At the height of the cold war, a Russian named Victor Veselago took a close look at something called the refractive index. At its most simple, the refractive index is the reason why the speed of light is what it is (even vacuum has a refractive index). What Veselago saw was that a positive refractive index is the product of the details of a material's response to the electric and magnetic components of the light field. But if one could play with material structures on the scale of the wavelength of light, it might be possible to create materials that had a negative refractive index—or no refractive index at all.
Late last century, fabrication techniques finally caught up, and Veselago's work started getting the attention that it deserved. Negative index meta-materials were demonstrated and, with that, transformation optics became the funnest game in town—all the cloaking device stories involve transformation optics at some level. In all the excitement, the idea of setting the refractive index to zero wasn't entirely forgotten, but it didn't grab the spotlight in the same way. But zero index meta-materials should have some rather special properties of their own, as a couple of recent papers illustrate nicely.
Let the madness eat your brain
Just to drive home how hard it is to think about these meta-materials, let's go through a couple of examples. Imagine I have two blocks of material: a normal one with a refractive index of one, and another with a refractive index of -1. I shine light on both of them and observe the consequences. One thing that I would notice is that, although the speed of light was exactly the same in both materials, it seems to be in opposite directions. That is, the light in the negative index meta-material appears to be going backwards. Yet the direction of energy flow remains unchanged—both materials transmit the energy from the light field in the same direction—it's just that one makes the light moonwalk.
Well, that was a negative index meta-material, but what happens when the refractive index is zero? In this case, you might think that the speed of light would drop to zero, but it doesn't (that actually happens with a very large refractive index). No, in this case, the speed of light seems to be infinite. Funnily enough, though, this looks eerily like the light is standing still.
That's because, if I were to examine how the fields were distributed in space, I would find that they never change. But, yet again, the energy flow—if I were to momentarily increase the light intensity and measure the time for that pulse to appear at the other end of the meta-material—is no faster than the speed of light in a vacuum.
This seems a bit contradictory. If I play with the phase of the incoming light, then that change can't change the field distribution inside the meta-material—yet, these phase changes will, eventually, appear in the output.
Lovely theory, where's the evidence?
That's the prediction, at least. To see if this understanding was really correct, a group of researchers has constructed zero index materials and had a look at the propagation of light through them. The material was constructed by combining layers of negative index material with layers of positive index material, which gives an average refractive index that is zero, but only for a small range of light frequencies.
To analyze the behavior, they basically performed the experiments described above: split light from a laser in two, send part through the zero index material and part through a normal material, then recombine the two laser beams at the end. The output depends on the effective distance the light has travelled through each sample. If both distances are the same, then they will add up in phase and give a bright light beam. On the other hand, if they are a half wavelength different, then the two light fields add up out of phase to give no light at all.
So, in one arm we have a normal silicon waveguide, and in the other we have layers of silicon interleaved with layers of silicon with holes drilled in it (the negative index material)—a zero index meta-material. If this is truly a zero index material, then, as far as the light is concerned, it isn't there at all. In other words, it should have a zero length, at least for the appropriate wavelengths of light.
We can watch how the output light intensity changes as we change the wavelength. For the wavelengths where the refraction index is normal, the interference changes slowly from constructive to destructive, since the refractive index varies with wavelength in normal materials. However, once the input wavelength enters the part of the spectrum where the meta-material is supposed to have a zero refractive index, the dips and peaks in intensity become much smaller. This is because one refractive index is no longer changing, so the intensity differences only depend on the normal arm.
Compare that to a model of the expected output and you get fairly good agreement between experiment and theory. The authors probably have made a zero index material and, yes, it behaves as if it has zero length.
That is pretty cool. Now, what might we use that for?
Would you like fusion with your zero index meta-material
The second paper is seemingly outlandish—I admit it, my eyes got a lot of exercise as I read the paper. But even if it's so technically challenging that what it proposes may never see the light of day, that doesn't make it worth ignoring. Yes, they want to use zero index meta-materials in laser-induced fusion facilities to improve the efficiency of fusion.
A quick recap: in laser-induced fusion, one drops a pellet of deuterium (a hydrogen atom with an extra neutron) through the combined focus of a couple hundred laser beams. If the laser pulses all arrive simultaneously, their combined might crushes the pellet to pressures significant to fuse some fraction of the deuterium.
There are two critical points to this process. The lasers should have the smallest combined focus possible. This makes the pressure largest and will allow more of the pellet to fuse. It is also necessary to have the laser pulses arrive at the same time. All of these events happen in time scales of picoseconds and nanoseconds—late arriving pulses create a hole through which deuterium is ejected, reducing the amount available for fusion.
In a zero index meta-material, the field distribution never changes, so maybe it can help create a good focus? If we enclose the vacuum chamber where fusion takes place in a spherical shell of zero index meta-material, then we have a starting point that is always the same. This will, if you choose everything correctly, always focus to the same location. Indeed, this is what these and other researchers have shown, that a spherical shell of zero index meta-material acts like a perfect focusing lens.
Oh, wait a minute. If I change the input distribution of laser beams—say one is slightly misaligned—the output distribution will change (even though the distribution inside the meta-material remains constant), so surely this doesn't help, right? Not so fast, say Zhai and colleagues. The solution is to place the lasers inside the zero index meta-material. Once this is completed, then the only thing the lasers can do is contribute to the unchanging field distribution, no matter what direction they are pointed.
That is when the laserboy in me says: "you want to do what?" At the start of the paper, I was envisaging the survival of a delicate meta-material in the face of 200 odd high energy lasers—you know, ones that, in a different life, might be used to cut steel. But you can make arguments about the meta-material being well out of the focus, so it has a good chance of surviving. I could get that... just about.
But making the laser in the zero index material... That's genius and, at the moment, totally undoable. There are several problems that must be overcome. Lasers are very sensitive to things like light absorption and scattering losses. Meta-materials are created by creating lots of little scatterers in an ordered pattern. The typical through-put of a layer of meta-material is much less than half of the input, and no laser can survive that. Then there is the issue of physical scale. These are big lasers, so you need to make your meta-material over a very wide area. With current fabrication techniques, that simply isn't going to happen—oh, and you can't use silicon either, so don't count on using a normal fab to get this done.
There are other problems that spring to mind as well, but I think if they can solve the first two, then I would recommend giving them the money to solve the others as well.
Like I said, a crazy idea, and one that will probably never work. But still quite neat, and certainly worth keeping in mind as meta-materials get better and better.
Nature Photonics, 2011, DOI: 10.1038/NPHOTON.2011.129
Optics Letters, 2011, DOI: 10.1364/OL.36.002689
Listing image by Photograph by Samuel M. Livingston
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