Shaping the beam polarisation profile for new opportunities in XUV science

Light is defined not only by its wavelength and intensity but also by its polarisation state – the direction in which its electric field oscillates. Polarisation plays a crucial role in controlling and understanding light-matter interactions: in everyday life, it enables Polaroid sunglasses to block horizontally polarised glare for clearer vision; in condensed matter physics, it provides a means to probe magnetic ordering and electronic anisotropy in materials; and in optics, it determines conditions for phenomena such as total internal reflection, which underpin technologies like fibre-optic communication. While in most applications optical beams are uniformly polarised, Maxwell’s equations also admit exotic solutions such as vortex beams and, more generally, Poincaré beams, where the spatial structure of the polarisation is non-uniform and can encode topological properties. At visible wavelengths, Poincaré beams have found applications in areas such as high-resolution imaging, material processing, and the exploration of novel physical effects – including optical skyrmions – as well as in charged-particle acceleration and optical tweezing.

For the first time, Poincaré beams have now been realised at a free-electron laser (FEL) in the extreme-ultraviolet (XUV) spectral region. The experiment was carried out at the FERMI FEL by an international team of researchers from LCLS and FERMI. Extending structured polarisation into the XUV domain opens new opportunities for science, such as spatially-resolved scattering, local mapping of magnetic order, and the investigation of molecular chirality.

At XUV and X-ray wavelengths, conventional optical components such as waveplates or polarisation converters cannot be employed to efficiently manipulate the polarisation state of light. The innovation at FERMI lies in generating the structured polarisation directly at the light source. As shown in Fig. 1a, by combining two collinear FEL pulses – one with right-handed circular polarisation in a Gaussian mode and another with left-handed circular polarisation carrying a helical phase and a ring-shaped intensity profile – the experimental team produced a superposed beam with a spatially varying polarisation distribution: a so-called “star” Poincaré beam.

Figure 1: Generation and characterisation of XUV Poincaré beams at FERMI. (a) Schematic of the FEL configuration used to generate two pulses with orthogonal circular polarisations and distinct spatial profiles, which combine to form the structured beam. (b) Experimental setup to characterise the polarisation profile at the DiProI beamline of FERMI. (c) Intensity recorded before the polariser, showing a filled central profile (first panel). Spiral structure observed after reflection from a polariser, revealing the underlying polarisation pattern (other panels). (d) Reconstructed polarisation map of the beam, where local polarisation ellipses are overlaid on the measured intensity, confirming the expected “star” distribution. (e) The polarisation distribution mapped onto the Poincaré sphere.

The polarisation profile of this novel light was characterised at the DiProI beamline of FERMI. A linear polariser, realised via reflection near Brewster’s angle, revealed a distinct difference between the intensity of the whole beam (that includes all polarisation components) and the intensity of its linearly polarised part (Fig. 1b). Indeed, before the polariser, the intensity appeared centrally filled (Fig. 1c, first panel). After reflection, however, a spiral pattern emerged, directly evidencing the spatially non-uniform polarisation (Fig. 1c, second panel). By adjusting the relative phase of the two superimposed modes, the spiral (and therefore the polarisation pattern) rotated as a whole (Fig. 1c). From these images, spatially resolved Stokes parameters were reconstructed, providing a full map of the polarisation distribution.

As shown in Fig. 1d, the beam is right-circularly polarised at the centre and gradually evolves into elliptical and linear states toward the edges, producing the expected star-shaped pattern. A subtle twist in the local polarisation ellipses carries a direct signature of the two FEL pulses coming from slightly separated emission points. While the overall structure closely matches theoretical predictions, small asymmetries were observed, consistent with minor differences in the relative amplitudes and alignment of the modes. Projecting the Stokes parameters onto the Poincaré sphere (Fig. 1e) shows that nearly all polarisation states are represented in a single FEL pulse, confirming both the high quality of the beam and the robustness of its polarisation topology.

The experiment performed at FERMI demonstrates that FELs can be used to generate complex vector beams directly, without the need for optical elements. The method can be extended to even shorter wavelengths and adapted to different FEL schemes, including those based on self-amplified spontaneous emission (SASE). This achievement provides new experimental capabilities for ultrafast and polarisation-resolved studies, opening pathways toward applications ranging from magnetism and chirality to the development of more advanced vector beam topologies, which might unlock further applications in manipulation and in the topological diagnosis of inhomogeneous media at the nanometre scale.

Jenny Morgan¹, Primož Rebernik Ribič², Flavio Capotondi², Alexander Brynes², Michele Manfredda², Giovanni De Ninno^2,3, Luka Novinec², Matteo Pancaldi^2,4, Emanuele Pedersoli², Alberto Simoncig², Carlo Spezzani², Marco Zangrando^2,5 and Erik Hemsing¹

¹ SLAC National Accelerator Laboratory, Menlo Park, CA, US
² Elettra - Sincrotrone Trieste S.C.p.A., Trieste, Italy
³ University of Nova Gorica, Nova Gorica, Slovenia
⁴ Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, Venezia, Italy
⁵ CNR - Istituto Officina dei Materiali (IOM), Trieste, Italy

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