Generalized Veselago-Pendry lenses via complex transformation optics

Field solutions for a conventional Veselago-Pendry (VP) flat lens with ϵ=-ϵ ₀ and μ=-μ ₀ can be derived based on transformation optics (TO) principles. The TO viewpoint makes it clear that perfect imaging by a VP lens is a consequence of multivalued nature of the particular coordinate transformation involved. This transformation is equivalent to a "space folding" whereby one point in the transformed domain (source point) is mapped to three different points in the physical domain (the original source point plus two focal points). In theory, a VP lens would enable the recovery of the entire range of spectral components, i.e. both propagating and evanescent fields, thus characterizing a "perfect lens". Such lens, if lossess, is indeed "perfect" for monochromatic waves; however, for any realistic wave packet the space folding interpretation provided by TO makes it clear that a VP lens violates primitive causality constraints, which precludes any practical realization. Here, we utilize complex transformation optics (CTO) to derive generalized Veselago-Pendry (GVP) lenses without requiring a multivalued transformation. Unlike the conventional VP lens, the proposed lenses can fully recover the evanescent spectra under more general conditions that include the presence of (anisotropic) material loss/gain.