We present theoretical and numerical studies of near- and far-field scattering properties of planar and cylindrical uniaxially anisotropic metamaterials having hyperbolic dispersion relations. The imaging properties of single-layer and bilayer lenses consisting, respectively, of one and two anisotropic layers are studied with a view to fabrication. In order to facilitate understanding of the influence of material parameters on near-field imaging properties, a Green's function analysis for a uniaxially anisotropic slab is derived. We introduce a multiplexer that can be demonstrated by illuminating a slab composed of a metal-insulator multi-layer stack through a small aperture, and use this example to evaluate the performance of the analytic model. The theory for inductive and capacitive elements realized from anisotropic slabs is furthermore developed. These elements are shown to have low sensitivity to angle of incidence and non-dispersive performance. Low-pass filtering and anti-reflection examples are given. We present an optical leaky waveguide, which can support both forward and backward leaky waves. The radiation behavior is analyzed with a transverse resonance approach, and supported by finite element simulation results. The backward leaky nature can be exploited to develop a sub-diffraction limit imaging system. Finally, we extend our focus to the field behavior inside cylindrically anisotropic materials, and derive a Green's function and resulting formation for resonance cones, which provides a basis for two optical devices, an optical multiplexer based on the dispersive properties of a metal-insulator stack, and a far-field bilayer subwavelength imaging system.
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