The idea of optical cloaking, or more generally the concept of invisibility, has gone from science fiction trope to serious topic of physics research to subfield of optical science in its own right in a remarkably short period of time.
One of the most fascinating aspects of the “cloaking craze,” as I have referred to it before, is that the optics of cloaks and the mathematics used to design them have implications far beyond the simple idea of hiding an object. Lessons learned from cloaking have been used to design such exotic devices as “perfect” lenses, space-time cloaks, and optical black holes. The number of ingenious applications has been growing at a rapid pace (although most are still purely theoretical), and others almost certainly still wait to be discovered.
Of all the ideas suggested, my favorite is one that has gotten relatively little attention: the ability to make “perfect” optical illusions. In principle, it is possible to wrap an object in an illusion cloak to make that object look like a completely different one. A simple illustration of the idea is shown below, in which an apple is surrounded by a cloak that makes it look exactly like an orange.
It is important to realize that this illusion is three-dimensional: the apple ends up looking like an orange from all directions of observation. The disguise is far more complex and effective than simply draping the apple in a tarp with a picture of an orange on it!
This surprising trick is an inevitable consequence of the existence of (theoretically) perfect invisibility cloaks, and in turn it leads to even more surprising possibilities! In this post we look at how such illusions are possible, and what implications they have for future optical devices.
A little bit of history is helpful in order to explain how “invisibility” leads to “illusion,” and we should say a few words about the research that started the current “craze.” The two foundational theoretical papers on optical cloaks appeared in 2006, one by Leonhardt1 and the other by Pendry, Schurig and Smith2, and they used strikingly similar reasoning to envision their devices. Both cloaks use carefully-designed optical materials to guide light around a central cloaked region and return it to its original trajectory on the other side. The original (and often reprinted) figure from Pendry, Schurig and Smith’s paper is shown below; the black lines indicate rays of light passing through the cloak and around the hidden region.
The means by which this works is based on the fact that a ray of light changes direction when it passes from one medium to another, in the process of refraction. If the optical properties of the medium vary continuously in space, a ray will follow a curved trajectory, as illustrated below.
By designing an appropriate gradient refractive index medium, one can curve light around a region, therefore making it cloaked.
But how does one determine the correct material properties? Light rays also follow curved trajectories under the influence of gravity, and one can take advantage of the well-established mathematics of general relativity — in which space and time are curved by the presence of matter — to plan how one would like light rays to behave. It is then straightforward to determine the material properties from the bending of space. For example, the figure below shows the hypothetical bending of space used by the Pendry, Schurig and Smith cloak, which effectively “pushes” space out away from the center of the region. A light ray is also shown in the picture.
This technique of using simulated warpings of space to design optical devices is now known as transformation optics, and it is a subfield of optics in its own right.
What was truly remarkable about the cloaking papers is that, before they came out, cloaking was generally thought to be impossible! It turns out that the existence of invisible objects has significance beyond simply hiding things from light, and years before cloaking was studied the more general possibility of invisibility was of great importance in a surprisingly different field.
In 1973, Godfrey N. Hounsfield revolutionized medical science with the introduction of what is now typically known as “computed tomography,” a diagnostic technique by which x-rays are used to image the interior of the human body.
CT, of course, has become a standard medical tool, and it inspired a variety of other imaging methods such as magnetic resonance imaging (MRI). All of these techniques, however, involve taking a large amount of data and combining it on a computer (hence the “computed” in “computed tomography”) using sophisticated algorithms to produce an image. A natural question arose: How do we know that we have enough data to produce an accurate image? Or, to put it another way, suppose we illuminate an object with radiation (light, x-rays, or even acoustic waves) from a large number of directions and measure the scattered radiation for a large number of directions. How much data (directions) do we need to uniquely and unambiguously generate an image?
This question of uniqueness is directly connected to the existence of invisible objects. If invisible objects exist, then the inverse scattering problem is nonunique. This is not terribly difficult to understand: suppose we are taking an image of the human skeleton using x-rays. If the inverse problem is unique, then we expect to be able to get a reliable image of the skeleton.
However, if invisible objects exist, our imaging device will not see them! All sorts of things could be present that we simply cannot see, and our reconstruction will be a highly inaccurate representation of what is really there…
If one envisions an “invisible tumor,” one can see why this would be a really big problem in medical imaging. Fortunately, a pair of theoretical papers were produced around 1990, one by Nachman3 and one by Habashy and Wolf4, that seemed to show that perfectly invisible objects do not exist.
When the cloaking papers came out in 2006, researchers in inverse scattering problems — including myself — had our doubts, thanks to the theoretical papers mentioned above. However, the cloak researchers had answers to these doubts. Leonhardt simply stated what should have been obvious: “nearly perfect” cloaking is just as good as “perfect” cloaking.
The response by Pendry, Schurig and Smith was more surprising: perfect cloaking is possible, if one uses materials that are both anisotropic and magnetic. The aforementioned theoretical demonstrations that invisibility is impossible were only done for isotropic and non-magnetic materials, and therefore had what might be considered a “loophole.” This was not a weakness of those earlier theories, as almost all materials in nature are isotropic and non-magnetic for visible light; rather, other researchers (again, such as myself) failed to recognize that they did not apply to all possible materials.
Magnetic materials are those which have a strong magnetic response to electromagnetic waves. The optical properties of most natural materials are due to an electrical response of the atoms and molecules.
So what are anisotropic materials? A simple example is optical calcite, also known as Iceland Spar. Calcite exhibits the phenomenon of double refraction, in which two images are seen when viewed through the crystal.
The behavior of light in anisotropic materials is sensitive to the polarization of light. As there are two independent polarizations of a light wave, there are two images formed by a piece of calcite.
With this explanation of cloaking out of the way, we now turn to the possibility of illusion! We have said that the nonexistence of invisible objects implies the uniqueness of the inverse scattering problem. If we consider the opposite scenario, the existence of invisible objects implies the nonuniqueness of the inverse scattering problem. This means that it is possible to find many different objects that all look exactly the same from all directions. Returning to our example at the beginning of this post, it is in principle possible to find complex objects of many different shapes and structures that would look exactly the same as an apple. It should also be possible to place an “illusion device” next to another object to simultaneously hide the object and make it look like something else!
This is, in essence, what was demonstrated by the authors of the first 2009 paper5 on “illusion optics.” As shown in the simulation below, they were able to demonstrate that a dielectric spoon could be concealed by an illusion device to scatter waves exactly as a metal cup would.
The first image shows the waves, coming from the left, and how they’re scattered by the spoon. The second image shows the field scattered from the combined spoon-illusion device, and the third image shows the field of a pure cup. It can be seen that the field scattered by the illusion is essentially the same as that of the cup.
So how does this work? The illusion device consists of two parts: a spoon-cancelling cloaking element and a spatially-compressed cup-creating element. These are illustrated below.
The details of how this works gets rather thorny. Suffice to say that transformation optics is used to take the image of the cup and “squash” it upwards out of the way of the spoon, and other strategies are used to design the spoon-cancelling element.
Illusion optics represents a sort of missed opportunity for me! When it became clear that optical cloaking could in principle be perfectly achieved, I quickly drew on my inverse scattering knowledge and realized that it could be used to make perfect illusions. However, I didn’t get around to acting on my intuition and got scooped by other researchers!
I actually suspect that illusion optics might be a better way to hide things than a perfect cloak. It seems to me that an imperfect disguise would survive scrutiny better than an imperfectly invisible object, the latter of which would look much more bizarre to a suspicious observer. Beyond this, though, the authors of the original cloaking paper have introduced another remarkable application of their idea: the ability to see through solid walls!
It should be noted that the spoon-cup illusion shown above does not have to surround the spoon, but works just fine with the device right to its side. Suppose, however, that instead of cancelling out a spoon, we design the device to cancel out a section of a wall! The device creates an illusion of a hole in the wall, and light will pass through what would have been an otherwise opaque barrier.
If it is possible to create a virtual hole where one does not exist, it is also possible to hide a hole that does exist! This is the idea behind “superscatterers,” which are essentially illusion devices that appear much bigger than they actually are. Superscatterers have actually been proposed6 to hide an open portal! This is illustrated roughly below.
Does this all seem too good (or bizarre) to be true? Well, to some degree, it is! The cloaking devices discussed above only function perfectly at a single frequency (color) of light, and effectively over a very small range of frequencies. This is also true of the illusion devices discussed, at least in their initial forms. Furthermore, the illusion devices and superscatterers have only been simulated for relatively small sizes — the spoon that was disguised above is only about three wavelengths long, which at optical frequencies would be about a millionths of a meter! It also seems clear that there must be a limit to the apparent size of superscatterers — it is almost certainly not possible to design a grain of sand that appears to be the size of the universe, for example.
Nevertheless, the idea of illusion optics demonstrates that the implications and consequences of cloaking are much broader than originally imagined. Who knows what sort of strange things we’ll see coming out of optics in the next few years? And whether or not those things will actually be there?
1 Leonhardt, U. (2006), ‘Optical conformal mapping’, Science 312, 1777–1780.
2 Pendry, J., Schurig, D. & Smith, D. (2006), ‘Controlling electromagnetic fields’, Science 312, 1780–1782.
3 Nachman, A. (1988), ‘Reconstructions from boundary measurements’, Annals Math. 128, 531–576.
4 Wolf, E. & Habashy, T. (1993), ‘Invisible bodies and uniqueness of the inverse scattering problem’, J. Mod. Opt. 40, 785–792.
5 Lai, Y., Ng, J., Chen, H., Han, D., Xiao, J., Zhang, Z.-Q. & Chan, C. (2009), ‘Illusion optics: the optical transformation of an object into another object’, Phys. Rev. Lett. 102, 253902.
6 Luo, X., Yang, T., Gu, Y., Chen, H. & Ma, H. (2009), ‘Conceal an entrance by means of superscatterer’, Appl. Phys. Lett. 94, 223513.