Analytical solution of the almost-perfect-lens problem

The problem of imaging for a slab of a lossless left-handed material with refractive index n=-(1-sigma)(1/2) is solved analytically for \sigma\much less than1. The electromagnetic field behavior is determined largely by singularities arising from the excitation of surface polaritons with wave vector q-->(+/-infinity). Depending on the sign of sigma, the near-field is either odd or even with respect to the lens middle plane. Consistent with other nonanalytical studies, the resolution depends logarithmically on \sigma\. With minor alterations, these results apply as well to the electrostatic limit. (C) 2004 American Institute of Physics.