Spatial Distribution of Nitrogen Fluorescence Emission Induced by Femtosecond Laser Filamentation in Air

As a major component in the air, nitrogen emits fluorescence when it interacts with intensive laser field. The fluorescence comes from the first negative band system (\begin{document}${{\rm{B}}^{{2}}}\Sigma _{\rm{u}}^{{ + }} \to {{\rm{X}}^{{2}}}\Sigma _{\rm{g}}^{{ + }}$\end{document} transition) of \begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document} and the second positive band system (\begin{document}${{\rm{C}}^{{3}}}\Pi _{\rm{u}}^{{ + }} \to {{\rm{B}}^{{3}}}\Pi _{\rm{g}}^{{ + }}$\end{document} transition) of \begin{document}${{\rm{N}}_{{2}}}$\end{document}. Under the action of high-intensity femtosecond laser, \begin{document}${{\rm{N}}_{{2}}}$\end{document} can be directly photo-ionized into \begin{document}${\rm{N}}_{{2}}^{{ + }}{{(}}{{\rm{B}}^{{2}}}\Sigma _{\rm{u}}^{{ + }})$\end{document}, which results in fluorescence emission of \begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document}. In the process of femtosecond laser filament formation, the dynamic processes such as ionization and excitation of nitrogen molecules are affected by the laser intensity distribution and laser polarization direction. The products show different distributions in the propagation direction and radial space, which, in turn, affects its light emission. Therefore, it is necessary to further ascertain its generation mechanism through the spatial distribution of nitrogen fluorescence. In this experiment, the spatial distribution of the nitrogen fluorescence emission generated by linearly polarized femtosecond laser pulse filaments in air is measured. By changing the polarization direction of the laser to study the distribution of nitrogen fluorescence in the radial plane, it is found that the fluorescence emission of \begin{document}${\rm{N}}_2^ + $\end{document} is more intense in the direction perpendicular to the laser polarization, while it is weaker in the direction parallel to the laser polarization. The nitrogen fluorescence emission has the same intensity in all directions. The ionization probability of a linear molecule depends on the angle between the laser polarization direction and the molecular axis, which is maximum (minimum) when the angle is \begin{document}${{{0}}^{\rm{o}}}$\end{document}(\begin{document}${{9}}{{{0}}^{\rm{o}}}$\end{document}). The \begin{document}${{\rm{N}}_{{2}}}$\end{document} gas is more likely to be ionized in the laser polarization direction, the nitrogen molecular ions \begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document} and electrons are separated in the direction parallel to the laser polarization. Therefore, more ions (\begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document}) are generated in the direction parallel to the laser polarization, and the fluorescence emission of \begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document} is more intense. Along the propagation direction of the laser, it is found that the fluorescence of \begin{document}${{\rm{N}}_{{2}}}$\end{document} appears before the fluorescence of \begin{document}${\rm{N}}_2^ + $\end{document} and disappears after the fluorescence of \begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document} has vanished. This is due to the fact that \begin{document}${{\rm{N}}_{{2}}}$\end{document} can be ionized into \begin{document}${\rm{N}}_{{2}}^{{ + }}{{(}}{{\rm{B}}^{{2}}}\Sigma_{\rm{u}}^{{ + }})$\end{document} at the position of high enough laser intensity, thus emitting fluorescence of \begin{document}${\rm{N}}_2^ + $\end{document}. However, the laser energy is not enough to ionize nitrogen at the beginning and end of laser transmission, but it can generate \begin{document}${\rm{N}}_2^ * $\end{document}, which emits nitrogen fluorescence through the process of intersystem crossing \begin{document}${\rm{N}}_2^*\xrightarrow{{{\rm{ISC}}}}{{\rm{N}}_2}({{\rm{C}}^3}\Pi _{\rm{u}}^ + )$\end{document}. The spatial distribution of nitrogen fluorescence emission during femtosecond laser filament formation shows that in the case of short focal length, the intersystem crossing scheme can explain the formation of \begin{document}${{\rm{N}}_{{2}}}{{(}}{{\rm{C}}^{{3}}}\Pi _{\rm{u}}^{{ + }})$\end{document}. This research is helpful in understanding the mechanism of nitrogen fluorescence emission.