Generalized Surface Conductivity Model for Anisotropic Phonon Polaritons in van der Waals Slabs

Recent advancements of anisotropic phonon polaritons (PhPs) in low-dimensional van der Waals (vdW) materials enable efficient control of long-wavelength light at nanoscale with ultrahigh confinement and low loss. The theoretical analysis based on the two-dimensional (2D) surface conductivity model has been widely exploited, for its simplicity, to understand fundamental phenomena at the surface of vdW slabs, which, however, neglects the intrinsic higher-order waveguide modes excited therein. Here, we report a generalized surface conductivity model which can allow us to include all waveguide modes, by taking into account the out-of-plane dimensions. In doing so, we can separate and examine each individual waveguide mode in vdW slabs with 2D models, and to further clarify the contribution of each polaritonic mode in near-field light matter interactions. As a concrete example, we examine the enhancement of photonic local density of states by PhPs in the α-phase molybdenum trioxide and hexagonal boron nitride plates and show that higher-order waveguide PhPs, instead of fundamental ones, surprisingly dominate the enhancement of light-matter interactions close to the surface. Our findings provide fundamentally relevant insights into anisotropic polaritons in vdW materials and beyond, important in near-field energy and information transport and other nanophotonic phenomena.