SUPPLEMENTARY INFORMATION
Laser-driven XUV sources are currently reaching a bottleneck in the race for ultrahigh intensity. Reaching such intensities requires fully coherent, highly energetic beams (0.1
to 1 mJ), with short duration (20-100 fs) and good wave front to ensure near diffractionlimited focusing. To our knowledge, none of the currently achieved laser-driven sources has
the potential to produce ultra-high intensity. High Harmonic Generation (HHG) has
demonstrated a regular wave front1, full coherence2, and ultra-short pulse duration from 20 fs
down to 0.1 fs3. However, the highest energy achieved to-date is 0.3 µJ at 30 nm4 i.e. three
orders of magnitude lower than required. It is even lower while considering shorter
wavelengths down to 10 nm due to the intrinsic drop of conversion efficiency with photon
energy5. On the other hand, laser-driven X-ray lasers (XRL) exhibit a large output up to 7
mJ6, but with poor optical qualities and long pulse duration (the shortest being about 2.5 ps 7).
No proper coherence has been measured and the wave front is not regular 8. Low XRL quality
is intrinsic of the way they are run (amplification of spontaneous emission –ASE). The selfemission (i.e. noise) is amplified in single pass along the laser medium without any filtering,
generating an intense but noisy beam. Improvement of the X-ray laser beam quality, while
keeping the high output energy, has been theoretically9 and experimentally10 studied by
several laboratories with no clear success.
The major improvement of the x-ray laser architecture used for this work consists in
extrapolating to the XUV the most advance architectures for visible lasers. For a laser chain,
each stage has a specific function: the oscillator delivers a pulse having perfect spectral,
temporal and spatial properties while amplifiers are set only for increasing the beam energy.
High harmonic generation delivers high quality pulses as required for the seed, while X-ray
laser amplifying medium are well suited to be an amplifier stage. To our knowledge, only one
experiment of HHG amplification 11 has been performed prior to our work with mitigated
results. This previous experiment was conceptually very far from the work reported in this
article. Indeed, the choice of the amplifying medium is very stringent and should be done
according to the following criteria. (i) Although it is preferable to achieve a high amplification
factor (output energy/ input energy), this is not the key criterion. Indeed, a succession of
amplifiers might be set such as to reach the targeted energy. The most important criterion is
that amplification does not deteriorate the seed properties otherwise post-amplification beam
filtering will be required leading to a low net amplification. (ii) As for visible lasers, it is
crucial to keep the amplifier self-emission (ASE), which is an unusable beam, as weak as
possible compared to the seeded laser output. On the previous experiment, the ASE was much
stronger than the seeded x-ray laser. (iii) One also has to consider the spectral gain narrowing
that induces a pulse broadening and the loss of beam homogeneity. (iv) X-ray laser amplifiers
being a plasma the beam might be depolarised due to local magnetic fields12. Also, beam
decoherence may arise from elastic collisions between ions and free electrons.
Clearly, the choice of the amplifier is the heart of the design of a seeded x-ray laser.
The main limitations for amplifying in a plasma come from the strong refraction sampled by
the seeding beam while propagating along the amplifying medium. For plasmas created by the
interaction of an intense laser with a solid density target, refraction might be so high that the
x-ray laser is pushed out of the gain region after few millimetres of propagation artificially
reducing the net amplification13. On the Ditmire’s experiment11 the small-signal gain
coefficient was too low (3cm-1) to compensate for the losses induced by the refraction leading
to a much weaker amplification (a factor of 3) than expected (220). This shows that the
amplifier must exhibit refraction as low as possible. Gas targets have the advantage to be at
low density (about 1/1000th of solid density) preventing from any significant refraction.
Optical Field Ionisation (OFI) x-ray laser has been chosen because it is the only one able to
fulfil all the experimental requirements: Considering developements of applications the
repetition rate has to be as high as possible. OFI XRL has the highest repetition rate over all
x-ray lasers (10 Hz compared to about 10-3 Hz for other laser-driven XRLs). OFI XRL being
pumped by the same laser than the seed ensures the a jitter-free synchronisation of the seed
and the pumping of the XRL amplifier. OFI x-ray laser is generated in a gas as required from
the above refraction considerations. Furthermore, small-signal gain as high as 78 cm-1 has
been demonstrated up to the saturation level14 ensuring strong amplification. Using an
amplifier with a large small-signal gain coefficient prevents from using long targets to achieve
a strong amplification. This intrinsically reduce the ASE level. Also this is favorable for
reducing the refraction. The beam is shifted out of gain region by the refraction 15 with a
displacement varying as L2, L being the plasma length. Consequently, the target has to be
kept as small as possible. On the previous work, the target was 2 cm long, while it is only
0.4 cm long for this study.
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