  A novel type of discrete basis for paraxial beams is proposed, consisting of
monomial vortices times polynomials of Gaussians in the radial variable. These
bases have the distinctive property that the effective size of their elements
is roughly independent of element order, meaning that the optimal scaling for
expanding a localized field does not depend significantly on truncation order.
This behavior contrasts with that of bases composed of polynomials times
Gaussians, such as Hermite-Gauss and Laguerre-Gauss modes, where the scaling
changes roughly as the inverse square root of the truncation order.
