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Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction

We report experimental results concerning the propagation at high intensity of Laguerre- Gaussian beams in a nonlinear Kerr medium. We show that such patterns are remarkably stable and allow the beam to transport several times the critical power for self focusing before critical breakdown. We study the influence of the azimuthal order of the beam on the spatial and temporal averaging of the nonlinear phase shifts.