Maxwell-consistent, symmetry- and energy-preserving solutions for ultrashort-laser-pulse propagation beyond the paraxial approximation
Journal article, 2018

We analytically and numerically investigate the propagation of ultrashort tightly focused laser pulses in vacuum, with particular emphasis on Hermite-Gaussian and Laguerre-Gaussian modes. We revisit the Lax series approach for forward-propagating linearly polarized laser pulses, to obtain Maxwell-consistent and symmetry-preserving analytical solutions for the propagation of all field components beyond the paraxial approximation in four-dimensional geometry (space and time). We demonstrate that our solution conserves the energy, which is set by the paraxial-level term of the series. The full solution of the wave equation towards which our series converges is calculated in the Fourier space. Three-dimensional numerical simulations of ultrashort tightly focused pulses validate our analytical development.


Pedro González De Alaiza Martínez

University of Bordeaux

G. Duchateau

University of Bordeaux

B. Chimier

University of Bordeaux

R. Nuter

University of Bordeaux

Illia Thiele

Chalmers, Physics, Subatomic and Plasma Physics

Stefan Skupin

Université de Lyon

V. Tikhonchuk

University of Bordeaux

Czech Academy of Sciences

Physical Review A

2469-9926 (ISSN) 2469-9934 (eISSN)

Vol. 98 4 043849

Subject Categories

Computational Mathematics

Other Physics Topics

Mathematical Analysis



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