Strong spatial dispersion in wire media in the very large wavelength limit

Abstract

It is found that there exist composite media that exhibit strong spatial dispersion even in the very large wavelength limit. This follows from the study of lattices of ideally conducting parallel thin wires ͑wire media͒. In fact, our analysis reveals that the description of this medium by means of a local dispersive uniaxial dielectric tensor is not complete, leading to unphysical results for the propagation of electromagnetic waves at any frequencies. Since nonlocal constitutive relations have been usually considered in the past as a secondorder approximation, meaningful in the short-wavelength limit, the aforementioned result presents a relevant theoretical interest. In addition, since such wire media have been recently used as a constituent of some discrete artificial media ͑or metamaterials͒, the reported results open the question of the relevance of the spatial dispersion in the characterization of these artificial media. Causality imposes that all material media must be dispersive. In most cases this behavior results in local dispersive constitutive relations, i.e., in frequency-dependent constitutive permittivity and permeability tensors. Nonlocal dispersive behavior ͑i.e., spatial dispersion͒, which results in constitutive operators depending also on the spatial derivatives of the mean fields ͑or, for plane electromagnetic waves, on the wave-vector components͒, is usually considered as a small effect, meaningful in the short-wavelength limit. Specifically, spatial dispersion will always appear when the higher-order terms in the series expansion of the constitutive parameters in power series of the dimensionless parameter a/ (a is the lattice constant of the crystal and the wavelength inside the medium͒ are not neglected.

Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties

“…1(a) has been described for an incident electric field parallel to the wires as an artificial dielectric [18][19][20] with an isotropic effective plasma-like relative permittivity ε eff r = 1 − f 2 P /f 2 , where f is the signal frequency, f p is the plasma frequency which depends on the wire diameter and interspacing, see [21][22][23][24] (such medium is assumed to be lossless, which is a reasonable approximation at microwave frequencies). Spatial dispersion should be additionally taken into account when the waves travel at a slant angle to the wire axes [25,26]. For waves propagating normally to the wires, and in the absence of losses, a homogenized wire medium exhibits negative effective permittivity at f < f p (see Fig.…”

Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime

“…An excellent possibility to realize the canalization regime for p-polarization is provided by a wire medium, a material formed by a lattice of parallel conducting wires [30,31,32,33]. This material supports very special type of eigenmodes, so-called transmission line modes [33], which transfer energy strictly along wires with the speed of light and can have arbitrary transverse wave vector components.…”

“…This material supports very special type of eigenmodes, so-called transmission line modes [33], which transfer energy strictly along wires with the speed of light and can have arbitrary transverse wave vector components. It means that such modes correspond to completely flat isofrequency contour which is the main requirement for implementing the canalization regime.…”

“…This is a subwavelength optical telegraph which operates completely in the same principle as the slab of wire medium at microwaves. It is known that the wire medium [33] can be described by spatially dispersive permittivity tensor of the form…”

Triple wire medium for use in isotropic metamaterials

“…The wire mesh has a period a, and the wires have radius r w . It has been shown that a general wire medium (single, double or triple) suffers from a spatial dispersion [10], [11], nevertheless it can be considered as an isotropic negative permittivity medium near the plasma frequency [12]. A spatial dispersion can be defined as a nonlocal dispersive behavior of the material, i.e., the constitutive permittivity and permeability tensors depend not only on the frequency, but also on the spatial derivatives of the electric and magnetic field vectors or, for plane electromagnetic waves, on the wave-vector components determining the direction of propagation.…”