Enhancement of High Harmonics Generation by Floquet Engineering*

High hramonic generation (HHG) in gaseous systems and solids is well studied. Since periodically driven systems can produce harmonic response, it is important to study the influence of external driving on the HHG power spectrum. We formulate a theory of high-harmonic current using Floquet theory of periodically driven systems. As an application of our theory, we study HHG in the Su-Schrieffer-Heeger (SSH) model with and without periodic drive. We find that there is a significant enhancement in higher harmonincs when the system is driven. Moreover, this enhancement peaks for an optimal harmonic at a value that increases when the intensity of the laser is reduced. This means HHG can be generated even at lower pulse intensities in a Floquet system. We obtain analytical expressions for HHG power spectrum in the high-frequency approximation for driven SSH model. Further, we study the effects of laser polarization and occupation of Floquet bands on HHG in two dimensional systems. We also investigate the consequences of spatiotemporal symmetries and Floquet topology for HHG in Floquet systems.