# Fundamental Limits to the Coupling between Light and 2D Polaritons by Small Scatterers

## TL;DR

This paper quantifies the fundamental limits of light coupling to 2D polaritons in van der Waals materials, revealing maximum efficiencies and how resonators can enhance coupling for practical applications.

## Contribution

It provides universal analytical expressions for photon-polariton coupling cross sections and establishes fundamental constraints on maximum coupling efficiencies in 2D materials.

## Key findings

- Maximum photon-to-plasmon conversion efficiency is ~10^{-6} for point scatterers and ~10^{-4} for line scatterers in graphene.
- Mie resonators can significantly boost light-to-polariton coupling to near unity.
- Universal formulas for scattering, extinction, and coupling cross sections are derived.

## Abstract

Polaritonic modes in two-dimensional van der Waals materials display short in-plane wavelengths compared with light in free space. As interesting as this may look from both fundamental and applied viewpoints, such large confinement is accompanied by poor in/out optical coupling, which severely limits the application of polaritons in practical devices. Here, we quantify the coupling strength between light and 2D polaritons in both homogeneous and anisotropic films using accurate rigorous analytical methods. In particular, we obtain universal expressions for the cross sections associated with photon-polariton coupling by point and line defects, as well as with polariton extinction and scattering processes. Additionally, we find closed-form constraints that limit the maximum possible values of these cross sections. Specifically, the maximum photon-to-plasmon conversion efficiency in graphene is $\sim10^{-6}$ and $\sim10^{-4}$ for point and line scatterers sitting at its surface, respectively, when the plasmon and photon energies are comparable in magnitude. We further show that Mie resonators placed at an optimum distance from the film can boost light-to-polariton coupling to order unity. Our results bear fundamental interest for the development of 2D polaritonics and the design of applications based on these excitations.