Transverse-mode dependence of femtosecond filamentation

We theoretically investigate the transverse-mode dependence of femtosecond filamentation in Ar gas. Three different transverse modes, Bessel, Gaussian, and Laguerre modes, are considered for incident laser pulses. By solving the extended nonlinear Schrödinger equation coupled with the electron density equation, we find that the lengths of the filament and the plasma channel induced by the Bessel incident beam is much longer than the other transverse modes with the same peak intensity, pulse duration, and beam diameter. Moreover we find that the temporal profile of the pulse with the Bessel incident mode is nearly undistorted during the propagation. Since the pulse energy that the Bessel beam can carry is more than one order of magnitude larger than the other modes for the same peak intensity, pulse duration, and beam diameter, the Bessel beam can be a very powerful tool in ultrafast nonlinear optics involving propagation in a Kerr medium.