Simulating macroscopic high-order harmonic generation driven by structured laser beams using artificial intelligence

Abstract

Artificial intelligence, and in particular deep learning, is becoming a powerful tool to access complex simulations in intense ultrafast laser science. One of the most challenging tasks to model strong-field physics, and in particular, high-order harmonic generation (HHG), is to accurately describe the microscopic quantum picture—that takes place at the sub-nanometer/attosecond spatiotemporal scales—together with the macroscopic one—at the millimeter/femtosecond scales—to reproduce experimental conditions. The exact description would require to couple the laser-driven wavepacket dynamics given by the three-dimensional time-dependent Schrödinger equation (3D-TDSE) with the Maxwell equations, to account for propagation. However, such simulations are beyond the state-of-the-art computational capabilities, and approximations are required. Here we introduce the use of artificial intelligence to compute macroscopic HHG simulations where the single-atom wavepacket dynamics are described by the 3D-TDSE. We use neural networks to infer the 3D-TDSE microscopic HHG response, which is coupled with the exact solution of the integral Maxwell equations to account for harmonic phase-matching. This method is especially suited to compute macroscopic HHG driven by structured laser beams carrying orbital angular momentum within minutes or even seconds. Our work introduces an alternative and fast route to accurately compute extreme-ultraviolet/x-ray attosecond pulse generation.