Research ArticlePHYSICS

Optics-less focusing of XUV high-order harmonics

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Science Advances  05 Apr 2019:
Vol. 5, no. 4, eaau7175
DOI: 10.1126/sciadv.aau7175
  • Fig. 1 Far-field XUV beam size.

    Measurement of the XUV beam size (FWHM) in the far field (i.e., 2.9 m after the IR focus) as a function of the longitudinal gas jet position with respect to the IR focus position. Harmonics are generated in a neon jet with a maximum intensity at focus of 5.6 × 1014 W/cm2, and IR laser beam Rayleigh length of 2.7 cm.

  • Fig. 2 Position and size of the XUV waists.

    (A) Calculated positions of the XUV beam waists, z0_XUV, relative to the IR focus and (B) size of the harmonic beam waist, W0_XUV. The IR focus is at z = 0, and negative positions imply a jet located before the IR focus. The shaded area represents the zone where the jet is within the IR beam Rayleigh range.

  • Fig. 3 Calculated diameters (FWHM) of the Gaussian XUV beams at a distance of 2.9 m after the IR focus position.

    The shaded area represents the zone where the jet is within the IR beam Rayleigh range.

  • Fig. 4 Spatial chirp of harmonic 29.

    Far-field spatially resolved normalized spectra of the harmonic 29 generated in neon for three positions of the generating medium (A) zjet = −70 mm, (B) zjet = −35 mm, and (C) zjet = +25 mm. HHG was performed with a fundamental beam that was spatially chirped in the generating medium. The tilt of the spatially resolved harmonic spectra is the signature of a spatial chirp in the XUV beam in the far field.

  • Fig. 5 Far-field XUV spatial chirp.

    Far-field spatially resolved high-order harmonic spectra obtained with a spatially chirped IR beam. The neon jet is located at various longitudinal positions (A) 25 mm after IR focus, (B) at IR focus, and (C) 50 mm before IR focus. The harmonic orders vary between 29 and 45 for the first order of diffraction of the XUV grating, and we observe the second orders of diffraction for harmonics 59 and higher. The tilt of the harmonic beams is the signature of a spatial chirp in the XUV beams in the far field. For the position zjet = −50 mm, where the XUV beam is small, the spatial scale has been expanded.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/4/eaau7175/DC1

    Section S1. Experimental setup

    Section S2. Characterization of the IR spatial chirp near focus

    Section S3. Evolution of the HHG efficiency with the jet longitudinal position

    Section S4. Evolution of the beam size for higher-order harmonics

    Section S5. Impact of qeff and α on the numerical results

    Section S6. Impact of the longitudinal evolution of α

    Section S7. Normalized focus shift

    Section S8. Simulations with non-Gaussian XUV beams

    Fig. S1. Spatial profile of the fundamental beam.

    Fig. S2. Experimental setup.

    Fig. S3. Characterization of the spatial chirp near the focus of the IR beam.

    Fig. S4. Integrated XUV emission.

    Fig. S5. Diameter of the XUV beam in the far field.

    Fig. S6. Parametric evolution of the XUV beam size.

    Fig. S7. Influence of the α parameter.

    Fig. S8. Beam size evolution for several peak intensities.

    Fig. S9. Normalized focus shift.

    Fig. S10. Non-Gaussian XUV beam size evolution.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Experimental setup
    • Section S2. Characterization of the IR spatial chirp near focus
    • Section S3. Evolution of the HHG efficiency with the jet longitudinal position
    • Section S4. Evolution of the beam size for higher-order harmonics
    • Section S5. Impact of qeff and α on the numerical results
    • Section S6. Impact of the longitudinal evolution of α
    • Section S7. Normalized focus shift
    • Section S8. Simulations with non-Gaussian XUV beams
    • Fig. S1. Spatial profile of the fundamental beam.
    • Fig. S2. Experimental setup.
    • Fig. S3. Characterization of the spatial chirp near the focus of the IR beam.
    • Fig. S4. Integrated XUV emission.
    • Fig. S5. Diameter of the XUV beam in the far field.
    • Fig. S6. Parametric evolution of the XUV beam size.
    • Fig. S7. Influence of the α parameter.
    • Fig. S8. Beam size evolution for several peak intensities.
    • Fig. S9. Normalized focus shift.
    • Fig. S10. Non-Gaussian XUV beam size evolution.

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