Abstract
We investigate a two-dimensional metamaterial template constructed from different pixels through a conservation law of effective indices: If the product of refractive indices along the principal axes is invariant for different anisotropic materials in a two-dimensional space, the product of indices of the effective medium remains constant after mixing these materials. Such effective media of constant indices product can be implemented using metamaterial structures. The orientation of the metamaterial structure in a single pixel controls the direction of the principal axis of the effective medium. Different pixels are assembled into an array to obtain reconfigurable anisotropy of the effective medium. These considerations would be useful for constructing reconfigurable metamaterials and transformation media with area-preserving maps.
Highlights
Homogenization of composite materials is an important topic in optics for understanding wave propagation and is currently with a renewed interest due to the developments of metamaterials [1]
By establishing an index conservation law in mixing anisotropic effective media of constant indices product, we can design reconfigurable effective media with microstructures composed of isotropic dielectrics and anisotropic metal bars
The results presented in this paper hold for fixed frequency homogenization wherein the wavelength is much larger than the size of the periodic cell
Summary
Homogenization of composite materials is an important topic in optics for understanding wave propagation and is currently with a renewed interest due to the developments of metamaterials [1]. We first point out a mixing law for anisotropic effective medium theory in which the product of principal indices of an effective medium remains constant throughout the homogenization process with specific conditions. In this law, the constant property of mixture is independent of the filling ratio and is independent of the shape of material inclusions (established through two-scale convergence), which is guaranteed in the long wavelength limit.
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