### Vaseva I. Федорук М.П. Рубенчик А.М. Турицын С.К.

## Light Self-Focusing in the Atmosphere. Simplified Description.

### Reporter: Vaseva I.

The ground based pulsed laser system is a promising way to mitigate the space debris problem [1]. Recently it was demonstrated that for typical parameters of a laser pulse the self-focusing in the atmosphere could degrade the laser beam quality, decrease the laser intensity on the target [2].

The key features of the beam evolution (diffraction and Kerr nonlinearity) can be described using the standard paraxial approximation for the envelope of the electric field - the nonlinear Schrodinger equation. Even with powerful modern computers the complete modeling of the self-focusing requires some effort and in situations when one have a lot of parameters and the optimal regime must be found it is desirable to have a simplified description of the process.

We consider the propagation of the laser beam through the nonlinear layer of the finite thickness, and the collapse point is located beyond this region, where the propagation is linear. In this case, the self-focusing effect can greatly modify the laser beam but without the catastrophic collapse of all the energy into a small volume.

Here we show that the situation can be accurately modeled within the “thin window” model [3]. We suggest the analytical formula determining the field structure at the exit of a thin non-linear medium. It can be used as an initial condition to compute the subsequent optical field using linear propagation. The numerical calculations confirm the applicability of the used analytical model.

1. Phipps C. R., Baker K. L., Libby S. B., Liedahl D. A, Olivier S. A. et al. Removing orbital debris with lasers // Advances in Space Research. 2012. Vol. 49, iss. 9. P. 1283–1300.

2. Rubenchik A.M., Fedoruk M.P., Turitsyn S.K. The effect of self-focusing on laser space-debris cleaning // Light: Science & Applications. 2014. Vol. 3, e159.

3. Marburger J. H. Self-focusing: Theory // Progress in Quantum Electronics. 1975. Vol. 4. P. 35-110.

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