All-optical reconstruction of valley polarization through helicity-resolved high-harmonic generation
We theoretically investigate valley-resolved high-order harmonic generation in gapped graphene driven by elliptically polarized laser fields. Using two-band density-matrix simulations and an electron-hole recombination trajectory model, we find that the two inequivalent valleys emit harmonics with opposite helicities. Under an elliptically polarized field, these emissions occur predominantly in different half cycles of the laser field. Time-dependent density functional theory calculations for monolayer MoS$_2$ show the same temporal separation of harmonic emissions with opposite helicities, supporting the generality of this valley-dependent chiral response. We further propose an all-optical scheme to reconstruct valley polarization from helicity-resolved harmonic signals. A circularly polarized pulse first prepares a valley population imbalance. A subsequent elliptically polarized laser induces different changes in the harmonic intensities of opposite helicities through Pauli blocking. The ratio of these intensity changes provides a direct measure of the valley polarization. Our results demonstrate that chiral high-harmonic emission can serve as an all-optical probe of ultrafast valley-dependent carrier dynamics.