## Invisibility physics: Hiding and seeking, all at once!

When the first papers on the idea of a “cloaking” device came out in 2006, lots of people were immediately worried that the CIA would soon be peering right over their shoulder from the shelter of invisibility cloaks.  Many scientists, including myself, pointed out the flaw in that reasoning: a “perfect” cloak would direct all light around the outside of the cloak.  This meant that, although the spy couldn’t be seen in the cloak, he couldn’t see anything from inside!

###### An illustration of one of the original cloaking concepts from J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006): rays of light are guided around the interior region, which sees no light.

A recent paper in Physical Review Letters, however, suggests that this “mutual invisibility” can be overcome.  The research described suggests that a different type of cloaking device could be used to enclose a sensing device, and that the sensor would not only be (almost) invisible, but it would be able to detect radiation just as well as when outside the cloak!  The research is intriguing (though it still won’t help the CIA quite yet), and it illustrates a different, earlier, technique for making something “not be seen”.

The recent research by Andrea Alù and Nader Engheta is based on an optical invisibility idea they first1 published in 2005, a year before the sensation-causing papers appeared in Science. Their cloak is arguably less effective than the Science cloaks, as (a) the theory has only been developed in detail for very small objects, (b) the cloak must be specifically tailored for the object it intends to hide, and (c) it is not a “perfect” cloak, which the Science cloaks are, at least in principle.  This latter result, however, allows it to be used effectively with a sensor.

In short, the Alù and Engheta cloak involves covering the object to be hidden with an appropriately chosen thin shell of special material, either a material that supports surface plasmons or a layer of metamaterials.  The shell produces a scattered field which is very nearly the “opposite” of the scattered field of the hidden object, and the two fields cancel out.  The net result is that the cloaked object has little visible influence on an illuminating field, i.e. it becomes invisible.

It’s difficult to explain exactly how this works, as the technique really involves playing with the mathematics until a solution is found.  We can go into a bit more detail, enough to draw a picture at least, if we describe a little about how matter interacts with light waves.

Suppose we have a single hydrogen atom all by itself in some otherwise empty region of space.  If we adopt a loosely quantum mechanical picture of the atom, we may imagine it to be a positively-charged nucleus surrounded by an electron ‘cloud’:

The atom is electrically neutral, and because it is spherically symmetric, it produces no electric field outside of the electron cloud: the electric field of the nucleus is perfectly canceled by the electric field of the electron.

Now we  apply a uniform, static electric field $\bf E$ across this atom.  This field pulls the nucleus in the direction of the field, and pulls the electron cloud in the direction opposite of the field.  The net effect, to good approximation, is that the atom now appears to as a positive charge and a negative charge separated by some distance d:

A vector $\bf p$ is defined as the dipole moment of the atom, and points from the negative charge to the positive charge. The combination of a negative charge with an equal and opposite charge separated by a small distance is known as an electric dipole.

Because the charges are now separated, the dipole produces its own electric field, which appears roughly as follows:

If we apply an electric field to some larger object consisting of many atoms, the field turns each atom into its own little dipole.  If the field is uniform throughout the material, the net effect is to make the object look like a very big dipole:

Most objects will behave essentially like an electric dipole when excited by a uniform electric field.  To summarize:  when a static electric field is applied to a material, electric dipoles are induced, and the matter produces its own electric field, which looks mostly like a dipole field.

The preceding reasoning is relevant when a static electric field is applied to a material; we may, however, extend this discussion to understand the effect of light on materials.  As we’ve noted many times before, a light wave is a transverse electromagnetic wave:  the electric and magnetic fields oscillate in directions perpendicular to the direction of motion:

When the electric field from a light wave hits an object, it induces electric dipoles in the material just like a static electric field does.  If the object is comparable in size or smaller than the wavelength of light, it acts mostly like an electric dipole. It is different from the static electric field case in that a dipole excited by light oscillates at the same frequency as the electromagnetic wave.  This oscillating dipole produces a secondary electromagnetic wave, which is what we refer to as the scattered field.  The scattering process is basically the same as that discussed in my recent post on X-ray polarization.

How does the behavior of the oscillating dipole relate to the behavior of the illuminating electric field?  For ordinary materials (which are weak absorbers of light), the induced dipole points in the same direction as the electric field.  For plasmonic materials or negative refractive index metamaterials, however, the electric field points in the opposite direction as the electric field:

For an ordinary material, the dipole points up when the illuminating field points up; for a metamaterial, the dipole points down when the illuminating field points up!

If we take an ordinary material of size comparable to the wavelength of light, and surround it by a plasmonic material or metamaterial shell, the dipole moments of the two materials will always be pointing in opposite directions.  Since the scattered field radiated by a dipole is proportional to the dipole behavior itself, this means that the scattered fields produced by the shell and object will partially cancel each other out:

This is a fundamentally different approach to cloaking than that presented in the Science articles.  The cloaks presented in the Science articles work by guiding light around the “hidden” object.  The Alù/Engheta cloak lets the illuminating light field scatter off of the cloaked object, but cancels this scattered field with the scattered field from the metamaterial cloak. It hides the object by the use of destructive interference.

As already noted, the Alù/Engheta suffers from several limitations: it has, as yet, only been demonstrated theoretically for very small objects (the math gets very difficult for larger objects), the cloak design must be tailored to the specific object to be cloaked, the cloaking is not in principle “perfect”, and light is not perfectly blocked from the interior of the cloak.

This latter property, however, allows the cloak to hide a sensor!  In their recent article in Physical Review Letters, Alù and Engheta study what happens when their cloak is used to shield a receiver antenna.  When illuminated by electromagnetic radiation at its operating frequency, an antenna will typically be a strong scatterer: the properties of the antenna which make it receptive to collecting radiation also make it scatter that radiation.  By surrounding the antenna with a cloak, however, that scattered field could in principle be largely canceled out by the scattered field of the cloaking material!  Simulations by the researchers suggest that the amount of energy scattered by the sensor/cloak can be reduced by a factor of more than 1500!

For me, the most surprising result of this research is that the sensitivity of the sensor is more or less unaffected by the cloaking; that is, it detects radiation just as well as when the cloak is not present!  At first glance, this seems almost crazy: one might expect that, because “cloaking” implies “reduction of scattering”, that little light would impinge on the antenna, and the cloak would necessarily reduce the detector sensitivity.  If we were using a 2006 Science-type cloak, this would be true, as no light would reach the enclosed detector at all.  The Alù/Engheta cloak, however, attempts to minimize the field scattered outside of the object/cloak combination, by having the cloak produce a scattered field which counteracts the scattered field of the object.  The important distinction is that the object itself still scatters light strongly, and can therefore be a very sensitive detector.  The Alù/Engheta cloak is related to the idea of nonradiating sources, which I have been discussing in my ‘history of invisibility posts‘ and will come back to in more detail later.

Again, though, it is to be noted that the technology has to develop quite a bit before we have to worry about invisible men peeking over our shoulders at the computer!  The cloaked sensors considered in the paper had an outer radius of 23 mm, and operated at a frequency of 1 GHz, which is in the microwave regime.  In other words, the sphere was still of comparable size to a wavelength.  This means, with current theory, the largest size cloaked sensor we can imagine with visible light would be about a thousandth of a millimeter in diameter!

Those interested in getting a different, slightly more technical, perspective on this paper can read the nice APS Viewpoint article about it here.

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1 A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72 (2005), 016623.

Alù, A., & Engheta, N. (2009). Cloaking a Sensor Physical Review Letters, 102 (23) DOI: 10.1103/PhysRevLett.102.233901

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### 2 Responses to Invisibility physics: Hiding and seeking, all at once!

1. stuwat says:

Great explanation and very useful diagrams. Thanks as always for the effort you’ve put into explaining this research.

I’m still left scratching my head a little bit and was wondering if you could give some clarification. Are we to understand that there is some asymmetry in the cloaking material, so that it is tailored to work in a one way fashion?

• stuwat wrote: “Are we to understand that there is some asymmetry in the cloaking material, so that it is tailored to work in a one way fashion?”

Thanks for the question! There is no asymmetry in the cloaking material — it is assumed to be, unlike the ‘perfect’ cloaks of 2006 — an isotropic medium.

Perhaps a better way to describe what’s happening is to say that the cloak converts the dipole into a quadrupole. Our object has a dipole induced in it, which produces a radiation pattern. The cloak is not designed to “block” the illuminating field, but rather to have the opposite dipole induced in it. If the cloak is chosen properly, one could in principle produce a near-perfect quadrupole. Because the original quadrupole moment of the object is expected to be small, the radiation produced by the object should be very small.

One might be expected to continue the process for larger objects. By introducing more layers to the cloak, one might be able to cancel the quadrupole moment as well, leaving only the octupole moment, and so forth. Such calculations haven’t been done yet, to the best of my knowledge, though, so it is still speculation…