Vacuum birefringence in the head-on collision of XFEL and optical high-intensity laser pulses

TL;DR

This paper derives compact analytical formulas for vacuum birefringence signals in head-on collisions of XFEL and high-intensity lasers, aiding experimental design and understanding of the effect's dependence on beam parameters.

Contribution

It provides new analytical expressions for the differential number of polarization-flipped photons, including effects of beam waists, pulse durations, and offsets, enhancing previous approximations.

Findings

Analytical expressions for polarization-flipped photon signals.

Insights into how beam parameters affect birefringence signals.

Formulas for far-field angular decay and divergence of signal photons.

Abstract

The focus of this article is on providing compact analytical expressions for the differential number of polarization flipped signal photons constituting the signal of vacuum birefringence in the head-on collision of x-ray free electron (XFEL) and optical high-intensity laser pulses. Our results allow for unprecedented insights into the scaling of the effect with the waists and pulse durations of both laser beams, the Rayleigh range of the high-intensity beam, as well as transverse and longitudinal offsets. They account for the decay of the differential number of signal photons in the far-field as a function of the azimuthal angle measured relative to the beam axis of the probe beam in forward direction, typically neglected by conventional approximations. Moreover, they even allow us to extract an analytical expression for the angular divergence of the perpendicularly polarized signal photons. We expect our formulas to be very useful for the planning and optimization of experimental scenarios aiming at the detection of vacuum birefringence in XFEL/high-intensity laser setups, such as the one put forward at the Helmholtz International Beamline for Extreme Fields (HIBEF) at the European XFEL.