Polarization-modulated population distribution of nitrogen molecular ions in a strong laser field

We investigate the dependence of $N_2{}^{+}$ lasing radiation on the polarization ellipticity of the pump laser with the 900- and 980-nm wavelengths. Our results show that the 391-nm lasing radiation is stronger with the elliptically polarized laser in the 900-nm pumping case, while the lasing signal decays monotonically with the increasing ellipticity in the 980-nm pumping case. In contrast, the strongest 428-nm lasing appears with the linear polarization laser for both pumping cases. The theoretical simulations reproduce key observations and reveal that the physical origin underlying the ellipticity-dependent behaviors is the sensitivity of photoexcitation of different channels on the wavelength and polarization of the pump laser. At the 900-nm pump wavelength, one-photon excitation from $X{{}^2\Sigma }_g^{+}$ to $A{}^2{\Pi }_u$ of $N_2{}^{+}$ plays a dominant role in the population inversion. The elliptically polarized laser is beneficial to the perpendicular transition between the two states. In the 980-nm pumping case, the three-photon excitation from $X{{}^2\Sigma }_g^{+}$ to $B{{}^2\Sigma }_u^{+}$, which prefers linear polarization pumping, dominates the population inversion. The 428-nm lasing gain mainly depends on the population on the $B{{}^2\Sigma }_u^{+}$ state, thus the strongest radiation always occurs in the case of linear polarization. The polarization-dependent behaviors of $N_2{}^{+}$ lasing reflect the complex population inversion mechanism in the strong-field-prepared ionic system.