Self-focusing of a light beam in a medium with relativistic nonlinearity: new analytical solutions

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.