  In this paper, an existence theory is established for ring-profiled optical
vortex solitons. We consider such solitons in the context of an electromagnetic
light wave propagating in a self-focusing nonlinear media and governed by a
nonlinear Schr\"odinger type equation. A variational principle and constrained
minimization approach is used to prove the existence of positive solutions for
an undetermined wave propagation constant. We provide a series of explicit
estimates related to the wave propagation constant, a prescribed energy flux,
and vortex winding number. Further, on a Nehari manifold, the existence of
positive solutions for a wide range of parameter values is proved. We also
provide numerical analysis to illustrate the behavior of the soliton's
amplitude and wave propagation constant with respect to a prescribed energy
flux and vortex winding number.
