Framework Programme of the European Research Council (FP7- Marie Curie IOF) under grant agreement no. 328853CMC-BSiCS.

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Authors and Affiliations

  1. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Yi Yang, Aviram Massuda, Charles Roques-Carmes, Thomas Christensen, Steven G. Johnson, John D. Joannopoulos, Ido Kaminer & Marin Soljačić

  2. Institute for Soldier Nanotechnologies, Cambridge, MA, USA

    Steven E. Kooi & John D. Joannopoulos

  3. Department of Applied Physics and Energy Sciences Institute, Yale University, New Haven, CT, USA

    Owen D. Miller

  4. Andrew and Erna Viterbi Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

    Ido Kaminer

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  1. Yi Yang
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Contributions

Y.Y., O.D.M., I.K. and M.S. conceived the project. Y.Y. developed the analytical models and numerical calculations. A.M. prepared the sample under study. Y.Y., A.M., C.R.-C., S.E.K. and I.K. performed the experiment. Y.Y., T.C. and O.D.M. analysed the asymptotics and bulk loss of the limit. S.G.J., J.D.J., O.D.M., I.K. and M.S. supervised the project. Y.Y. wrote the manuscript with input from all authors.

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Correspondence to Yi Yang, Owen D. Miller or Ido Kaminer.

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Yang, Y., Massuda, A., Roques-Carmes, C. et al. Maximal spontaneous photon emission and energy loss from free electrons. Nature Phys 14, 894–899 (2018). https://doi.org/10.1038/s41567-018-0180-2

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