When a femtosecond laser is sufficiently strong to undergo filamentation in air, perturbation theory cannot be used to analyze the interaction because the laser intensity inside the filament is comparable to the Coulomb field intensity inside the molecule. The interaction between the strong laser field and molecule then produces a series of nonlinear phenomena, such as molecular alignment, ionization, high-order harmonics, terahertz radiation, and fluorescence radiation. These nonlinear phenomena are closely related to particle motion under strong fields. For example, by collecting the resulting high-order harmonics, ionized electrons, and dissociated ion signals, the internal structure of the material or dynamic process can be experimentally detected. In addition, these nonlinear phenomena have broad application prospects; for instance, filament-induced fluorescence can be used for atmospheric remote sensing, and high-order harmonics generated by laser-molecule interactions can be used to obtain high-intensity purple rays and attosecond lasers. Therefore, an in-depth study of molecular dynamics under a strong field can facilitate the elucidation of the nonlinear mechanism in the filamentation process as well as provide a theoretical basis for innovation and application.

This study presents a review of the main research progress concerning strong field molecular dynamics of femtosecond laser filamentation in air, including molecular alignment, molecular strong field ionization, electron-ion recombination, and population of molecular energy levels. As regards molecular alignment, researchers have conducted extensive research on its basic mechanism and have successfully used many methods to improve the alignment of molecules in experiments. Therefore, increasing research focus has been placed on more complex molecular alignment problems, such as three-dimensional alignment. In the field of molecular strong field ionization, there are many methods and models for calculating single-electron ionization, and the theoretical and experimental results are in agreement. With regard to filament-induced fluorescence radiation, substantial research has been conducted on measuring the spatial distribution of fluorescence radiation, and new technologies for environmental monitoring and atmospheric remote sensing have been proposed using this mechanism, such as filament-induced nonlinear spectroscopy. In the study of high-order harmonics, researchers can now directly generate high-order harmonics inside the filament and extract relevant information. Finally, in the study of air lasers, a series of methods have been proposed to realize the population inversion of particles, thus driving the experimental generation of air lasers.

Although strong-field molecular dynamics in the background of filamentation has been widely studied, many problems remain unsolved. As regards molecular alignment, combining molecular alignment with other technologies remains a problem worth considering. For molecular strong field ionization, there is no ideal model or method that can completely restore the ionization behavior of multiple electrons. In addition, the study of the complex motion of electrons after molecular ionization in filaments is crucial for the generation of new extreme ultraviolet or terahertz waves using common laser light sources, and its regulation must be further optimized. For filament-induced fluorescence radiation, the reason for the fluorescence gain in the filament is still controversial, and research has mainly focused on common gas molecules. Further research is needed to apply filament-induced fluorescence to practical application scenarios, such as large pollutant detection. With regard to higher harmonics, the basic mechanism of its generation needs to be elucidated, and improving its conversion efficiency is currently a difficult problem. Finally, regarding air lasers, many methods can be used to generate population inversion; however, these methods often have significant limitations. For example, an atomic air laser must be excited by a high-intensity ultraviolet pump laser; however, ultraviolet light is easily absorbed in air, thus limiting its application prospects. Although a few researchers have suggested that the rare gas argon with weak absorption of ultraviolet light can be used as the gain medium, prior studies have shown that the argon atom laser can be observed only when the mole fraction of argon reaches more than 10%, which is evidently different from that in the real air environment. In addition, the phenomenon of air laser reflects the quantum coherence of molecules under the action of a strong field. However, few studies have combined quantum optics with ultrafast laser, and further exploration and research are required in this field. Therefore, many unknowns remain to be explored regarding strong field molecular dynamic problems in filaments.