# High-order harmonic generation in atomic and molecular systems

## TL;DR

This paper presents an analytical extension of the strong-field approximation to describe high-order harmonic generation in atomic and molecular systems, enabling direct study of target and laser pulse effects with good accuracy.

## Contribution

It introduces an analytical method using a non-local separable potential to calculate key matrix elements in HHG, improving understanding of physical mechanisms and interference effects.

## Key findings

- Analytical expressions match numerical solutions for atomic systems.
- Method captures interference features in multicenter molecular systems.
- Enables direct analysis of target and pulse influence on HHG spectra.

## Abstract

High-order harmonic generation (HHG) results from strong-field laser matter interaction and it is one of the main processes that are used to extract electron structural and dynamical information about the atomic or molecular targets with sub-femtosecond temporal resolution. Moreover, it is the workhorse for the generation of attosecond pulses. Here we develop an analytical description of HHG, which extends the well established theoretical strong-field approximation (SFA). Our approach involves two innovative aspects: i) First, using a model non-local, but separable potential, we calculate the bound-free dipole and the rescattering transition matrix elements analytically for both atomic and molecular multicenter systems. In comparison with the standard approaches to the HHG process, these analytic derivations of the different matrix elements allows us to study directly how the HHG spectra depend on the atomic target and laser pulse features. We can turn on and of contributions having distinct physical origins or corresponding to different physical mechanisms. Our SFA results are compared, when possible, with the direct numerical integration of the time-dependent Schr\"odinger equation (TDSE) in reduced and full dimensionality. Excellent agreement is found for single and multielectronic atomic systems, modeled under the single active electron approximation, and for simple diatomic molecular systems. Our model captures also the interference features, ubiquitously present in every strong-field phenomenon involving a multicenter target.