The photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams

TL;DR

This paper derives analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams using a locally constant field approximation, relevant for studying vacuum birefringence in high-intensity laser experiments.

Contribution

It provides the first analytical formulas for the photon polarization tensor in these specific laser beam modes within the locally constant field approximation.

Findings

Analytical expressions for the photon polarization tensor in Hermite- and Laguerre-Gaussian beams.

Results applicable to current laboratory laser configurations.

Relevance for vacuum birefringence studies with high-intensity lasers.

Abstract

In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.