Marshall N. Rosenbluth Outstanding Doctoral Thesis Award Talk: The Ultrafast Nonlinear Response of Air Molecules and its Effect on Femtosecond Laser Plasma Filaments in Atmosphere

When exceeding the critical power $P_{cr}$, an intense laser pulse propagating in a gas collapses into one or multiple ``filaments,'' which can extend meters in length with weakly ionized plasma and local intensity $\sim $ 10$^{13}$ W/cm$^{2}$ radially confined in a diameter of $<$ 100 $\mu $m [1]. While it has been generally accepted the nonlinear self-focusing of the laser pulse leading to beam collapse is stabilized by plasma generation [2], neither the field-induced nonlinearity nor the plasma generation had been directly measured. This uncertainty has given rise to recent controversy about whether plasma generation does indeed counteract the positive nonlinearity [3, 4]. For even a basic understanding of femtosecond filamentation and for applications, the focusing and defocusing mechanisms---nonlinear self-focusing and ionization---must be understood. By employing a single-shot, time-resolved technique based on spectral interferometry [5] to study the constituents of air, it is found that the rotational responses in O$_{2}$ and N$_{2}$ are the dominant nonlinear effect in filamentary propagation when the laser pulse duration is longer than $\sim $ 100fs. Furthermore, we find that the instantaneous nonlinearity scales linearly up to the ionization threshold [6], eliminating any possibility of an ionization-free negative stabilization [3] of filamentation. This is confirmed by space-resolved electron density measurements in meter-long filaments produced with different pulse durations, using optical interferometry with a grazing-incidence, ps-delayed probe [7].\\[4pt] [1] A. Braun \textit{et al}., Opt. Lett. \textbf{20}, 73 (1995).\\[0pt] [2] A. Couairon and A. Mysyrowicz, Phys. Rep. \textbf{441}, 47 (2007).\\[0pt] [3] V. Loriot \textit{et al}., Opt. Express \textbf{17}, 13429 (2009).\\[0pt] [4] P. B\'{e}jot \textit{et al}., Phys. Rev. Lett. \textbf{104}, 103903 (2010).\\[0pt] [5] Y.-H. Chen \textit{et al}., Opt. Express \textbf{15}, 7458 (2007); Opt. Express \textbf{15}, 11341 (2007).\\[0pt] [6] J. K. Wahlstrand \textit{et al}., Phys. Rev. Lett. \textbf{107}, 103901 (2011).\\[0pt] [7] Y.-H. Chen \textit{et al}., Phys. Rev. Lett. \textbf{105}, 215005 (2010).