Nonadiabaticity of cavity-free neutral nitrogen lasing

We report on a theoretical study of cavity-free lasing of neutral nitrogen molecules in femtosecond laser filaments with a nonadiabatic Maxwell-Bloch model, compared with recent pump-seed experiments. The nonadiabaticity of the lasing process is revealed and it is found that electron-neutral collisions dominate the dipole dephasing rate. Moreover, we show that the asymmetry between forward and backward lasing not only depends on the different amplification lengths but also on the temporal dynamics of electron-neutral collisions. The comparison of the nonadiabatic model with simulations based on the adiabatic approximation (such as radiative transfer equations) explicitly sets a bound on the validity of the latter model for cavity-free nitrogen lasing phenomenon, which holds a unique potential in optical remote sensing applications.

Figure 1

(a), (c) Forward and (b), (d) backward amplified seed (red dotted line/black continuous line) and ASE (blue continuous line) modeled using constant values for the dipole dephasing rate, $\gamma =8.3\times {10}^{11}{\mathrm{s}}^{-1}$ (upper panel) and $\gamma ={10}^{11}{\mathrm{s}}^{-1}$ (lower panel). Comparison with experiments [9] (e), (f) shows that a constant dipole dephasing rate cannot explain the experimental results.

Figure 2

Temporal evolution of the dipole dephasing rate induced by electron-neutral collisions (solid blue line). The two constant dipole dephasing rates used in Fig. 1 are depicted (dashed-dotted blue line) for comparison.

Figure 3

(a) Forward and (b) backward amplified seed (red dotted line/black continuous line) and ASE (blue continuous line) modeled using a time-dependent dipole dephasing rate, induced by electron-neutral collisions (depicted in Fig. 2). The experimental results [9] for (c) forward and (d) backward emission of neutral molecular nitrogen are shown below.

Figure 4

Comparison of the adiabatic (upper panel) and nonadiabatic (lower panel) polarization for the (a), (c) forward and (b), (d) backward cases. (a) and (c) depict in the red dotted line the forward amplified seed and in the blue continuous line the ASE. The adiabatic approximation cannot explain the temporal profiles of the amplified pulses, with the disagreement in the backward case being more dramatic.

Figure 5

Experimental amplification curve (black dots) and modeled amplification curves using the adiabatic approximation (blue concentric circles) and the nonadiabatic polarization (red circles).