Is it possible to hide something within an invisible cloak? It has already been over four years since the first groundbreaking theoretical papers on invisible cloaking devices were published, stirring up a near frenzy in the physics and optics communities. Since then, new results have come at a rapid and genuinely surprising pace, and news articles on the recent developments have been a bit overwhelming, even for a worker in the field. In this post, I thought I'd take a look at some of the fascinating results that have been published on invisibility, giving some perspective on how far we've come and how far we have to go!
Let's start with the fundamental cloaking papers of June 2006. Two theoretical papers appeared back-to-back in the journal Science, one by Ulf Leonhardt1 of the University of St. Andrews and one by Pendry, Schurig and Smith2 of Imperial College and Duke University. The papers were strikingly similar in their central premise, a great example of how ideas in science can be independently developed by different researchers.
So how do the Pendry/Leonhardt cloaks work? When a ray of light enters a material medium, it changes direction, in a phenomenon known as refraction. This refraction can be traced to the slowing of the light as it enters the medium, and the speed of light is reduced from c (the vacuum speed) to c/n, where n is the so-called refractive index of the medium.
Image Left: Illustrating the idea of refraction; in passing from a rarer medium (such as air) to a denser medium (such as glass), a light ray is bent towards the normal to the surface. The angles and refractive indices of the two media are related by Snell's law. (Figure by Dr. SkySkull)
When light enters a medium with a non-uniform refractive index (an index that depends upon position), its path tends to curve in the direction of higher refractive index. This can, and has been, used as a technique to guide light in a material.
Image Right: A ray passing diagonally through a gradient medium will find its direction bent towards the denser medium. (Figure by Dr. SkySkull)
The same idea was employed in the development of both invisibility cloaks. A central, cloaked, region is surrounded by a medium with a radially varying refractive index that guides light around the central region and allows it to continue along its original path, like water flowing around a rock in a stream. A simulation from the original Pendry et al. paper illustrates the idea nicely.
Image Left: 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 Ref. , taken from BBC News.
This is such a simple and elegant idea, it is quite surprising that it wasn't tried long ago. In fact, a weird fiction novel from 1923, A. Merritt's The Face in the Abyss, uses exactly the water in the stream image to explain invisibility:
Conceive something that neither absorbs light nor throws it back. In such case the light rays stream over that something as water in a swift brook streams over a submerged boulder. The boulder is not visible. Nor would be the thing over which the light rays streamed.
There is a very good reason why physicists didn't investigate such cloaks earlier, however; they had seemingly been proven to be impossible some years before! Imaging techniques such as CAT scans and MRIs, in use since the early 1970s, detect the internal structure of patients by measuring electromagnetic waves scattered from them. If invisible objects existed, however, these techniques would be extremely unreliable: imagine "invisible" tumors not showing up on a CAT scan. In 1988, a mathematician named Nachman provided a rigorous proof3 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 (including myself) 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.
Image Right: The phenomenon of double refraction in calcite. Light of perpendicular polarizations travel at different speeds and refract differently, resulting in two images of the text beneath. Picture from Wikipedia.
The Pendry, Schurig and Smith cloak is an anisotropic cloak, and not subject to Nachman's impossibility theorem. In 2007, other researchers4 showed through more rigorous calculations that this design is, in principle, perfectly invisible.
A few points are worth making about these early cloaks. First, 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.
Second, these cloaks work only for a single wavelength (color) of light, or a very small range of colors. 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.
Third, 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 2008, Li and Pendry5 described a modification of the three-dimensional cloak -- if the object to be concealed is sitting on top of a flat surface, it is possible to put a different type of cloak on top of it that, in essence, makes the object look like the flat surface! This has been referred to as "hiding under the carpet", and may roughly understood in terms of rays like the original cloaks.
Image Right: Illustration of the idea of "hiding under the carpet". Light rays entering the cloak are bent to reemerge as if they had reflected from the flat surface beneath; no light interacts with the object hidden below. (Figure by Dr. SkySkull)
One important advantage of "hiding under the carpet" is that such cloaks do not require an anisotropic material. They are therefore in principle much easier to construct, and also have the advantage of being more amenable to broadband cloaking.
One problem with all of the cloaks mentioned so far is that they completely block light from the cloaked region: an outside observer won't see a cloaked person, but the cloaked person won't see anything! In June of 2009, however, Alu and Engheta proposed6 a technique for cloaking a sensor that allows the sensor to detect, but not to be seen!
The idea is a relatively simple one: the sensor scatters light because the electromagnetic field induces oscillating electric charges (dipoles) that reradiate light. If one surrounds the sensor by a "cloak" that induces "opposing" dipoles, the cloak will produce a scattered field that cancels the scattered field of the sensor.
Image Left: 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. (Figure by Dr. SkySkull)
The limitation of this cloak, as it stands, is that it is necessarily very small: the theory requires the cloak to be comparable in size to the wavelength of light. This means that a cloaked sensor would have to be roughly a thousandth of a millimeter in size!
Perhaps the problem with the cloaks described so far is that they have a very narrow view of cloaking, assuming that the cloaked object has to be inside the cloak! In March of 2009, Lai, Chen, Zhang and Chan introduced7 a "complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell".
The trick to such a device is again the use of metamaterials, specifically objects with a negative refractive index. If one wants to hide an object outside of the external cloak, one must embed within the cloak an "anti-object". The scattering effects of the "anti-object" cancel out the scattering effects of the object, rendering it invisible.
Image Right: Schematic of "external cloaking". A negative refractive index material has embedded in it an "anti-object" that mirrors the object to be hidden. Light rays shining on the line A will effectively "skip" the region between A and B and emerge from B unchanged. (Figure by Dr. SkySkull)
The biggest limitation of this type of cloak is that it must be tailored specifically for the object that it is intended to hide. The "anti-object" is a mirror image, of sorts, of the object itself.
One of the most fascinating ideas to come out of cloaking so far came from a group of researchers in Hong Kong8 in 2009, the idea of making "optical illusions"! Earlier in this post, we noted that the non-existence of invisible objects was important for imaging techniques such as CAT and MRI. This non-existence of invisibility directly implies that the image we form is an accurate representation of the object. This argument may be turned on its head, however: 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.
Image Left: A schematic of "illusion optics". An uncloaked apple will look like an apple, while a cloaked apple can be made to look like anything imaginable, even an orange. (Figure by Dr. SkySkull)
We noted that "transformation optics" uses the tools of Einstein's general relativity to design these unusual devices. In July of last year, Chen, Miao and Li9 took this connection to the next logical step and designed an optical device that mimics the behavior of light outside of a type of black hole! The analogy is not perfect, as a black hole warps time as well as space, but such devices may allow some optics of cosmological systems to be studied in the laboratory.
The problem with all of the schemes described so far, however, is that they all require the use of optical metamaterials, which we have noted involves modifying the structure of matter on the scale of a billionth of a meter. This cannot be done in a practical manner as of yet, but some of the ideas described here have been tested nevertheless.
In November of 2006, soon after the publication of the first cloaking papers, one of the groups demonstrated10 a crude cloaking device that operates at microwave wavelengths, roughly 3.5 cm. The cloak was fabricated out of simple metamaterial "cells" that were roughly 3 mm square.
Image Right: A photograph of the first microwave cloak, described in Ref. . Image from Gizmo Watch.
It is dangerous to make long-term predictions about a field of study as surprising and rapidly developing as transformation optics, but I suspect it will be a few years still before anyone demonstrates a three-dimensional cloak that works at visible wavelengths. Progress is still being made, however; as of this writing, two papers appeared on the Arxiv.org, here and here, which demonstrate an experimental realization of the "hiding under the carpet" strategy!
1 U. Leonhardt, "Optical conformal mapping," Science 312 (2006), 1777.
2 J.B. Pendry, D. Schurig and D.R. Smith, "Controlling electromagnetic fields," Science 312 (2006), 1780.
3 A.I. Nachman, "Reconstructions from boundary measurements," Annals Math. 128 (1988), 531.
4 H. Chen, B.-I Wu, B. Zhang and J.A. Kong, "Electromagnetic wave interactions witha metamaterial cloak," Phys. Rev. Lett. 99 (2007), 063903.
5 J. Li and J.B. Pendry, "Hiding under the carpet: a new strategy for cloaking," Phys. Rev. Lett. 101 (2008), 203901.
6 A. Alu and N. Engheta, "Cloaking a sensor," Phys. Rev. Lett. 102 (2009), 233901.
7 Y. Lai, H. Chen, Z.-Q Zhang and C.T. Chan, "Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell," Phys. Rev. Lett. 102 (2009), 093901.
8 Y. Lai, J. Ng, H.Y. Chen, D. Han, J. Xiao, Z.-Q Zhang and C.T. Chan, "Illusion optics: the optical transformation of an object into another object," Phys. Rev. Lett. 102 (2009), 253902.
9 H. Chen, R.-X Miao and M. Li, "Transformation optics that mimics the system outside a Schwarzschild black hole," Opt. Exp. 18 (2010), 15183.
10 D. Schurig, J.J. Mock, B.J. Justice, S.A. Cummer, J.B. Pendry, A.F. Starr and D.R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314 (2006), 977.
About the Author: Greg Gbur is an associate professor of Physics and Optical Science at the University of North Carolina at Charlotte, specializing in research on theoretical classical optics. Since August of 2007 he has blogged as "Dr. SkySkull" at Skulls in the Stars, where he covers optics, the history of physics, historical weird fiction, and the interconnection of these subjects. Greg also co-founded the history of science blog carnival The Giant's Shoulders. He has over 60 peer-reviewed publications and is the author of the upcoming textbook, "Mathematical Methods for Optical Physics and Engineering".
The views expressed are those of the author and are not necessarily those of Scientific American.