Transformation-designed optical elements

We describe transformation design of optical elements which, in addition to image transfer, perform useful operations. For one class of operations, including translation, rotation, mirroring and inversion, an image can be generated that is ideal in the sense of the perfect lens (combining both near- and far-field components in a flat, unit transfer function, up to the limits imposed by material imperfection). We also describe elements that perform magnification, free from geometric aberrations, even while providing free-space working distance on both the input and output sides. These magnifying elements also operate in the near- and far-field, allowing them to transfer near field information into the far field, as with the hyper lens and other related devices, however in contrast to those devices, insertion loss can be much lower, due to the matching properties accessible with transformation design. The devices here described inherently require dispersive materials, thus chromatic aberration will be present, and the bandwidth limited.