Spatial dispersion in a wire mesh metamaterial D. Felbacq, a B. Guizal, a G. Bouchitt´ e, b and C. Bourel b a University of Montpellier 2 Groupe d’Etude des Semiconducteurs UMR-CNRS 5650 Bat. 21 CC074 34095 Montpellier Cedex 05, France; b Universite du Sud-Toulon-Var Laboratoire IMATH BP 20132 - 83957 La Garde Cedex, France ABSTRACT The homogeneous and transport properties of a set of metallic fibers was studied. The existence of a plasma frequency was shown and a precise formula was derived. A homogenized system for finite length ohmic wires was derived. Some numerical simulations were made to study the influence of disorder. Keywords: Metamaterials, Homogenization, Spatial Dispersion 1. INTRODUCTION Metamaterials are artificial objects made of microscopic elements whose effective properties are not found in nature. 1 For instance, it has been show that it was possible to design dielectric or metallic structures possess- ing an artificial magnetic activity. 2–9 In the long wavelength regime the heterogeneous material behaves as if homogeneous with an effective permeability, this comes under homogenization theory. 10–14 It was also shown that it was possible to design materials with a tailorable plasma frequency out of ohmic or infinitely conducting wires. 15–22 These structures prove to have very interesting application for imaging. 23–26 In the present paper, we study the effective behavior of a set of ohmic wires, such as that depicted in fig.1. Throughout the article, we consider time-harmonic fields (dependence in e -iωt ) in s-polarization (electric field linearly polarized along the direction of the wires). 2. PLASMA FEQUENCY IN A WIRE METAMATERIAL 2.1 Some numerical experiments We start with a simple numerical experiment. We consider a finite set of infinitely conducting wires disposed periodically with a square symmetry (a/d =1/100) as in fig. (1), and we plot the transmission through the structure for an incident gaussian beam. The spectrum is given in fig.(2). It can clearly be seen that above λ/d = 5, the transmitted field is strongly damped. In fact, it can be shown that the set of wires is equivalent to a homogeneous medium with a dispersive effective permittivity given by: ε eff =1 - λ 2 λ 2 p , (1) where λ p is the plasma wavelength. It is interesting to note that this effect is an emergent property, in the sense that each wire does not possess it. Rather, it is the interaction between the wires that produces it. Even more interestingly, it turns out that this effect is not due to periodicity. Indeed, in fig.(3) we plot the transmission spectrum for a set of wires where the position have been modified with a uniform disorder along the horizontal and vertical directions. We have used three different values for the disorder: 10%, 20% and 30%. It is clearly seen that the disorder only plays a marginal role in the global behavior of the set of wires: the curves are almost superimposed, whatever the disorder. Invited Paper Metamaterials IV, edited by Vladimir Kuzmiak, Peter Markoš, Tomasz Szoplik, Proc. of SPIE Vol. 7353, 735302 · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.820560 Proc. of SPIE Vol. 7353 735302-1