Modular multiscale approach to modelling high-harmonic generation in gases

TL;DR

The paper presents a modular, open-source toolbox for high-harmonic generation in gases that unifies macroscopic IR propagation, microscopic 1D-TDSE responses, and XUV diffraction-based propagation into a coherent multiscale framework. It introduces three core components—CUPRAD for radially symmetric IR propagation, CTDSE for 1D TDSE calculations, and HANKEL for XUV diffraction—interfaced via a unified HDF5 data archive to enable HPC-ready, pipeline-style simulations. The work demonstrates practical usage through tutorials and physical examples (gas-cell and gas-jet geometries, pre-ionization strategies, and custom input fields) and provides Python-based tooling for interactive analysis of microscopic electron dynamics. Beyond its current capabilities (linear polarization, cylindrical symmetry), the authors outline concrete plans to extend to 3D TDSE, vectorial propagation, and advanced microscopic models, aiming to deliver a versatile platform for designing and interpreting HHG experiments in realistic laboratory settings.

Abstract

We present a modular user-oriented simulation toolbox for studying highharmonic generation in gases. The first release consists of the computational pipeline to 1) compute the unidirectional IR-pulse propagation incylindrical symmetry, 2) solve the microscopic responses in the whole macroscopic volume using a 1D-TDSE solver, 3) obtain the far-field harmonic field using a diffraction-integral approach. The code comes with interfaces and tutorials, based on practical laboratory conditions, to facilitate the usage and deployment of the code both locally and in HPC-clusters. Additionally, the modules are designed to work as stand-alone applications as well, e.g., 1D-TDSE is available through Pythonic interface.

Figures (10)

• Figure 1: General MMA scheme showing the coupling of the macroscopic field propagation governed by the macroscopic Maxwell's equations together with microscopic dynamics given by TDSE. It presents the idea of the full feedback loop, which poses a great computational challenge in a general case.
• Figure 2: The MMA approach unfolds the intrinsically coupled description of the problem outlined in Fig. \ref{['fig:MMA_scheme_intro']} into a pipeline of consecutive tasks. Here we schematically summarise the core ideas of the respective physical models: 1) the NLSE that governs the propagation of the driving (ionizing) IR field including plasma generation and Kerr effect and provides the laser field in the whole macroscopic volume; 2) the microscopic TDSE that is solved at each macroscopic point $\boldsymbol{r}$ of the medium, describing the atomic microscopic dynamics (spatial variable $x_m$) resulting into the source term in the XUV range; and 3) the diffraction-integral approach to obtain the macroscopic XUV signal.
• Figure 3: The HDF5-archive structure showing some of the CUPRAD inputs.
• Figure 4: A schematic representation of the archive structure after all modules have completed their computations is shown. The red groups indicate the mandatory inputs required prior to the execution of each module, while the pink groups correspond to optional inputs. The remaining groups contain the output data generated by the respective modules.
• Figure 5: The initially Gaussian pulse in time $t$ and radial coordinate $\rho$ expressed in the units of harmonic cut-off in panel a) propagates through 1 cm long and 25 mbar argon gas cell leading to a distorted pulse b). The bottom panels c,d) shows the respective free electron profiles.