Dynamical symmetries governing harmonic generation in laser-solid interactions

In previous work we have shown how high harmonic generation in laser-solid interactions that involve more than one spectral dimension can be described as an enhanced beat-wave process [1], and how this description can be exploited to obtain tuneable 1-D frequency combs from HHG in two spectral dimensions. To strengthen the foundations of our approach, we investigate here 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 various theorems by Noether, Mathieu and Jacobi-Anger, as well as well-known spectral theorems from solid-state physics by Laue, Floquet and Bloch. The specific nature of our approach to harmonic spectra allows these connections to be revealed. We will apply our results to examples from existing literature and discuss the practical consequences.

[1] R. Trines et al., Nature Communications 15, 878 (2024).

[2] R. Trines et al., arXiv:2410.03599 (2024).

[3] R. Trines et al., arXiv:2507.08635 (2025).