Abstract

Homogenization of layered media beyond the asymptotic (long-wavelength) limit remains a challenge (see e.g. [1, 2] ad references therein). In [3–5], we developed local and nonlocal homogenization procedures valid for any reasonable size and composition of a periodic lattice cell. On the fine scale, fields are approximated via a basis set of Bloch waves propagating in different directions, while the coarse-scale basis consists of the corresponding generalized plane waves. To satisfy Maxwell’s boundary conditions as accurately as possible, the amplitudes of the plane waves are calculated as surface averages of the Bloch waves, whereupon the dispersion relations are approximated by solving a least-squares problem [3, 5]. In general, the effective tensor contains, in addition to the permittivity and permeability entries, magnetoelectric coupling terms.

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