Metamaterials | History
We Measure Artificial Magnetism
It was towards the end of 1999, and time to start writing up a manuscript. But there was a problem. While all the measurements supported our interpretation that the rings were magnetic, we hadn't really proved that they were actually magnetic. We had assumed that the electric permittivity, ε, didn't matter. If we tried to publish our result as a scientific paper, a reviewer was bound to criticize us as having not really made the case. With our equipment, all we could do is measure the amplitude of the reflected and transmitted waves - two measurements. A material is characterized by at least four parameters: ε and μ, which tell you how the material transmits and reflects waves, and ε and μ, which tell you how the material absorbs waves. To properly characterize a material, we would need four measurements. We could have potentially done such a measurement with a device called a vector network analyzer, but we didn't have one. So, one could argue that we had misinterpreted our results, that the rings were actually an electric material and that it was ε that was negative where the material became opaque, not μ. Our measurements were not sufficient to differentiate between electric and magnetic response.
The night after we had completed the measurements on the rings, I obsessed about the problem. We were stuck. We could probably find a vector network analyzer somewhere to use, but it would take a long time to arrange and our momentum would fall off rapidly. It wasnt even clear if we could do the experiments in the parallel plate waveguidewe might have to build entirely new samples and set up something like an antenna chamber. That would become a serious effort, and the more I thought about what had to be done, the less likely it all seemed we could actually do it. We had to find a different way.
I felt almost desperate, trying to think of any experiment that would help us unambiguously assert that the ring structure was effectively magnetic, using our relatively primitive equipment. What if we were to embed the rings in another material? Suppose we encased the rings in plastic, for example. Plastic has a positive ε, and all that would happen is that the spectrum would shift in frequency - the frequency shift wouldn't help us conclude anything about whether the rings were magnetic or electric.
What if the surrounding ε were negative?
With that thought, all of a sudden, things started to fall in place!
The refractive index of a material, n, is the square root of ε multiplied by μ. In order to be able to take the square root, ε and μ both need to be positive. If either ε or μ of a material is negative, their product is negative and you can't take the square root, meaning the material is opaque. But, if both ε and μ were simultaneously negative, then their product would be positive, and the material would be transparent! And we knew how to make a negative ε - that was easy. We could use the wire medium. The experiment was suddenly obvious: Interleave a wire medium with the ring medium. The opaque region that we were measuring should become transparent once the wires were added, and the transparent frequency regions around the frequency gap should turn into opaque regions.
That night, I tried a couple really simple calculations and confirmed the idea. It should work!
The next day I told everyone about the idea, and David Vier immediately tried some simulations to verify the effect. We had been calculating dispersion diagrams, which told us (among other things) at what frequencies the material was transparent (or where there was a mode) and at what frequencies the material was opaque. When David added wires to the rings in the simulations, the transparent and opaque regions were swapped, exactly as expected.
And there was something else. The dispersion diagrams we were calculating consisted of lines that tell you how quickly a pulse should travel within the material. Normally, the lowest line starts at zero and has a positive slope. For the rings and wires, though, there was a gap that extended from zero up to some frequency, and then a line appeared that had a negative slope. I had never seen anything like this, even after calculating and researching band structures for years. Band structures can have bands with negative slopes, but I'd never seen a case where the lowest band had a negative slope. There was something special about this structure that I'd have to follow up on later. For now, though, we could at least do the experiment to confirm the simulations.
When I told Shelly about the wires, he seemed to become a lot more interested, sensing that we had found a system with unusual physics. Always on the lookout for funding opportunities, Shelly told me that a new term was being bounced around the physics community, called metamaterials, and that the stuff we were doing looked like it might be a good match. He had heard his program manager mention it, and had suggested to Shelly that he attend a talk about metamaterials being given at an upcoming meeting of the American Physical Society in Minneapolis. With any luck, maybe our work would eventually have a path to funding.
Willie, David and I talked about how to make the sample, with David doing lots of simulations to find a structure that would be easy to fabricate. In the end, relatively thick posts could be used, with strips of rings placed in between. Willie made an aluminum plate with an array of brass posts, and cut a rectangular groove in the bottom plate of the parallel plate waveguide. The wire medium - the brass posts - could then be dropped into the chamber and measured, and then measured again with the split rings added.
It worked! While the data wasn't great, the rings and wires together produced a transparent frequency region that, for the rings alone, had been an opaque region. This experiment combined with the simulations was now very strong and persuasive evidence that the array of conducting rings behaved like a magnetic material. For an unfunded, "hobby" project, we had actually produced a pretty nice little experiment and set of interpretations. We had gone through a lot of trouble to prove the rings had a magnetic response, but the result was satisfying and definitely enough to write a manuscript. I felt there was enough unique physics contained in this little study that I thought we should submit the work Physical Review Letters, the most prestigious physics journal. Willie and I wrote up the manuscript, and I sent it off in December of 1999.
We Discover Negative Index
Our manuscript was rejected immediately, with a form letter that said, among other things, "this work is not important enough for Physical Review Letters."
Actually, the rejection was not surprising. We were bouncing microwaves off of copper to prove that rings with little gaps in them could be interpreted as forming an artificial magnetic medium. The entire experiment seemed much more engineering than physics to start with. There was nothing really fundamental from a physics point-of-view, at least not anything that immediately grabbed your attention. It wasn't clear where else we could submit the paper, though. I knew we wouldn't fare well in an engineering journal, since our measurements were - by engineering standards - sloppy and primitive. We really were focusing on a concept, but did not have the right equipment or training to do a proper job of it.
But the strange slope of the line on the dispersion curve still nagged at me and made me feel like there was more physics to be uncovered. Clearly, the medium with negative ε and μ was somehow special. Could we really have been the first to discover it? Had anyone else ever reported such a thing? I needed to find out what other mysteries this artificial material held.
After receiving the rejection from PRL, I figured the first thing I should do was a literature search on the key words "negative permittivity and negative permeability." Using the online search tool at UCSD, only one paper showed up, published in 1968 by a Russian physicist named Victor Veselago. The title of the paper was "The electrodynamics of substances with simultaneously negative ε and &mu." That was promising! I sent the link over to Willie, and he ordered a copy from the library.
A few hours later, Willie walked into my office, practically trembling.
"I can't believe it, every time I read through this paper I get more excited! Willie handed me a copy of the Veselago paper.
It was stunning. The artificial material we had put together just to demonstrate that the rings were magnetic, was actually much more than we realized. It was a material that had been hypothesized by Victor Veselago more than thirty years before. Veselago had actually contemplated the physics of a medium that had both negative ε and negative μ, which he had called a "left-handed medium" at the time, and had made some very startling predictions. Among the most basic predictions was that the refractive index of such a material would actually be negative that a beam of light striking the interface to a material with negative ε and μ would actually be bent the wrong way. For this reason, materials with negative ε and μ are also known as negative index materials. Veselago showed that all of geometrical optics would need to be reconsidered in the context of negative index, with new optical devices being possible.
But Veselago didn't stop at negative refraction. He noted that all electromagnetic and optical phenomena would be be impacted by negative index materials. The Doppler shift would be reversed, for example. The direction of Cerenkov radiation--the light emitted by a charged particle passing through a material--would be reversed. Radiation pressure would be modified. It was truly amazing. Veselago went on further to point out that no such material had ever been synthesized or reported; he suggested possible ideas to creating a negative index material, including magnetic semiconductors. So, the Veselago paper showed that the artificial material we had made in the lab had only been predicted to exist in 1968, with no actual material ever having been demonstrated before then. What about after 1968? I looked at the number of times his paper had been cited: three. Three times in the past thirty-plus years, and two of those cites were by Veselago in subsequent papers. There were clearly no negative index materials that had ever been reported.
We had made the first one! The first negative index material!
For Shelly, the Veselago paper changed everything. Sensing that we had stumbled onto a major discovery, Shelly now became completely involved. Shelly and I rewrote the abstract of the PRL manuscript, paraphrasing Veselago's predictions and making the paper more about the discovery of negative index rather than just about proving that the split rings were an artificial magnetic material. Shelly was convinced that our structure could also be considered a metamaterial, so we included the term metamaterial in the abstract and discussion. We resubmitted the manuscript, and after a couple of months, it was accepted for publication.
The acceptance of the PRL was a great triumph for us; I was happy that we had succeeded in generating some intriguing physics. But, I really didn't see much practical use for the negative index material, and I also didn't think that microwaves scattering from artificial metal structures had much of a future. I figured engineers had probably worked everything out that was of importance decades before and that, if anything, we were probably rediscovering things that were well known in another context. I sent our manuscript to John Pendry, thanking him for giving us the go-ahead to work on the split rings, and told him we were probably done with artificial materials. I had to get back to studying optical plasmons. In my opinion, no one was likely to be interested in funding this sort of work.
I had completely underestimated the level of curiosity in the scientific community.
