Optical theorem for 2d magnetoelectric quadrupolar arrays

TL;DR

This paper derives comprehensive Green function dyadics for 2D magnetoelectric quadrupolar arrays, including radiative and non-radiative parts, and introduces an energy-conserving approximation scheme for long wavelengths.

Contribution

It provides a concise analytic form for the Green function dyadics of 2D arrays including electric, magnetic, and quadrupolar interactions, with a new approximation scheme respecting energy conservation.

Findings

Derived explicit Green function dyadics including radiative and non-radiative parts.

Developed an energy-conserving approximation scheme for long wavelengths.

Extended static approximation with dynamic corrections for better accuracy.

Abstract

We present all the periodic Green function dyadics that enter a description of a 2d array of emitters at the level that includes the electric dipole, magnetic dipole and electric quadrupole moment of each emitter. We find a concise analytic form for the radiative contributions to the periodic Green function dyadics that give rise to radiation reaction fields, and we give the non-radiative contributions that do not affect energy balance in the form of rapidly converging series. Finally, we present an approximation scheme for evaluating periodic Green function dyadics at long wavelengths that rigorously respects energy conservation. The scheme extends the range of validity of the usual static approximation by the inclusion of a simple dynamic correction.