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

Abstract

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.

Applicability of effective medium description to photonic crystals in higher bands: Theory and numerical analysis

“…We can introduce the notations ∆ = P − P and Π = βq 4 . This is what we can expect to happen in triangular lattices with C 6 symmetry.…”

“…As a result, the function ∆(q) and the summation result {g} F [{g}]∆(q) are not circularly-symmetric. We can write the result for σ (c) 4 in a form similar to that used in lower orders if we account for the identity q The terms of the form (9) appear only in the sixth order of the perturbation theory. The corresponding coefficients are very complicated and we do not compute them here.…”

“…The theory of homogenization of periodic electromagnetic media continues to attract significant attention [1][2][3][4][5] due to the proposed important applications such as subwavelength optical imaging 6 . However, some fundamental questions remain open in this field of research.…”

Enhancement and interplay of first- and second-order spatial dispersion in metamaterials with moderate-permittivity inclusions

“…Following the approach reported in Ref. [10], we obtain the effective constitutive relationships for TM waves propagating in a multilayered metamaterial, viz.,…”

“…The reader is referred to [4][5][6][7][8] for a representative sampling of nonlocal homogenization approaches available in the topical literature. It is worth stressing that two cornerstones in metamaterial science, namely, artificial electromagnetic chirality and optical magnetism, are manifestations of firstand second-order spatial dispersion, respectively [9,10]. Artificial electromagnetic chirality (due to 3-D, 2-D and 1-D geometrical chirality [11]) yields interesting phenomena, such as giant optical activity, asymmetric transmission, and negative refractive index [12].…”