Supplementary Information to “Coherent Kiloelectronvolt X-ray Emission from
Laser-Driven Atoms” by J. Seres et. al.
The ultrashort laser pulses used for the X-ray generation in our experiments were
produced with an all-solid-state laser system based on a titanium:sapphire oscillator and
three titanium:sapphire multipass amplifier stages. The laser system delivers pulses with
an energy of 3 mJ and a duration of 12 fs at a repetition rate of 1 kHz. The pulses are
subsequently spectrally broadened in a hollow fiber of 1-m length and 0.3-mm core
diameter filled with neon gas at a pressure of ~1.5 bar. Temporal compression in a
dispersive delay line consisting of ultrabroad-band chirped multilayer mirrors finally
yields 5-fs, 1-mJ pulses carried at a wavelength of 720 nm as revealed by the
autocorrelation and spectrum shown in the insets in Fig. S1.
Fig. S1
In our experiments the 5-fs laser pulses were focused into a 0.4-mm helium gas jet
(pressure: 0.5 bar). Its 1/e2-diameter is 2w0 = 60 mm at the beam waist, yielding a peak
intensity of ~ 1.4x1016 W/cm2 on the optical axis. A series of thin metal filters prevents
the laser beam and low-order (vacuum ultraviolet and extreme ultraviolet) harmonics at
photon energies below 200 eV from reaching the detector.
The spatial coherence of the X-ray beam was assessed by measuring the beam divergence
with a knife-edge scanned across the X-ray beam 60 cm downstream from the helium gas
jet. Fig. 2 depicts the EUV/SXR power passing by a knife-edge scanned across the beam
versus distance of edge from the beam axis (red line). The measurement reveals two
distinctly different beams with a large and small diameter, which are attributed to photons
in the 18-24 eV band and the >200 eV region transmitted by the helium background
atmosphere and the 100-nm aluminum filter used in this measurement. Fig. S2 shows
also the intensity distribution of the SXR beam (Eph > 200 eV) and the EUV beam (10 eV
< Eph < 24 eV) evaluated by assuming a Gaussian radial profile in both spectral ranges.
From the data we evaluate a beam divergence of u ~ 0.2 mrad and u ~ 3.6 mrad for the
high-energy and low-energy beam, respectively.
Fig. S2
The divergence u of a Gaussian beam is related to the wavelength l and the beam radius
at the beam waist w0 by the simple expression
  M2

w 0
(1)
where M2 ≥ 1 quantifies the deviation from a diffraction-limited beam. The radius w0,x of
the X-ray beam is substantially smaller than that of the pumping laser beam w0,L = 30
mm, decreasing with increasing photon energy. From these considerations and the knifeedge measurement we obtain a safe upper limit M2 < 5 at a photon energy of 1 keV.
The spectrum of the generated EUV/SXR radiation was analyzed with an energydispersive (EDX) as well as a wavelength-dispersive (WDX) spectrograph. The EDX
spectrograph consisted of a liquid-nitrogen-cooled Si(Li) detector and a multichannel
pulse height analyzer with 50eV resolution (limited by thermal noise). WDX
spectrometry was performed with a grazing-incidence grating spectrograph (248/310G,
McPherson) equipped with a 1200-line/mm platinum-coated grating. Fig. S3 shows a
spectrum transmitted through a 100-nm copper foil and recorded with the grating
spectrograph.
Fig. S3