Desing and model of piezoelectromagnetic metamaterials
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"This dissertation introduces a novel theory of piezoelectromagnetic crystal homogenization which provides the basis to characterize media with nonlocal piezoelectric and piezomagnetic properties, normally described by material tensors. The introduced formalism extends the conventional homogenization theory which can not predict the dispersion of certain resonant structures of the electromagnetoelastic medium beyond the long wavelength limit. Specifically, the existence of the negative refraction index for photonic crystals and negative dynamic mass density and bulk modulus for phononic crystals can not be predicted by classical formalisms. The new theory is able to describe accurately the physical parameters of the homogenized electromagnetoelastic medium, even for wavelengths comparable with the characteristic period of the crystal lattice. The results of the novel theory application to the photonic and phononic crystals show a very good correspondence with those of other homogenization theories with the assumption of weak piezoelectric and piezomagnetic efects. Furthermore, a metamaterial transformation of the nonlocal response of the homogenized piezoelectromagnetic medium is proposed. The developed theory of the metamaterial response was applied to well-known metamaterials (2D system of metallic wires, split-ring resonators) and for introducing a new symmetric window resonators metamaterials with enhanced properties. The experimental study of the window resonators proved the correctness of the new formalism predictions. An important advantage of the proposed homogenization theory is that it allows to calculate reflectivity and transmission coefficients for finite-size samples in the nonlocal regime."
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