Sub-diffraction light propagation and imaging in planar negative refraction waveguides

In this dissertation we study the electromagnetic properties of planar waveguides with non-magnetic strongly anisotropic dielectric cores. We develop an analytical description of the mode propagation in these systems and show that the index of refraction can be either positive or negative depending on the specific material parameters. Propagating modes are supported even when the waveguide size is much smaller than the wavelength allowing light propagation and beam steering in micro- and nano-scale areas. We further demonstrate that it is possible to combine same-sized planar waveguide structures to build a planar lens. We determine the far-field resolution limit of such a lens and show that it is feasible to achieve resolution better than the free-space diffraction limit. For example, with incident light at the optical wavelength, lambda = 1.5mum, we obtain an image with resolution Delta ≈ 0.3mum.;We further study the coupling to and from sub-wavelength planar waveguides of different sizes and compare the transmission through a negative-index structure to the behavior of positive index waveguides. We use numerical simulations to model electromagnetic wave propagation in arbitrary waveguide configurations. Included is a derivation of analyical expressions for the transmission and reflection coefficients along with a comparison of these expressions to our numerical results. The extension of the planar lens is explored with three-dimensional imaging in chosen waveguide configurations with a focus on designing and optimizing planar-waveguide based beam-steering photonic devices. These results bring forth applications including sub-diffraction planar lens imaging, photonic funnels, high-performance optical sensing, and all-optical computing.