Scientific Method / Science & Exploration

Give me the right phase and an amplitude and I will lift the Moon

Two research groups provide elegant demonstrations of how directly controlling …

Way, way, way back in the ancient times of, umm, 2007, some colleagues of mine published a paper. And it was good. In fact, it caught the imagination of physicists and has led to a string of similar publications. For those of you too lazy to click the links, those are all stories about how to make light focus either inside an opaque material, or while passing through.

As you might expect from an introduction like that, this story is also about focusing light, but it has a twist to it. It shows that a light pulse can be focused in space and time despite having passed through an opaque material. A related paper is a little more complicated, but it essentially shows that you can do the focusing trick with surface plasmons as well. This may sound counterintuitive, but the very short summary would be that these researchers have shown that light behaves like light.

These are part of an on-going series of elegant experiments. As far as the physics goes, I don't think there is anything new here—instead, the real story is about control, which is much of modern physics research.

The lingering question for some of you will be, "How do you focus light through an opaque material?" The answer is fairly simple. Most opaque materials are white-ish, meaning that they don't really absorb much light; instead, they scatter the light in every conceivable direction. This scattering makes the material appear white, and by the time light reaches your eye, any spatial information that it might have carried—like who is on the other side of a frosted window—is gone.

The heart of these experiments

What researchers at the University of Twente realized is that, in these systems, there are a number of paths through the material that all have different lengths. If you control the phase and amplitude of the light entering these paths, you can get the light exiting the material to have the phase relationship that you desire. In principle, you could use this to send images through a sugar cube, for instance.

Principles are cheap though. The reality is that you don't know the relationship between these paths, so you can't know what phases or amplitudes to set for any of them. The solution is to choose something simple, like focusing a beam of light, and carefully adjust the amplitude and phase of the light in each path until that is achieved.

In practice, this is achieved by passing light through a liquid crystal screen. Each pixel modifies the phase and amplitude of the light passing through it, creating a beam of light with an arbitrary phase and amplitude distribution. The light from each pixel follows its own path through the scattering material, and a camera on the other side tells the experimenter how much light is falling on a given pixel. Maximize one of these values by altering the liquid crystal screen, and you have created a focus.

It works in time, too

A group of Israeli researchers has followed this up by showing that this works in both space and time. The idea is that if you have pulses of light that are just 100 femtoseconds (fs) in duration then, spatially, these are only something like 30 micrometers long. The different paths have a distribution of lengths that might span the entire length of the pulse or more. Although the entry pulse might be 100fs long, the exit pulse, even if it is focused in space, might have a duration of 1 picosecond (1,000fs).

Electronic devices are way too slow to tell you if you are optimizing the pulse duration. To get around this, the researchers used something called two photon absorption. The idea is that you have some molecule that might absorb photons at a wavelength of 400nm (blue) and later emit a photon at 500nm (green). But if you shine enough photons with a wavelength of 800nm on the molecule, it can absorb two photons simultaneously and still glow green. This really depends on having a lot of photons around at the same moment in time, so it is a good indirect measure of pulse duration.

The experimental setup is nearly identical—just shift the camera out of the focus you want to create and replace it with a screen painted with molecules that undergo two photon fluorescence. Now, optimize the intensity from the smallest possible spot on the screen and you have created a spatial and temporal focus through an opaque material.

The researchers showed that they can do that. They can also take a laser pulse that has been stretched out when passing through some glass and use the scattering medium to shorten the pulse back to its shortest possible length. 

Am I surprised by this finding? No. I would have been more shocked if it hadn't worked at all. It is surprising that it works so well, because the paths through the material must be chosen such that they have identical lengths. That these paths exist is no surprise; that the authors can efficiently couple to them is no surprise; that they get nearly the same efficiency in the non-pulsed case, though, is a bit surprising.

If you are wondering what this is good for, there isn't a simple answer. A researcher may tell you that what they want to do is image through scattering tissue like skin or bone. But the big issue is that this sort of imaging requires you to be able to steer the focus in a known way. If you don't know the relationship between the paths—the optimization trick just tells you that you have it right, but nothing about the actual paths themselves—then you can't steer the focus. As the game is currently played, the device would steer to wherever the nearest fluorescent molecule was and would stay there, which is not a lot of use.

I'm not saying it can't be done. Instead, I am saying that you need a secondary observation system that tells you where the focus is. But no one has any real idea on how to implement that yet.

But can you do that trick with plasmons?

So we now know that you can focus light in space and time using a scattering material and some feedback. The real physics is that light is focused by controlling the relative phase of the light wave in a spatially dependent manner—if you have control of the phase and amplitude, you have control of everything. This is what a group of researchers in the Netherlands has demonstrated.

They used a spatial light modulator to create four beams of light that form a square. Each light beam can have its phase and amplitude controlled independently. These were focused onto a metal substrate that had an array of holes drilled into it. The holes serve two purposes: they provide the scattering necessary to excite plasmons, and they also provide the scattering necessary to image where the plasmons are on the surface.

And, yes, by controlling the relative phase and amplitude of the four beams of light, the researchers could produce a focus anywhere inside the square formed by the beams. I find that absolutely unsurprising, too. The nice thing about it, though, is that the etched structures are only necessary to create the plasmon; they aren't necessary to focus. 

If you have to etch a specific structure to create a lens, then it will have limited use, just as any single ordinary lens has. In a bulk optical setup, exchanging a lens is generally no big deal. On the other hand, changing a plasmonic lens involves the redesign of an entire substrate, since all the other optical elements must be etched onto the same substrate. Since this new approach allows the researchers to choose their focus as and when they will, it's more akin to exchanging lenses in a normal optical setup.

The other big thing is that etched structures always allow the plasmon to re-radiate as light, meaning that things like lenses end up reducing the intensity of the plasmon. This avoids that problem as well, which may open the door to new experiments that require high intensity, focused surface plasmons.

The summary: these are very interesting experiments that demonstrate some well-known physics principles and provide a nice step in the direction of new applications.

Nature Photonics, 2011, DOI:10.1038/NPHOTON.2011.72

Nature Photonics, 2011, DOI:10.1038/NPHOTON.2011.57

Listing image by Image from Pink Floyd's 'Dark Side of the Moon' album.

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