Comparative analysis of two models for phonon polaritons in van der Waals materials: 2D and 3D.

Phonon polaritons with ultralow losses and high confinement in extremely anisotropic media have opened up new avenues for manipulating the flow of light at the nanoscale. Recent advances in var der Waals (vdW) materials reveal unprecedented dispersion characteristics of polaritons using a two-dimensional (2D) model, treating the slab as a surface without thickness. However, the difference between the 2D and three-dimensional (3D) models of hyperbolic polaritons remains largely unexplored. Herein, we compare the polaritonic difference between these two models for biaxial vdW slabs. In addition, we demonstrate that the fundamental mode in slab configuration corresponds to the polaritonic mode in surface sheet and higher-order modes vanish in the latter configuration. In particular, we reveal that the difference in in-plane polaritons along the [100] and [001] crystal directions between the two models is associated with the inverse of the dielectric function along these two directions. For example, we compare the near-field radiative heat transfer (NFRHT) between two vdW slabs based on these two models. It is found that when the attenuation length of the higher-order hyperbolic mode is less than the gap distance, the enhancement achieved using the 3D model comes from only the fundamental mode, resulting in a negligible difference between these two models. Therefore, our findings may help to understand in-plane anisotropic polaritons and provide guidance for the application of the 2D model in the analysis of vdW materials.