Effective parameters of metamaterials: a rigorous homogenization theory via Whitney interpolation

Tsukerman, Igor

doi:10.1364/josab.28.000577

Cited by 41 publications

(84 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The general solution to (3.16) for a non-diagonal tensor can be expressed in terms of two 6 × n matrices, Ψ m,DB and Ψ m,EH , whose columns α are equal to k Here '+' denotes the Moore-Penrose pseudoinverse. This is very similar to the expressions in our earlier publications [17][18][19], where the Ψ matrices had an analogous meaning but were not the same as here. In practice, the minimization problem (3.22) is expected to be overdetermined (i.e.…”

Section: (B) Approximation Of Coarse-level Fieldssupporting

confidence: 88%

See 1 more Smart Citation

A non-asymptotic homogenization theory for periodic electromagnetic structures

Tsukerman

Markel

2014

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: (B) Approximation Of Coarse-level Fieldssupporting

confidence: 88%

“…where the term δ represents the approximation error referred to as the 'out-of-the-basis error' in [17][18][19] and c mα are expansion coefficients. We expect that the basis contains enough functions so that δ is small.…”

Section: Non-asymptotic (Trefftz) Homogenizationmentioning

confidence: 99%

A non-asymptotic homogenization theory for periodic electromagnetic structures

Tsukerman

Markel

2014

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

show abstract

“….. Equations (6) together with Eqs. (11) and (12) can be used to evaluate the rapidly varying fields of order n + 1 once those of order n are known and these fields are linearly dependent on the slowlyvarying fields. Therefore, the discussed homogenization technique allows to obtain an effective medium description of the metamaterial respose up to the desired order in η.…”

Section: A Electromagnetic Field Multiscale Analysismentioning

confidence: 99%

Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality

Ciattoni¹,

Rizza

2015

Phys. Rev. B

127

View full text Add to dashboard Cite

We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order. Specifically, by resorting to a suitable multiscale technique, we show that medium effective permittivity tensor and the first and second order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly-varying fields each satysifing electrostatic-like equations within the metamaterial unit cell. For metamaterials with negligible second-order spatial dispersion, we exploit the equivalence of first-order spatial dispersion and reciprocal bianisotropic electromagnetic response to deduce a simple expression for the metamaterial chirality tensor. Such an expression allows us to systematically analyze the effect of the composite spatial symmetry properties on electromagnetic chirality. We find that even if a metamaterial is geometrically achiral, i.e. it is indistinguishable from its mirror image, it shows pseudo-chiral-omega electromagnetic chirality if the rotation needed to restore the dielectric profile after the reflection is either a 0• or 90• rotation around an axis orthogonal to the reflection plane. These two symmetric situations encompass two-dimensional and one-dimensional metamaterials with chiral response. As an example admitting full analytical description, we discuss one-dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures.

show abstract

“…A rigorous homogenization theory via the Whitney interpolation developed in Ref. [29] allows us to reproduce the well-known Maxwell Garnett formula and introduce artificial magnetism.…”

Section: Introductionmentioning

confidence: 99%