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 radially polarized modes (i.e. the electric field is only radial) with the same perfect focusing properties as the Maxwell fish-eye (MFE) lens. An approximate version of that device, comprising a thin waveguide with a homogeneous core, paves the way to experimentally attaining perfect imaging in the MFE lens.