The interaction between a metamaterial cylindrical structure and an incident plane wave is investigated. The structure is comprised of two cylinders, one embedded into the other, whose effective characteristics vary with the operating frequency following similar laws. Such a model can be used to describe periodic structures, constituting metamaterials, with slightly different features. The well-known eigenfunction expansions are adopted, while the boundary conditions are manipulated with help of the translation theorem for cylindrical coordinates. A first-order perturbation solution is obtained leading to simple and computationally efficient formulas. The fluctuations of near-field and far-field responses with respect to the position of the internal cylinder, the permittivities and the frequency are observed and discussed.
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