Extreme-Ultraviolet Vortices from a Free-Electron Laser

Extreme-ultraviolet vortices may be exploited to steer the magnetic properties of nanoparticles, increase the resolution in microscopy, and gain insight into local symmetry and chirality of a material; they might even be used to increase the bandwidth in long-distance space communications. However, in contrast to the generation of vortex beams in the infrared and visible spectral regions, production of intense, extreme-ultraviolet and x-ray optical vortices still remains a challenge. Here, we present an in-situ and an ex-situ technique for generating intense, femtosecond, coherent optical vortices at a free-electron laser in the extreme ultraviolet. The first method takes advantage of nonlinear harmonic generation in a helical undulator, producing vortex beams at the second harmonic without the need for additional optical elements, while the latter one relies on the use of a spiral zone plate to generate a focused, micron-size optical vortex with a peak intensity approaching ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, paving the way to nonlinear optical experiments with vortex beams at short wavelengths.

Popular Summary

Light typically travels as a wave whose wave fronts are flat, similar to ocean waves gently coming ashore. But it is possible to make light whose wave fronts twist as they move forward. Such light beams are said to carry “orbital angular momentum.” A beam of light carrying these helically shaped wave fronts—known as optical vortices—has a donutlike intensity. In the visible spectrum, optical vortices have been used to trap and rotate small objects, increase the resolution in optical microscopes, and enhance data transmission in optical communications. At short wavelengths (ultraviolet and x rays), optical vortices are predicted to trigger new phenomena, such as loops of electric current in spherical molecules or violations of the standard rules that determine how an atom is ionized by light. Here, we demonstrate two methods for generating intense optical vortices at wavelengths approaching the x-ray spectral region using a free-electron laser (FEL).

In a FEL, powerful laserlike pulses are generated by relativistic electrons wiggling inside an undulator—a periodic magnet structure. In the first setup, we exploit the fact that harmonics emitted by electrons on a spiral trajectory through a helical undulator carry orbital angular momentum to produce intense optical vortices at the second harmonic of the FEL resonant frequency. The second method is based on the use of a spiral zone plate, which simultaneously focuses the FEL beam and imprints a helical structure onto its phase profile, generating a high-intensity focused optical vortex.

We expect that these methods will allow researchers to perform recently proposed experiments involving vortex beams in different areas of fundamental and applied physics such as characterization of materials and even long-distance space communication.

Figure 1

Generation of coherent optical vortices through nonlinear harmonic generation at a FEL (not to scale). A transversely Gaussian seed density modulates the e-beam using a combination of an undulator (modulator) and a dispersive section (D.S.) so that it emits coherent XUV light in the radiator. The interaction between FEL radiation at the fundamental wavelength and the e-beam induces bunching at the second harmonic, which is amplified along the radiator chain, leading to emission of intense, coherent optical vortices in the XUV spectral range. A Zr filter is placed at the FEL output to suppress the fundamental Gaussian mode, transmitting only the optical vortex.

Figure 2

A typical single-shot interference pattern of the FEL emission from a chain of six undulators. Top panel: Experiment. Bottom panel: Calculation (obtained assuming emission only at the fundamental wavelength).

Figure 3

Left panel: A typical single-shot image of an optical vortex generated at 15.6 nm. The multiple-ring pattern comes from the interference of the emission from six undulators. Middle panel: Calculation. Right panel: A single-spiral pattern obtained by interference of the optical vortex with a Gaussian mode (in a single-shot measurement), confirming the $l=1$ charge of the vortex beam.

Figure 4

Left panel: A typical single-shot image of the donut-shaped intensity pattern obtained by increasing the e-beam size. Middle panel: Calculation. Right panel: A single-spiral pattern obtained by interference of the optical vortex with a Gaussian mode (in a single-shot measurement), confirming the $l=1$ charge of the vortex beam.

Figure 5

SEM images of ZPs with charges of $l=0$ (left panel), $l=1$ (middle panel), and $l=2$ (right panel).

Figure 6

Generation of intense, coherent XUV vortices at the fundamental FEL wavelength with a SZP. The fundamental, transversely Gaussian FEL beam was sent onto the SZP, producing a micron-size optical vortex in the focal plane, which was detected using the PMMA imprint method; see text for details. The spiral phase of the vortex was measured in the far field (80 cm from the focal plane) with a WFS.

Figure 7

Measured far-field intensity (left column) and phase (middle column), and the intensity distribution in the focal plane (right column) for ZPs with charges from 0 (top row) to 3 (bottom row). Because of the relatively long distance from the focus (800 mm), the phase gradients were below the detection threshold of the WFS far from the beam axis. We therefore had to limit the reconstruction of the phase to a circle with a radius of around 3 mm from the singularity point, as shown for $l=1$, 2, and 3. All measurements were done in single-shot mode.