Role of localized electronic states in high-order harmonic generation from doped semiconductors

We investigate high-order harmonic generation (HHG) in sparsely doped semiconductors. The doping in semiconductors breaks the periodic translation invariance in space and introduces localized electronic states (LESs), which leads to two additional electron transition channels, namely, the nonvertical transitions and transitions from LESs. By involving these channels, one can intuitively understand the enhancement of the harmonic yield and the extension of the cutoff energy found in previous works. Moreover, the transition from LESs is space localized and shows self-probed behavior under strong laser fields, encoding the structure information into the HHG. To demonstrate this, we analyze the HHG process in a doped semiconductor with a pair of impurities, where the recombination process of the electron from LESs can be interpreted as a two-center interference. This imprints the internuclear separation between the impurities into the minima of the harmonic spectra. Our work reveals the underlying physical mechanisms in HHG from doped semiconductors and suggests all-optical metrology for structural and dynamic information of LESs.