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, λ = 1.5µm, we obtain an image with resolution
∆ ≈ 0.3µm.
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 expresssions 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, highperformance
optical sensing, and all-optical computing
