Similarity parameter for the process of mid-IR light bullet formation

We study the influence of the ratio of diffraction and dispersion lengths of a femtosecond mid-IR wave packet on the filamentation threshold power and the light bullet (LB) formation upon nonlinear optical interaction with solid-state dielectrics under the conditions of anomalous group velocity dispersion. It is found that the ratio of the threshold power of filamentation and LB formation to the critical power of stationary self-focusing is independent of the radiation wavelength and the medium characteristics and is determined by the similarity parameter, equal to the ratio of the diffraction length to the dispersion one. With an increase in the similarity parameter, the threshold power of filamentation and light bullet formation increases.