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−σ)1/2 is solved analytically for |σ|≪1. The electromagnetic field behavior is determined largely by singularities arising from the excitation of surface polaritons with wave vector q→±∞. Depending on the sign of σ, 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 |σ|. With minor alterations, these results apply as well to the electrostatic limit.