Generalized homogenization theory and inverse design of periodic electromagnetic metamaterials

Liu, Xing-Xiang
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Artificial metamaterials composed of specifically designed subwavelength unit cells can support an exotic material response and present a promising future for various microwave, terahertz and optical applications. Metamaterials essentially provide the concept to microscopically manipulate light through their subwavelength inclusions, and the overall structure can be macroscopically treated as homogeneous bulk material characterized by a simple set of constitutive parameters, such as permittivity and permeability. In this dissertation, we present a complete homogenization theory applicable to one-, two- and three-dimensional metamaterials composed of nonconnected subwavelength elements. The homogenization theory provides not only deep insights to electromagnetic wave propagation among metamaterials, but also allows developing a useful and efficient analysis method for engineering metamaterials. We begin the work by proposing a general retrieval procedure to characterize arbitrary subwavelength elements in terms of a polarizability tensor. Based on this system, we may start the macroscopic analysis of metamaterials by analyzing the scattering properties of their microscopic building blocks. For one-dimensional linear arrays, we present the dispersion relations for single and parallel linear chains and study their potential use as sub-diffractive waveguides and leaky-wave antennas. For two-dimensional arrays, we interpret the metasurfaces as homogeneous surfaces and characterize their properties by a complete six-by-six tensorial effective surface susceptibility. This model also offers the possibility to derive analytical transmission and reflection coefficients for metasurfaces composed of arbitrary nonconnected inclusions with TE and TM mutual coupling. For three-dimensional metamaterials, we present a generalized theory to homogenize arrays by effective tensorial permittivity, permeability and magneto-electric coupling coefficients. This model captures comprehensive anisotropic and bianisotropic properties of metamaterials. Based on this theory, we also modify the conventional retrieval method to extract physically meaningful effective parameters of given metamaterials and fundamentally explain the common non-causality issues associated with parameter retrieval. Finally, we conceptually propose an inverse design procedure for three-dimensional metamaterials that can efficiently determine the geometry of the inclusions required to achieve the anomalous properties, such as double-negative response, in the desired frequency regime.