Abstract
Here, we present an overview of a first principles homogenization theory of periodic metamaterials. It is shown that in a rather general context it is possible to formally introduce effective parameters that describe the time evolution of macroscopic (slowly-varying in space) initial states of the electromagnetic field using an effective medium formalism. The theory is applied to different types of characterized by a strong spatial dispersion in the long wavelength limit. It is highlighted that the spatial dispersion may tailor in unique ways the wave phenomena in wire metamaterials leading to exotic tunneling effects and broadband lossless anomalous dispersion.
Highlights
The interactions between waves and matter play a fundamental role in most physical processes
To illustrate some of the unusual opportunities created by the spatial dispersion in wire metamaterials, we review in the subsections the effects of anomalous light refraction and anomalous light tunneling
We presented an overview of a first principles homogenization approach based on an effective Hamiltonian that describes exactly the time evolution of the wave packet envelope when the initial state is less localized than the lattice period
Summary
The interactions between waves and matter play a fundamental role in most physical processes. Effective medium theories are successful when the wavelength is large with respect to the characteristic spatial period of the composite material. In this case, the material may be regarded as a continuum, and the homogenization formalism gives a simplified and insightful picture of the wave propagation. This contrasts with natural media where the ratio, λ/a, is several orders of magnitude larger than that value, even at optical frequencies This property imposes restrictions on the application of classical homogenization theories to artificial materials [5, 7, 18, 19] due to the emergence of spatial dispersion.
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