We theoretically show that a single free electron in circular motion radiates an electromagnetic wave possessing helical phase structure, which is closely related to orbital angular momentum carried by it. We experimentally demonstrate it by interference and double-slit diffraction experiments on radiation from relativistic electrons in spiral motion. Our results indicate that photons carrying orbital angular momentum should be created naturally by cyclotron/synchrotron radiations or Compton scatterings in various situations in cosmic space. We propose promising laboratory vortex photon sources in various wavelengths ranging from radio wave to gamma-rays.

The recent development of novel extreme ultraviolet (XUV) coherent light sources bears great potential for a better understanding of the structure and dynamics of matter 1,2 . Promising routes are advanced coherent control and nonlinear spectroscopy schemes in the XUV energy range, yielding unprecedented spatial and temporal resolution 3,4 . However, their implementation has been hampered by the experimental challenge of generating XUV pulse sequences with precisely controlled timing and phase properties. In particular, direct control and manipulation of the phase of individual pulses within a XUV pulse sequence opens exciting new possibilities for coherent control and multidimensional spectroscopy 4 , but has

22 23 24 Photons have fixed spin and unbounded orbital angular momentum (OAM). While the 25 former is manifested in the polarization of light, the latter corresponds to the spatial 26 phase distribution of its wave front [1]. The distinctive way in which the photon spin dictates the electron motion upon light-matter interaction is the basis for numerous well-established spectroscopies that reveal the electronic, magnetic and structural 29 properties of matter. In contrast, imprinting OAM on a matter wave, specifically on a propagating electron, is generally considered very challenging and the anticipated effect undetectable [2]. Indeed, this amounts to transferring the phase of a classical electromagnetic wave, defined within several hundreds of nanometres, to a quantum particle localized within the few angstroms of an atom. In addition, the centre of symmetry of irradiated atoms does not in general coincide with the axis of the photon beam. In [3], the authors provided evidence of OAM-dependent absorption of light by a cold trapped atom, located in the centre of the light beam. Off-centre excitation was studied in [4]. Here we seek to observe an OAM-dependent dichroic photoelectric effect, using an extended sample of He atoms. Surprisingly, we find experimentally, and confirm theoretically, that the OAM of an optical field can be imprinted coherently onto a propagating electron wave, and that this phase information survives ensemble averaging out to macroscopic distances, where the electron is detected. We also show that electronic transitions, which are otherwise optically inaccessible due to selection rules, are essential for this process to occur. Our results reveal new aspects of light-matter interaction and point to a new kind of single-photon electron spectroscopy for accessing electronic optical transitions that are usually forbidden by symmetry. In our experiment, He atoms are ionized by XUV radiation, generated by a freeelectron laser (FEL) [5], in the presence of an intense infrared (IR) laser field, see Fig.

2160-3308=20=10(3)=031070(14) 031070-1 Published by the American Physical Society involving absorption and emission of an infrared photon is extracted. Our method can be used for extraction of a phase difference between single-photon and two-photon pathways and provides a new tool for attosecond science, which is complementary to RABBITT.

X-ray free electron lasers (FELs), which amplify light emitted by a relativistic electron beam, are extending nonlinear optical techniques to shorter wavelengths, adding element specificity by exciting and probing electronic transitions from core levels. These techniques would benefit tremendously from having a stable FEL source, generating spectrally pure and wavelength-tunable pulses. We show that such requirements can be met by operating the FEL in the so-called echo-enabled harmonic generation (EEHG) configuration. Here, two external conventional lasers are used to precisely tailor the longitudinal phase space of the electron beam before emission of X-rays. We demonstrate high-gain EEHG lasing producing stable, intense, nearly fully coherent pulses at wavelengths as short as 5.9 nm (~211 eV) at the FERMI FEL user facility. Low sensitivity to electron-beam imperfections and observation of stable, narrow-band, coherent emission down to 2.6 nm (~474 eV) make the technique a prime candidate for generating laser-like pulses in the X-ray spectral region, opening the door to multidimensional coherent spectroscopies at short wavelengths.

No abstract

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, extremeultraviolet 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 W=cm 2 , paving the way to nonlinear optical experiments with vortex beams at short wavelengths.

We discuss a two-color self-amplified spontaneous emission free-electron laser (FEL) amplifier where the emission is obtained from two orthogonally polarized undulators with different periods and field intensities. Nonaveraged and averaged equations are compared. The two radiations have not only different frequencies, but also different polarizations, while the total length of the device does not change with respect to usual single-color FELs. The wavelengths of two different colors can be changed by choosing different periods, while variation in the magnetic strengths can be used to modify the gain lengths.