Role of the radiation-reaction electric field in the optical response of two-dimensional crystals

TL;DR

This paper develops a classical theory for radiating 2D crystals, deriving an expression for the radiative-reaction electric field that links microscopic and macroscopic fields, highlighting its essential role in optical response.

Contribution

It introduces a new classical framework for 2D crystal radiation, explicitly deriving the radiative-reaction electric field and clarifying its role in optical boundary conditions.

Findings

Derived an explicit expression for the radiative-reaction electric field.

Showed the radiative-reaction field equals the macroscopic radiated field.

Connected microscopic dipole fields to macroscopic optical response.

Abstract

A classical theory of a radiating two-dimensional crystal is proposed and an expression for the radiative-reaction electric field is derived. This field plays an essential role in connecting the microscopic electromagnetic fields acting on each dipole of the crystal to the macroscopic one, via the boundary conditions for the system. The expression of the radiative-reaction electric field coincides with the macroscopic electric field radiating from the crystal and, summed to the incident electric field, generates the total macroscopic electric field.