Metamaterials Analysis, Modeling, and Design in the Point Dipole Approximation
This dissertation is focused on applying the discrete dipole approximation to modeling metamaterial structures and devices. In particular, it is focused on modeling the linear and nonlinear behavior of one particular kind of metasurface, called a film-coupled metasurface. Film-coupled metasurfaces are periodic structures of metamaterial elements where the elements are placed a deeply subwavelength distance away from a metal film. The optical nanopatch antenna is an example of a particularly interesting film-coupled metasurface, and it is explored in depth in this dissertation. Starting with fundamental coupled mode theory approaches, fully predictive, analytic formula are developed that solve for the polarizabilities of the elements, which in turn are used to compute the reflective properties of the metasurface, including the effects of spatial dispersion using the language of effective medium theory. The theory is able to explain Wood's anomalies of the structure from an effective medium standpoint, again using purely analytic results that show excellent agreement with experiments and full-wave simulations. fThe linear optical theory is extended in later chapters to applications in nonlinear optics including bistability and lasing in four-level systems. The final chapter is devoted to solving for surface modes of the structure with complex eigenfrequencies, which may be useful in future work for explaining recent experiments that show lasing in modes that are spatially coherent across the surface.
Modeling other metamaterial devices using the discrete dipole approximation, including radio frequency metamaterial antennas, is discussed in the appendices.
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