Modular multiscale approach to modelling high-harmonic generation in gases

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.

💡 Research Summary

The paper introduces a modular, user‑oriented simulation toolbox designed to model high‑harmonic generation (HHG) in gases with a level of detail that matches typical laboratory experiments. The authors describe a three‑stage computational pipeline that links macroscopic infrared (IR) pulse propagation, microscopic atomic response, and far‑field XUV (extreme‑ultraviolet) field reconstruction. Each stage is implemented as an independent module that can also be run as a stand‑alone application, and the modules communicate through a common HDF5 data format, enabling seamless integration on both local workstations and high‑performance computing (HPC) clusters.

The first module, named CUPRAD (Complex Unidirectional Propagator, RADial symmetry), solves the propagation of an intense IR laser pulse under the assumption of cylindrical symmetry. It uses a scalar envelope formulation based on the slowly varying envelope approximation (SVEA) applied to the nonlinear Schrödinger‑type equation. Linear dispersion, third‑order Kerr nonlinearity, and ionization‑induced plasma effects are included. Ionization can be modeled either with a simple multiphoton rate or with the more sophisticated Perelomov‑Popov‑Terent’ev (PPT) theory. The free‑electron response is treated with a Drude model, while recombination and diffusion are neglected for the femtosecond timescales of interest. The output of this stage consists of the complex IR field envelope and the spatially resolved electron density, both stored in an HDF5 file.

The second module solves the one‑dimensional time‑dependent Schrödinger equation (1D‑TDSE) for each radial position in the gas. Implemented as an MPI‑parallel application with a Pythonic interface, it receives the IR envelope from CUPRAD, propagates the electronic wavefunction in time, and computes the induced dipole moment d(t)=⟨ψ|r|ψ⟩. By Fourier transforming d(t) the module provides the microscopic high‑harmonic source spectrum for every radial slice. This dipole data is written back to the same HDF5 container, preserving the full spatio‑temporal correlation between the macroscopic field and the microscopic response.

The third module reconstructs the far‑field XUV field using a diffraction‑integral (Fresnel/Fraunhofer) approach. Implemented in Python, it reads the dipole distribution from the HDF5 file, applies the appropriate Green’s function for cylindrical geometry, and outputs the spatial profile and spectrum of the high‑harmonic beam at a detector plane. Users may also supply custom dipole data, allowing the module to be employed for analytic or experimentally measured sources.

A key strength of the toolbox is its modularity and extensibility. Because each component adheres to a common data schema, researchers can replace the SVEA‑based IR propagator with a full unidirectional pulse propagation equation (UPPE) solver, swap the 1D‑TDSE for a multi‑dimensional quantum‑mechanical code, or couple the diffraction step to a full Maxwell solver for XUV propagation in complex media. The authors provide Docker images, detailed documentation, and Jupyter notebooks that demonstrate typical workflows, from setting up a gas‑jet geometry to visualizing the final harmonic spectrum.

The current release is limited to linearly polarized fields, cylindrical symmetry, and third‑order nonlinearities (with optional fifth‑order terms omitted for clarity). The authors acknowledge that few‑cycle pulses, vectorial fields (e.g., circular polarization), and higher‑order plasma dynamics are not yet supported, but they outline plans to incorporate these capabilities in future versions.

In summary, the presented toolbox offers a comprehensive, end‑to‑end simulation environment for HHG that bridges the gap between microscopic quantum dynamics and macroscopic laser propagation. Its open‑source nature, HPC readiness, and clear user interfaces make it a valuable resource for optimizing HHG efficiency, designing XUV pump‑probe experiments, and exploring new regimes of strong‑field physics.