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Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation


Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light–matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses—from linear to circular—and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.

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Fig. 1: Bicircular HHG in the presence of simultaneous SAM–OAM conservation (SAM–OAM HHG).
Fig. 2: Experimental generation and theoretical confirmation of SAM–OAM EUV vortices in the presence of simultaneous SAM–OAM conservation.
Fig. 3: Separation of EUV high-harmonic vortex beams with opposite circularities through the OAM of the bicircular vortex driver.
Fig. 4: Control over the OAMs of the bicircular driver yields full control of the polarization state of APTs in SAM–OAM HHG.
Fig. 5: Circularly polarized high-harmonic vortex beams with equal, low-charge OAM.

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Data availability

The datasets and analysis routines utilized to prepare the data presented in this manuscript are available, free of charge, from the corresponding authors under reasonable request.


  1. Beth, R. A. Mechanical detection and measurement of the angular momentum of light. Phys. Rev. 50, 115–125 (1936).

    Article  ADS  Google Scholar 

  2. Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).

    Article  ADS  Google Scholar 

  3. Yao, A. M. & Padgett, M. J. Orbital angular momentum: origins, behavior and applications. Adv. Opt. Photon. 3, 161–204 (2011).

    Article  Google Scholar 

  4. Calvo, G. et al. Measuring the complete transverse spatial mode spectrum of a wave field. Phys. Rev. Lett. 100, 173902 (2008).

    Article  ADS  Google Scholar 

  5. Ballantine, K. E., Donegan, J. F. & Eastham, P. R. There are many ways to spin a photon: half-quantization of a total optical angular momentum. Sci. Adv. 2, e1501748 (2016).

    Article  ADS  Google Scholar 

  6. Cardano, F. & Marrucci, L. Spin-orbit photonics. Nat. Photon. 9, 776–778 (2015).

    Article  ADS  Google Scholar 

  7. Willner, A. E. et al. Optical communication using orbital angular momentum beams. Adv. Opt. Photon. 7, 66–106 (2015).

    Article  Google Scholar 

  8. Torres, J. P. & Torner, L. Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley-VCH, Bristol, 2011).

  9. Beaulieu, S. et al. Photoexcitation circular dichroism in chiral molecules. Nat. Phys. 14, 484–489 (2018).

    Article  Google Scholar 

  10. Padgett, M. & Bowman, R. Tweezers with a twist. Nat. Photon. 5, 343–348 (2011).

    Article  ADS  Google Scholar 

  11. Marrucci, L., Manzo, C. & Paparo, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006).

    Article  ADS  Google Scholar 

  12. Eichmann, H. et al. Polarization-dependent high-order two-color mixing. Phys. Rev. A 51, R3414 (1995).

    Article  ADS  Google Scholar 

  13. Fleischer, A., Kfir, O., Diskin, T., Sidorenko, P. & Cohen, O. Spin angular momentum and tunable polarization in high-harmonic generation. Nat. Photon. 8, 543–549 (2014).

    Article  ADS  Google Scholar 

  14. Ferré, A. et al. A table-top ultraviolet light source in the extreme ultraviolet for circular dichroism experiments. Nat. Photon. 9, 93–98 (2015).

    Article  ADS  Google Scholar 

  15. Hickstein, D. D. et al. Non-collinear generation of angularly isolated circularly polarized high harmonics. Nat. Photon. 9, 743–750 (2015).

    Article  ADS  Google Scholar 

  16. Lambert, G. et al. Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources. Nat. Commun. 6, 6167 (2015).

    Article  Google Scholar 

  17. Ellis, J. L. et al. High harmonics with spatially varying ellipticity. Optica 5, 479–485 (2018).

  18. Huang, P.-C. et al. Polarization control of isolated high-harmonic pulses. Nat. Photon. 12, 349–354 (2018).

    Article  ADS  Google Scholar 

  19. Zürch, M. et al. Strong-field physics with singular light beams. Nat. Phys. 8, 743–746 (2012).

  20. Hernández-García, C. et al. Attosecond extreme ultraviolet vortices from high-order harmonic generation. Phys. Rev. Lett. 111, 083602 (2013).

    Article  ADS  Google Scholar 

  21. Gariepy, G. et al. Creating high-harmonic beams with controlled orbital angular momentum. Phys. Rev. Lett. 113, 153901 (2014).

    Article  ADS  Google Scholar 

  22. Géneaux, R. et al. Synthesis and characterization of attosecond light vortices in the extreme ultraviolet. Nat. Commun. 7, 12583 (2016).

    Article  ADS  Google Scholar 

  23. Rego, L., San Román, J., Picón, A., Plaja, L. & Hernández-García, C. Nonperturbative twist in the generation of extreme-ultraviolet vortex beams. Phys. Rev. Lett. 117, 163202 (2016).

    Article  ADS  Google Scholar 

  24. Kong, F. et al. Controlling the orbital angular momentum of high harmonic vortices. Nat. Commun. 8, 14970 (2017).

    Article  ADS  Google Scholar 

  25. Gauthier, D. et al. Tunable orbital angular momentum in high-harmonic generation. Nat. Commun. 8, 14971 (2017).

    Article  ADS  Google Scholar 

  26. Turpin, A., Rego, L., Picon, L., Roman, J. S. & Hernandez-Garcia, C. Extreme ultraviolet fractional orbital angular momentum beams from high harmonic generation. Sci. Rep. 7, 43888 (2017).

    Article  ADS  Google Scholar 

  27. Hernández-García, C. et al. Extreme ultraviolet vector beams driven by infrared lasers. Optica 4, 520–526 (2017).

  28. Schafer, K. J., Yang, B., DiMauro, L. F. & Kulander, K. C. Above threshold ionization beyond the high harmonic cutoff. Phys. Rev. Lett. 70, 1599–1602 (1993).

    Article  ADS  Google Scholar 

  29. Corkum, P. B. Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993).

    Article  ADS  Google Scholar 

  30. McPherson, A. et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases. J. Opt. Soc. Am. B 4, 595 (1997).

    Article  ADS  Google Scholar 

  31. Ferray, M. et al. Multiple-harmonic conversion of 1064-nm radiation in the rare gases. J. Phys. B 21, L31–L35 (1998).

  32. Fan, T. et al. Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism. Proc. Natl Acad. Sci. USA 111, 14206–14211 (2015).

  33. Rundquist, A. et al. Phase matching of soft X-ray harmonic emission in hollow-core fibers. Science 280, 1412–1415 (1998).

  34. Popmintchev, T. et al. Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers. Science 336, 1287–1291 (2012).

  35. Dorney, K. M. et al. Helicity-selective enhancement and polarization control of attosecond high-harmonic waveforms driven by bichromatic circularly polarized laser fields. Phys. Rev. Lett. 119, 063201 (2017).

    Article  ADS  Google Scholar 

  36. Jiménez-Galán, Á. et al. Control of attosecond light polarization in two-color bicircular fields. Phys. Rev. A 97, 023409 (2018).

  37. Hernández-García, C. A twist in coherent X-rays. Nat. Phys. 13, 327–329 (2017).

  38. Hernández-García, C. et al. High-order harmonic propagation in gases within the discrete dipole approximation. Phys. Rev. A 82, 033432 (2010).

    Article  ADS  Google Scholar 

  39. Chen, C. et al. Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology. Sci. Adv. 2, e1501333 (2016).

    Article  ADS  Google Scholar 

  40. Hernández-García, C. et al. Schemes for generation of isolated attosecond pulses of pure circular polarization. Phys. Rev. A 93, 043855 (2016).

    Article  ADS  Google Scholar 

  41. Hernández-García, C., San Román, J., Plaja, L. & Picón, A. Quantum-path signatures in attosecond helical beams driven by optical vortices. New J. Phys. 17, 093029 (2015).

    Article  ADS  Google Scholar 

  42. Alon, O. E., Averbukh, V. & Moisevev, N. Selection rules for the high harmonic generation spectra. Phys. Rev. Lett. 80, 3743–3746 (1998).

  43. Pisanty, E., Sukiasyan, S. & Ivanov, M. Spin conservation in high-order harmonic generation using bicircular fields. Phys. Rev. A 90, 043829 (2014).

    Article  ADS  Google Scholar 

  44. Paufler, W., Böning, B. & Fritzsche, S. Tailored orbital angular momentum in high-order harmonic generation with bicircular Laguerre-Gaussian beams. Phys. Rev. A 98, 011401(R) (2018).

  45. Bliokh, K. Y., Rodríguez-Fortuño, F. J., Nori, F. & Zayats, A. V. Spin-orbit interactions of light. Nat. Photon. 9, 796–808 (2015).

    Article  ADS  Google Scholar 

  46. Milošević, D. B., Becker, W. & Kopold, R. Generation of circularly polarized high-order harmonics by two-color coplanar field mixing. Phys. Rev. A 61, 063403 (2000).

    Article  ADS  Google Scholar 

  47. Medišauskas, L., Wragg, J., van der Hart, H. & Ivanov, M. Y. Generating elliptically polarized attosecond pulses using bichromatic counterrotating circularly polarized laser fields. Phys. Rev. Lett. 115, 153001 (2015).

    Article  ADS  Google Scholar 

  48. Milošević, D. B. Generation of elliptically polarized attosecond pulse trains. Opt. Lett. 40, 2381–2384 (2015).

  49. Milošević, D. B. & Becker, W. Attosecond pulse trains with unusual nonlinear polarization. Phys. Rev. A 62, 011403(R) (2000).

  50. Sanson, F. et al. Hartmann wavefront sensor characterization of a high charge vortex beam in the XUV spectral range. Opt. Lett. 43, 2780–2783 (2018).

    Article  ADS  Google Scholar 

  51. Beaurepaire, E., Merle, J.-C., Daunois, A. & Bigot, J.-Y. Ultrafast spin dynamics in ferromagnetic nickel. Phys. Rev. Lett. 76, 4250–4253 (1996).

  52. Boeglin, C. et al. Distinguishing the ultrafast dynamics of spin and orbital moments in solids. Nature 465, 458–461 (2010).

  53. Chen, C. et al. Distinguishing attosecond electron–electron scattering and screening in transition metals. Proc. Natl Acad. Sci. USA 114, E5300–E5307 (2017).

  54. Tengdin, P. et al. Critical behavior within 20 fs drives the out-of-equilibrium laser-induced magnetic phase transition in nickel. Sci. Adv. 4, 9744 (2018).

    Article  Google Scholar 

  55. Cireasa, R. et al. Probing molecular chirality on a sub-femtosecond timescale. Nat. Phys. 11, 654–658 (2015).

    Article  Google Scholar 

  56. Fujita, H. & Sato, M. Ultrafast generation of skyrmionics defects with vortex beams: printing laser profiles on magnets. Phys. Rev. B 95, 054421 (2017).

    Article  ADS  Google Scholar 

  57. van Veenendaal, M. Interaction between X-ray and magnetic vortices. Phys. Rev. B 92, 245116 (2015).

    Article  ADS  Google Scholar 

  58. Picón, A. et al. Transferring orbital and spin angular momenta of light to atoms. New J. Phys. 12, 083053 (2010).

    Article  ADS  Google Scholar 

  59. Eckart, S. et al. Ultrafast preparation and detection of ring currents in single atoms. Nat. Phys. 14, 701–704 (2018).

    Article  Google Scholar 

  60. van Veenendaal, M. & McNulty, I. Prediction of strong dichroism induced by X rays carrying orbital angular momentum. Phys. Rev. Lett. 98, 157401 (2007).

    Article  ADS  Google Scholar 

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The authors are thankful for useful and productive conversations with E. Pisanty, C. Durfee, D. Hickstein, S. Alperin and M. Siemens. H.C.K. and M.M.M. graciously acknowledge support from the Department of Energy BES Award No. DE-FG02–99ER14982 for the experimental implementation, as well as a MURI grant from the Air Force Office of Scientific Research under Award No. FA9550–16–1–0121 for the theory. J.L.E., N.J.B. and Q.L.N. acknowledge support from National Science Foundation Graduate Research Fellowships (Grant No. DGE-1144083). C.H.-G., J.S.R. and L.P. acknowledge support from Junta de Castilla y León (SA046U16) and Ministerio de Economía y Competitividad (FIS2013–44174-P, FIS2016–75652-P). C.H.-G. acknowledges support from a 2017 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation. L.R. acknowledges support from Ministerio de Educación, Cultura y Deporte (FPU16/02591). A.P. acknowledges support from the Marie Sklodowska-Curie Grant, Agreement No. 702565. We thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (RES-AECT-2014–2–0085). This research made use of the high-performance computingresources of the Castilla y León Supercomputing Center (SCAYLE,,financed by the European Regional Development Fund (ERDF). Certain commercial instruments are identified to specify the experimental study adequately. This does not imply endorsement by the National Institute of Standards and Technology (NIST) or that the instruments are the best available for the purpose.

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C.H.-G., K.M.D., M.M.M., H.C.K., L.R. and L.P. conceived and designed the SAM–OAM HHG experiment. K.M.D., N.J.B., C.-T.L., J.L.E. and Q.L.N. conducted the experiment. K.M.D. analysed the experimental data. C.H.-G., L.R., J.S.R., A.P. and L.P. performed the theoretical simulations and analysed the resulting data. J.M.S. prepared the EUV MCD sample. C.H.-G., L.P., M.M.M. and H.C.K. supervised the theoretical simulations and experimental work and developed the required facilities and measurement capabilities. C.H.-G., K.M.D., L.R., J.S.R., M.M.M. and L.P. wrote and prepared the manuscript, to which all authors provided constructive improvements and feedback.

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Correspondence to Kevin M. Dorney or Carlos Hernández-García.

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M.M.M. and H.C.K. have a interest in KMLabs. The other authors declare no competing interests.

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Dorney, K.M., Rego, L., Brooks, N.J. et al. Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation. Nature Photon 13, 123–130 (2019).

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