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

TL;DR

This paper develops Maxwell-consistent analytical solutions for ultrashort laser pulse propagation beyond the paraxial approximation, ensuring energy conservation and symmetry preservation, validated by numerical simulations.

Contribution

It introduces a novel approach using the Lax series to derive comprehensive solutions that include all field components beyond the paraxial approximation.

Findings

Energy is conserved in the solutions.

Analytical solutions match numerical simulations.

Solutions are valid for Hermite-Gaussian and Laguerre-Gaussian modes.

Abstract

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, in order 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.