  High-harmonic generation by a highly non-linear interaction of infrared laser
fields with matter allows for the generation of attosecond pulses in the XUV
spectral regime. This process, well established for atoms, has been recently
extended to the condensed phase. Remarkably well pronounced harmonics up to
order ~30 have been observed for dielectrics. We present the first ab-initio
multi-scale simulation of solid-state high-harmonic generation. We find that
mesoscopic effects of the extended system, in particular the realistic sampling
of the entire Brillouin zone, the pulse propagation in the dense medium, and
the inhomogeneous illumination of the crystal have a strong effect on the
formation of clean harmonic spectra. Our results provide a novel explanation
for the formation of clean harmonics and have implications for a wide range of
non-linear optical processes in dense media.
