Diverging and converging schemes of approximations to describe fundamental EM Gaussian beams beyond the paraxial approximation

Gérard Gouesbet (1) , Jianqi Shen (2) , Leonardo Ambrosio (3)

1 CORIA - Complexe de recherche interprofessionnel en aérothermochimie
2 University of Shanghai for Science and Technology
3 USP - Universidade de São Paulo = University of São Paulo

EM Gaussian beams are the most celebrated and used kind of laser beams. Their description beyond paraxial regimes has a long and venerable history, culminating may be with the building of a scheme of approximations which can be named the Davis scheme of approximations whose convergence has been considered as granted. Strange as it may be, a paper by Wang and Webb demonstrated that, actually, the Davis scheme is divergent. This quite unexpected result has been dramatically overlooked. This is the motivation for the present paper which reviews diverging and converging schemes of approximations to describe fundamental EM Gaussian beams. One of the new results obtained in the present framework is that a scheme of approximations known as the improved standard scheme, introduced more than two decades ago, is diverging as well. These divergences are the result of the behavior of asymptotic series similar to the ones encountered in quantum electrodynamics.

Mots clés: Gaussian beams; Davis scheme of approximations; Standard beams; Localized approximations; Light scattering; Asymptotic series; Quantum electrodynamics

Domaines: Physique [physics]

Gérard Gouesbet, Jianqi Shen, Leonardo Ambrosio. Diverging and converging schemes of approximations to describe fundamental EM Gaussian beams beyond the paraxial approximation. Journal of Quantitative Spectroscopy and Radiative Transfer, 2022, 291, pp.108344. ⟨10.1016/j.jqsrt.2022.108344⟩. ⟨hal-03793128⟩