A method for solving the problem of nonlinear optical self-focusing in an infinite half-space

A numerical method for solving the problem of nonlinear optical self-focusing in an infinite half-space is proposed. Some numerical results obtained for the propagation of light beams in a linear medium and in a medium with the Kerr-type nonlinearity and with the three-photon absorption are discussed. These numerical results are compared with the results obtained by a previously proposed method for a domain bounded along the transverse coordinate. The work was supported by the Russian Foundation for Basic Research (project No. 08-01-00285).