Coherent soft x-ray pulses from an echo-enabled free-electron laser

The free-electron laser (FEL) FERMI is a unique facility, providing users with laser-like pulses in the XUV spectral range. At FERMI, the generation of highly coherent pulses, with tunable spectro-temporal properties, relies on the so-called high-gain harmonic generation (HGHG) technique. In the latter, a (single) infrared seed laser is used to shape the electron-beam properties and trigger the amplification process. Amplification occurs at one selected harmonic, h, of the seed. However, in HGHG, the seed energy required to prepare the electron beam for FEL emission becomes larger and larger for higher harmonics (i.e., shorter FEL wavelengths). For high harmonics, the resulting strong electron-beam energy modulation reduces the FEL gain, limiting the scheme to h<15 (wavelengths of about 10-20 nm) for a single HGHG scheme, or to h of the order of 60-70 (i.e., 4-5 nm), in case of two-stage HGHG. Moreover, at such high h, the sensitivity to the shape of the electron-beam phase space becomes critical and may severely affect the FEL radiation in terms of longitudinal coherence, pulse energy, and shot-to-shot stability. In addition, the HGHG scheme cannot cover the whole harmonic range, as the final harmonic number is a product between the harmonic numbers of the individual stages. Last, but not least, the two-stage setup uses a relatively large portion of the e-beam to accommodate the double seeding process, which makes the implementation double-pulse operation difficult.
The drawbacks of the two-stage HGHG can be overcome by using a recently proposed technique called echo-enabled harmonic generation (EEHG), where the electron-beam is shaped using two seed lasers to enable FEL emission at high harmonics. The method requires a much weaker energy modulation compared to HGHG and is also intrinsically less sensitive to the initial electron-beam imperfections, making it a strong candidate for producing highly stable, nearly fully coherent, and intense FEL pulses, down to soft x-ray wavelengths.
The EEHG principle is illustrated in Fig. 1. In the experiment we performed, we demonstrated the first high-gain lasing of an EEHG FEL in the soft-x-ray region at 7.3 nm (about 169 eV) and 5.9 nm (about 211 eV), i.e., the 36thand 45thharmonics of the seed wavelength. At > 45, the limitation of the present FERMI setup did not allow us reaching saturation by the radiator’s end. Still, we could observe coherent harmonic emission with relatively clean spectra up to h = 101, as shown in Fig. 2. The left panel shows the spectrum at λ = 3.1 nm (about 394 eV), i.e., = 84. Within the resolution, the spectrum is a narrow single-line with relatively weak pedestal structures, even at this high harmonic number. The right panel shows EEHG optimized for emission at λ = 2.6 nm (about 474 eV), i.e., = 101. The observation of coherent emission at harmonics in the range from 84 to 101 indicates the possibility to extend the lasing to wavelengths as short as 2 nm (620 eV) or less, either by using EEHG directly (in a setup optimised for this purpose), or with a cascade employing both EEHG and HGHG schemes. Such a layout has the potential to set the stage for entirely new experiments using x-ray nonlinear optical techniques.

Figure 1.    The EEHG scheme together with the e-beam phase space at different stages of the evolution. The 1st seed laser with a wavelength λ1 imprints a sinusoidal energy modulation with an amplitude ΔE<3σE,  σE is the initial uncorrelated energy spread, onto the relativistic e-beam in the 1st modulator. After passing through a strong 1st chicane, the electrons with different energies move relative to each other, resulting in a striated phase space with multiple energy bands. Importantly, the energy spread within a single band is much smaller than σE. The electrons then pass through the 2nd modulator, where their energy is again periodically modulated using a 2nd seed laser with λ2= λ1 and ΔE2ΔE1. After traversing a weaker 2nd chicane, the e-beam phase space is rotated, transforming the sinusoidal energy modulation into a periodic density modulation, with high-frequency components. As the energy spread within a single band is much smaller than σE, only a moderate ΔE2 is required to reach very high harmonics. The e-beam is then injected into the radiator, tuned to emit light at a high harmonic of the 2nd seed laser.



Figure 2.  EEHG at high harmonics. Coherent emission spectra at λ= 3.1 nm (394 eV) (left) and λ= 2.6 nm (474 eV) (right). Insets show the raw CCD images.



This research was conducted by the following research team:


Primož Rebernik Ribič1,2, Alessandro Abrami1, Laura Badano1, Maurizio Bossi1, Hans-Heinrich Braun3, Niky Bruchon4, Flavio Capotondi1, Davide Castronovo1, Marco Cautero1, Paolo Cinquegrana1, Marcello Coreno5, Marie Emmanuelle Couprie6, Ivan Cudin1, Miltcho Boyanov Danailov1, Giovanni De Ninno1,2, Alexander Demidovich1, Simone Di Mitri1, Bruno Diviacco1, William M. Fawley1, Chao Feng7, Mario Ferianis1, Eugenio Ferrari3, Laura Foglia1, Fabio Frassetto8, Giulio Gaio1, David Garzella1,9, Amin Ghaith6, Fabio Giacuzzo1, Luca Giannessi1,10, Vanessa Grattoni11, Sandi Grulja1, Erik Hemsing12, Fatma Iazzourene1, Gabor Kurdi1, Marco Lonza1, Nicola Mahne1,13, Marco Malvestuto1, Michele Manfredda1, Claudio Masciovecchio1, Paolo Miotti8, Najmeh S. Mirian1, Ivaylo Petrov Nikolov1, Giuseppe Maria Penco1, Gregory Penn14, Luca Poletto8, Mihai Pop15, Eduard Prat3, Emiliano Principi1, Lorenzo Raimondi1, Sven Reiche3, Eléonore Roussel16, Roberto Sauro1, Claudio Scafuri1, Paolo Sigalotti1, Simone Spampinati1, Carlo Spezzani1, Luca Sturari1, Michele Svandrlik1, Takanori Tanikawa17, Mauro Trovó1, Marco Veronese1, Davide Vivoda1, Dao Xiang18, Maurizio Zaccaria1, Dino Zangrando1, Marco Zangrando1,13and Enrico Massimiliano Allaria1


Elettra-Sincrotrone Trieste, Area Science Park, Trieste, Italy. 
University of Nova Gorica, Nova Gorica, Slovenia. 
Paul Scherrer Institut, Villigen PSI, Switzerland. 
Department of Engineering and Architecture, Università degli Studi di Trieste, Trieste, Italy. 
ISM-CNR, Istituto di Struttura della Materia,  LD2 Unit, Trieste, Italy. 
Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, Gif-sur-Yvette, France. 
Shanghai Advanced Research Institute,  Chinese Academy of Sciences, Shanghai, China.
Institute for Photonics and Nanotechnologies CNR-IFN, Padova, Italy. 
CEA/DRF/LIDYL, Université Paris-Saclay, Saclay, France. 
10 ENEA C.R. Frascati, Frascati, Italy. 
11 Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany. 
12 SLAC National Accelerator Laboratory, Menlo Park, CA, USA. 
13 Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, Basovizza, Italy. 
14 Lawrence Berkeley National Laboratory, Berkeley, CA, USA. 
15 MAX-IV, Lund University, Lund, Sweden. 
16 Université Lille, CNRS, UMR 8523 - PhLAM, Lille, France. 
17 European XFEL, Schenefeld, Germany. 
18 Key Laboratory for Laser Plasmas, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China


Contact persons:

P. R. Ribič, e-mail:
E. Allaria, e-mail:


P.R. Ribič et al., “Coherent soft x-ray pulses from an echo-enabled harmonic generation free-electron laser”, to be published in Nature Photonics, DOI: 10.1038/s41566-019-0427-1,

Last Updated on Thursday, 16 January 2020 16:23