Formation of an extended homogeneous optical channel in a nonlinear medium with focusing of the laser radiation by an axicon

It is shown theoretically that, when a laser beam is focused by an axicon (a conical lens) in a Kerr-type nonlinear medium with nondissipative saturation of a square-root nonlinearity, an extended homogeneous optical channel may form and its length may be comparable with the length of the axicon caustic.