Spatial distribution of nitrogen fluorescence emission induced by femtosecond laser filamentation in air

Abstract

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 (<inline-formula><tex-math id="M7">\begin{document}${{\rm{B}}^{{2}}}\Sigma _{\rm{u}}^{{ + }} \to {{\rm{X}}^{{2}}}\Sigma _{\rm{g}}^{{ + }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M7.png"/></alternatives></inline-formula> transition) of <inline-formula><tex-math id="M8">\begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M8.png"/></alternatives></inline-formula> and the second positive band system (<inline-formula><tex-math id="M9">\begin{document}${{\rm{C}}^{{3}}}\Pi _{\rm{u}}^{{ + }} \to {{\rm{B}}^{{3}}}\Pi _{\rm{g}}^{{ + }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M9.png"/></alternatives></inline-formula> transition) of <inline-formula><tex-math id="M10">\begin{document}${{\rm{N}}_{{2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M10.png"/></alternatives></inline-formula>. Under the action of high-intensity femtosecond laser, <inline-formula><tex-math id="M11">\begin{document}${{\rm{N}}_{{2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M11.png"/></alternatives></inline-formula> can be directly photo-ionized into <inline-formula><tex-math id="M12">\begin{document}${\rm{N}}_{{2}}^{{ + }}{{(}}{{\rm{B}}^{{2}}}\Sigma _{\rm{u}}^{{ + }})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M12.png"/></alternatives></inline-formula>, which results in fluorescence emission of <inline-formula><tex-math id="M13">\begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M13.png"/></alternatives></inline-formula>. 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 <inline-formula><tex-math id="M14">\begin{document}${\rm{N}}_2^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M14.png"/></alternatives></inline-formula> is more intense in the direction perpendicular to the laser polarization, while it is weaker in the direction parallel to the laser polarization. The nitrogen fluorescence emission has the same intensity in all directions. The ionization probability of a linear molecule depends on the angle between the laser polarization direction and the molecular axis, which is maximum (minimum) when the angle is <inline-formula><tex-math id="M15">\begin{document}${{{0}}^{\rm{o}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M15.png"/></alternatives></inline-formula>(<inline-formula><tex-math id="M16">\begin{document}${{9}}{{{0}}^{\rm{o}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M16.png"/></alternatives></inline-formula>). The <inline-formula><tex-math id="M17">\begin{document}${{\rm{N}}_{{2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M17.png"/></alternatives></inline-formula> gas is more likely to be ionized in the laser polarization direction, the nitrogen molecular ions <inline-formula><tex-math id="M18">\begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M18.png"/></alternatives></inline-formula> and electrons are separated in the direction parallel to the laser polarization. Therefore, more ions (<inline-formula><tex-math id="M19">\begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M19.png"/></alternatives></inline-formula>) are generated in the direction parallel to the laser polarization, and the fluorescence emission of <inline-formula><tex-math id="M20">\begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M20.png"/></alternatives></inline-formula> is more intense. Along the propagation direction of the laser, it is found that the fluorescence of <inline-formula><tex-math id="M21">\begin{document}${{\rm{N}}_{{2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M21.png"/></alternatives></inline-formula> appears before the fluorescence of <inline-formula><tex-math id="M22">\begin{document}${\rm{N}}_2^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M22.png"/></alternatives></inline-formula> and disappears after the fluorescence of <inline-formula><tex-math id="M23">\begin{document}${\rm{N}}_{{2}}^{{ + }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M23.png"/></alternatives></inline-formula> has vanished. This is due to the fact that <inline-formula><tex-math id="M24">\begin{document}${{\rm{N}}_{{2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M24.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M24.png"/></alternatives></inline-formula> can be ionized into <inline-formula><tex-math id="M25">\begin{document}${\rm{N}}_{{2}}^{{ + }}{{(}}{{\rm{B}}^{{2}}}\Sigma_{\rm{u}}^{{ + }})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M25.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M25.png"/></alternatives></inline-formula> at the position of high enough laser intensity, thus emitting fluorescence of <inline-formula><tex-math id="M26">\begin{document}${\rm{N}}_2^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M26.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M26.png"/></alternatives></inline-formula>. However, the laser energy is not enough to ionize nitrogen at the beginning and end of laser transmission, but it can generate <inline-formula><tex-math id="M27">\begin{document}${\rm{N}}_2^ * $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M27.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M27.png"/></alternatives></inline-formula>, which emits nitrogen fluorescence through the process of intersystem crossing <inline-formula><tex-math id="M28">\begin{document}${\rm{N}}_2^*\xrightarrow{{{\rm{ISC}}}}{{\rm{N}}_2}({{\rm{C}}^3}\Pi _{\rm{u}}^ + )$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M28.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M28.png"/></alternatives></inline-formula>. The spatial distribution of nitrogen fluorescence emission during femtosecond laser filament formation shows that in the case of short focal length, the intersystem crossing scheme can explain the formation of <inline-formula><tex-math id="M29">\begin{document}${{\rm{N}}_{{2}}}{{(}}{{\rm{C}}^{{3}}}\Pi _{\rm{u}}^{{ + }})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M29.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20201704_M29.png"/></alternatives></inline-formula>. This research is helpful in understanding the mechanism of nitrogen fluorescence emission.