Toward a constructive homogenization theory of composite metamaterials
- PDF / 225,750 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 4 Downloads / 197 Views
0919-J03-02
Toward a constructive homogenization theory of composite metamaterials Alexandru I Cabuz, and Didier Felbacq Groupe d'Etude des Semiconducteurs , Université Montpellier II, Montpellier, 34095, France ABSTRACT In the homogenization of composite metamaterials the role played by the relative positions of the wires and resonators is not well understood, though essential. We present an effective medium approach which can systematically account for these effects. It involves independently homogenizing rows of wires and planes of resonators as slabs with negative permittivity and permeability respectively. The metamaterial is then treated as a 1D single negative anisotropic stack. Using this approach we show that it is in principle possible to satisfy the requirements of Pendry’s superlens, µ = ε = −1 , up to losses. We propose a class of structure geometries which seems promising for achieving this holy grail of metamaterial science. INTRODUCTION Ever since Pendry’s revival of Veselago’s left handed material lens [1, 2], extensive research efforts have focused on the possibility of constructing media with simultaneously negative permittivity and negative permeability. More particularly, Pendry’s requirement for his super-lens was that the values of these two parameters satisfy µ = ε = −1 . Various building blocks have been proposed in order to obtain the required negative constitutive parameters. Thin wire media have held almost complete monopoly on the negative permittivity half of the problem [3], at least until the very recent proposal of electric resonating elements by the Duke University group [4]. The former can be described accurately by a diagonal dielectric tensor, be it spatially dispersive [5, 6]. The latter is not yet as well understood at this time though, and we set it aside for now. As for the negative permeability, there have been two main proposals, both due to Pendry’s group: metallic ring resonators [7] and high dielectric fibers [8]. Both of them implement negative permeability along only one direction. However, the resonators seem to have been preferred by most workers, perhaps due to their ease of fabrication, in contrast to the difficulty of finding dielectrics with the required high dielectric constants, though this difficulty has been addressed in recent years [9, 10]. The 1D stack approach then involves arranging the wires and resonators in layers. One can distinguish three steps to the homogenization of the composite. First the rows of wires are replaced by negative permittivity slabs. Second, the planes of resonators are replaced by negative permeability slabs. Finally the resulting single negative anisotropic stack is homogenized to obtain the effective medium of the composite metamaterial. In what follows we discuss the first and the third steps.
1D EFFECTIVE MEDIUM THEORY
Figure 1). The structure we study is a 1D medium, invariant in the xz plane. a). We differentiate four ~ ~ ~ ~ polarization types : Ex, Hx, Ey and Hy. b) The crystal period. ε 1 , ε 2 , µ 1 and µ 2 are 3x3 d
Data Loading...
