  We report on the lasing action of atmospheric air pumped by an 800 nm
femtosecond laser pulse with peak power up to 4 TW. Lasing emission at 428 nm
increases rapidly over a small range of pump laser power, followed by
saturation above ~ 1.5 TW. The maximum lasing pulse energy is measured to be
2.6 uJ corresponding to an emission power in the MW range, while a maximum
conversion efficiency of is measured at moderate pump pulse energy. The optical
gain inside the filament plasma is estimated to be excess of 0.7/cm. The lasing
emission shows a doughnut profile, reflecting the spatial distribution of the
pump-generated white-light continuum that acts as a seed for the lasing. We
attribute the pronounced saturation to the defocusing of the seed in the plasma
amplifying region and to the saturation of the seed intensity.
