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This dissertation encompasses homogenization methods, with a special interest into their applications to metamaterial homogenization. The first method studied is the Floquet-Bloch method, that is based on the assumption of a material being infinite periodic. Its field can then be expanded in terms of spatial harmonics, which are used for homogenization, along with the dispersion equation, also a property of infinite periodic structures. The spatial harmonic relative weights are subsequently used to asses the dominance of the individual harmonics. This has been done for a 1D magnetodielectric Bragg stack.The second method is analogous to the Floquet-Bloch method, with that difference, that it treats finite structures. A finite structure cannot strictly be expanded in spatial harmonics, but the field can be Fourier transformed, and expanded with a set of sinc basis functions, constituting a set of pseudo spatial harmonics. From expressions of the exact field in the 1D Bragg stack, the Fourier transform is computed, and a numerical inversion is performed to determine the relative weight of the sinc bassis functions.The third method, the so-called Nicolson-Ross-Weir (NRW) method, is based on scattering parameters, and is not only treating 1D configurations. It has been implemented to work with CST, a computational software suite that is able to simulate almost any structure, making the combination a versatile tool. It is investigated, how this method can homogenize with different harmonics, much like the Floquet-Bloch based methods.The fourth method studied, is a method developed specially for metamaterial homogenization, the general retrieval method (GRM). It considers bianisotropic materials, and retrieves the electric and magnetic polarizabilities in addition to the permittivity, permeability and the bianisotropic parameter.Lastly the methods are compared by homogenizing a triangular prism made of a magneto-dielectric Bragg stack, and a rectangular lens made of magneto-dielectric spheres. A wave refracted through either will reveal, by the pattern of the refracted wave, what effective material parameter should be assigned. The Floquet-Bloch method is used for the triangular prism, to decide which harmonic is most suitable. The general retrieval method (GRM) is compared to the Nicolson-Ross-Weir (NRW) method for the rectangular lens, also to investigate which harmonic to use for the latter method.
|Place of Publication
|Technical University of Denmark
|Number of pages
|Published - 2014
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- 1 Finished
01/06/2011 → 18/03/2015