  We analyze the crystal orientation-dependent polarization state of extreme
ultraviolet (XUV) high-order harmonics from bulk magnesium oxide crystals
subjected to intense linearly polarized laser fields. We find that only along
high-symmetry directions in crystals high-order harmonics follow the
polarization direction of the laser field. In general, the polarization
direction of high-order harmonics deviates from that of the laser field, and
the deviation amplitude depends on the crystal orientation, harmonic order and
the strength of the laser field. We use a real-space electron trajectory model
to understand the crystal orientation-dependent polarization state of XUV
harmonics. The polarization analysis allows us to track the motion of
strong-field-driven electron in conduction bands in two dimensions. These
results have implications in all-optical probing of atomic-scale structure in
real-space, electronic band-structure in momentum space, and in the possibility
of generating attosecond pulses with time-dependent polarization in a compact
setup.
