Maxwell-consistent, symmetry-and energy-preserving solutions for ultrashort laser pulse propagation beyond the paraxial approximation
Résumé
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 revisite the Lax series approach for forward-propagating linearly-polarized laser pulses, in order to obtain Maxwell-consistent, symmetry-and energy-preserving analytical solutions for the propagation of all field components beyond the paraxial approximation in four-dimensional geometry (space and time). Our solution converges towards an exact solution of the wave equation. Three-dimensional numerical simulations of ultrashort tightly-focused pulses validate our analytical development.
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