Macroscopic Spin-Orbit Interaction through Strong-Field Pumping of Inhomogeneously Aligned Molecular Ensemble

We study the strong-field interaction of a helical bi-chromatic pump with an anisotropic and inhomogeneous molecular system in the form of planar distribution of radially aligned molecular ensemble. This setting gives rise to macroscopic spin-orbit interaction where High Harmonic radiation is emitted while imbued with Orbital Angular Momentum (OAM) whose sign is directly dictated by the helicity of the pump field. We demonstrate this phenomenon in ensembles of $H_2^+$ and $N_2$ molecules with Time-Dependent Density Functional Theory (TDDFT) simulations.

💡 Research Summary

In this work the authors explore a novel route to generate orbital angular momentum (OAM) in high‑harmonic generation (HHG) by exploiting a macroscopic spin‑orbit interaction in a radially aligned molecular gas. The system consists of a planar layer of homonuclear diatomic molecules (H₂⁺ and N₂) whose axes point radially outward from a common centre, forming a molecular analogue of a q‑plate. The molecules are first aligned with a strong, linearly polarized “alignment pulse” that creates a spatially varying polarization pattern (radial linear polarization) and then, after the rotational revival, are interrogated by an ultrashort bi‑chromatic circularly polarized (BCCP) pump. The pump is composed of two counter‑rotating circular components: a fundamental field at frequency ω₀ with right‑handed circular polarization (RHC) and its second harmonic at 2ω₀ with left‑handed circular polarization (LHC). By swapping the helicities of the two components the overall helicity of the pump can be reversed.

The theoretical approach is two‑fold. First, real‑time time‑dependent density‑functional theory (RT‑TDDFT) is used to calculate the microscopic response of a single aligned molecule to the BCCP field. For H₂⁺ a pure time‑dependent Schrödinger equation (TDSE) treatment is employed, while N₂ is treated with TDDFT using the asymptotically corrected LB exchange functional. The time‑dependent dipole moments along the y and z axes are Fourier‑transformed to obtain the amplitude and phase of each harmonic for a range of molecular alignment angles θ. Second, the dipole emission from many molecules arranged on five concentric circles (spacing chosen so that the outermost radius is comparable to the harmonic wavelength) is propagated to the far field (10 λ_q). The resulting far‑field pattern is decomposed onto a basis of Laguerre‑Gaussian (LG) modes (azimuthal index l = −4…4, radial index p = 0…4) to quantify the OAM content.

Key findings are: (i) With a linearly polarized pump no OAM appears, confirming that a simple linear field lacks the required phase‑amplitude asymmetry. (ii) The BCCP pump generates clear OAM in selected harmonics (e.g., the 5th order), with the sign of the OAM directly following the helicity of the pump. Reversing the helicity flips the OAM sign, demonstrating a macroscopic spin‑orbit coupling. (iii) For N₂ the harmonic phase varies almost linearly with the alignment angle, which ensures that the collective emission from the radially ordered ensemble adds constructively to produce integer‑valued OAM modes. (iv) An analytical point‑source model based on SAM selection rules and the molecule’s anisotropic polarizability reproduces the observed SAM‑OAM relationship, confirming that each molecule acts as a localized source whose additional polarization component is phase‑locked to its orientation.

The authors therefore show that a structured molecular ensemble can function as a “molecular q‑plate” in the strong‑field regime, imprinting OAM onto HHG beams across a wide spectral range (from UV to XUV). This capability opens new avenues for ultrafast structured‑light applications, such as vortex‑beam generation for attosecond spectroscopy, optical manipulation of nanoscale objects, and encoding of quantum information in the OAM degree of freedom at extreme frequencies. The work also highlights the broader potential of macroscopic spin‑orbit photonics in strong‑field physics, suggesting that engineered spatial patterns of molecular alignment could become a versatile toolbox for tailoring the angular momentum properties of high‑intensity laser‑matter interactions.