  We crossed two femtosecond extreme ultraviolet (EUV) pulses in a beta - Ga2O3
(001) single crystal to create transient gratings (TG) of light intensity with
sub-100 nm spatial periodicity. The EUV TG excitation launches phonon modes,
whose dynamics were revealed via the backward diffraction of a third,
time-delayed, EUV probe pulse. In addition to the modes typically observed in
this kind of experiment, the phase-matching condition imposed by the TG,
combined with the sharp penetration depth of the EUV excitation pulses,
permitted to generate and detect phonons with a wavevector tangibly larger
(approximately 1 nm-1) than the EUV TG one, via stimulated Brillouin
back-scattering (SBBS) of the EUV probe. While SBBS of an optical probe was
reported in previous EUV TG experiments, the extension of SBBS to short
wavelength radiation can be used as a contact-less experimental tool for
filling the gap between the wavevector range accessible through inelastic hard
X-ray and thermal neutron scattering techniques, and the one accessible through
Brillouin scattering of visible and UV light.
