  We report a novel experimental scheme for single-pass second harmonic
generation (SHG) of vector vortex beam in the blue. Using an ultrafast
Ti:Sapphire laser of pulse width ~17 fs and a set of spiral phase plates in
polarization based Mach-Zehnder interferometer (MZI) we have generated vector
vortex beams of order as high as lp = 12 at an average power of 860 mW. Given
the space-variant polarization of the vector vortex beam, and the dependence of
nonlinear frequency conversion processes on the polarization of the interacting
beams, using two contiguous bismuth borate crystals with optic axis orthogonal
to each other, we have frequency-doubled the near-IR vector vortex beam into
visible vector vortex beams with order as high as lsh=24. The maximum output
power of the vector vortex beam of order, lsh =2 is measured be as high as 20.5
mW at a single-pass SHG efficiency of 2.4 %. Controlling the temporal delay in
the MZI, we have preserved the vector vortex nature of the beams at both pump
and frequency-doubled beams at ultrafast timescales. The measurement on mode
purity confirms the generation of high quality vector vortex beams at pump and
SHG wavelengths. The generic experimental scheme can be used to generate vector
vortex beams across the electromagnetic spectrum.
