Optical vortex trapping and annihilation by means of nonlinear Bessel beams in nonlinearly absorbing media

In nonlinear Kerr media at intensities such that multiphoton absorption is significant, a vortex of topological charge $m$ in the center of a high-order nonlinear Bessel beam (NBB) can be stable and subsist endlessly. We show that the $m$-charged NBB is not only stable but is formed spontaneously from any other $n$-charged NBB and $N$ "foreign" vortices of total charge $s$ randomly nested in the beam cross section if $n+s=m$. All nested vortices merge in the center of the original NBB, which undergoes a mode conversion to the NBB that preserves the topological charge and the inward-directed power current that sustains the diffraction-free and attenuation-free propagation in the medium with nonlinear absorption. We foresee different applications such as the creation of stable, multiply charged vortices without tight alignment requirements but by spontaneous vortex combination, mixing waves or particles that the vortices can guide, fast annihilation of vortex dipoles, and cleaning of speckled beams by massive annihilation of vortices.