Special ECONAM session at Metamaterials'2009 Print E-mail

Progress of ECONAM project session and other relevant sessions

This special session was organized at the 3rd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, London, UK, Aug 30th-Sept 4th, 2009. Organized and chaired by Alex Schuchinsky (QUB) and Constantin Simovski (Aalto). The purpose of the session was to provide a review of the state-of-the-art in characterisation of artificial electromagnetic materials. The papers presented by the experts in the field have been focused on the definition and determination of the physical parameters suitable for the meaningful description of the metamaterial properties.

Here is the list of presented papers (click on the title to download papers):

Classical mixing rules for composites with spherical inclusions have been reviewed, and their applicability and limitations for different kinds of mixtures have been presented. It has been demonstrated that the plasmonic resonances are especially important in negative parameter composites. It has been shown that the classical mixing rules can be very useful for predicting the (quasistatic) effective permittivity of two-phase composites also when one constituent has negative permittivity, but the relative merits of different rules can be very different from the positive permittivity case. Moreover, the differences between regular lattices and different kinds of random mixtures are also important regardless of the sign of the permittivity.

The convergence of the procedure for retrieval of the optical parameters has been studied as the number of layers increases for the weakly and strongly coupled metamaterials. A detailed study of the weakly and strongly coupled fishnets has been presented to provide insight into the origin of negative n, as well the mechanism of low losses (that is, high figure of merit (FOM)) for the strongly coupled fishnets. The convergence of the retrieved parameters (ε, μ, and n) as the number of unit cells (layers) increases has been analysed. It has been found that for the weakly coupled structures, the convergence results for n and FOM are close to the single unit cell. As expected, for the strongly coupled structures, hybridization is observed and the retrieval results for n and FOM are completely different from the single unit cell. It has been demonstrated that the high value of FOM for the strongly coupled structure can be attributed to the periodicity effects.�

Challenges and opportunities for creating magnetically active metamaterials in the optical part of the spectrum have been discussed. The emphasis is on the sub-wavelength periodic metamaterials whose unit cell is much smaller than the optical wavelength. The conceptual differences between microwave and optical metamaterials are demonstrated. Miniaturization limits of metallic metamaterials have been discussed, and the role of plasmonic effects (electrostatic resonances) explained. The plasmonic effects have been quantified using a recently introduced plasmonic parameter. Several theoretical techniques for calculating the effective parameters of plasmonic metamaterials have been presented: the effective dielectric permittivity and magnetic permeability. Examples of negative permittivity and negative permeability plasmonic metamaterials have been used to illustrate the theory. A new application of complimentary metamaterials to developing ”perfect absorbers” of infrared and visible light supporting experimental results have been presented. Such metamaterials are characterized by a complex reflectivity that can be extracted from transmission/reflection coefficients and validated using semi-analytic theory.
The theoretical techniques for calculating the band structures and effective parameters of several negative index plasmonic structures have been applied to the analysis of a split-ring resonator and a SPOF structure. A novel absorber based on complimentary plasmonic metamaterials has been analyzed in terms of its effective parameters.

In this presentation the previously developed homogenization model of metamaterials formed by resonant electric and magnetic dipoles has been extended to the study of Drude transition layers. It has been shown that the material parameters of Drude transition layers satisfy the basic physical requirement of locality. The locality means that these parameters should not depend on the incidence angle and must be helpful to formulate the boundary value problem for a metamaterial slab. However, they cannot be described in terms of bulk material parameters such as permittivity and permeability, and only the description in terms of the refraction index and wave impedance is possible. The examples have shown that the parameters of Drude transition layers for some metamaterial slabs satisfy to the locality requirements, albeit they are not bulk material parameters since the locality was shown only for the refraction index and wave impedance of Drude layers. Moreover, these parameters are mesoscopic. Nevertheless, the obtained set of four local material parameters (two bulk parameters of the effective medium inside the metamaterial slab and two parameters of Drude layers) are useful for solving the boundary value problems of the metamaterial slab at the wave oblique incidence and for wave beams.

The problem of the boundary conditions for metamaterial interface has been studied. Since metamaterials are, in general, inhomogeneous media, this problem is connected with the homogenisation theory. It is shown that any homogenisation theory of infinitely extended media is, strictly speaking, inadequate for solutions of scattering problems. The reason is that it is possible to homogenize the refraction index but not the impedance, which behaves as a mesoscopic quantity. For metamaterials with electrically non-negligible cell sizes and small numbers of cells in a sample, this leads to serious disagreements between experiments and numerical simulations. Different approaches to fix the problem have been suggested: introduction of a transition layer or account of the dependence of the permittivity operator kernel on the surrounding medium. It has been shown that the mesoscopic nature of the homogenized impedance results in failure of the commonly accepted Maxwell boundary conditions. To fix the problem, it has been suggested to introduce a transition layer whose properties differ from the bulk homogenized properties of the medium. Since there is no unique algorithm to address this problem, several different approaches have been discussed.

Also we do recommend the materials of the following relevant sessions at is event:


Special session 8A: Homogenization and Bulk Metamaterials

Special session 1: Theoretical modeling of Metasurfaces