Description
In recent years, we have developed a novel framework to describe laser harmonic generation in plasma as an advanced beatwave process [1]. In our framework, all laser pulses are decomposed into modes with pure circular polarisation and “signed” frequencies and wave numbers. Each spectral step in the harmonic generation process can then be described as the beating between two such modes. The resulting harmonic spectrum will then show peaks with regular distribution along a 1-D line or a 2-D grid. We have also developed a novel method to analyse the harmonic radiation that will bring out this regular spectral structure. We apply our framework to the problem of generating harmonics via the interaction of a powerful laser pulse with solid targets with a structured surface and aperture targets with a structured inner edge [1]. We show that regular harmonic spectra are obtained in all cases, and that the spectral peak spacing can be tuned via the structure of the target. We also show how a laser frequency comb can be obtained by first generating a 2-D harmonic spectrum (e.g. frequency and OAM level, or frequency and transverse wave number) and then preferentially selecting a 1-D subset from this spectrum, for which the harmonic peak spacing is wider than in the full 2-D spectrum [2]. The wide range of configurations returning a 2-D harmonic spectrum (laser hitting a complex aperture or a corrugated target, or two laser beams hitting a flat target) guarantees a wide choice of potential frequency combs. Finally, we elucidate the role of symmetries of the original laser-target configuration in predicting the resulting harmonic spectrum [3]. Including these symmetries in our framework allows us to show the connection between our work and well-known mathematical theorems (Noether, Jacobi-Anger) as well as various spectral theorems known from solid-state physics (Laue, Mathieu, Floquet, Bloch).
[1] R. Trines et al., Nature Communications 15, 6878 (2024).
[2] R. Trines et al., arXiv:2410.03599 (2024).
[3] R. Trines et al., arXiv:2507.08635 (2025).