Sub-diffraction light propagation in fibres with anisotropic dielectric cores

We present a detailed study of light propagation in waveguides with anisotropic metamaterial cores. We demonstrate that in contrast to conventional optical fibres, our structures support free-space-like propagating modes even when the waveguide radius is much smaller than the wavelength. We develop analytical formalism to describe mode structure and propagation in strongly anisotropic systems and study the effects related to waveguide boundaries and material composition.