Self-Focusing of a Light Beam in a Medium with Relativistic Nonlinearity: New Analytical Solutions

Abstract

In contrast to the existing theories of the relativistic self-focusing of a light beam in a plasma, the problem of a steady self-focusing light beam with a given input Gaussian radial intensity distribution has been analytically solved approximately with the use of a renormalization group approach. Depending on the parameters of the plasma and laser beam, solutions describing its longitudinal–radial waveguide structure have been obtained. These solutions demonstrate three characteristic types of relativistic self-focusing: (i) self-focusing on an axis, (ii) self-focusing in the form of a tubular channel, and (iii) self-trapping distribution.