Quantum-trajectory-based analysis of far-field spatial profiles in high-order harmonic generation from single-layer...

Recently, the divergent features in the spatial profiles of solid-state high-order harmonic generation (HHG) have attracted significant attention in both experimental and theoretical studies. However, the understanding of their origins-particularly those related to microscopic quantum trajectories-remains incomplete. In this work, we reveal the relationship between spatially resolved HHG and the microscopic response by employing a propagation model combined with quantum-trajectory resolved induced-current phase. We simulate the far-field macroscopic HHG from single-layer ZnO under a Gaussian laser beam using the Huygens-Fresnel principle and show how its divergence features vary with the target position and laser intensity. We extract the phase coefficients of various quantum trajectories from the quantum-path intensity distributions. These distributions are calculated from the microscopic current across different momentum channels. The phase coefficients are then incorporated into the propagation model. This enables us to accurately explain the variations in both on-axis and off-axis components of the far-field macroscopic HHG spatial distributions as the target position changes. Our work provides new insights into analyzing the spatial structure of solid-state HHG in both experiment and theory and offers a novel perspective for probing the microscopic properties of solid-state high harmonics.