Testing the Role of Recollision in ${\mathrm{N}}_2^{+}$ Air Lasing

It has been known for many years that during filamentation of femtosecond light pulses in air, gain is observed on the $B$ to $X$ transition in ${\mathrm{N}}_2^{+}$. While the gain mechanism remains unclear, it has been proposed that recollision, a process that is fundamental to much of strong field science, is critical for establishing gain. We probe this hypothesis by directly comparing the influence of the ellipticity of the pump light on gain in air filaments. Then, we decouple filamentation from gain by measuring the gain in a thin gas jet that we also use for high harmonic generation. The latter allows us to compare the dependence of the gain on the ellipticity of the pump with the dependence of the high harmonic signal on the ellipticity of the fundamental. We find that gain and harmonic generation have very different behavior in both filaments and in the jet. In fact, in a jet we even measure gain with circular polarization. Thus, we establish that recollision does not play a significant role in creating the inversion.

Figure 1

The population transfer from $X^2{\mathrm{\Sigma }}_g^{+}({\nu }_{\mathrm{i}}=0)$ to $B^2{\mathrm{\Sigma }}_u^{+}({\nu }_{\mathrm{f}}=0,1,2)$ in ${\mathrm{N}}_2^{+}$ via recollision using linear polarization at 800 nm and $7\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$. The kinetic energy at the time of recollision (also shown) is calculated using the classical electron trajectories and the electron wave function expansion is estimated in the absence of the Coulomb potential. Inelastic scattering cross sections [25] are used to calculate the population transfer.

Figure 2

(a) An experimental diagram of the calibration measurement in air. (b) An experimental diagram of the gain measurement in air. (c) The normalized transmission intensity (color scale) of the unfocused 800 nm beam as a function of the quarter wave plate (QWP) and polarizer angle in degrees. (d) The intensity of 428 nm emission (color scale) from the air filament as a function of the QWP and polarizer angle in degrees.

Figure 3

(a) A spectrum of the forward emission showing continuum and ion lines at 428 nm and 471 nm. Regions of the continuum next to (431–455 nm) and far from (479–531 nm) the emission at 428 nm are highlighted using vertical lines. (b) The intensity integrated over the regions highlighted in Fig. 3, and 428 nm intensity divided by the continuum next to the emission ($\propto e^{gL}-1$) showing that the gain is maximum at an ellipticity of $\sim 0.45$.

Figure 4

(a) An experimental diagram showing the collinear pump and probe focusing into the supersonic gas jet. The pump is elliptically polarized and the seed is linearly polarized. The amplified seed is monitored on a spectrometer as a function of delay. High harmonics from the pump are measured using an XUV spectrometer. (b) Gain ($gL$) at 391 nm in the gas jet as a function of pump ellipticity at two seed delay times (0.45 and 3.78 ps) for a pump intensity of $\sim 7\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$. (c) Normalized gain at both 391 and 428 nm as a function of pump ellipticity at a delay of $\sim 0.45\mathrm{ps}$ and pump intensity of $\sim 4.5\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$. Integrated high harmonic intensity (H11–H21) is also shown as a function of pump ellipticity.