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The scattering parameter extraction method of metamaterial homogenization is reviewed to show that the only ambiguity is the one related to the choice of the branch of the complex logarithmic function (or the complex inverse cosine function), whereas it has no ambiguity for the sign of the wave number and intrinsic impedance. While the method indeed yields two signs of the intrinsic impedance, and thus the wave number, the signs are dependent, and moreover, both sign combinations lead to the same permittivity and permeability, and are thus permissible. This observation is in distinct contrast to a number of statements in the literature where the correct sign of the intrinsic impedance and wave number, resulting from the scattering parameter method, is chosen by imposing additional physical requirements such as passivity. The scattering parameter method is reviewed through an investigation of a uniform plane wave normally incident on a planar slab in free-space, and the severity of the branch ambiguity is illustrated through simulations of a known metamaterial realization. Several approaches for proper branch selection are reviewed and their suitability to metamaterial samples is discussed.

[1] An antenna configuration consisting of an arbitrarily located electric line source radiating in the presence of a pair of concentric metamaterial cylinders is investigated analytically and numerically. The near-and far-field properties of these structures are analyzed through an investigation of such parameters as the total radiated power, directivity, and total as well as differential scattering cross sections. The results obtained for these metamaterial structures are compared to those for the corresponding structures made of conventional materials. It is shown that electrically small concentric metamaterial structures can be designed to be resonant and to possess advantageous radiation and scattering characteristics in contrast to the corresponding structures made of conventional materials. More specifically, it is shown that metamaterial structures lead to significant enhancements of the total radiated power as well as the total and differential scattering cross sections. Moreover, the feasibility of controlling the directivity pattern of the electrically small metamaterial structures through appropriate locations of the electric line source is demonstrated. The effects of the dispersion and loss present in the metamaterials are taken into account to study the bandwidth properties of these resonant configurations.Citation: Arslanagic, S., R. W. Ziolkowski, and O. Breinbjerg (2007), Analytical and numerical investigation of the radiation and scattering from concentric metamaterial cylinders excited by an electric line source, Radio Sci., 42, RS6S15,

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