# Radiation-reaction electromagnetic fields in metasurfaces, a complete description of their optical properties

## TL;DR

This paper develops a comprehensive macroscopic model for metasurfaces by deriving electric and magnetic fields and susceptibilities from microscopic dipole scatterers, incorporating both retarded and advanced fields for accuracy.

## Contribution

It introduces a complete description of metasurface optical properties by including radiation-reaction fields and advanced fields in the macroscopic modeling process.

## Key findings

- Macroscopic fields are the sum of incident and radiation-reaction fields.
- Both local and radiation-reaction fields are essential for determining surface susceptibilities.
- The model accounts for the influence of microscopic dipoles on macroscopic optical properties.

## Abstract

This paper derives the macroscopic electric and magnetic fields and the surface susceptibilities for a metasurface, starting from the microscopic scatterer distribution. It is assumed that these scatterers behave as electric and magnetic dipoles under the influence of the incident radiation. Interestingly not only the retarded electromagnetic fields from oscillating dipoles are relevant to pass from the microscopic to the macroscopic representation, but the advanced fields must be considered too. It is found that the macroscopic fields are the sum of the incident fields plus the radiation-reaction fields acting on a single scatterer. Both the local fields and the radiation-reaction fields are necessary to fix the electric and magnetic surface susceptibilities.