Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy. 
We use metamaterials with extreme anisotropy to solve the fundamental problem of light transport in deep subwavelength apertures.  By filling a simply connected aperture with an anisotropic medium, we decouple the cutoff frequency and the group velocity of modes inside apertures.  In the limit of extreme anisotropy, all modes become purely transverse electromagnetic modes, free from geometrical dispersion, propagate with a velocity controlled by the transverse permittivity and permeability, and have zero cutoff frequency.  We analyze physically realizable cases for a circular aperture and show a metamaterial design using existing materials.