Spherical perfect lens: Solutions of Maxwell’s equations for spherical geometry

It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the subwavelength 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 $\varepsilon \mathrm{}\left(r\right)\mathrm{}\sim 1/r$ and $\mu \mathrm{}\left(r\right)\mathrm{}\sim 1/r.$ We concentrate on lenslike solutions for the extreme near-field limit. Then the conditions for the TM and TE polarized modes become independent of $\mu$ and $\varepsilon ,$ respectively.