  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.
