  We report on generation and control of tunable, broad orbital angular
momentum (OAM) spectrum of a vortex beam. Using two spiral phase plates (SPPs),
we have converted the Gaussian beam of Yb-fiber femtosecond laser at 1064 nm
into optical vortices of orders, l=1-6, with conversion efficiency >95%. By
adjusting the transverse shift of the SPPs with respect to the incident
Gaussian beam axis, we have transformed the symmetric (intensity distribution)
optical vortex of order, l, into an asymmetric vortex beam of broad OAM
spectrum of orders, l, l-1, l-2,..,0. While the position of the SPPs determines
the weightage of the OAM modes, however, the weightage of the higher OAM modes
transfer to lower OAM modes with the shift of SPPs and finally resulting a
Gaussian beam (l=0). Using single pass frequency doubling of asymmetric
vortices in a 5-mm-long bismuth triborate crystal, we have transferred the pump
OAM spectra, l, l-1, l-2, ..., 0, into the broad spectra of higher order OAM
modes, 2l, 2l-1, 2l-2, ...,0 at green wavelength, owing to OAM conservation in
nonlinear processes. We have also observed that the conversion efficiency of
the frequency-doubled vortices of all orders increases with the increase in the
asymmetry of the pump vortices. Using pump power of 4.6 W, we have generated
symmetric vortices at green wavelength of output powers, 1.2, 0.76, 0.47, 0.4,
0.32, and 0.3 W and orders of ls=2, 4, 6, 8, 10, and 12, respectively.
