Pump-laser-wavelength dependence of population inversion in N₂+

We investigate the pump wavelength dependence of population inversion in a nitrogen ion when nitrogen gas is irradiated by a femtosecond laser pulse in the wavelength range from ultraviolet to near-infrared. It is found that the population inversions corresponding to the transitions at 391 and 428 nm are very sensitive to the laser wavelength, with extreme values near 400 and 1000 nm. For the ultraviolet pump, the population inversions for 391 and 428 nm transitions occur at different wavelengths: a maximum inversion for the first corresponds to a minimum for the second. This is attributed to the near-resonance single-photon transition combined with the Raman process. A significantly stronger inversion is observed for the near-infrared laser, with the maximum depending on the laser intensity, ascribed to the ac Stark effect. The Floquet theory confirms this conclusion and reveals that the three-photon transition assisted by the strong laser field leads to this enhanced population inversion. This study provides the optimal conditions for air lasing based on ionic transitions of nitrogen molecules.