Second-harmonic generation in the air-based femtosecond plasma under loose focusing

We used filamentation of 940 nm, 90 fs, up to 6.5 mJ pulse to measure the spatial and spectral distributions of the second harmonic with 10^{-9} conversion efficiency in comparatively long focusing geometry (40 cm and 100 cm focal lengths, ≥1 cm filament), as well as spectral distributions of the second harmonic with about an order of magnitude higher conversion efficiency in tight focusing geometry (8 cm focal length, ∼1mm filament). Through integration of the vectorial second-order current over the (t,r,z)-simulated plasma channel, we identified the second-harmonic generation region, outside of which the ω-2ω phase mismatch quenches the second-harmonic energy increment. The unified description of the even harmonic emission based on the vectorial second-order current shows that the two lobes of the terahertz beam broken along the laser polarization are oriented perpendicularly to the two lobes of the second harmonic beam, in agreement with the experiment.