Complementary media of electrons

The concept of complementary media, which cause negative refraction and make perfect lenses, was first introduced to electromagnetic waves. This paper extends it to general waves by expressing the complementarity in terms of a transfer matrix. As an example, complementary media of electrons are discussed theoretically. An application of complementary media to subsurface imaging by scanning tunnelling microscopy is described. For realistic materials the formulation of complementary media is extended to take account of the scattering at interfaces, and effectively complementary systems formed by interfaces are discussed. Interfaces of the graphitic lattice forming complementary systems are designed.