Nonlinear unbalanced bessel beams: stationary conical waves supported by nonlinear losses

Nonlinear losses accompanying self-focusing substantially impact the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D + 1 nonlinear Schr?dinger equation, which are stable against radial collapse. These are featured by linear, conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as a strong attractor for the self-focusing dynamics in Kerr media.