  We report a systematic investigation into the processes behind a near
hundredfold enhanced second harmonic wave generated from a laser-induced air
plasma, by examining the temporal dynamics of the frequency conversion
processes, and the polarization of the emitted second harmonic beam. Contrary
to typical nonlinear optical processes, the enhanced second harmonic generation
efficiency is only observed within a sub-picosecond time window and found to be
nearly constant across fundamental pulse durations spanning from 0.1 ps to over
2 ps. We further demonstrate that with the adopted orthogonal pump-probe
configuration, the polarization of second harmonic field exhibits a complex
dependence on the polarization of both input fundamental beams, contrasting
with most of the previous experiments with a single-beam geometry.
