  We experimentally study the field-intensity dependence of high-harmonic
generation in bulk gallium arsenide in reflection geometry. We find the
oscillatory behavior at high fields where a perturbative scaling law no longer
holds. By constructing a theoretical framework based on the Luttinger-Kohn
model, we succeed in reproducing the observed oscillatory behavior. The
qualitative agreement between the experiment and theory indicates that
field-induced dynamic band modification is crucial in the nonperturbative
regime. We consider the origin of the oscillatory behavior in terms of
dynamical localization based on the Floquet subband picture.
