Flat lens without optical axis: Theory of imaging

We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction. This medium is characterized by two intrinsic parameters sigma and kappa. Imaging can be achieved with both negative and positive wave vector refraction if sigma is a positive constant. The Veselago-Pendry lens is a special case with sigma = 1 and kappa = 0. A general law of refraction for anisotropic media is revealed. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.