On the stability of self-channeling of light beams

For transparent media with Kerr and saturable nonlinearities of refractive index, the self-channeling regimes with an exactly symmetric intensity dist ribution and a single (tangential) component of the electric field strength are shown to be unstable. The increments of perturbations are calculated. In particular, the calculations are made for the beams whose width is compa rable to a wavelength of light. The perturbations with topological (azimuth al) indices m = 2 and 3 are found to grow with the highest rate.