Theory of a filament initiated nitrogen laser

We present the theoretical model for a single-pass, discharge-type standoff nitrogen laser initiated by a femtosecond filament in nitrogen gas. The model is based on the numerical solution of the kinetic equation for the electron energy distribution function self-consistently with balance equations for nitrogen species and laser equations. We identify the kinetic mechanisms responsible for a buildup of population inversion in the filament afterglow plasma and determine the dependence of population inversion density and the parameters of nitrogen lasing at a 337 nm wavelength corresponding to the transition between the C-3 Pi(u) (v = 0) excited and the X-1 Sigma(g) (v = 0) ground electronic states in a nitrogen molecule on the polarization and wavelength of the driver laser pulse used to produce the filament. We show that population inversion is achieved on an ultrafast time scale of approximate to 10 ps and decays within the time: <100 ps. We derive the low-signal gain 2.2 cm(-1) for lasing from a circularly polarized 0.8 mu m near-IR filament and 0.16 cm(-1) for a linearly polarized 4 mu m mid-IR filament. The results of the numerical simulations demonstrate good quantitative agreement with the experimental measurements.