Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Poincaré beams from a free electron laser

Abstract

Poincaré beams are light beams that have spatially inhomogeneous polarization structure that spans a finite portion of the Poincaré sphere. This feature bestows the beams with intriguing topological properties and has led to a surge in research on their fundamental characteristics, their controlled generation and on emerging applications. Here we present an experimental demonstration of a Poincaré beam generated in the extreme ultraviolet (16.7 nm) at the FERMI free electron laser (FEL). The ‘star’ type Poincaré beam is generated by exploiting the phase and intensity structure intrinsic to FEL radiation without relying on optical elements. We controlled the spatial polarization distribution through a precise overlap and power balance between two FEL pulses, each with different transverse phase distributions and orthogonal circular polarizations. The spatial polarization structure was mapped in detail and shows extensive coverage of the Poincaré sphere, in agreement with analytic predictions. This method of in situ Poincaré beam production in FELs enables straightforward flexibility in the orientation and balance of polarization states, and can readily be extended to other vector beams and to shorter wavelengths enabling novel science applications in modern light sources.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Polarization distribution for a superposition of Laguerre–Gaussian modes.
Fig. 2: Illustration of experimental set-up.
Fig. 3: Poincaré beams before and after linear polarizer.
Fig. 4: Mapping the polarization distribution of the FEL Poincaré beam and analysis of polarization topology.

Similar content being viewed by others

Data availability

Source data used to generate Figs. 3 and 4 are publicly available via figshare at https://figshare.com/projects/Poincar_Beams_from_a_Free_Electron_Laser/248654 (ref. 56). The intensity dataset from the complete phase scan is also available at the same location. Additional data supporting the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Zhan, Q. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1, 1–57 (2009).

    Article  Google Scholar 

  2. Beckley, A. M., Brown, T. G. & Alonso, M. A. Full Poincaré beams. Opt. Express 18, 10777–10785 (2010).

    Article  ADS  Google Scholar 

  3. Galvez, E. J., Khadka, S., Schubert, W. H. & Nomoto, S. Poincaré-beam patterns produced by nonseparable superpositions of Laguerre–Gauss and polarization modes of light. Appl. Opt. 51, 2925–2934 (2012).

    Article  ADS  Google Scholar 

  4. Rubinsztein-Dunlop, H. et al. Roadmap on structured light. J. Opt. 19, 013001 (2016).

    Article  ADS  Google Scholar 

  5. Bouchard, F. et al. Polarization shaping for control of nonlinear propagation. Phys. Rev. Lett. 117, 233903 (2016).

    Article  ADS  Google Scholar 

  6. Nesterov, A. V. & Niziev, V. G. Laser beams with axially symmetric polarization. J. Phys. D 33, 1817–1822 (2000).

    Article  ADS  Google Scholar 

  7. Hao, X., Kuang, C., Wang, T. & Liu, X. Effects of polarization on the de-excitation dark focal spot in STED microscopy. J. Opt. 12, 115707 (2010).

    Article  ADS  Google Scholar 

  8. Sick, B., Hecht, B. & Novotny, L. Orientational imaging of single molecules by annular illumination. Phys. Rev. Lett. 85, 4482–4485 (2000).

    Article  ADS  Google Scholar 

  9. Novotny, L., Beversluis, M. R., Youngworth, K. S. & Brown, T. G. Longitudinal field modes probed by single molecules. Phys. Rev. Lett. 86, 5251–5254 (2001).

    Article  ADS  Google Scholar 

  10. Shvedov, V. et al. Visualizing polarization singularities in Bessel–Poincaré beams. Opt. Express 23, 12444–12453 (2015).

    Article  ADS  Google Scholar 

  11. Salla, G. R., Kumar, V., Miyamoto, Y. & Singh, R. P. Scattering of Poincaré beams: polarization speckles. Opt. Express 25, 19886–19893 (2017).

    Article  ADS  Google Scholar 

  12. Han, W., Cheng, W. & Zhan, Q. Flattop focusing with full Poincaré beams under low numerical aperture illumination. Opt. Lett. 36, 1605–1607 (2011).

    Article  ADS  Google Scholar 

  13. Rajput, R. & Senthilkumaran, P. Optical currents in Poincaré beams. Phys. Rev. A 102, 013509 (2020).

    Article  ADS  Google Scholar 

  14. Lochab, P., Senthilkumaran, P. & Khare, K. Propagation of converging polarization singular beams through atmospheric turbulence. Appl. Opt. 58, 6335–6345 (2019).

    Article  ADS  Google Scholar 

  15. Lochab, P., Senthilkumaran, P. & Khare, K. Designer vector beams maintaining a robust intensity profile on propagation through turbulence. Phys. Rev. A 98, 023831 (2018).

    Article  ADS  Google Scholar 

  16. Wei, C., Wu, D., Liang, C., Wang, F. & Cai, Y. Experimental verification of significant reduction of turbulence-induced scintillation in a full Poincaré beam. Opt. Express 23, 24331–24341 (2015).

    Article  ADS  Google Scholar 

  17. Galvez, E. J. et al. Multitwist Möbius strips and twisted ribbons in the polarization of paraxial light beams. Sci. Rep. 7, 13653 (2017).

    Article  ADS  Google Scholar 

  18. Suárez-Bermejo, J. C., González de Sande, J. C., Santarsiero, M. & Piquero, G. Mueller matrix polarimetry using full Poincaré beams. Opt. Lasers Eng. 122, 134–141 (2019).

    Article  Google Scholar 

  19. Suárez-Bermejo, J. C., de Sande, J. C. G., Santarsiero, M. & Piquero, G. Analysis of the errors in polarimetry with full Poincaré beams. In Proc. 2019 Photonics & Electromagnetics Research Symposium – Spring (PIERS-Spring) 2621–2627 (2019).

  20. Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020).

    Article  ADS  Google Scholar 

  21. Donati, S. et al. Twist of generalized skyrmions and spin vortices in a polariton superfluid. Proc. Natl Acad. Sci. USA 113, 14926–14931 (2016).

    Article  ADS  Google Scholar 

  22. Ornelas, P., Nape, I., de Mello Koch, R. & Forbes, A. Non-local skyrmions as topologically resilient quantum entangled states of light. Nat. Photon. 18, 258–266 (2024).

    Article  ADS  Google Scholar 

  23. Shen, Y. et al. Optical skyrmions and other topological quasiparticles of light. Nat. Photon. 18, 15–25 (2023).

    Article  ADS  Google Scholar 

  24. Nye, J. F. Lines of circular polarization in electromagnetic wave fields. Proc. R. Soc. Lond. A 389, 279–290 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  25. Saleh, B. E. A. & Teich, M. C. Fundamentals of Photonics (Wiley, 2007).

  26. Ribic, P. R. & Margaritondo, G. Status and prospects of X-ray free-electron lasers (X-FELs): a simple presentation. J. Phys. D 45, 213001 (2012).

    Article  ADS  Google Scholar 

  27. McNeil, B. W. J. & Thompson, N. R. X-ray free-electron lasers. Nat. Photon. 4, 814–821 (2010).

    Article  ADS  Google Scholar 

  28. Hemsing, E., Stupakov, G., Xiang, D. & Zholents, A. Beam by design: laser manipulation of electrons in modern accelerators. Rev. Mod. Phys. 86, 897–941 (2014).

    Article  ADS  Google Scholar 

  29. Niziev, V. G., Chang, R. S. & Nesterov, A. V. Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer. Appl. Opt. 45, 8393–8399 (2006).

    Article  ADS  Google Scholar 

  30. Chen, S. et al. Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere. Opt. Lett. 39, 5274–5276 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Matsuba, S. et al. Generation of vector beam with tandem helical undulators. Appl. Phys. Lett. 113, 021106 (2018).

    Article  ADS  Google Scholar 

  33. Luttmann, M. et al. Nonlinear up-conversion of a polarization Möbius strip with half-integer optical angular momentum. Sci. Adv. 9, eadf3486 (2023).

    Article  Google Scholar 

  34. Morgan, J., Hemsing, E., McNeil, B. W. J. & Yao, A. Free electron laser generation of X-ray Poincaré beams. New J. Phys. 22, 072001 (2020).

    Article  ADS  Google Scholar 

  35. Sasaki, S. & McNulty, I. Proposal for generating brilliant X-ray beams carrying orbital angular momentum. Phys. Rev. Lett. 100, 124801 (2008).

    Article  ADS  Google Scholar 

  36. Rebernik Ribič, P. et al. Extreme-ultraviolet vortices from a free-electron laser. Phys. Rev. X 7, 031036 (2017).

    Google Scholar 

  37. Hemsing, E. Coherent photons with angular momentum in a helical afterburner. Phys. Rev. Accel. Beams 23, 020703 (2020).

    Article  ADS  Google Scholar 

  38. Allaria, E. et al. The FERMI free-electron lasers. J. Synchrotron Radiat. 22, 485–491 (2015).

    Article  Google Scholar 

  39. Yu, L. H. Generation of intense UV radiation by subharmonically seeded single-pass free-electron lasers. Phys. Rev. A 44, 5178–5193 (1991).

    Article  ADS  Google Scholar 

  40. Murphy, J., Pellegrini, C. & Bonifacio, R. Collective instability of a free electron laser including space charge and harmonics. Opt. Commun. 53, 197–202 (1985).

    Article  ADS  Google Scholar 

  41. Bonifacio, R., De Salvo, L. & Pierini, P. Large harmonic bunching in a high-gain free-electron laser. Nucl. Instrum. Methods Phys. Res. A 293, 627–629 (1990).

    Article  ADS  Google Scholar 

  42. Penco, G. et al. Nonlinear harmonics of a seeded free-electron laser as a coherent and ultrafast probe to investigate matter at the water window and beyond. Phys. Rev. A 105, 053524 (2022).

    Article  ADS  Google Scholar 

  43. Maroju, P. K. et al. Attosecond pulse shaping using a seeded free-electron laser. Nature 578, 386–391 (2020).

    Article  ADS  Google Scholar 

  44. Bahrdt, J. et al. First observation of photons carrying orbital angular momentum in undulator radiation. Phys. Rev. Lett. 111, 034801 (2013).

    Article  ADS  Google Scholar 

  45. Lopez-Mago, D. On the overall polarisation properties of Poincaré beams. J. Opt. 21, 115605 (2019).

    Article  ADS  Google Scholar 

  46. Khan, S. et al. Evolution of density-modulated electron beams in drift sections. Phys. Rev. Accel. Beams 27, 040702 (2024).

    Article  ADS  Google Scholar 

  47. Peters, C., Cox, M., Drozdov, A. & Forbes, A. The invariance and distortion of vectorial light across a real-world free space link. Appl. Phys. Lett. 123, 021103 (2023).

    Article  ADS  Google Scholar 

  48. McLaren, M., Konrad, T. & Forbes, A. Measuring the nonseparability of vector vortex beams. Phys. Rev. A 92, 023833 (2015).

    Article  ADS  Google Scholar 

  49. Selyem, A., Rosales-Guzmán, C., Croke, S., Forbes, A. & Franke-Arnold, S. Basis-independent tomography and nonseparability witnesses of pure complex vectorial light fields by Stokes projections. Phys. Rev. A 100, 063842 (2019).

    Article  ADS  Google Scholar 

  50. Pancaldi, M. et al. The COMIX polarimeter: a compact device for XUV polarization analysis. J. Synchrotron Radiat. 29, 969–977 (2022).

    Article  Google Scholar 

  51. Fanciulli, M. et al. Observation of magnetic helicoidal dichroism with extreme ultraviolet light vortices. Phys. Rev. Lett. 128, 077401 (2022).

    Article  ADS  Google Scholar 

  52. Rouxel, J. R. et al. Hard X-ray helical dichroism of disordered molecular media. Nat. Photon. 16, 570–574 (2022).

    Article  ADS  Google Scholar 

  53. Allaria, E. et al. Highly coherent and stable pulses from the FERMI seeded free-electron laser in the extreme ultraviolet. Nat. Photon. 6, 699–704 (2012).

    Article  ADS  Google Scholar 

  54. Capotondi, F. et al. Invited Article: Coherent imaging using seeded free-electron laser pulses with variable polarization: first results and research opportunities. Rev. Sci. Instrum. 84, 051301 (2013).

    Article  ADS  Google Scholar 

  55. Allaria, E. et al. Control of the polarization of a vacuum-ultraviolet, high-gain, free-electron laser. Phys. Rev. X 4, 041040 (2014).

    Google Scholar 

  56. Morgan, J. et al. Poincaré beams from a free electron laser. figshare https://figshare.com/projects/Poincar_Beams_from_a_Free_Electron_Laser/248654 (2025).

Download references

Acknowledgements

This work was supported by US Department of Energy Contract 218 number DE-AC02-76SF00515 and award number 2021-SLAC-100732. We thank W. Fawley, E. Allaria and L. Giannessi for useful discussions and suggestions, and the FERMI operations team for their contributions to this project.

Author information

Authors and Affiliations

Authors

Contributions

J.M. and E.H. proposed the experiment. The experiment was designed by J.M., E.H., F.C. and P.R.R., with contributions from G.D.N. and A.B. The end station was prepared by F.C., M.P. and E.P., with M.Z., M.M., A.S. and L.N. responsible for transporting the radiation beam. C.S. and G.D.N. prepared the machine for the experiment. The experiment was conducted by J.M., E.H., P.R.R., F.C., A.B. and M.P. Data analysis and paper preparation were carried out by J.M. and E.H., with input from all authors.

Corresponding author

Correspondence to Jenny Morgan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Giuseppe Sansone and Shigemi Sasaki for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Spiral intensity profile from uniformly polarised undulators.

Intensity profile of the radiation captured after the Zr filter with all undulators emitting the same polarisation.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Morgan, J., Rebernik Ribič, P., Capotondi, F. et al. Poincaré beams from a free electron laser. Nat. Photon. 19, 946–951 (2025). https://doi.org/10.1038/s41566-025-01737-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41566-025-01737-7

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing