This article is cited in 2 papers

Conservative finite-difference scheme for the problem of a femtosecond laser pulse with an axially symmetric profile propagating in a medium with cubic nonlinearity

A. G. Volkov, V. A. Trofimov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: Conservative finite-difference schemes are constructed for the problem of a femtosecond laser pulse propagating in a cubically nonlinear medium in the axially symmetric case with allowance for temporal dispersion of the nonlinear response of the medium. The process is governed by the nonlinear Schrödinger equation involving the time derivative of the nonlinear term. The invariants of the differential problem are presented. It is shown that the difference analogues of these invariants hold for the solution to the finite-difference schemes proposed for the problem. As an example, the numerical results obtained for the self-focusing of a femtosecond light beam are presented.

Key words: femtosecond laser pulse, combined nonlinear Schrödinger equation, axially symmetric case, self-focusing, cubic nonlinearity.

UDC: 519.634

Received: 27.03.2007

 English version: Computational Mathematics and Mathematical Physics, 2007, 47:10, 1681–1701

Bibliographic databases:

• 
•