Non-diffracting and non-attenuating vortex light beams in media with nonlinear absorption of orbital angular momentum

We show that a high-order Bessel beam propagating in a medium with nonlinear absorption is not completely absorbed, but survives in the form of a new propagation invariant vortex beam in which the beam energy and orbital angular momentum are permanently transferred to matter and at the same time refueled by spiral inward currents of energy and angular momentum. Unlike vortex solitons and dissipative vortex solitons, these vortex beams are not supported by specific dispersive nonlinearities (self-focusing or self-defocusing) and do not require gain. Propagation invariance in presence of multiple absorption of photons carrying (possibly high) orbital angular momentum makes these beams attractive for optical pumping of angular momentum over long distances.