FERMI | DiProl Transverse polarisation structure in extreme-ultraviolet light Generation of light with spatially varying polarisation, known as Poincaré beams, is well established at visible wavelengths. These beams are used in applications ranging from imaging and material processing to studies of atomic states, optical currents, and emerging topological phenomena like optical skyrmions. Poincaré beams, with their distinctive polarization structure, are promising for applications such as single-shot polarisation scans and spatially resolved scattering. Extending these beams into the extreme-ultraviolet (EUV) and x-ray regions could enable new scientific techniques, from mapping magnetic behaviour to probing chirality. Unfortunately, conventional optics cannot shape polarisation at these short wavelengths. However, Free Electron Lasers (FELs), provide a natural solution for producing structured polarisation states directly from the light source. The experimentally demonstrated method for producing EUV Poincaré beams relies on combining two FEL pulses with orthogonal circular polarisations and distinct transverse phase profiles. One pulse is emitted into a Gaussian mode, while the other carries a ring-shaped intensity profile with a helically varying transverse phase. When these pulses are overlapped at the same wavelength, their spatial superposition produces a beam with a structured polarisation distribution known as a ‘star’ Poincaré beam. The layout used to generate this beam is illustrated in Fig. 1 (a). The electron beam is first modulated by a seed laser and bunched using a magnetic chicane. In the radiator, five helical undulators induce nonlinear harmonic bunching through interaction of the electron beam with the on-axis fundamental radiation. At the second harmonic, the resulting emission is helically phased and radiated off-axis with left-handed circular polarisation. A short magnetic chicane introduces a delay before the beam enters a final undulator, which is tuned such that its fundamental matches the second harmonic of the earlier undulators, emitting righthanded circularly polarised radiation in a Gaussian mode at the same wavelength. This configuration ensures the two modes are overlapped with controlled relative phase. A filter downstream removes the longer-wavelength Gaussian emission from the first five undulators, isolating the superposed modes that form the structured beam. Detection of the beam’s polarisation structure, Fig. 1 (b), was carried out on the DiProI beamline. A linear polariser, realised via reflection near Brewster’s angle, was used to selectively reflect the component of the beam with linear polarisation in the plane of incidence. As shown in Fig. 1 (c), the intensity profile recorded upstream of the polariser appears centrally filled, indicating a superposition of the transverse modes without any visible spiral features in the total intensity. In contrast, downstream of the polariser, a distinct spiral pattern emerges in the reflected light. Scanning the phase between the orthogonally polarised modes with the phase shifter rotates the entire Poincaré beam polarisation pattern, resulting in a corresponding rotation of the spiral structure observed after the polariser. This was captured with a downstream camera and used to reconstruct the polarisation state across the transverse beam profile. From this data, the spatially resolved Stokes parameters were calculated, mapping the full polarisation distribution of the beam. The measured polarisation structure is shown in Fig. 1 (d), where local polarisation ellipses are overlaid on the beam’s intensity profile. The beam is right-circularly polarised at the centre and gradually evolves into elliptical and linear polarisation states toward the edges, forming the expected ‘star’ pattern. The orientation of the ellipses shows a subtle twist across the beam, reflecting the spatial separation between the emission points of the two FEL pulses. While the measured structure closely matches theoretical predictions, a small imbalance in the distribution is observed, with a slight bias toward linear horizontal polarisation and an increased density of right-circularly polarised states near the centre. These features are consistent with minor asymmetries in the relative mode amplitudes and alignment at the source. Fig. 1 (e) shows the measured Stokes parameters projected onto the Poincaré sphere, with each point corresponding to a different position in the beam. The broad coverage indicates that most polarisation states are represented in the FEL pulse. To quantify the distribution of polarisation states, the concurrence was calculated from the measured Stokes parameters. This value, also referred to as the vector quality factor, ranges from zero for a uniformly polarised beam to one for a fully structured vector beam, and was found to be 0.91. The high concurrence confirms that the generated FEL beam exhibits strong spatial variation in polarisation. As a metric, concurrence characterises the global polarisation topology and is invariant under propagation and nonpolarising optical elements, suggesting benefits such as increased robustness to turbulence. This method of producing structured polarisation beams directly from a FEL opens a pathway to generate other vector beam topologies, such as cylindrical vector beams, without the use of optical elements. It can be readily extended to shorter wavelengths and adapted to a range of FEL configurations, including those based on SASE. Such beams offer exciting prospects for applications in ultrafast magnetism, polarisation-sensitive scattering, and chiral spectroscopy, where spatially varying polarisation can provide new experimental capabilities. Elettra Highlights 2024–2025 150
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