Exact description of self-focusing in highly nonlinear geometrical optics

TL;DR

This paper shows that laser beam self-focusing in highly nonlinear media can be accurately described by geometrical optics, leading to analytical solutions that improve understanding and prediction of self-focusing phenomena.

Contribution

The authors derive exact analytical solutions of the eikonal equation for self-focusing, replacing empirical formulas and aiding experimental and numerical studies.

Findings

Analytical solutions match experimental data accurately.

Provides a first-principles method to determine self-focusing position.

Offers a benchmark for numerical simulations of nonlinear optics.

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 benchmark solution for numerical simulations, and iii) a tool for the experimental determination of the high-order nonlinear susceptibility. Successful comparison with several experiments is presented.