A spherical perfect lens

It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the sub-wavelength image information contained in the evanescent modes of a source. Here we elaborate on perfect lens solutions to spherical shells of negative refractive material where magnification of the near-field images becomes possible. The negative refractive materials then need to be spatially dispersive with $\epsilon® \sim 1/r$and$\mu®\sim 1/r$. We concentrate on lens-like solutions for the extreme near-field limit. Then the conditions for the TM and TE polarized modes become independent of $\mu$ and $ϵ$ respectively.