Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Samuel Schöpa, Falk-Erik Wiechmann, Franziska Fennel, Dieter Bauer

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.

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

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 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.

Paper Structure

This paper contains 32 equations, 5 figures.

Figures (5)

  • Figure 1: High-harmonic spectrum of a TLS for different field-strengths.
  • Figure 2: Spectral intensity as a function of the ratio between transition frequency $\omega_{10}$ and laser frequency $\omega_L$ and harmonic order $\omega/\omega_L$. The plotted intensity is capped to the range $\left[10^{-14}, 10^{4}\right]$.
  • Figure 3: The phase of the different harmonics plotted against the ratio between transition energy and laser frequency. The dashed lines indicate $\omega_{10}/\omega_L = 7.5$ (green) and $\omega_{10}/\omega_L=9.5$ (blue), which are the relevant frequency ratios for the model in Fig. \ref{['fig:HHG_intensity_model']} and \ref{['fig:HHG_phase_model']}.
  • Figure 4: Intensity of the harmonics in the four-level model system with two decoupled two level systems as a function of the polarization angle of the driving field.
  • Figure 5: Polarization of the harmonics in the four-level model system with two decoupled two level systems as a function of the polarization of the driving field.