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  • Open Access

Back reflection in dipole fields and beyond

Maksim Valialshchikov1,2,*, Felix Karbstein1,3,4,†, Daniel Seipt1,3,2,‡, and Matt Zepf1,3,2

  • *Contact author: maksim.valialshchikov@uni-jena.de
  • †Contact author: felix.karbstein@uni-jena.de
  • ‡Contact author: d.seipt@hi-jena.gsi.de
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Phys. Rev. D 112, 116012 – Published 15 December, 2025

DOI: https://doi.org/10.1103/129l-c43n

Abstract

Quantum reflection is a fascinating signature of the quantum vacuum that emerges from inhomogeneities in the electromagnetic fields. In pursuit of the prospective real-world implementation of quantum reflection in the back-reflection channel, we provide the first numerical estimates for the light-by-light scattering with dipole pulses, which are known to provide the tightest focusing of light possible. For an all-optical setup with a dipole pump and Gaussian probe of the same frequency, we find that the dominant signal signature is related mainly to the back-reflection channel from 4-wave mixing. Focusing on this, we study the particular case of a multiple focusing pulses configuration (belt configuration) as an approximation to the idealized dipole pulse. Using Bayesian optimization methods, we determine optimal parameters that maximize the detectability of a discernible back-reflection signal. Our study indicates that the optimization favors a three-beam collision setup, which we further investigate both numerically and analytically.

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Phys. Rev. D 112, 116012– Published 15 December, 2025
  • Received 15 October 2025
  • Accepted 17 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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