Perfect-lens-material condition from adjacent absorptive and gain resonances

We suggest, based on the principle of causality and for a material exhibiting adjacent absorptive and gain resonances, that there can be an intervening frequency where perfect imaging is in theory possible. At this frequency, both the dielectric constant and the permeability are negative, leading to a negative refractive index, and there is no loss. In such a material exhibiting a double resonance, the gain must be at the higher frequency. Through appropriate tuning of the refractive index, all propagating and evanescent fields from the object could then in principle be reconstructed at the image plane, subject to practical implementation limits.