  We report on a new class of exact solutions of the scalar Helmholtz equation
obtained by carefully engineering the form of the angular spectrum of a Bessel
beam. We consider in particular the case in which the angular spectrum of such
generalized beams has, in the paraxial zone, the same radial structure as
Laguerre-Gaussian beams. We investigate the form of these new beams as well as
their peculiar propagation properties.
