  We present a novel approach to generate Bessel-Gauss modes of arbitrary
integer order and well-defined optical angular momentum in a gradient index
medium of transverse parabolic profile. The propagation and coherence
properties, as well as the quality factor, are studied using algebraic
techniques that are widely used in quantum mechanics. It is found that imposing
the well-defined optical angular momentum condition, the Lie group $SU(1,1)$
comes to light as a characteristic symmetry of the Bessel-Gauss beams.
