Perfect imaging with geodesic waveguides

Transformation optics is used to prove that a spherical waveguide filled with an isotropic material with radial refractive index n=1/r has radial polarized modes (i.e. the electric field has only radial component) with the same perfect focusing properties as the Maxwell Fish-Eye lens. The approximate version of that device using a thin waveguide with a homogenous core paves the way to experimentally prove perfect imaging in the Maxwell Fish Eye lens.