# Introductory Summary of Invisibility, Metamaterials and Transformative Optics

Illustration of the idea of a “Pendry cloak”. Light rays illuminating the cloak are bent around the central region and allowed to continue on their original path. Figure from BBC News.

An introductory overview of invisibility cloaking work and transformative optics

In 1988, a mathematician named Nachman provided a rigorous proof that invisible objects do not exist: if one shines enough light on an object from enough directions, it will be detectable.

Nachman’s theorem, though rigorous, had two big “loopholes” in it that were overlooked by researchers of the time but were caught by the 2006 researchers. Leonhardt correctly noted that Nachman’s theorem only precluded perfectly invisible objects; a cloak that is 99.9% invisible, however, might very well be possible. Pendry, Schurig and Smith observed that Nachman’s theorem only applies to isotropic materials, in which light travels at the same speed regardless of its direction and polarization. Anisotropic materials, such as calcite crystals, behave differently depending on the nature of the light traveling through them, and give rise to phenomena such as double refraction.

The Pendry, Schurig and Smith cloak is an anisotropic cloak, and not subject to Nachman’s impossibility theorem. In 2007, other researchers showed through more rigorous calculations that this design is, in principle, perfectly invisible.

A few points are worth making about these early cloaks.

1. They require the fabrication of materials with a wide range of refractive indices and spatial variations that are not found in nature. The construction of a cloak that would work for visible light therefore requires the use of so-called metamaterials, materials that derive their properties from modification of their structure on the scale of a billionth of a meter. As it stands, nobody really knows how to make such materials reliably and efficiently.

2. These cloaks work only for a single wavelength (color) of light, or a small range of colors. Note: There is work to expand the rangse. Looking at the image of the Pendry cloak, light that intersects the middle of the cloak has to travel farther than light that hits the edge of the cloak. If the cloak is designed to make all of the light “synch up” when it reemerges at one wavelength, it will in general not be synched at another wavelength; there is no good solution to this problem as yet either.

3. The behavior of light inside these cloaks is in many ways analogous to the behavior of light in a gravitational field under Einstein’s general theory of relativity. A new subfield of optics known as transformation optics has been developed that applies the mathematical tools of general relativity to design new cloaks and other unusual optical devices.

So what other kind of optical devices have been imagined? It seems that it is possible to make light do almost anything these days — at least theoretically

In June of 2009, however, Alu and Engheta proposed a technique for cloaking a sensor that allows the sensor to detect, but not to be seen. Idea behind “cloaking a sensor”. The light scattered by the cloak is out of phase with the light scattered by the sensor, resulting in a partial cancellation of the total field scattered by the object.

The existence of metamaterial invisibility devices implies that we can also construct a cloak that makes one object look like a completely different object. This is potentially more useful than a true invisibility cloak: an imperfectly invisible object would likely draw much more attention than an imperfectly imaged mundane object. A group of researchers in Hong Kong in 2009 had the idea of making “optical illusion” using transformation optics and metamaterials