Phase-matched generation of spatially resolved, elliptically polarized, high-order harmonics during macroscopic propagation in an atomic gas medium
Phys. Rev. A 113, 023109 – Published 12 February, 2026
DOI: https://doi.org/10.1103/5vgl-bxmv
Abstract
We investigate the generation of spatially resolved, elliptically polarized high-order harmonics in argon gas, driven by a two-dimensional laser field, using extended macroscopic propagation theory. By only varying the gas pressure while keeping other parameters fixed, the intense cutoff harmonics exhibit a high degree of circular polarization (DCP) and are spatially separated from the lower-order harmonics at the gas-medium exit under the optimal condition. For different harmonic orders, we demonstrate that the spatial distributions of harmonic intensity, DCP, and emission angle within the gas medium, as well as the absorption length, differ significantly, while the electron trajectories and DCP in the single-atom response also vary markedly, accounting for the observed harmonic features under phase-matching conditions. We further examine dependence of the spatial features of elliptically polarized high-order harmonic generation (HHG) on gas pressure. Finally, we present far-field spatial profiles of cutoff harmonics with large DCP values, which become increasingly separated from the driving laser field at higher gas pressures, forming an annular harmonic beam with a divergence angle of 5 mrad. This work provides a theoretical foundation for understanding and optimizing elliptically polarized HHG in atoms.
