A Julia implementation of Floquet-Bloch theory for high-harmonic generation in periodic systems

Abstract

We present a flexible Julia codebase implementing Floquet-Bloch theory for high-harmonic generation (HHG) in periodic tight-binding systems. Using the frequency-domain Fourier-Sambe formalism, the package maps the time-dependent Schroedinger equation onto a static eigenvalue problem. This allows direct computation of Floquet states, quasienergy bands, and harmonic currents for 1D, 2D, or 3D lattices under arbitrary light polarizations. The implementation supports both analytical Fourier-Bessel expansions (via Peierls substitution) and numerical Fast Fourier Transforms (FFT). We validate the code against a canonical 1D two-band model and showcase its capabilities on 2D honeycomb systems: gapped graphene mapping HHG cutoff scaling with hopping parameters and the Kane-Mele model, exploring field-induced quasienergy gaps and topological transitions under linear and circular driving fields. In addition to the theoretical presentation, we provide a flexible and efficient open-source Julia implementation of the Floquet formalism: https://github.com/Ashwin-A-Pillai/Floquet-Fourier-Numericals/tree/main.