Numerical Modelling of High Harmonic Generation in Gases

Abstract

High harmonic generation is a highly nonlinear phenomenon produced in high-intensity laser-matter interactions, which results in the emission of wideband light in the extreme-ultraviolet or soft X-ray spectrum. The emitted light consists of harmonics – spectral peaks at integer multiples of the frequency of the driving laser. The intensity of the generated harmonics is approximately constant over a wide range of frequencies, yielding a wideband spectrum and high frequency emission. The large bandwidth together with the coherence of the emitted light leads to the generation of attosecond duration pulses that have applications in measuring physical systems with ultrafast dynamics, such as that of electrons in atoms and molecules. Due to the highly nonlinear and quantum-mechanical nature of high harmonic generation, the theoretical modeling of high harmonic generation must include single atomic responses in the presence of laser light as well as nonlinear wave propagation equations. This requires numerical simulations in order to calculate quantities relevant for experiments, such as conversion efficiency and the harmonic spectrum. In this work, a numerical simulation code called HarP has been developed to simulate high harmonic generation in gases. The code utilizes the Crank-Nicolson numerical scheme to solve the wave propagation equations and combines theoretical models and tabulated data for the microscopic response of the atoms. This approach reduces computational cost compared with non-tabulated approaches and complexity while maintaining accuracy. To validate HarP, benchmarks were performed against another high-harmonic code utilizing a different methodology, as well as against established simulation results from the literature. More specifically, these benchmarks focus on ionisation rates, pulse profiles for different pressures and propagation lengths, and conversion efficiencies in argon. The result demonstrates overall good agreement for ionisation, laser pulse propagation, and conversion efficiency, with only minor differences observed.