Hyperbolic transition of phonon polaritons from volume to surface modes in β-Ga2O3

As hybrid quasi-particles formed by the coupling of photons with lattice vibrations, phonon polaritons (PhPs) play a crucial role in nanophotonics due to their intense field confinement and long lifetimes. Exotic polaritonic behaviors were achieved by manipulating the in-plane anisotropy of crystals. However, the influence of the out-of-plane permittivity to the manipulation of polaritons needs further exploration, due to its significant impact on light behaviors. Here, we find a transition of phonon polaritons from volume to surface modes in a finite-thickness β -Ga 2 O 3 flake, which arises from the sign reversals of the out-of-plane permittivities at different frequencies. Through theoretical analysis, the volume mode and the surface mode of PhPs are distinguished, and the relationship between the surface-bulk properties and the field distribution of PhPs is revealed. Finally, we provide a comprehensive explanation of the thickness-dependent behavior of PhPs. Our findings deepen the understanding of the propagation behavior of PhPs in van der Waals crystals.