We use meta-materials with extreme anisotropy to solve the fundamental problem of light transport in deep sub-wavelength 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 electro-magnetic modes, free from geometrical dispersion, propagate with a velocity controlled by the transverse permittivity and permeability,

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... have zero cutoff frequency. We analyze physically realizable cases for a circular aperture and show a meta-material design using existing materials.