No abstract

A method is described for the determination of the effective electromagnetic parameters of a metamaterial based only on external measurements or simulations, taking boundary effects at the interfaces between a conventional material and metamaterial into account. Plane-wave reflection and transmission coefficients at the interfaces are regarded as additional unknowns to be determined, rather than explicitly dependent on the material parameters. Our technique is thus analogous to the line-reflect-line (LRL) calibration method in microwave measurements. The refractive index can be determined from S-parameters for two samples of different thickness. The effective wave impedance requires the additional assumption that generalized sheet transition conditions (GSTCs) account for the boundary effects. Expressions for the bulk permittivity and permeability then follow easily. Our method is validated by comparison with the results using the Nicolson-Ross-Weir (NRW) for determining properties of an ordinary material measured in a coaxial line. Utilizing S-parameters obtained from 3-D full wave simulations, we test the method on magnetodielectric metamaterials. We compare the results from our method and the conventional one that does not consider boundary effects. Moreover, it is shown that results from our method are consistent under changes in reference plane location, whereas the results from other methods are not.

Abstract-A low-loss passive metamaterial exhibiting negative refractive index or "double negative" electromagnetic properties at microwave frequencies is proposed. The metamaterial is a lattice of spherical particles made up of multiple dielectric materials in concentric layers. Because no magnetic constituents (that tend to have higher losses) are involved, the negative-index behavior is possible with very low values of attenuation. A negative-index metamaterial based on dielectric-coated metal spheres is also proposed, and is predicted to have lower attenuation than other structures based on metallic scatterers. Numerical results and design principles are given.

Abstract-In this paper we investigate boundary effects and other consequences of spatial dispersion by analyzing in detail the response of a metamaterial half-space to a monochromatic plane wave normally incident from free-space. The metamaterial is composed of an orthorhombic lattice of identical particles, each of which exhibits both an electric and magnetic response. Rather than relying on the conventional boundary conditions and the Clausius-Mossotti equations, we use instead the point-dipole interaction model and an expansion of polarization in eigenmodes to determine the structure's dispersion relation and electromagnetic response. Using the nearestneighbor approximation, we show how truncating the crystal lattice excites an "ordinary" mode and two "extraordinary" modes that are necessary to satisfy the boundary conditions at the interface. For most cases, the extraordinary modes are evanescent, and thus form a thin transition layer at the surface. However, under certain conditions, typically near particle resonances, either one or both of these modes can be propagating.

Abstract-In this paper, we present the extraction for effective material parameters for a metamaterial from TE or TM waveguide measurements with generalized sheet transition conditions (GSTCs) used to provide electric and magnetic surface susceptibilities that approximate boundary effects between the metamaterial and air. The retrieval algorithm determines the effective material properties via scattering data obtained from the metamaterial in a waveguide. The effective refractive index is expressed as a function of S-parameters for two samples of different length. The effective wave impedance is given in terms of S-parameters and the refractive index, assuming that GSTCs account for the boundary effects. The effective permittivity and permeability can then be determined through the refractive index and wave impedance. By use of S-parameters generated by commercial three-dimensional (3-D) full-wave simulation software our present equations are tested for two cases of metamaterials: magneto-dielectric (ε r = µ r ) and dielectric (TiO 2 ) particles. We also conduct S-parameter measurements on dielectric cubes with an S-band (WR-284) waveguide to compute the effective material properties. Furthermore, our results are compared to those derived from another retrieval method used in the literature, which does not account for boundary effects.