Optical theorems and physical bounds on absorption in lossy media

TL;DR

This paper derives two versions of optical theorems for lossy media, providing fundamental bounds on absorption using elementary optimization, applicable to arbitrary geometries and materials, including bianisotropic ones.

Contribution

It introduces two novel optical bounds for absorption in lossy media, generalizing previous results and applicable to arbitrary shapes and complex materials.

Findings

Derived a variational bound based on polarization currents.

Established a T-matrix based bound for arbitrary scatterers.

Numerical examples demonstrate the bounds' complementary nature.

Abstract

Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary optimization techniques. The first version is formulated in terms of polarization currents (or equivalent currents) inside the scatterer and generalizes previous results given for a lossless medium. The corresponding bound is referred to here as a variational bound and is valid for an arbitrary geometry with a given material property. The second version is formulated in terms of the T-matrix parameters of an arbitrary linear scatterer circumscribed by a spherical volume and gives a new fundamental upper bound on the total absorption of an inclusion with an arbitrary material property (including general bianisotropic materials). The two bounds are fundamentally different as they are based on different assumptions regarding the structure and the material property. Numerical examples including homogeneous and layered (core-shell) spheres are given to demonstrate that the two bounds provide complimentary information in a given scattering problem.