Scattering and depletion in a flying focus from conformal transformations

TL;DR

This paper demonstrates how flying focus fields can be generated via conformal transformations of plane waves, enabling simplified calculations of photon emission amplitudes in focused laser fields within strong-field QED.

Contribution

It introduces a method to incorporate focusing effects into strong-field QED calculations using conformal transformations, simplifying the computation of scattering amplitudes.

Findings

Photon emission amplitudes can be derived from plane wave amplitudes with a Gaussian average.

Focusing effects can be incorporated into strong-field QED calculations 'for free'.

Initial results for partial depletion and anti-self-dual limit are presented.

Abstract

We show that flying focus fields can be obtained from complex conformal transformation of plane waves, and that solutions of the massless wave equation in the so-obtained fields are, correspondingly, conformal transformations of the Volkov solutions. This leads to the result that photon emission amplitudes in a totally depleting flying focus beam may be computed directly from the corresponding plane wave amplitudes by taking a simple Gaussian average over certain momentum variables. In effect, this gives a way of introducing focussing effects into strong-field QED calculations `for free'. The extension of these results to scattering amplitudes including only partial depletion is discussed and some first results presented in the anti-self-dual limit.