Sub-diffraction imaging with compensating bilayers

We derive a general expression for the material properties of a compensating bilayer, which is a pair of material layers which transfer the field distribution from one side of the bilayer to the other with resolution limited only by the deviation of the material properties from specified values. One of the layers can be free space, a special case of which is the perfect lens, but the layers need not have equal thickness. Compensating a thick layer of free space with a thin layer creates a focusing device with increased working distance, and employs an anisotropic material. It is also possible to achieve compensation of materials with property tensors that are neither positive nor negative definite. In this case, we refer to such media as indefinite, and we analyse, in detail, bilayers of these media which support coupling of internal propagating waves to incident waves of any transverse wave vector. In this case, we find that the enhanced spatial resolution provided by large transverse wave vectors is far less sensitive to loss than that of the perfect lens.