Abstract
We demonstrate that laser beam collapse in highly nonlinear media can be described, for a large number of experimental conditions, by the geometrical optics approximation within high accuracy. Taking into account this fact we succeed in constructing analytical solutions of the eikonal equation, which are exact on the beam axis and provide (i) a first-principles determination of the self-focusing position, thus replacing the widely used empirical Marburger formula, (ii) a mathematical condition for obtaining the filament intensity, (iii) a benchmark solution for numerical simulations, and (iv) a tool for the experimental determination of the high-order nonlinear susceptibility. Successful comparison with experiment is presented.
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