  We analyze the transverse structure of the Gouy phase shift in light beams
carrying orbital angular momentum and show that the Gouy radius $r_G$
characterizing the transverse structure grows as $\sqrt{2p+|\ell|+1}$ with the
nodal number $p$ and photon angular momentum number $\ell$. The Gouy radius is
shown to be closely related to the root-mean-square radius of the beam, and the
divergence of the radius away from the focal plane is determined. Finally, we
analyze the rotation of the Poynting vector in the context of the Gouy radius.
