  The generation of optical beams with multiple, mutually-coherent
orbital-angular-momentum (OAM) modes using phase gratings is analyzed from the
perspective of energy distribution and radial mode composition. We show that
phase gratings designed with equally-weighted Laguerre-Gauss (LG) modes will
generate beams with uneven energy distribution among OAM components. This
unwanted outcome cannot be corrected by adjusting the width of the illuminating
beam. We propose a way to design phase gratings that will produce a uniform
energy distribution among the constituent OAM states after illumination, while
minimizing the content of high radial modes. This method is based on a
generalized definition for the LG modes that takes advantage of the freedom to
select their radial scales.
