Regularities of femtosecond filamentation in the case of superposition of Gaussian and annular laser beams

The self-action of high-power femtosecond laser beams with a radiation wavelength of 800 nm (formed by superposition of Gaussian and annular beams) in air is theoretically modelled. A detailed analysis of self-focusing and filamentation of this radiation is performed based on the numerical solution of the spectral equation of the unidirectional propagation of a wave packet with allowance for the nonlinearity of the medium, and by tracing averaged diffraction-optical rays. It is shown that, in terms of the diffraction-beam optics, the outer annulus forms a waveguide, which facilitates self-trapping of the central part of the combined beam, supplying the light energy to the filament. The spatial stability of this waveguide depends on the energy stored in the annulus and on the distance from the latter to the beam axis.