Fourier Crystal for Polaritonic Dispersion Engineering

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, despite the advantages in terms of strong field confinement and momentum tunability, these high-momentum modes suffer from a combination of the inherent material-mediated losses and the severe scattering losses at sharp edges and surface defects. Consequently, the realization of polaritonic crystals with pronounced wave phenomena is a non-trivial task.<br/>Two approaches have been demonstrated so far to create a polaritonic crystal: patterning the polaritonic waveguide and patterning the dielectric substrate, where conventional nanofabrication methods result in sharp material edges. Using this approach, researchers demonstrated 2D polaritonic crystals for hyperbolic phonon-polaritons (HPhP) in hexagonal boron nitride (hBN) and alpha-phase molybdenum trioxide (α-MoO₃) that support collective Bloch modes. However, hBN and α-MoO₃ slabs of finite thickness support a practically infinite number of polaritonic modes due to their hyperbolic nature. Therefore, a severe scattering of propagating polaritons at the sharp patterned edges leads to an excitation of multiple higher-order modes, so that the band structure of such polaritonic crystals is filled with mode branches, hindering the band engineering and manifestation of polaritonic bandgaps for individual modes.<br/>We suggest a new concept of polaritonic Fourier crystal for mid-IR HPhP in hBN based on the continuously varying metallic Fourier surface which bypasses the aforementioned limitations of conventional patterning methods. We employ a holographic inscription method to fabricate a wafer-scale Fourier surface which is then covered with gold, acting as a substrate for a pristine polaritonic material. The proximity of the 2D polaritonic waveguide to a highly conductive metal leads to a coupling of the polariton to its mirror image and formation of an “image polariton”. Since the momentum of image polariton depends on the distance between the mirror and the waveguide, polaritons in the Fourier crystal experience a harmonic modulation of their wavevector. Most importantly, due to the stronger field confinement in the hBN layer, higher-order modes experience lesser modulation depth, while the intermode scattering is minimized due to the adiabatically varying geometry of the structure.<br/>In our device with a 106 nm-thick hBN, the momentum of the fundamental HPhP mode decreases by approximately 50% as the air gap between hBN and gold expands from 0 to 70 nm. At the same time, more confined higher-order modes are increasingly less sensitive to the variation of the gap size and thus experience much weaker modulation (less than 25%). Besides, these high-momentum modes are expected to be damped in the absence of coupling mechanisms such as scattering at sharp material edges. Indeed, our near-field experiments and full-wave numerical simulations demonstrate that the polaritonic Fourier crystal predominantly supports the fundamental Bloch mode in the hBN slab. Furthermore, we show that the momentum modulation of the fundamental mode would lead to a manifestation of a wide polaritonic bandgap for this mode even in a relatively lossy naturally abundant hBN crystal used in our experiments.