  We find that, for sufficiently strong mid-IR fields, transitions between
different conduction bands play an important role in the generation of
high-order harmonics in a dielectric. The transitions make a significant
contribution to the harmonic signal, and they can create a single effective
band for the motion of an electron wave packet. We show how high harmonic
spectra produced during the interaction of ultrashort laser pulses with
periodic solids provide a spectroscopic tool for understanding the effective
band structure that controls electron dynamics in these media.
