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Controlling free electrons with optical whispering-gallery modes


Free-electron beams are versatile probes of microscopic structure and composition1,2, and have revolutionized atomic-scale imaging in several fields, from solid-state physics to structural biology3. Over the past decade, the manipulation and interaction of electrons with optical fields have enabled considerable progress in imaging methods4, near-field electron acceleration5,6, and four-dimensional microscopy techniques with high temporal and spatial resolution7. However, electron beams typically couple only weakly to optical excitations, and emerging applications in electron control and sensing8,9,10,11 require large enhancements using tailored fields and interactions. Here we couple a free-electron beam to a travelling-wave resonant cavity mode. The enhanced interaction with the optical whispering-gallery modes of dielectric microresonators induces a strong phase modulation on co-propagating electrons, which leads to a spectral broadening of 700 electronvolts, corresponding to the absorption and emission of hundreds of photons. By mapping the near-field interaction with ultrashort electron pulses in space and time, we trace the lifetime of the the microresonator following a femtosecond excitation and observe the spectral response of the cavity. The natural matching of free electrons to these quintessential optical modes could enable the application of integrated photonics technology in electron microscopy, with broad implications for attosecond structuring, probing quantum emitters and possible electron–light entanglement.

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Fig. 1: Experimental scheme.
Fig. 2: Electron spectral broadening induced by WGMs.
Fig. 3: Spectral and temporal properties of the interaction between free electrons and WGMs.

Data availability

The data supporting the findings of this study are available within the paper and at the Open Science Framework repository at Source data for Figs. 13 are provided with the paper.


  1. 1.

    Oh, S. H., Kauffmann, Y., Scheu, C., Kaplan, W. D. & Rühle, M. Ordered liquid aluminum at the interface with sapphire. Science 310, 661–663 (2005).

    ADS  CAS  PubMed  Google Scholar 

  2. 2.

    Kimoto, K. et al. Element-selective imaging of atomic columns in a crystal using STEM and EELS. Nature 450, 702–704 (2007).

    ADS  CAS  PubMed  Google Scholar 

  3. 3.

    Glaeser, R. M. How good can cryo-EM become? Nat. Methods 13, 28–32 (2016).

    CAS  PubMed  Google Scholar 

  4. 4.

    Barwick, B., Flannigan, D. J. & Zewail, A. H. Photon-induced near-field electron microscopy. Nature 462, 902–906 (2009).

    ADS  CAS  PubMed  Google Scholar 

  5. 5.

    Peralta, E. A. et al. Demonstration of electron acceleration in a laser-driven dielectric microstructure. Nature 503, 91–94 (2013).

    ADS  CAS  PubMed  Google Scholar 

  6. 6.

    Breuer, J. & Hommelhoff, P. Laser-based acceleration of nonrelativistic electrons at a dielectric structure. Phys. Rev. Lett. 111, 134803 (2013).

    ADS  PubMed  Google Scholar 

  7. 7.

    Carbone, F., Kwon, O.-H. & Zewail, A. H. Dynamics of chemical bonding mapped by energy-resolved 4D electron microscopy. Science 325, 181–184 (2009).

    ADS  CAS  PubMed  Google Scholar 

  8. 8.

    Cai, W., Sainidou, R., Xu, J., Polman, A. & García de Abajo, F. J. Efficient generation of propagating plasmons by electron beams. Nano Lett. 9, 1176–1181 (2009).

    ADS  CAS  PubMed  Google Scholar 

  9. 9.

    Kfir, O. Entanglements of electrons and cavity photons in the strong-coupling regime. Phys. Rev. Lett. 123, 103602 (2019).

    ADS  CAS  PubMed  Google Scholar 

  10. 10.

    Di Giulio, V., Kociak, M. & García de Abajo, F. J. Probing quantum optical excitations with fast electrons. Optica 6, 1524–1534 (2019).

    ADS  Google Scholar 

  11. 11.

    Schwartz, O. et al. Laser phase plate for transmission electron microscopy. Nat. Methods 16, 1016–1020 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  12. 12.

    García de Abajo, F. J. Optical excitations in electron microscopy. Rev. Mod. Phys. 82, 209–275 (2010).

    ADS  Google Scholar 

  13. 13.

    Talebi, N. Interaction of electron beams with optical nanostructures and metamaterials: from coherent photon sources towards shaping the wave function. J. Opt. 19, 103001 (2017).

    ADS  Google Scholar 

  14. 14.

    García de Abajo, F. J. & Kociak, M. Probing the photonic local density of states with electron energy loss spectroscopy. Phys. Rev. Lett. 100, 106804 (2008).

    ADS  PubMed  Google Scholar 

  15. 15.

    Nelayah, J. et al. Mapping surface plasmons on a single metallic nanoparticle. Nat. Phys. 3, 348–353 (2007).

    CAS  Google Scholar 

  16. 16.

    Talebi, N. et al. Excitation of mesoscopic plasmonic tapers by relativistic electrons: phase matching versus eigenmode resonances. ACS Nano 9, 7641–7648 (2015).

    MathSciNet  CAS  PubMed  Google Scholar 

  17. 17.

    Hörl, A. et al. Tomographic imaging of the photonic environment of plasmonic nanoparticles. Nat. Commun. 8, 37 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  18. 18.

    Bosman, M. et al. Surface plasmon damping quantified with an electron nanoprobe. Sci. Rep. 3, 1312 (2013).

    PubMed  PubMed Central  Google Scholar 

  19. 19.

    García de Abajo, F. J. & Kociak, M. Electron energy-gain spectroscopy. New J. Phys. 10, 073035 (2008).

    ADS  Google Scholar 

  20. 20.

    Pomarico, E. et al. meV resolution in laser-assisted energy-filtered transmission electron microscopy. ACS Photonics 5, 759–764 (2018).

    CAS  Google Scholar 

  21. 21.

    Das, P. et al. Stimulated electron energy loss and gain in an electron microscope without a pulsed electron gun. Ultramicroscopy 203, 44–51 (2019).

    CAS  PubMed  Google Scholar 

  22. 22.

    Asenjo-Garcia, A. & García de Abajo, F. J. Plasmon electron energy-gain spectroscopy. New J. Phys. 15, 103021 (2013).

    ADS  Google Scholar 

  23. 23.

    Wang, K. et al. Coherent interaction between free electrons and a photonic cavity. Nature (2020).

  24. 24.

    Feist, A. et al. Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 521, 200–203 (2015).

    ADS  CAS  PubMed  Google Scholar 

  25. 25.

    Madan, I. et al. Holographic imaging of electromagnetic fields via electron-light quantum interference. Sci. Adv. 5, eaav8358 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  26. 26.

    Vanacore, G. M. et al. Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields. Nat. Mater. 18, 573–579 (2019).

    ADS  CAS  PubMed  Google Scholar 

  27. 27.

    Priebe, K. E. et al. Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy. Nat. Photon. 11, 793–797 (2017).

    ADS  CAS  Google Scholar 

  28. 28.

    Morimoto, Y. & Baum, P. Diffraction and microscopy with attosecond electron pulse trains. Nat. Phys. 14, 252–256 (2018).

    CAS  Google Scholar 

  29. 29.

    Kozák, M., Schönenberger, N. & Hommelhoff, P. Ponderomotive generation and detection of attosecond free-electron pulse trains. Phys. Rev. Lett. 120, 103203 (2018).

    ADS  PubMed  Google Scholar 

  30. 30.

    Park, S. T., Lin, M. & Zewail, A. H. Photon-induced near-field electron microscopy (PINEM): theoretical and experimental. New J. Phys. 12, 123028 (2010).

    ADS  CAS  Google Scholar 

  31. 31.

    Constant, E. et al. Optimizing high harmonic generation in absorbing gases: model and experiment. Phys. Rev. Lett. 82, 1668–1671 (1999).

    ADS  CAS  Google Scholar 

  32. 32.

    Breuer, J., McNeur, J. & Hommelhoff, P. Dielectric laser acceleration of electrons in the vicinity of single and double grating structures—theory and simulations. J. Phys. B 47, 234004 (2014).

    ADS  Google Scholar 

  33. 33.

    Kozák, M. et al. Acceleration of sub-relativistic electrons with an evanescent optical wave at a planar interface. Opt. Express 25, 19195–19204 (2017).

    ADS  PubMed  Google Scholar 

  34. 34.

    Dahan, R. et al. Observation of the stimulated quantum Cherenkov effect. Preprint at (2019).

  35. 35.

    Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    ADS  Google Scholar 

  36. 36.

    Brasch, V. et al. Photonic chip-based optical frequency comb using soliton Cherenkov radiation. Science 351, 357–360 (2016).

    ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  37. 37.

    Vollmer, F. & Arnold, S. Whispering-gallery-mode biosensing: label-free detection down to single molecules. Nat. Methods 5, 591–596 (2008).

    CAS  PubMed  Google Scholar 

  38. 38.

    Arnold, S., Khoshsima, M., Teraoka, I., Holler, S. & Vollmer, F. Shift of whispering-gallery modes in microspheres by protein adsorption. Opt. Lett. 28, 272–274 (2003).

    ADS  CAS  PubMed  Google Scholar 

  39. 39.

    Aoki, T. et al. Observation of strong coupling between one atom and a monolithic microresonator. Nature 443, 671–674 (2006).

    ADS  CAS  PubMed  Google Scholar 

  40. 40.

    Shomroni, I. et al. All-optical routing of single photons by a one-atom switch controlled by a single photon. Science 345, 903–906 (2014).

    ADS  CAS  PubMed  Google Scholar 

  41. 41.

    García de Abajo, F. J., Asenjo-Garcia, A. & Kociak, M. Multiphoton absorption and emission by interaction of swift electrons with evanescent light fields. Nano Lett. 10, 1859–1863 (2010).

    ADS  PubMed  Google Scholar 

  42. 42.

    Liu, J. et al. Ultralow-power chip-based soliton microcombs for photonic integration. Optica 5, 1347 (2018).

    ADS  CAS  Google Scholar 

  43. 43.

    Bechler, O. et al. A passive photon–atom qubit swap operation. Nat. Phys. 14, 996–1000 (2018).

    CAS  Google Scholar 

  44. 44.

    He, L., Özdemir, Ş. K., Zhu, J., Kim, W. & Yang, L. Detecting single viruses and nanoparticles using whispering gallery microlasers. Nat. Nanotechnol. 6, 428–432 (2011).

    ADS  CAS  PubMed  Google Scholar 

  45. 45.

    Feist, A. et al. Ultrafast transmission electron microscopy using a laser-driven field emitter: femtosecond resolution with a high coherence electron beam. Ultramicroscopy 176, 63–73 (2017).

    CAS  PubMed  Google Scholar 

  46. 46.

    Polyanskiy, M. N. Refractive Index Database (2015).

  47. 47.

    Balac, S. WGMode: a Matlab toolbox for whispering gallery modes volume computation in spherical optical micro-resonators. Comput. Phys. Commun. 243, 121–134 (2019).

    ADS  CAS  Google Scholar 

  48. 48.

    García de Abajo, F. J. Multiple excitation of confined graphene plasmons by single free electrons. ACS Nano 7, 11409–11419 (2013).

    Google Scholar 

  49. 49.

    Yang, Y. et al. Maximal spontaneous photon emission and energy loss from free electrons. Nat. Phys. 14, 894–899 (2018); correction 14, 967 (2018).

    CAS  Google Scholar 

  50. 50.

    Hörl, A., Trügler, A. & Hohenester, U. Tomography of particle plasmon fields from electron energy loss spectroscopy. Phys. Rev. Lett. 111, 076801 (2013).

    ADS  PubMed  Google Scholar 

  51. 51.

    Boyd, R. W. Nonlinear Optics (Academic Press, 2003).

  52. 52.

    Hansen, J. E. Spherical Near-field Antenna Measurements (IET, 1988).

  53. 53.

    Balac, S. & Féron, P. Whispering Gallery Modes Volume Computation in Optical Micro-Spheres. Report 01279396 (HAL, 2014);

  54. 54.

    Vanacore, G. M. et al. Attosecond coherent control of free-electron wave functions using semi-infinite light fields. Nat. Commun. 9, 2694 (2018); correction 10, 1069 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

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We acknowledge the joint effort of the UTEM team in Göttingen and especially the support of M. Möller, J. H. Gaida, T. Danz and T. Domröse. We thank J. Liu for productive discussions. O.K. gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement number 752533. T.R.H. acknowledges the support of a postdoctoral fellowship from the Alexander von Humboldt Foundation and its sponsor, the German Federal Ministry for Education and Research. This work was funded by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center ‘Atomic Scale Control of Energy Conversion’ (DFG-SFB 1073, project A05) and the Priority Program ‘Quantum Dynamics in Tailored Intense Fields’ (DFG-SPP 1840).

Author information




O.K. conceived the experiment. C.R. directed the study. O.K. and H.L.-M. conducted the experiment with contributions from A.F. and T.R.H.; O.K., H.L.-M., G.S. and M.S. prepared the samples. O.K. analysed the data with contributions from A.F.; O.K. and C.R. wrote the manuscript with contributions from T.J.K., H.L.-M., A.F. and M.S. and based on discussions with all authors.

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Correspondence to Ofer Kfir or Claus Ropers.

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The authors declare no competing interests.

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Peer review information Nature thanks Nahid Talebi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Kfir, O., Lourenço-Martins, H., Storeck, G. et al. Controlling free electrons with optical whispering-gallery modes. Nature 582, 46–49 (2020).

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