We carry out a combined theoretical and experimental investigation on the population distributions in the ground and excited states of tunnel-ionized nitrogen molecules at various driver wavelengths in the near- and midinfrared range. Our results reveal that efficient couplings (i.e., population exchanges) between the ground N_{2}^{+}(X^{2}Σ_{g}^{+}) state and the excited N_{2}^{+}(A^{2}Π_{u}) and N_{2}^{+}(B^{2}Σ_{u}^{+}) states occur in strong laser fields. The couplings result in a population inversion between the N_{2}^{+}(X^{2}Σ_{g}^{+}) and N_{2}^{+}(B^{2}Σ_{u}^{+}) states at wavelengths near 800 nm, which is verified by our experimental observation of the amplification of a seed at ∼391  nm. The result provides insight into the mechanism of free-space nitrogen ion lasers generated in remote air with strong femtosecond laser pulses.

Since the first observation of odd and even high-order harmonics generated from ZnO crystals in 2011, the dependence of the harmonic yields on the orientation of the laser polarization with respect to the crystal axis has never been properly interpreted. This failure has been traced to the lack of a correct account of the phase of the transition dipole moment between the valence band and the conduction band. Using a simple one-dimensional two-band model, here we demonstrate that the observed odd harmonics is directly related to the orientation dependence of the magnitude of the transition dipole, while even harmonics is directly related to the phase of the transition dipole. Our result points out the essential role of the complex transition dipole moment in understanding harmonic generation from solids that has long been overlooked so far.

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