Optical gain in the $P$ branch of ${{\mathrm{N}}_2}^{+}$ lasing by polarization-modulated laser pulses

A near-infrared laser pulse generates lasing of $\mathrm{N}{{}_2}^{+}$ during filamentation, while the underlying mechanism of optical gain is still under debate. Here, we study the rotational lasing spectra by manipulating the polarization properties of the pump laser with the polarization gating (PG) method. The independent enhancement of lasing emission was observed in the $P$ branch when the pump laser was modulated by linear polarization gating (LPG). The increased gain is attributed to the promoted population inversion degree between rotational states located on the $B^2{\mathrm{\Sigma }}_u^{+}(v=0)$ and $X^2{\mathrm{\Sigma }}_g^{+}(v=0)$ states. Based on a stimulated emission mechanism, we simulated the lasing spectra and population distributions on the rotational states. The results suggest that the rotational inversion-induced lasing emission mainly contributes to the $P$ branch, which agrees well with the experimental observations.

Figure 1

(a) Schematic of the polarization gating (PG), where $\phi$ is the angle between the multiorder quarter-wave plate (MQP) optical axis (OA) and the horizontally linear polarization direction, $\theta$ is the angle between the OA of the MQP and the zero-order quarter-wave plate (ZQP). The insets are the sketch of the electric fields of a linearly polarized pulse ($\phi =0^{\circ }$, $\theta =0^{\circ }$) and a modulated pulse with $\phi ={45}^{\circ }$, $\theta =0^{\circ }$. (b),(c) The temporal evolved spectra obtained by using these two kinds of pump pulses, respectively. The intensities of the spectra are normalized.

Figure 2

The forward lasing spectra generated by a LPG-modulated pump pulse with (a) continuous $\phi$ and (b) dissociative $\phi$. The insets in (b) are the sketch of the electric fields of related pump pulses, respectively.

Figure 3

(a) The side fluorescence spectra measured when only the linearly polarized pump pulse exists. (b)–(e) and (f)–(i) are the population differences and stimulated spectra calculated by Eq. (4) and Eq. (3) with different ratios of $N_{X0}$ to $N_{B0}$, respectively. $N_{X0}$ and $N_{B0}$ are the total population of the $\mathrm{N}{{}_2}^{+}(B^2{\mathrm{\Sigma }}_u^{+},v=0)$ and $\mathrm{N}{{}_2}^{+}(X^2{\mathrm{\Sigma }}_g^{+},v=0)$ states, respectively.

Figure 4

(a)–(c) The forward-lasing spectra generated by EPG. The electric fields of the related pump pulses are sketched in them. (d)–(f) The front views of the falling edges of these electric fields. The gradual, curved arrows demonstrate the orientation of time. The orange dashed lines mark the polarization direction of the modulated pump pulse at zero time, and the black dashed lines mark the major axis of the pulse at infinite time. The polarization states are sketched near these lines.