High-harmonic generation from two weakly coupled molecules: a simple tight-binding model

TL;DR

This work investigates high-harmonic generation from a minimal two-molecule tight-binding dimer to understand how laser polarization and weak intermolecular coupling influence harmonic yields. It combines exact TDSE calculations with an adiabatic framework that decomposes the response into adia-intra and adia-inter contributions, clarifying the roles of intraband and interband transitions. The study shows that low-order harmonics favor polarization along the molecular axes, while high-order harmonics peak when the field aligns with the intermolecular axis, with the flip in optimal polarization order shifting as the coupling $|t_1|$ changes; the HOMO-LUMO gap plays a crucial role in the intermolecular response. Although the adiabatic picture captures the qualitative trends, it underestimates the intermolecular contribution near the HOMO-LUMO transition, highlighting the importance of transitions between adiabatic states for a complete description. Overall, the results offer mechanistic insight into HHG in weakly coupled molecular crystals and validate a simple, flexible model for probing coupling-dependent electron dynamics in organic molecular solids.

Abstract

The generation of high harmonics is a strongly nonlinear effect that allows to probe properties of the target and to study electron dynamics in matter. It has been investigated in many different kinds of targets, including molecular gases, liquids and solids. Recently, high-harmonic generation was studied in organic molecular crystals by Wiechmann et al. [Nat. Commun. 16, 9890 (2025)]. It was found that the laser-polarization-dependent harmonic yield is sensitive to the weak couplings between nearest- and next-nearest-neighbor molecules. In this paper, the impact of the laser polarization angle and the intermolecular interaction on the harmonic yield is examined in detail using a simple but insightful two-dimensional tight-binding system that models a molecular dimer, i.e. two weakly coupled molecules. We find that the intensities of lower harmonic orders tend to maximize for a laser polarization direction aligning with the molecular axes, whereas higher harmonic orders rather show the strongest yield for a polarization direction along the intermolecular axis. We further demonstrate that the harmonic order at which the maximum flips from the molecular to the intermolecular direction strongly depends on the intermolecular coupling strength. To gain a deeper insight into the origins of the findings, we include a detailed adiabatic analysis, showing that the flipping of the maximum yield towards the intermolecular direction is already contained qualitatively in the adiabatically following states.

Figures (9)

• Figure 1: (a) Sketch of the model system. The blue circles depict the tight-binding sites. The sites $0$ and $1$ ($2$ and $3$) form a molecule with the intramolecular coupling $t_0$. The molecules are connected by the intermolecular coupling $t_1$. The distances $l$ and $d$ and the angles $\alpha_{\textrm{mol}}$ and $\alpha_{\textrm{inter}}$ specify the geometry of the target. The electric laser field with the polarization direction $\varphi$ is indicated by the red arrow. (b) Schematic representation of the energy levels of the unperturbed target system. Note that for the default settings, the splitting between the two lower (upper) levels is even smaller than depicted. In the ground state, the two lowest energy levels are doubly populated. The red arrows illustrate the energy of the fundamental laser photons. The dipole-allowed transitions are indicated by the purple and orange arrows.
• Figure 2: Normalized harmonic intensities as a function of the laser polarization direction $\varphi$. The black solid (dashed) line indicates the angle of the molecular (intermolecular) axis.
• Figure 3: High-harmonic spectra for laser polarization directions perpendicular to the intermolecular (solid line) and molecular (dashed line) direction. The vertical dash-dotted gray line marks the frequency corresponding to the HOMO-LUMO gap of the unperturbed system.
• Figure 4: (a) Normalized harmonic intensities as a function of the laser polarization angle for the reduced intermolecular coupling of $t_1=0.002\,t_0$. (b) Yield-maximizing laser polarization angle for the different harmonic orders color-coded as a function of the intermolecular coupling strength $t_1$ (given in units of the intramolecular coupling strength $t_0$). The light blue corresponds to polarization angles close to $\alpha_{\textrm{inter}}$, whereas the dark shades indicate polarization directions close to the orientation of the molecular axes, as also illustrated in panel (a).
• Figure 5: Harmonic intensities as a function of the intermolecular coupling strength $t_1$ for a laser polarization perpendicular to the intermolecular axis (solid lines) and perpendicular to the molecular axes (dashed lines). The diamonds indicate where the yield for $\varphi \perp \alpha_{\textrm{mol}}$ starts to exceed the yield for $\varphi \perp \alpha_{\textrm{inter}}$.