Homogenizing metamaterials by the plane wave expansion method
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Increasingly complex metamaterial structures has revitalized the interest in homogenization and effective medium theories, with the intention of finding better ways to model and understand their electromagnetic complexity. This thesis describes an implementation of the plane wave expansion method in MATLAB, employed for simulating the electric field inside one- and two-dimensional periodic metamaterial unit cells. The electric field is excited by an unlocalized plane wave source, and is used to determine the significance of higher order multipoles of the averaged microscopic polarization density through a scheme that employs two different source polarizations. The simulated electric fields in three different unit cells are discussed, and the significance of the simulated higher order terms is interpreted in context of this discussion. The simulations that have been performed in this thesis is used to argue that higher order terms are significant, and have been used in an article that was submitted to Phys. Rev. B in January 2017. The effective permeabilities obtained from two different homogenization formalisms are simulated for two unit cells and used to support the previous results suggesting that higher order terms are significant.