I’ve spent a lot of time on this blog talking about the optics of invisibility, both hypothetical and actual. Though a number of forms of invisibility have been considered in both science and fiction for over a hundred years, the study of the subject really exploded in 2006 with the publication of two theoretical papers introducing designs for “invisibility cloaks.”
The principle behind one of these cloaks is illustrated below, taken from the original paper by Pendry, Schurig and Smith. The cloak guides light around the central region and sending it along its original path, like water flowing around a boulder in a stream. The lines in the illustration represent rays of light being deflected and returned to their original trajectories.
The device is passive; it “works its magic” by virtue of the materials it is built out of, and guides light around the hidden region by what amounts to refraction.
It is fun to talk about the unusual implications of optical invisibility, but it is hard to show it! Cloaks are complicated, and there are relatively few experimental realizations to date — and those that do exist are not easily reproducible without a lot of resources.
Fortunately, there exists a simple trick, suggested by my colleagues*, that can be used to demonstrate the principle of cloaking in a striking way! I assembled a version of this trick myself for use in a recent popular talk on invisibility physics that I gave; a short video of it is shown below.
A finger placed behind the device is readily visible, but a finger placed within the cloak vanishes!
For about $50, you too can make your own “cloaking device”, albeit an oversimplified and crude one! Let’s take a look at how it is done.
The device is constructed out of eight glass right-angle prisms arranged as shown in the top-down photograph below.
The operation of the cloak is really simple to explain. Suppose we look through the device from the bottom up; light coming from above bounces through the system as shown in the following image. (Rays have been color-coded to clearly show path of travel.)
The illusion is obviously not perfect — looking at the “cloak” from any direction other than directly in front of one of the flat faces will not provide any effect, other than a highly distorted image. This is not exactly a flaw, as more recent cloaking investigations have focused on such “directional” cloaks as a way to simplify the design requirements.
But an interesting question arises: the prisms are made of clear glass: why doesn’t some of the light passing through the system just go right through the side of the prism and into the diamond-shaped cloaked region? For that matter, why doesn’t some of the light escape out through the sides of the cloak as it bounces around? The answer is that the light is totally internally reflected at the glass interfaces, and none escapes until it hits the exit surface head on.
What is total internal reflection? As discussed in my “basics” post on refraction, when light crosses a flat interface between two media, it changes direction: this is the phenomenon of refraction. When light goes from a rarer medium (like air) to a denser medium (like glass), the ray gets bent towards the line perpendicular to the surface. When it goes the other way, from a denser medium to a rarer medium, it gets bent away from the perpendicular; this is illustrated below.
Refraction satisfies Snell’s law, which says that the angles of the rays and the refractive indices (labelled by n) satisfy the relation:
We won’t worry about Snell’s law in detail right now, but the important thing to note is that light coming from glass to air exits the interface at a bigger angle than it hit the interface. But this means that there is some critical angle at which the light is refracted parallel to the surface!
This means that any light hitting the interface at greater than the critical angle will not be refracted at all: in fact, it will be completely reflected inside the glass, and no light will escape. This is total internal reflection, and it is also, loosely speaking, how fiber optic cables can transmit light over long distances with little loss. The light is trapped inside the glass cable and cannot escape except at the ends.
A glass with a refractive index of n = 1.5 will have a critical angle of 41.8°, meaning that any light hitting the interface with an angle larger than this will be totally reflected. In our prism cloak, light is hitting the boundary at 45°, so all the light is funneled from one side of the cloak to the other without escaping.
Though this device is not even close to a perfect cloak and is certainly not invisible, it does demonstrate two important aspects of the original invisibility cloak design. First, it guides light around a hidden region, as a perfect cloak would be expected to do. Second, it hides the interior region by total internal reflection, and this is essentially what happens in a perfect cloak as well. In fact, a perfect cloak in principle would have a refractive index of zero on the interior edge, meaning that all rays of light, regardless of angle, must be trapped within.
The effect is also good enough to impress people and convey that invisibility is scientifically feasible, if not possible — yet!
* A special thanks to Mike Fiddy and Robert Ingel of UNC Charlotte for suggesting this idea.
Although I like the demo a lot on its own, I think it’s a pretty unconvincing argument for the potential feasibility of metamaterial cloaking devices. In fact, it’s fundamentally different physics and therefore very misleading. It’s like “proving” that an antigravity machine could work by pointing to a hot air balloon. Not that cloaking is equivalent to antigravity, but using one effect to convince people that another would work seems wrong to me.
Hmm… I kinda completely disagree with your comment, which I also find a bit uncharitable. First of all:
I’m not really sure how it’s fundamentally different physics. A cloaking device is a specially designed material structure that guides light around a central region and sends it on its way effectively without distortion. This is essentially the same thing that the prism cloak is doing, albeit in a cruder and much more limited way. The physics of a cloak is light-guiding around the hidden region, this guiding can only be done in a “perfect” manner with the appropriate materials, such as metamaterials.
You’ll notice that I didn’t even use the word “metamaterials” in the post at all. “Metamaterials” are somewhat of a red herring in the discussion of cloaking: if evolution had given us vision in a longer-wavelength range of the spectrum, we would be likely using all-natural materials to build these cloaks.
In fact, the whole progression of cloaking optics over the past six years has been towards designs that use simpler, even natural, materials for cloaking. The introduction of the “carpet cloak” in 2008 was motivated in large part by the desire to create cloaks that do not need extreme material parameters and can be fashioned very simply. The carpet cloak demonstrated by Zhang in the video at that link is in fact made entirely of natural materials: it is a pair of cut pieces of natural optical calcite glued together!
If true metamaterials are needed to really demonstrate the cloaking concept, then every experiment done to demonstrate so far has been fatally flawed. The first experiment in 2006 by the Duke group used “reduced parameters” to generate their cloak — pure nonmagnetic dielectrics. This cloak was consequently not perfect, but was used to demonstrate that the basic transformation optics design could guide light around a central structure. Every experiment, save for a recent one in 2012, has also used reduced parameters to simulate the cloaking effect. That design, like the prism cloak, is also “unidirectional.”
To summarize: cloaking researchers have focused their experimental work on demonstrating that a cloaked region can be generated by guiding light around a hidden region, most of it without using anything that could really be called a “metamaterial.”
That isn’t to say that the “prism cloak” described here is doing exactly the same thing, but it is a simple illustration that light-guiding cloaks are not impossible. For illustrating the basic concept to the public, it doesn’t seem unreasonable.
I didn’t mean to offend you and I’m sorry if I came across harshly. But if you discuss the very novel work of Pendry et al. and then demonstrate something similar using technology that has been employed by magicians for as long as prisms and mirrors have existed, I can’t help but feel it’s misleading. This is, however, a terrific demo of classical optics.
Thanks for the follow-up comment. I think it can be misleading, but only if presented as something that it is not. When I’ve been using this in talks, and in this post, I’ve tried to make it clear that this is not a modern invisibility cloak: it is merely a trick that can be used to illustrate that light can be guided around an area to hide it, much in the manner that modern cloaks do. People I’ve encountered seem able to appreciate the difference between this trick and “true” invisibility.
I do agree with you. It is just a trick, not related to academics. Blog posts maybe need not too much accuracy? I think.
Although H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep., vol. 2, Feb. 2012 might disagree about tricks versus academics.
Very true! I need to blog about that, because the same researchers just announced new related results.