Exact and geometrical optics energy trajectories in twisted beams

Energy trajectories, that is, integral curves of the Poynting (current) vector, are calculated for scalar Bessel and Laguerre-Gauss beams carrying orbital angular momentum. The trajectories for the exact waves are helices, winding on cylinders for Bessel beams and hyperboloidal surfaces for Laguerre-Gauss beams. In the geometrical-optics approximations, the trajectories for both types of beam are overlapping families of straight skew rays lying on hyperboloidal surfaces; the envelopes of the hyperboloids are the caustics: a cylinder for Bessel beams and two hyperboloids for Laguerre-Gauss beams.