General and concise operator approach to the dyadic Green's function of layered media

TL;DR

This paper introduces an operator-based method for deriving dyadic Green's functions in layered media, simplifying analysis and enabling applications in nanophotonics.

Contribution

It presents a novel operator approach that expresses Green's functions through evolution operators and surface impedance tensors for anisotropic layered media.

Findings

Green's function expressed via transfer matrices and impedance tensors

Method simplifies conceptual understanding and practical calculations

Approach generalizable to spherical and cylindrical layers

Abstract

Dyadic Green's function is an important tool of computational photonics, giving deeper insights into light-matter interaction. We present an operator approach to the derivation of the dyadic Green's function of a generic anisotropic planarly-layered medium for both electric and magnetic fields. The resulting Green's function is expressed through the evolution operators (a kind of transfer matrices) of the comprising layers and the surface impedance tensors, the singular term being naturally separated from other terms. The operator approach to the Green's function simplifies both the conceptual understanding of the problem and the subsequent practical applications, some of which are demonstrated here. The proposed approach can be easily generalized to the case of spherical and cylindrical layers. The obtained results can be applied in nanophotonics engineering problems.