Theoretical analysis on small-scale self-focusing of multi-wavelength beams in an isotropic medium

An analytic model for nonlinear propagation theory is developed for multi-wavelength laser beams propagating in an isotropic media. The small-scale self-focusing theoretical solution of multi-wavelength beams is obtained and is superposed by eigenfunctions with multiple local fastest-growth frequency, so the traditional B-integral obtained from a single-wavelength beam cannot be used to describe the small-scale self-focusing of multi-wavelength beams. Some laws for multi-wavelength beams propagating in an isotropy medium are also found, such as the self-focusing distance decreasing, the large angle scattering increasing and the spatial distributions of each wavelength trending to be consistent. The theoretical laws are confirmed by integrated numerical simulations and provide an explanation for the final optics phenomenon in high power lasers. The results promote the understanding of self-focusing theory and provide a very promising tool for beam control, which can transfer information from one beam to another through isotropic media.