  We theoretically report that high-order sideband generation (HSG) from
Floquet matters driven by a strong terahertz light while engineered by weak
infrared light can achieve multiple plateau HSG. The Floquet-engineering
systems exhibit distinctive spectroscopic characteristics that go beyond the
HSG processes in field-free band-structure systems. The spatial-temporal
dynamics analyses under Floquet-Bloch and time-reversal-symmetry theories
clarify the spectral and its odd-even characteristics in the HSG spectrum. Our
work demonstrates the HSG of Floquet matters via Floquet engineering and
indicates a promising way to extract Floquet material parameters in future
experiments.
