Reply to the Comment on Perfect imaging with positive refraction in three dimensions

Exact time-dependent solutions of Maxwell's equations in Maxwell's fish eye show that perfect imaging is not an artifact of a drain at the image, although a drain is required for subwavelength resolution

Transformation Optics and the Geometry of Light

Metamaterials are beginning to transform optics and microwave technology thanks to their versatile properties that, in many cases, can be tailored according to practical needs and desires. Although metamaterials are surely not the answer to all engineering problems, they have inspired a series of significant technological developments and also some imaginative research, because they invite researchers and inventors to dream. Imagine there were no practical limits on the electromagnetic properties of materials. What is possible? And what is not? If there are no practical limits, what are the fundamental limits? Such questions inspire taking a fresh look at the foundations of optics and at connections between optics and other areas of physics. In this article we discuss such a connection, the relationship between optics and general relativity, or, expressed more precisely, between geometrical ideas normally applied in general relativity and the propagation of light, or electromagnetic waves in general, in materials. We also discuss how this connection is applied: in invisibility devices, perfect lenses, the optical Aharonov-Bohm effect of vortices and in analogues of the event horizon.Comment: 72 pages, 18 figures, preprint with low-resolution images. Introduction to transformation optics, to appear in Progress in Optics (edited by Emil Wolf