Bloch phonon-polaritons with anomalous dispersion in polaritonic Fourier crystals

The recently suggested concept of a polaritonic Fourier crystal (PFC) is based on a harmonically-corrugated mirror substrate for a thin pristine polaritonic crystal layer. The propagating polaritons in PFC experience a harmonic and mode-selective momentum modulation leading to a manifestation of Bloch modes with practically zero inter-mode scattering. PFC was first demonstrated for the hyperbolic phonon-polaritons in hexagonal boron nitride (hBN) within its Type II Reststrahlen band (RB-II) where the in-plane components of the dielectric permittivity tensor are isotropic and negative, while the out-of-plane component is positive. By contrast, a Type I Reststrahlen band (RB-I) is characterized by negative out-of-plane and positive in-plane permittivity components, and consequently, the inversion of field symmetry of phonon-polaritons compared to RB-II. Behavior of such RB-I modes in a polaritonic crystal is yet to be explored. Here, we employ a biaxial crystal alpha-phase molybdenum trioxide ({\alpha}-MoO3) and near-field imaging to study polaritonic Bloch modes in a one-dimensional PFC within the RB-I where the mid-infrared phonon-polaritons in {\alpha}-MoO3 have anomalous dispersion and negative phase velocity. Surprisingly, we observe a manifestation of Bloch waves as a dispersionless near-field pattern across the first Brillouin zone, in contrast to RB-II case demonstrated with in-plane isotropic hBN. We attribute this difference to the opposite field symmetry of the lowest-order phonon-polariton mode in the two RBs, leading to a different momentum modulation regime in the polaritonic Fourier crystal. Our results reveal the importance of mode symmetry for polaritonic crystals in general and for the emerging field of Fourier crystals in particular, which promise new ways to manipulate the nanolight.