Diffraction, self-focusing, and the geometrical optics limit in laser produced plasmas

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Abstract
The effect of diffraction on the self‐modulation of an intense laser beam in an initially uniform hydrogen plasma is investigated. A formalism is used in which the diffraction term in the paraxial wave equation can be arbitrarily reduced by the use of a weight factor ι. In the limit where ι approaches zero, it is shown that the paraxial wave equation correctly reduces to the geometrical optics limit and that the problem then becomes formally equivalent to solving the ray‐tracing equations. When ι=1, the paraxial wave equation takes its usual form and diffraction is fully accounted for. This formalism is applied to the simulation of self‐modulation of an intense laser beam in a hydrogen plasma, for which diffraction is shown to be significant.