Optical theorems and physical bounds on absorption in lossy media

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 (coreshell) spheres are given to demonstrate that the two bounds provide complimentary information in a given scattering problem.

Poles, physical bounds, and optimal materials predicted with approximated Mie coefficients

“…The resonant interaction between an electromagnetic wave and a scatterer is limited by physical bounds [29,[51][52][53]. Physical bounds can be described by the maximum of the electromagnetic radiation that can be absorbed by a scatterer in a homogeneous or complex environment [28,44,[54][55][56][57][58][59].…”

“…Physical bounds can also be described by the maximum of electromagnetic scattering. In the framework of the multipolar theory, this limit corresponds to the maximum of electromagnetic scattering in a single channel corresponding to a given multipolar order [29,[51][52][53]60], i.e. when the norm of this multipolar order is equal to 1, |a n | = 1 and |b n | = 1.…”

The Bianisotropic Formulation of the Plane Wave Method from Faraday’s and Ampere’s Laws

“…The notation is such that a subscript of D relates tensor parameters for the electric flux density vector, and the subscript B relates tensor parameters for the magnetic flux density vector. A 1/c has been pulled out of the magnetoelectric tensors as is common practice when dealing with bianisotropy [16] [17]. For a computation environment that is charge and current free, time dependence of the fields taken as e j t ω − and the constitutive relations in (1)-(2) are used, Faraday's and Ampere's laws can be expressed as:…”

“…The order of the matrix system is half that of matrix expression (13). The remaining terms in (16), not associated with [ ]…”

On the optical theorem and optimal extinction, scattering and absorption in lossy media

“…Perhaps counter-intuitive, the presence of external losses in the surrounding medium implies major difficulties in the formulation of an optical theorem for a general scattering object, and a reasonably simple analytical solution is typically available only for spheres [1], [2], [3], [4], see also [5], [6], [7]. Analytical solutions based on the spherical vector wave expansion (Mie theory) [3] have recently been used to formulate an optical theorem and to derive explicit formulas for the optimal multipole absorption, scattering and extinction of a spherical object embedded in a lossy medium [5], [6].…”