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

## TL;DR

This paper introduces a new model to study light-matter interactions in van der Waals materials by including all polariton modes, revealing that higher-order modes dominate near-surface interactions.

## Contribution

A generalized surface conductivity model that includes all waveguide polariton branches in van der Waals slabs.

## Key findings

- Higher-order waveguide phonon polaritons dominate near-field light-matter interactions in van der Waals materials.
- The generalized model allows separation and examination of individual polaritonic modes.
- The model provides insights into anisotropic polaritons for nanophotonic applications.

## Abstract

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.

Herein, we report a generalized surface conductivity model which includes all waveguide polariton branches, by taking into account the out‐of‐plane dimension. Using this generalized 2D model can separate and examine each individual polaritonic mode in van der Waals slabs and further clarify their contributions in near‐field light matter interactions.