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  • Letter
  • Open Access

Phase structure of below-threshold harmonics in aligned molecules: A few-level model system

Samuel Schöpa1, Lina Bielke1, Falk-Erik Wiechmann1,2, Franziska Fennel1,2, and Dieter Bauer1,2,*

  • *Contact author: dieter.bauer@uni-rostock.de
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Phys. Rev. Research 8, L022022 – Published 4 May, 2026

DOI: https://doi.org/10.1103/5fjm-8ps7

Abstract

We utilize few-level model systems to analyze the polarization and phase properties of below-threshold harmonics generated from aligned molecules. In a two-level system, we find that the phase of emitted harmonics undergoes a distinct change. For harmonics with photon energies below the transition energy between the dominant field-dressed states, the phase alternates by π between successive odd harmonic orders. In contrast, the phase remains constant for harmonics above the transition energy. Exploiting this behavior, we construct a four-level model composed of two uncoupled two-level systems aligned along orthogonal directions. We demonstrate that with selected transition frequencies lower-order harmonics follow the polarization of the linearly polarized driving field while higher-order harmonics exhibit a mirrored polarization. The model predicts that aligned systems with orthogonal transition dipoles may show analogous phase and polarization features in the below-threshold regime.

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Phys. Rev. Research 8, L022022– Published 4 May, 2026
  • Received 29 October 2025
  • Accepted 13 March 2026
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