Iterative projection algorithm for retrieval of angle-resolved single-molecule dipoles from high-harmonic spectra

Abstract

High-order harmonic spectroscopy (HHS), as an emerging technique, provides a way to detect molecular structures with \aa{}ngstr\"om spatial resolution and ultrafast electron dynamics in molecules on an attosecond timescale. However, the implementation of HHS still encounters great difficulties due to the coherent average of single-molecule emissions from different alignment angles. Here, we provide a machine learning algorithm based on the iterative projection method to fully retrieve the complex single-molecule dipole of a linear molecule from the harmonic spectra measured at different delays and polarization angles between the alignment and driving pulses. We demonstrated our algorithm both theoretically and experimentally using the ${\mathrm{N}}_{2}$ molecule. The results show that our algorithm can accurately retrieve the complex single-molecule dipole from the harmonic spectra with good noise stability and robustness. From the retrieved single-molecule dipole, the contributions of multiple orbitals in high harmonic generation are identified even with a low degree of alignment.