  Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that
do not carry orbital angular momentum (OAM). Such beams have a wide range of
applications in many fields including atomic optics, bio-photonics, atmospheric
science, and plasma physics. Till date, these beams have been generated using
linear optical elements. Here, we show a new way of generating HGBs by
three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of
photons having OAM and conservation of OAM in nonlinear processes, we
experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW
at 355 nm. This generic concept can be extended to any wavelength, timescales
(continuous-wave and ultrafast) and any orders. We show that the removal of
azimuthal phase of vortices does not produce Gaussian beam. We also propose a
new and only method to characterize the order of the HGBs.
