Filament propagation length of femtosecond pulses with different   transverse modes
  We experimentally studied intense femtosecond pulse filamentation and propagation in water for Gaussian, Laguerre-Gaussian, and Bessel-Gaussian incident beams. These different transverse modes for incident laser pulses were created from an initial Gaussian beam by using a computer generated hologram technique. We found that the length of the filament induced by the Bessel-Gaussian incident beam was longer than that for the other transverse modes under the conditions of the same peak intensity, pulse duration, and the size of the central part of the beam. To better understand the Bessel-Gaussian beam propagation, we performed a more detailed study of the filament length as a function of the number of radial modal lobes. The length increased with the number of lobes, implying that the radial modal lobes serve as an energy reservoir for the filament formed by the central intensity peak. 
N. Kaya, M. Sayrac, G. Kaya, J. Strohaber, A. A. Kolomenskii, and H.   A. Schuessler
physics.optics