Tineke Thio. American Scientist. Volume 94, Issue 1. Jan/Feb 2006.

With relentless regularity, consumers have seen the development of iPod-sized devices containing large collections, first of songs, then photographs and now movies as well. If past experience is any guide, the progress won’t cease here. The current Holy Grail of data-storage technology is “the terabit memory”-the capability of storing a thousand billion bits (or about 2,500 movies) on a square inch of the medium, implying that each bit occupies a spot about 25 nanometers across. At these tiny size scales, thermal fluctuations can easily flip a magnetically recorded bit between the “one” and “zero” states, so something else is needed. Many researchers are investigating optical data storage for this next big step in data density.

Currently, a DVD can hold one long movie on its tracks, where the bits are recorded using features that are about 500 nanometers across. For a terabit optical disk, each data bit would have to be written and read with a beam of light that is 25 nanometers in diameter, and for writing the intensity of the light must be high enough locally to melt the storage medium. The latter requirement is the reason why the optical terabit memory has not been achieved-at least not yet.

Boy Scout lore holds that you can use a lens to focus sunlight to such a high intensity that it can start a fire. And today’s DVD and CD-ROM writers indeed use lenses to focus laser light enough to “burn” data bits onto the disk. However, because light is an electromagnetic wave, the tiniest spot one can make in this way, even with the most sophisticated lenses, is about half the optical wavelength in diameter. Physicists call this minimum “the diffraction limit.” Consumer electronic devices typically use semiconductor lasers, which are cheap to make and reliable. Such lasers, which usually have wavelengths of 670 nanometers or longer, can be focused to a circle that is about 400 nanometers across. The diffraction limit prevents the light from being concentrated more narrowly. This problem is endemic in the field of nanophotonics, where one often wishes to restrict light to dimensions that are far less than the optical wavelength.

One possible solution is not to use a lens at all; instead pass the light through a tiny aperture in an opaque screen. That works, but diffraction causes the spot size to grow quickly with distance from the opening. So to benefit from this approach, the target must remain very close to the screen, which is why optical microscopes that get their extremely high resolution from the use of an aperture are considered “near-field” instruments.

Another even more unfortunate limitation is that apertures with diameters much smaller than the wavelength don’t let much power through. To put this concern in perspective, a typical metal needs to be at least 200 nanometers thick to be opaque; even a 50-nanometer aperture in such a metal film would pass only one ten-millionth of the light shone on it from a 670-nanometer laser. Thus, if you used a laser with 10 milliwatts of power, only 1 nanowatt would make it through the hole, which is not very useful for burning data bits.

Fortunately for those people who simply must carry all their favorite movies in their coat pockets, recent research has shown a way to boost the throughput of even subwavelength apertures quite substantially. As is often the case in science, the initial motivation for the work had little to do with practical applications. Rather, it began with an attempt to study isolated molecules.

Spellbound

The story begins in 1988, when Thomas W. Ebbesen, a physical chemist then at the Nippon Electric Company (NEC) Fundamental Research Laboratories in Tsukuba, Japan, decided he wanted to do single-molecule spectroscopy. He planned to place the molecules under study on a metal film perforated with millions of small holes arranged in a regular array and underlain by a transparent substrate-much like a microscopic muffin tin. Each compartment would contain a single molecule, which would ensure that it was well separated from its neighbors.

Before attempting spectroscopy on the isolated molecules, Ebbesen needed to characterize this rather unusual sample holder. What he discovered was so surprising that I don’t believe he ever carried out the single-molecule experiment he set out to perform: When he held up the perforated film to the light, he could see with nothing more than his two eyes that it was quite transparent, whereas from the tiny size of the holes one would have expected it more to resemble very dark sunglasses or perhaps even a welding mask.

Ebbesen then put his perforated film in a spectrometer and found that the optical throughput of his hole array varied wildly with wavelength. At the peaks, the fraction of light transmitted through the perforated film was a few times larger than the tiny fraction of the area occupied by the holes. This observation was astounding, considering that the holes were much smaller than the optical wavelength. The result was so far out of the realm of the ordinary that many physicists familiar with the principles of optics simply could not believe it. Their skeptical reactions prompted Ebbesen to do more experiments on his perforated films, varying such parameters as the hole diameter, the distance between the holes, and the substrate material. Those studies became easier in 1992 when Henri J. Lezec, who was then also at NEC in Tsukuba, became interested in these curious structures and started fabricating them with a focused ion beam, a versatile milling tool with a resolution of 5 nanometers.

The understanding of the unusual optical properties of hole arrays took a major step forward in 1995 when Ebbesen moved to the NEC Research Institute in Princeton, where Peter A. Wolff first suggested the possible role of electronic excitations at the metal surface, a phenomenon known to physicists as surface plasmons (a short version of the more correct term, surface plasmon polaritons). Although typical metal surfaces are electrically neutral on average, they can hold an excess of surface charge in places and a deficiency in other locations. Surface plasmons are nothing more than waves of varying charge density which travel along the surface of a metal in an orderly fashion.

Because metals shield electromagnetic fields quite well, such waves of charge density cannot penetrate very deeply. In the visible to near-infrared range of the spectrum, the fields typically extend only about 20 to 30 nanometers below the surface of silver, for example. They can’t escape into the space outside the metal either, because for a given optical frequency, the wavelength of a surface plasmon is slightly shorter than the wavelength of light in free space, and for a surface plasmon to convert into a free-space photon, their frequencies and wavelengths both have to match. Similarly, a photon of light impinging on a metal from free space doesn’t normally excite surface plasmons. But if surface plasmons don’t interact with light in such ways, why should they be relevant to the optical transmission of hole arrays? The answer to this key question was not entirely clear when Wolff first made his suggestion.

It was at this point that I got involved in studying this topic, together with Hadi F. Ghaemi, who was then a postdoc in my group at NEC’s Princeton lab. Ghaemi and I realized that when a metal surface contains a regularly spaced pattern of holes, grooves or other features, light incident on it can, in fact, interact with surface plasmons through a process known as grating coupling. We were thrilled to see that Ghaemi’s calculations matched the observed transmission peaks reasonably well without our having to fool with any adjustable parameters. This coup marked the birth of a quantitative “surface-plasmon model,” which explained how certain structures, particularly those with regularly spaced features, allow light to interact with surface plasmons. Our notion was that when the photons have the right energy (that is, color) and momentum (effective wavelength and direction) to match those of the surface plasmons on a corrugated surface, the interaction is resonant, giving rise to electromagnetic fields that are strongly enhanced relative to the intensity of the incident light. Resonance accounts for many physical phenomena, including the fact that you can get a child on a swing to go pretty high while giving only small pushes-so long as they are timed just right.

The reason to invoke resonance in this context was because the transmission enhancement Ghaemi and I found for the perforated metal films was so enormous: We estimated that the transmission of each individual hole in our array was 600 times larger than what would normally be expected for a single hole. Such a large enhancement was terribly exciting in terms of the possibilities it opened up for the design of various high-tech devices. So when Ebbesen, Lezec, Ghaemi, Wolff and I published these results in Nature in 1998, they made quite a splash.

Suspicion

For about five years, the surface-plasmon model seemed adequate to explain the extraordinary optical properties of perforated metal films, and it became the standard interpretation. But as early as 1999, Michael M. J. Treacy, who was also at the NEC Research Institute at that time, proposed an alternative model involving diffraction. And more work produced a growing body of results that did not easily fit the surface-plasmon view of things. For instance, Michaël Sarrazin at the University of Namur in Belgium did a numerical calculation for hole arrays in nonmetallic materials, which do not support surface plasmons at all, and he found that such films have transmission spectra quite similar to those observed for hole arrays in metallic films. And a numerical calculation done by Philippe Lalanne’s group at L’Institut d’Optique in Orsay, France, suggested that surface plasmons should, in fact, suppress the transmission of light rather than increase it.

In addition to these troubling results from theoreticians, there was a long-standing experimental enigma: The enhancement in the transmission of light was observed over a much larger range of wavelengths than would be expected from a consideration of the optical properties of the metal. This observation was puzzling because surface-plasmon resonances on a metal surface generally give rise to spectral peaks spanning a narrow range of wavelengths (so narrow that they can be used to probe subtle changes in the environment at the surface, which give rise to detectable shifts of the resonant wavelength). What, my colleagues and I wondered, was really going on?

All these loose ends were neatly tied up in a model that Lezec first proposed in 2003 when he was working with Ebbesen, who by this time had established a research group at Université Louis Pasteur in Strasbourg. Increasingly bothered by the inconsistencies in the data, Lezec decided to go back to the beginning and measure the transmission enhancement of a hole array. But he took a different approach than we had taken a decade before: This time he compared the transmission of a hole array not to a theoretical result but to a single, isolated hole. The lone hole he used was in every way identical to the ones in his arrays, and it was fabricated in the same metal film; the only difference was that it had nothing around it but the smooth metal surface. He was also careful to account for the fact that an array of holes sends light in a well-collimated beam (wave interference suppresses radiation in other directions), whereas a single subwavelength hole projects light into a hemisphere. As a consequence, the fraction of incident power that gets transmitted appears to depend on the size of the lens used to collect the light for measurement on the far side. One needs to correct for this effect to extract the true transmission coefficient (the total power radiating from the holes, whether or not it falls on the collection lens, divided by the power incident on the total area of the holes). Dividing this quantity by the transmission coefficient of a single hole gives the enhancement factor, which for historical reasons specialists call G.

Lezec’s careful experimental comparison between a hole array and a single hole led to two startling results. To begin with, the largest enhancement factor he observed was G=7, much less than the “orders of magnitude” stated in our influential Nature paper. However Lezec varied the parameters of his experiments (hole diameter, hole spacing, film thickness or material used), he never observed more than a sevenfold boost in transmission.

How could this result be squared with the 600-fold enhancement we reported earlier? Lezec and I went back to our closet of old data and found skeletons: Inexplicably and inexcusably, we never did check that the holes were actually the size we said they were. Such a test would require breaking the film, and in the early days we were squeamish about destroying our priceless samples. After some sleuthing we came to the conclusion that the hole diameter we had quoted for our original experiment was smaller than the actual diameter, which resulted in an overestimate of the enhancement factor by a large amount, because the transmission coefficient of a single subwavelength hole depends very strongly on its size. That one simple mistake explains why we had calculated a G of 600.

Interestingly, this degree of transmission enhancement, although often quoted, has never been reproduced, despite the fact that it constitutes one of the chief reasons physicists became interested in this area of research in the first place. It should be a credit to Lezec that his careful experimental work overturned many years of accepted wisdom on the subject. But sadly, his efforts to get at the truth are often met with hostility or (worse) indifference.

The second surprise was, if possible, even more stunning: Whereas the maximum transmission coefficient Lezec measured as he varied the wavelength was much less than we previously reported, the minimum transmission coefficient for a hole array proved to be smaller than that of a single hole (that is, G could be less than 1). This result cannot be explained by the resonance effects of the surface-plasmon model. Indeed, the observation of both transmission enhancement and suppression is more suggestive of wave interference.

Lezec’s further experiments confirmed that, just as Sarrazin had predicted, transmission spectra for arrays of holes in nonmetallic substrates are very similar to those produced in metals. Thus whatever mechanism one invokes to explain these curious transmission effects, it must work for both metals and nonmetals. And the surface-plasmon model can only be valid for the former, because only metals support such waves of surface electric charge. That consideration alone was enough to demonstrate that something was seriously wrong with the prevailing theory.

The Lady Vanishes

As Lezec set out to find a different way to account for his new results, his conceptual starting point was a single subwavelength feature, such as a bump or an indentation on a surface. In general, surface features of this sort are expected to scatter incoming light. An everyday example is frosted window glass, which owes its translucent properties to the roughness of its surface. Those irregularities scatter light every which way such that, although the total transmitted intensity is high, an image is not formed on the other side of the glass.

When the surface roughness takes the form of a periodic corrugation, say a series of regularly spaced grooves, wave diffraction and interference gives rise to color dispersion. This phenomenon is the basis of the diffraction gratings used for spectroscopy and, closer to home, explains why CDs and DVDs, especially the re-writable kind, throw spectacular rainbows when held in sunlight, their evenly spaced data tracks being bunched closely together. The same effect is responsible for the iridescence seen in the feathers of a peacock and the wings of some butterflies.

Although it doesn’t produce such stunning visual effects, a single feature on a surface, say a tiny dimple, has its own diffraction characteristics. When it is much smaller than the optical wavelength, it doesn’t interact with light much, and the surface appears completely smooth. In contrast, a feature that is larger than the wavelength will scatter lots of light, mostly into free space. And when the surface irregularity is only a little smaller than the wavelength, it also scatters some light into free space, but a significant fraction is converted into electromagnetic waves that are confined to the surface. Physicists refer to them as evanescent waves.

The evanescent waves created in this way are of the same frequency as the incoming light, but they can have different wavelengths (all shorter than the free-space wavelength). Because the total surface wave emanating from the scattering site is formed by their superposition, Lezec and I have dubbed them “composite diffracted evanescent waves,” a name that has proved so cumbersome that we often just use the acronym CDEW (which itself is a bit of a mouthful). Here I refer to them simply as evanescent waves.

A rigorous mathematical description of such waves is horribly complicated, but in the case of a long, narrow scattering feature, the physical interpretarion turns out to be charmingly simple. When, for example, a groove or a slit is illuminated, it launches an evanescent wave that travels along the surface in a direction perpendicular to the long dimension of the feature. The new wave has the same wavelength as the incident light but has its phase shifted by 90 degrees at the point of scattering. The amplitude of the evanescent wave decays as it moves away from the place where it is created, diminishing by a factor that is inversely proportional to the distance traveled.

If there is only one groove present, the evanescent waves it generates remain bound to the surface and thus cannot be seen or collected with a lens. True to their name, these are “vanishing” waves. However, if such a wave encounters another surface feature, it can scatter into free space, where it then becomes visible. Furthermore, the evanescent wave will interfere with the light that falls directly on the second scattering site. So the total intensity at that point will be different from what is supplied by the incident light alone: Constructive interference can enhance the light intensity, and destructive interference can diminish it. If the second scattering site is a hole, such wave interference leads to a modulation of the amount of light transmitted, which can be more or less than would be the case were the evanescent wave not present.

If there is more than one scattering site located near the hole, its transmission properties are affected by all of them. But because the amplitude of a diffracted evanescent wave decays so quickly with distance along the surface, the intensity of light at the entrance to the hole is affected only by features that are located nearby, typically within seven wavelengths. An interesting consequence is that changing the wavelength by even 5 to 10 percent does not significantly alter the phase of the evanescent waves arriving at the hole. So, for example, if a set of diffracted evanescent waves interfere constructively when they reach the hole, a modest shift in wavelength won’t destroy their additive effects. (Hence the observation that transmission enhancements have wide spectral width points to the action of evanescent waves rather than far reaching surface plasmons, which generally produce narrow spectral features.)

After passing through a subwavelength-size hole, light gets diffracted as it emerges, resulting in an evanescent wave that is similar to those launched by surface features on the illuminated side of the film. If the dark side is completely smooth (apart from the hole itself), the diffracted evanescent wave remains confined to the surface. However, if there are other features on the dark surface, they will scatter whatever evanescent waves impinge on them. And if the size of these features is comparable to the wavelength, that process can be quite efficient and can produce some impressive effects. For example, features spaced at regular intervals on the dark side can lead to a “beaming” of the transmitted light. Thus the light collected after passing through the film contains information not only about the structure on the illuminated surface, but also about what’s on the far side.

Shadow of a Doubt

I confess to having received the new model with extreme skepticism when I first heard Lezec speak about it at a conference: For five years, he and I had been co-authors on a string of papers that explained the experiments with the surface-plasmon model, and now he was telling me that the theory is wrong! I wasn’t going to accept such a challenge meekly. There followed a period of several months of transatlantic argument during which 1 hammered on his model with great determination to see whether it could stand up to the pounding and account for all the observations available. It did. And in response to all my probing, Lezec produced additional measurements that made the case for evanescent waves even more convincing.

Still, there remained an obvious question: What is the role of surface plasmons in all this? In an earnest search for a surface-plasmon contribution, I persuaded Lezec to prepare a film of silver with a single cylindrical hole, surrounded by a set of regularly spaced, ring-shaped grooves. That structure should have been optimal for revealing surface-plasmon effects, yet we saw no obvious manifestation of them. The measurements were, however, entirely consistent with the new model. To me, this test offered conclusive evidence that the contribution of surface plasmons must be negligible compared with that of diffracted evanescent waves. And Lezec, who is currently at the California Institute of Technology, has created samples for additional tests as well-all of which have provided us with data that support the new view of things.

Does the demise of the surfaceplasmon model mean that optical terabit memories are out of the question? Perhaps not. Whereas the transmission enhancement is less than a factor of seven for arrays of holes, it can be substantially higher for single holes that are surrounded by a set of circularly symmetric grooves. This is because a full circle is a more efficient scatterer than are the four nearest neighbors in a hole array with square symmetry. Indeed, Keishi Ohashi’s group at NEC in Japan has shown that the transmission enhancement for a bull’s-eye structure with a single hole at the center can be up to 400 times greater than for the equivalent hole in isolation. I expect that the enhancement can be raised to an even higher level of performance by further optimizing the geometries of the corrugation and of the hole itself, which should be very helpful for situations requiring high light intensity and a tiny spot size, such as for high-efficiency near-field microscopes or for reading and writing optical data bits packed at ultra-high density. And indeed, Ohashi’s team has already built a prototype device using this strategy.

The new model, which Lezec and I published together in 2004, is generally received enthusiastically, at least by those who have no preconceived ideas on the subject. But it has encountered considerable resistance from some proponents of the surface-plasmon explanation-people who are prepared to go through rather strenuous contortions in an attempt to explain with their model such enigmatic properties as the widths of the transmission peaks, the sensitivity to features placed on the dark side of the film, the occurrence of transmission suppression and even the similarity of the results one gets with nonmetallic systems, observations that the evanescent-wave formulation accounts for in a straightforward, rather elegant way.

Easy Virtue

Perhaps I shouldn’t be surprised that many investigators in this field remain reluctant to give up on the former explanation: I can’t deny that, if it weren’t incorrect, the surface-plasmon model would be exciting, slightly mysterious and, in a word, sexy. Perhaps the notion that all the observations can be accounted for by nothing more complicated than the effects of diffraction and interference seems a big let down.

I see things differently. Because diffraction is a property of waves in general, the new model should be relevant to other physical situations as well, not just to light shining on perforated films. For instance, I believe that an analogous scattering of acoustic surface waves can explain the enhanced transmission of sound through an acoustic grating, a phenomenon that Xiangdong Zhang of the Beijing Normal University recently reported. The new perspective might one day prove useful too for examining water waves and how they pass through, or are deflected by, segmented breakwaters. But for the moment, the most exciting implications are for the development of various optical devices.

One obvious application of the new understanding is to the lithographic masks employed in the manufacture of integrated circuits. These masks are used to project patterns onto silicon wafers that are coated with “photoresist,” a material that either hardens or becomes soluble when exposed to light. After such exposures, the photoresist can be selectively removed and the silicon etched, forming whatever tiny features are required. The size of the openings in such lithographic masks is currently just a few times the wavelength of the light used, so I would expect a significant generation of evanescent waves, particularly at sharp features such as corners. Although the semiconductor industry has worked out elaborate ways of correcting for the effects of diffraction, the contribution of evanescent waves is now largely being ignored.

Although the transmission enhancement of hole arrays is more modest than first thought, these structures are still very promising for optical switching or display devices. Possibilities arise for such applications because the transmission efficiency can easily be varied, either by manipulating the wavelength or by changing the physical environment of the film. Indeed, T. J. Kim, while he was in my group at NEC, used a liquid crystal to control how much light passes through a hole array at a fixed wavelength, demonstrating the principle for a single pixel. Whereas the polarizers and color filters found in conventional liquid-crystal displays allow only about 5 percent of the background illumination to reach the front of the screen, the throughput of a perforated metal can be higher than 50 percent. Such a gain would translate into vastly longer battery life for mobile display devices.

I would not at all mind being able to work on the plane ride from New York to Tokyo (a 12-hour flight) without having to carry extra batteries for my laptop. Or I could just relax in my seat while watching a few of my favorite Hitchcock movies-downloaded from the vast collection stored on my iPod, of course.