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.
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