Imaging Properties of Finite Maxwell Fish Eye Medium

The imaging properties of the Maxwell medium filling a spherical finite-radius domain have been analyzed. An analytical expression has been obtained for the field of the radial electric dipole inside the sphere. It is shown that the finite Maxwell medium of arbitrarily large size cannot overcome classical Abbe's diffraction limit in optical systems. Perfect imaging in the infinite Maxwell medium is the consequence of its electrodynamic closure, i.e., the absence of waves outgoing to infinity.