Relationship between elegant Laguerre-Gauss and Bessel-Gauss beams

We show that the elegant Laguerre-Gauss light beams of high radial order n are asymptotically equal to Bessel-Gauss light beams. The Bessel-Gauss beam equivalent to each elegant Laguerre-Gauss beam is found and shown to have almost identical propagation factors M-2. In the limit n --> infinity, elegant Laguerre-Gauss beams can be identified with Durnin's Bessel beam. Our results suggest a new experimental procedure for generating light beams with nondiffractinglike properties directly from the output of a stable resonator.