Complete Computation of Macroscopic High Harmonic Generation using Artificial Intelligence

Artificial intelligence, and in particular deep learning, is becoming a powerful tool to access complex simulations in strong-field, ultrafast science. One of the most challenging tasks in strong-field laser-matter interaction schemes is to combine microscopic quantum calculations that take place at the nanometer, subfemtosecond spatio temporal scales, with macroscopic simulations that take into account experimentally accessible setups. A paradigmatic example is the process of high-order harmonic generation (HHG), in which the highly nonlinear interaction of an intense infrared laser pulse with a gas target results in the generation of coherent radiation that extends from the extreme-ultraviolet to the soft x-rays, emitted in the form of attosecond pulses. The exact calculation of HHG is given by the solution of the time-dependent Schrödinger equation, which describes the laser-driven electronic wavepacket dynamics in the vicinity of each atom, coupled with the macroscopic Maxwell equations to take into account phase-matching. Those calculations are extremely challenging computationally, so approaches that rely on approximations are typically performed both at the microscopic level, such as the strong field approximation (SFA) [1], and/or at the macroscopic level [2].