Light bullets under conditions of third harmonics generation

An analytical study of the possibility of a two-color light bullet forming during generation of the third harmonics in a graded index waveguide with the focusing Kerr nonlinearity is carried out. It is shown that under conditions of phase and group matching, as well as the absence of group velocity dispersion at the third harmonic frequency, a stable light bullet can be formed under certain restrictions. This applies to the lower limit on the temporal duration of the light bullet and to the upper limit on its power. The most stringent condition is the double restriction on the transverse radius of the light bullet.