A non-asymptotic homogenization theory for periodic electromagnetic structures

Abstract

Homogenization of electromagnetic periodic composites is treated as a two-scale problem and solved by approximating the fields on both scales with eigenmodes that satisfy Maxwell's equations and boundary conditions as accurately as possible. Built into this homogenization methodology is an error indicator whose value characterizes the accuracy of homogenization. The proposed theory allows one to define not only bulk, but also position-dependent material parameters (e.g. in proximity to a physical boundary) and to quantify the trade-off between the accuracy of homogenization and its range of applicability to various illumination conditions.

Trefftz approximations in complex media: Accuracy and applications

“…where Euclidean vector norms and the Frobenius matrix norm are implied. In (40), ψ ref tot should ideally be the exact solution, which is not available; hence an overkill RCWA solution with N ref G = 1000 is used in its stead. Since FLAME-slab contains a few adjustable parameters, we study the dependence of the consistency error on these parameters separately.…”

“…which satisfy Maxwell's equations in a homogeneous but possibly anisotropic medium; subscript '0' indicates the field amplitudes to be determined. Further technical details of the procedure can be found in [40,39]. The final result is as follows.…”

“…Example A of a layered medium from[41,40]. The real part of R (left) and T (right) vs. the sine of the angle of incidence; non-asymptotic and nonlocal homogenization.…”

Classical and non-classical effective medium theories: New perspectives

“…The paper has three main parts. The first one is a condensed review of the homogenization framework of [8]. The second part extends the non-asymptotic framework to a nonlocal one.…”

“…A given periodic structure is to be replaced with a homogeneous sample of the same geometric shape and size, with some material tensor M to be defined, in such a way that reflection and transmission of waves (or, equivalently, the far-field pattern) remain, to the extent possible, unchanged. This informal description is made more precise in [8].…”