Optical filaments and optical bullets in dispersive nonlinear media

We have investigated the evolution of picosecond and femtosecond optical pulses governed by the amplitude vector equation in the optical and UV domains. We have written this equation in different coordinate frames, namely, in the laboratory frame, the Galilean frame, and the moving-in-time frame and have normalized it for the cases of different and equal transverse and longitudinal sizes of optical pulses or modulated optical waves. For optical pulses with a small transverse size and a large longitudinal size (optical filaments), we obtain the well-known paraxial approximation in all the coordinate frames, while for optical pulses with relatively equal transverse and longitudinal sizes (so-called light bullets), we obtain new non-paraxial nonlinear amplitude equations. In the case of optical fields with low intensity, we have reduced the nonlinear amplitude vector equations governing the light-bullet evolution to the linear amplitude equations. We have solved the linear equations using the method of Fourier transform. An unexpected new result is the relative stability of light bullets and the significant decrease in the diffraction enlargement of light bullets with respect to the case of long pulses in the linear propagation regime.