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Intrinsic chiral optical vortex emission from the interactions between free electrons with bound states in the continuum

Jing Li1,2,3,*, Zihan Wang1,2,*, Wu Wen1,2, Haoyu Mo1,2, Qingyao Liang1,2, Tianxiang Hong1,2, Yuhan Jiang1,2, and Yunquan Liu1,2,3,4,5,†

  • *These authors contributed equally to this work.
  • †Contact author: Yunquan.liu@pku.edu.cn

Phys. Rev. Research 7, 043049 – Published 15 October, 2025

DOI: https://doi.org/10.1103/9jmn-z1fj

Abstract

We present an approach for free-electron-driven optical vortex emission through interaction with the quasi-bound states in the continuum (quasi-BICs). Based on a unified framework for free electron-nanophotonic interaction and time domain simulations, we show that the free electron beam can efficiently excite the quasi-BIC under the phase-matching condition. The intrinsic k-space polarization anisotropy associated with the quasi-BIC imprints a geometric phase onto the emission, and thus generates an intrinsic optical vortex. We then reveal a link between the topological charge of the quasi-BIC and the emitted optical vortex by analyzing the far-field polarization structure and phase distribution. This mechanism offers a promising approach to creating nanoscale electron-beam-driven structured light sources without the need for complex chiral nanostructures, thereby advancing the interdisciplinary study of free-electron optics and nanophotonics.

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References (39)

  1. A. Polman, M. Kociak, and F. J. García De Abajo, Electron-beam spectroscopy for nanophotonics, Nat. Mater. 18, 1158 (2019).
  2. C. Roques-Carmes, S. E. Kooi, Y. Yang, N. Rivera, P. D. Keathley, J. D. Joannopoulos, S. G. Johnson, I. Kaminer, K. K. Berggren, and M. Soljačić, Free-electron–light interactions in nanophotonics, Appl. Phys. Rev. 10, 011303 (2023).
  3. A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, Quantum coherent optical phase modulation in an ultrafast transmission electron microscope, Nature (London) 521, 200 (2015).
  4. G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, H. Larocque, V. Grillo, E. Karimi, F. J. García De Abajo, and F. Carbone, Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields, Nat. Mater. 18, 573 (2019).
  5. K. Wang, R. Dahan, M. Shentcis, Y. Kauffmann, A. Ben Hayun, O. Reinhardt, S. Tsesses, and I. Kaminer, Coherent interaction between free electrons and a photonic cavity, Nature (London) 582, 50 (2020).
  6. J. Li, Y. Fang, and Y. Liu, Topologically protected strong-interaction of photonics with free electrons, Phys. Rev. Lett. 132, 073801 (2024).
  7. A. Feist, G. Huang, G. Arend, Y. Yang, J.-W. Henke, A. S. Raja, F. J. Kappert, R. N. Wang, H. Lourenço-Martins, Z. Qiu, J. Liu, O. Kfir, T. J. Kippenberg, and C. Ropers, Cavity-mediated electron-photon pairs, Science 377, 777 (2022).
  8. Y. Yang, C. Roques-Carmes, S. E. Kooi, H. Tang, J. Beroz, E. Mazur, I. Kaminer, J. D. Joannopoulos, and M. Soljačić, Photonic flatband resonances for free-electron radiation, Nature (London) 613, 42 (2023).
  9. L. W. W. Wong, X. Shi, A. Karnieli, J. Lim, S. Kumar, S. Carbajo, I. Kaminer, and L. J. Wong, Free-electron crystals for enhanced x-ray radiation, Light Sci. Appl. 13, 29 (2024).
  10. E. Akerboom, V. Di Giulio, N. J. Schilder, F. J. García De Abajo, and A. Polman, Free electron–plasmon coupling strength and near-field retrieval through electron energy-dependent cathodoluminescence spectroscopy, ACS Nano 18, 13560 (2024).
  11. G. Adamo, J. Y. Ou, J. K. So, S. D. Jenkins, F. De Angelis, K. F. MacDonald, E. Di Fabrizio, J. Ruostekoski, and N. I. Zheludev, Electron-beam-driven collective-mode metamaterial light source, Phys. Rev. Lett. 109, 217401 (2012).
  12. Y. Yang, A. Massuda, C. Roques-Carmes, S. E. Kooi, T. Christensen, S. G. Johnson, J. D. Joannopoulos, O. D. Miller, I. Kaminer, and M. Soljačić, Maximal spontaneous photon emission and energy loss from free electrons, Nat. Phys. 14, 894 (2018).
  13. Z. Wang, K. Yao, M. Chen, H. Chen, and Y. Liu, Manipulating Smith-Purcell emission with Babinet metasurfaces, Phys. Rev. Lett. 117, 157401 (2016).
  14. Y.-C. Lai, T. C. Kuang, B. H. Cheng, Y.-C. Lan, and D. P. Tsai, Generation of convergent light beams by using surface plasmon locked Smith-Purcell radiation, Sci. Rep. 7, 11096 (2017).
  15. N. Talebi, S. Meuret, S. Guo, M. Hentschel, A. Polman, H. Giessen, and P. A. Van Aken, Merging transformation optics with electron-driven photon sources, Nat. Commun. 10, 599 (2019).
  16. A. Karnieli, D. Roitman, M. Liebtrau, S. Tsesses, N. Van Nielen, I. Kaminer, A. Arie, and A. Polman, Cylindrical metalens for generation and focusing of free-electron radiation, Nano Lett. 22, 5641 (2022).
  17. C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Cerenkov radiation in photonic crystals, Science 299, 368 (2003).
  18. T. Coenen, E. J. R. Vesseur, and A. Polman, Angle-resolved cathodoluminescence spectroscopy, Appl. Phys. Lett. 99, 143103 (2011).
  19. J. Ni, C. Huang, L.-M. Zhou, M. Gu, Q. Song, Y. Kivshar, and C.-W. Qiu, Multidimensional phase singularities in nanophotonics, Science 374, eabj0039 (2021).
  20. G. Li, B. P. Clarke, J.-K. So, K. F. MacDonald, and N. I. Zheludev, Holographic free-electron light source, Nat. Commun. 7, 13705 (2016).
  21. N. van Nielen, M. Hentschel, N. Schilder, H. Giessen, A. Polman, and N. Talebi, Electrons generate self-complementary broadband vortex light beams using chiral photon sieves, Nano Lett. 20, 5975 (2020).
  22. M. Taleb, M. Hentschel, K. Rossnagel, H. Giessen, and N. Talebi, Phase-locked photon–electron interaction without a laser, Nat. Phys. 19, 869 (2023).
  23. M. Taleb, P. H. Bittorf, M. Black, M. Hentschel, W. Sigle, B. Haas, C. Koch, P. A. Van Aken, H. Giessen, and N. Talebi, Ultrafast phonon-mediated dephasing of color centers in hexagonal boron nitride probed by electron beams, Nat. Commun. 16, 2326 (2025).
  24. B. Wang, W. Liu, M. Zhao, J. Wang, Y. Zhang, A. Chen, F. Guan, X. Liu, L. Shi, and J. Zi, Generating optical vortex beams by momentum-space polarization vortices centered at bound states in the continuum, Nat. Photon. 14, 623 (2020).
  25. C. Huang, C. Zhang, S. Xiao, Y. Wang, Y. Fan, Y. Liu, N. Zhang, G. Qu, H. Ji, J. Han et al., Ultrafast control of vortex microlasers, Science 367, 1018 (2020).
  26. B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, Topological nature of optical bound states in the continuum, Phys. Rev. Lett. 113, 257401 (2014).
  27. Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, Analytical perspective for bound states in the continuum in photonic crystal slabs, Phys. Rev. Lett. 113, 037401 (2014).
  28. Y. Zhang, A. Chen, W. Liu, C. W. Hsu, B. Wang, F. Guan, X. Liu, L. Shi, L. Lu, and J. Zi, Observation of polarization vortices in momentum space, Phys. Rev. Lett. 120, 186103 (2018).
  29. H. M. Doeleman, F. Monticone, W. Den Hollander, A. Alù, and A. F. Koenderink, Experimental observation of a polarization vortex at an optical bound state in the continuum, Nat. Photon 12, 397 (2018).
  30. W. Ye, Y. Gao, and J. Liu, Singular points of polarizations in the momentum space of photonic crystal slabs, Phys. Rev. Lett. 124, 153904 (2020).
  31. J. Lee, B. Zhen, S.-L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, Observation and differentiation of unique high-q optical resonances near zero wave vector in macroscopic photonic crystal slabs, Phys. Rev. Lett. 109, 067401 (2012).
  32. A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, Lasing action from photonic bound states in continuum, Nature (London) 541, 196 (2017).
  33. M.-S. Hwang, H.-C. Lee, K.-H. Kim, K.-Y. Jeong, S.-H. Kwon, K. Koshelev, Y. Kivshar, and H.-G. Park, Ultralow-threshold laser using super-bound states in the continuum, Nat. Commun. 12, 4135 (2021).
  34. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9jmn-z1fj for the far-field radiation distribution at wider emission angles, the 41 × 41 unit cell PCS simulation, and the interaction between free electrons and merging BICs.
  35. P. Das, T. K. Chini, and J. Pond, Probing higher order surface plasmon modes on individual truncated tetrahedral gold nanoparticle using cathodoluminescence imaging and spectroscopy combined with FDTD simulations, J. Phys. Chem. C 116, 15610 (2012).
  36. Y. Cao, A. Manjavacas, N. Large, and P. Nordlander, Electron energy-loss spectroscopy calculation in finite-difference time-domain package, ACS Photonics 2, 369 (2015).
  37. A. Massuda, C. Roques-Carmes, Y. Yang, S. E. Kooi, Y. Yang, C. Murdia, K. K. Berggren, I. Kaminer, and M. Soljačić, Smith-Purcell radiation from low-energy electrons, ACS Photonics 5, 3513 (2018).
  38. W. Liu, B. Wang, Y. Zhang, J. Wang, M. Zhao, F. Guan, X. Liu, L. Shi, and J. Zi, Circularly polarized states spawning from bound states in the continuum, Phys. Rev. Lett. 123, 116104 (2019).
  39. J. Durnin, J. J. Miceli, and J. H. Eberly, Diffraction-free beams, Phys. Rev. Lett. 58, 1499 (1987).

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