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

TL;DR

This paper uses few-level models to analyze the phase and polarization of below-threshold harmonics in aligned molecules, revealing phase shifts and polarization behaviors linked to transition energies.

Contribution

It introduces a four-level model to explain phase and polarization features of below-threshold harmonics, extending understanding beyond two-level systems.

Findings

Phase of harmonics alternates by π between odd orders below transition energy.

Higher-order harmonics maintain constant phase above transition energy.

Aligned systems with orthogonal dipoles exhibit similar phase and polarization features.

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 $\pi$ 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.