This paper proposes an approximate method of describing and estimating how intensity affects the focusing parameters of radiation propagating in a weakly scattering nonlinear optical medium. The method uses the characteristics of the propagating radiation averaged over the cross section. A description and an estimate of the nonlinear effect are given for a weakly scattering medium with an activation shape of the dependence of the light scattering on the radiation intensity for weak focusing. The phenomenon of the penetration of a cylindrical transmission channel is predicted.
V. L. Komolov, A. V. Kulikov, S. G. PrzhibelÃ¢Â€Â™skii,, and V. N. Smirnov, "Formation of a waist in an intense radiation beam focused in a scattering medium," J. Opt. Technol. 70, 92-94 (2003)