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Abstract: We show that any pair of real symmetric tensors $\BGve$ and $\BGm$ can berealized as the effective electric permittivity and effective magneticpermeability of a metamaterial at a given fixed frequency. The constructionstarts with two extremely low loss metamaterials, with arbitrarily smallmicrostructure, whose existence is ensured by the work of Bouchitt{\-e} andBourel and Bouchitt\-e and Schweizer, one having at the given frequency apermittivity tensor with exactly one negative eigenvalue, and a positivepermeability tensor, and the other having a positive permittivity tensor, and apermeability tensor having exactly one negative eigenvalue. To achieve thedesired effective properties these materials are laminated together in ahierarchical multiple rank laminate structure, with widely separated lengthscales, and varying directions of lamination, but with the largest length scalestill much shorter than the wavelengths and attenuation lengths in themacroscopic effective medium.



Author: Graeme W. Milton

Source: https://arxiv.org/







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