Title: Polaritonic Fourier crystal

Abstract: Polaritonic crystals - periodic structures where the hybrid light-matter waves called polaritons can form Bloch states - promise a deeply subdiffractional nanolight manipulation and enhanced light-matter interaction. In particular, polaritons in van der Waals materials boast extreme field confinement and long lifetimes allowing for the exploitation of wave phenomena at the nanoscale. However, in conventionally patterned nanostructures, polaritons are prone to severe scattering loss at the sharp material edges, making it challenging to create functional polaritonic crystals. Here, we introduce a new concept of a polaritonic Fourier crystal based on a harmonic modulation of the polariton momentum in a pristine polaritonic waveguide with minimal scattering. We employ hexagonal boron nitride (hBN) and near-field imaging to reveal a neat and well-defined band structure of phonon-polaritons in the Fourier crystal, stemming from the dominant excitation of the first-order Bloch mode. Furthermore, we show that the fundamental Bloch mode possesses a polaritonic bandgap even in the relatively lossy naturally abundant hBN. Thus, our work provides a new paradigm for polaritonic crystals essential for enhanced light-matter interaction, dispersion engineering, and nanolight guiding.