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

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.