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Invisibility: After several years of research, it’s just gotten weirder

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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. [1], 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. [10]. 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, 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.


Comments 13 Comments

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  1. 1. jtdwyer 11:41 pm 01/11/2011

    It seems to me that the same optical effects occur in spacetime. While general relativity describes spacetime as being curved around massive objects, IMO spacetime can also be described as being radially contracted by the gravitational/velocity field around spherically symmetrical objects of mass.

    As such, light passing obliquely through a radially gradient velocity field is curved, as a function of its own velocity of self-propagation.

    This is similar to the illustrated effect of a "Pendry cloak" above since the effects imparted to light waves are essentially identical.

    While the potential energy contained within a singular, spherically symmetrical distribution of mass produces a radially gradient field of gravitational velocity effects, galactic gravitational lensing effects, produced most often by viewing a disperse spiral galaxy along its rotational axis, produces a highly distorted magnification of objects located behind the galaxy.

    The optical distortion produced in these circumstances are the result the aggregation of millions and even billions of individual gravitational velocity fields surrounding each of the galaxy’s stars and other masses. While an individual gravitational velocity field produces a smooth optical effect identical to a crystal ball, the aggregated fields of galaxies produce a distorted optical effect.

    While the optical lensing effect produced by spiral galaxies is often attributed to peripheral dark matter, it can be simply explained by the aggregation of gravitational lens effects produced by the galaxy’s innumerable peripheral stars, which are not normally individually considered.

    In contrast, if a spiral galaxy’s gravitational lens effect was produced by a spherical or even elliptical halo of dark matter, an optically smooth magnification would be produced.

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  2. 2. jtdwyer 12:12 am 01/12/2011

    One other thing… If the density of the universe diminishes in time as a function of universal expansion, wouldn’t light emitted in the early universe, reaching us now, most likely have been significantly curved by the gradient density of traversed spacetime?

    This curvature applied to the path of light might, in some cases depending on the directional alignment of expansion and light emission, eliminate the physical extension of light’s wavelength, identified by its redshift.

    In this case, light emitted in the earlier universe may traverse significant distances in rapidly expanding spacetime without incurring redshift. This is precisely the conditions observed in type Ia supernovae observations that are considered to support the conclusion that universal expansion is accelerating. IMO, it’s very possible that conditions producing those observed characteristic properties of light’s spectrum and luminosity have been misinterpreted.

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  3. 3. riborp2 10:04 am 01/12/2011

    I think the refraction theory needs to be updated a little… the refraction we see is not only due to the bending lights but actually the light rays tend to unite when they enter a denser medium. That is why a piece of wood in the sun gets heated earlier than the water.

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  4. 4. PaoloMagrassi 12:31 pm 01/12/2011

    Excellent post, Greg.

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  5. 5. jtdwyer 2:21 pm 01/13/2011

    I certainly agree with PaoloMagrassi that this is a very interesting article!

    In hopes of clarifying my previous comments; IMO the methods of transformation optics should be employed to formally evaluate galactic gravitational lensing.

    Gravitational lensing is often considered as evidence for the existence of dark matter. However, there seems to be quite a bit of conflicting analysis being done. As I understand, the are a large number of potential effects that may contribute to the observed effects produced by, especially, a spiral galaxy. These include the gravitational warping effect of a hypothetical spherical or elliptical dark matter ‘halo’ enveloping the galaxy, containing up to about 10x the galaxy’s ‘visible’ mass, the gravitational warping effect produced by the much more compact ‘visible’ matter, both of which may contribute strong gravitational lensing effects, and periodic microlensing effects producing High Magnification Events as the aggregated gravitational effects of individual objects of mass transverse a projected background image. For example, an interesting analysis is provided by the École polytechnique fédérale de Lausanne’s Laboratory of Astrophysics, "USING MICROLENSING : MICRO-IMAGING OF A QUASAR ACCRETION DISK";

    Some researchers express concern that current lensing analyses place too much emphasis on the spheroidal components of spiral galaxies, ignoring their large discs. Please refer to "Inclination Effects in Spiral Galaxy Gravitational Lensing";

    Some astronomers even consider that the location of projected background object images indicates the location of dark matter halos, although it seems to me the that their locations indicate the gravitational ‘curvature’ of peripheral spacetime.

    It can be hoped that the complex combinations of optical effects produced, especially by spiral galaxies, with their large disc components and hypothetically very massive dark matter components, may be better resolved though improved analytical methods.

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  6. 6. dmummert 2:20 pm 01/14/2011

    Two observations:

    (jtdwyer)"As such, light passing obliquely through a radially gradient velocity field is curved, as a function of its own velocity of self-propagation."

    This could probably be interpreted as light taking a short cut across the rubber-sheet model – which by definition cannot occur. Wave propagation through a gravitational field takes the long way ’round. It’s what validated Einstein’s general theory.

    The other observation re; dark matter. Since we have so few materials characteristics of the stuff, other than that it makes up the bulk of the universe along with dark energy, and that it interacts with normal matter so little, could we not posit that, however small the effect, it may possess meta-material effects and negative refractive indices?

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  7. 7. jtdwyer 5:26 pm 01/14/2011

    You may be right that some would interpret it in that way – perhaps I should find a better description. I don’t do math, but I think that if the velocity of light directed obliquely through a gravitational velocity field is vector-summed with a massive object’s radial gravitational velocity as the light progresses through the gravitational field, the result would be the curved path of light that is observed.

    As I understand, dark matter cannot interact with ordinary matter, including light, in any way except gravitationally – otherwise it could be directly detected. This is one of the requirements that dark matter must meet, since undetectable gravitational effects are required to compensate for the discrepancy between observed galactic rotational velocities and those predicted by the laws of Planetary Motion (even though they do not properly apply).

    As I understand, the effect being observed is understood to result from gravitational lensing only, with no material optical effects.

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  8. 8. verdai 5:32 pm 01/14/2011

    transformation optics may be a label somewhat like teleportation in that the original is neither transformed in fact or moved: rather, in the case of the latter is destroyed.

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  9. 9. jtdwyer 1:01 pm 01/16/2011

    By the way, the image illustrating the "Pendry cloak" does not precisely represent the effects of gravitation on light or other small objects. Light directed to a massive object will ‘collide’ with it. Otherwise we’d never receive any sunlight.

    Only light that is directed near enough to the periphery of a sufficiently massive object, obliquely directed to its external gravitational velocity field, will be curved around the massive object.

    However, sufficiently massive objects directed towards each other do not typically collide. Rather, they are redirected around each other to an eventual orbital trajectory. This occurs because each (spherical) massive object possesses an external field of radially directed velocity that is combined with their linear relative velocity: two opposingly directed fields of radially velocity prevent the completion of impact.

    Vector summation of the two fields and the objects’ relative velocity produces the orbital result. Only when orbital velocity of two massive objects decays is collision typically produced. Of course two massive objects directed to one another with sufficient linear relative velocity would collide immediately.

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  10. 10. dmummert 9:25 pm 01/20/2011

    Sigh… I was so looking forward to polishing off some of my backlog tonight. However, skimming the rest of the discussion, I think I can probably catch up on some of it. This will turn out to be a short post.

    Number One Concept – Understand the Theory. I see lots of words strung together, and very little actual basic science. The things that the authors are trying are complex optics experiments (and in at least one instance, a thought experiment), but…

    Number Two Concept – Stay On Topic!

    And, of course – if you don’t do math, you ought to. Dwyer – you’d probably make a very good theoretical physicist if you’d pick up a couple of basic physics books and work through them. I used to dislike physics in college because I got low grades in vector math, but now its different.

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  11. 11. jtdwyer 4:33 am 01/21/2011

    I’ll certainly consider coming to you for any personal advice based on your vastly superior life experiences. In the meantime, do you have any specific issues you can address, or only academic counseling?

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  12. 12. nandakumarcheiro.nandakumar@gm 9:48 pm 10/22/2011

    Dark matter could be viewed as invisible cloaking screen domain in which this stuff is stored which can be simulated by removing the invisible cloaking screen for a Possible vortex differentiation Propulsion system: The fixed point motion and deviation towards repulsive attractive natural force is observed in space with reference to meta material analogy that swing between + theta and – theta semi circular boundaries from Toa to s plane ring dynamics must have a meaning as the inner string current with reference to outer string current direction is changed between 1/2 Li2 and 1/2 cv2 where the induction energy and capacity energy is interchanged and a critical energy amplification is possible with reference to Nyquist gaining systems,this could be achieved.
    Thus this is as well well comparable with reference to multiple reflective photon energy gaining more voltage by analogy.Hence a repetitive polarity reversal will gain more amplification in any propulsion system as you squeeze the spiralling nozzle between the inner circle and outer circle out of eccentricity may act like a converging nozzle out side due centrifugal vortex flow or converging nozzle inside as centeripetal force ,thanks to Hall’s magneticfield quantisation vortex squeezing.
    Unfortunately, the below scenario violates the (several independently) verified fact that dark energy has positive energy density and negative pressure for which there is no electromagnetic analog available. The electromagnetic coil and tube device described below will not produce the negative pressure that is observed to produce the gravitationally repulsive effect that we call cosmological expansion. The dark energy negative pressure is exactly equal to the dark energy positive energy density which has been determined to 6 sigma. The only form of matter in this universe that has this type of equation of state is quantum vacuum energy. The energy density of dark energy is 1 nanoJoule per cubic meter, which means that its pressure is negative 1 nanoJoule per cubic meter.
    As for the energy density and pressure produced by electromagnetic devices, in every reference frame, the electromagnetic pressure and electromagnetic energy density will be positive and thus produce a gravitationally attractive force on something nearby. Also, the equation of state for electromagnetic radiation is such that the electromagnetic pressure is one-third of the electromagnetic energy density, and both quantities are positive. This is not observed in dark energy as noted above.
    Also, internal electromagnetic momentum in the system described below will act to compensate any external electromagnetic thrust produced, so the device will produce a net thrust of zero.
    But this could be simulated to produce Nyquist gain energy by multiple reversible dynamics along with reversible vortex analogy by giving an eccentricity in converging nozzles using Hall’s magneticfield quantization
    Sankaravelyudhan Nadakumar.
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  13. 13. AET RaDAL 12:41 pm 02/8/2012

    All of this is really quite quaint (the article, not the subsequent theoretical noodling from the comment section). The fact remains that I’ve been doing invisibility R&D since ’94. You want invisible attack helicopters? Invisible speed boats? How about increased environmental freedom for snipers? Whatever. I know how to do it all now. In the optical range, not microwaves like those posers from Duke University that claimed to have an “invisibility cloak” when all they really had was a microwave stealth system. But my work is not for sale to foreign governments. Period.

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