Giant laser could arrange particles into enormous space telescope

Sometimes scientists present stuff that just seems to hit a trifecta of awesomeness. In these cases, after I have finished giggling uncontrollably and making the guy next to me nervous, I start thinking about how I might describe it to others. Without further ado, let me present the trifecta of awesomeness: a seemingly ridiculous idea, one that works in a bizarre manner that has little to do with the justification given by the scientists, and—to really make matters special—it involves lasers in space.

I think you will agree that the idea of making a giant telescope mirror by using a giant laser to control tiny beads in space has a degree of ridiculousness exceeding all safety limits. Even if the experimental results turned out to be highly subjective and slightly dodgy, there was no way that I could let this pass.

Caught in a trap

So let's start at the beginning. Light can be used to trap objects. An easy explanation for one of the trapping mechanisms can be seen by considering how light is bent when it passes through a small glass sphere. A light beam traveling through the center of the sphere will not be deflected, while light that hits to one side is bent toward the center. (Yes, I just described a lens to you. Sorry.)

Now it gets a little complicated. A light beam usually has a nonuniform intensity: as we travel across the beam, it is brightest at the center and dimmer toward the edges. If our little glass bead is sitting off-center, then more light is deflected away from the center than is deflected toward the center. This gives the bead a tiny kick. Light carries momentum, so when the bead bends the light, it changes the light's momentum, and that requires a force. As a result, the bead moves to the center of the light beam, where the intensities are symmetrical about the bead and the forces balance.

That is optical trapping, and it is awesome in its own way (it is also widely used in biophysics and related areas). But, it gets more interesting when you have a large number of glass beads. In this case, they all want to move toward the center of a light beam. But they can't all occupy the center, so they arrange themselves into a two-dimensional hexagonal pattern across the light beam. As they come into contact with each other, they stick together through electrostatic forces. The result is that a thin membrane self assembles and, if disturbed, puts itself back together.

If the beads were made out of the right material, the membrane would make a self-assembling mirror. But, given that the surface would be rough, it's not obvious that it would be possible to use it in an imaging system. Yet, this is the idea: self-assemble a bunch of beads and use this as the enormous mirror in a space telescope.

In this work, a trio of physicists actually tried to show that the imaging quality would be okay. They used a laser to trap and self assemble a group of polystyrene beads in water. The beads did indeed form a flat mirror—not only was it flat, but it formed against the wall of the vessel. The researchers did not use the slightly more complicated laser beam geometry required to form a 3D trap, nor did they try to obtain a curved membrane.

In any case, to show that such a membrane would reflect the light without overly distorting the image, they used it as part of an imaging system. And, the results were pretty sucky. To show that the mirror worked, they had to subtract the images formed by all the glass walls of the water vessel. So, they took an image with the membrane in place and an image without the membrane in place and subtracted the two from each other. In each image, there is a blurry number eight visible, which shows that the light reflected by the membrane was not too badly distorted.

But, as experimental demonstrations go, it was not the most convincing set of pictures that I have ever seen. And, indeed, I was hoping to see some characterization of imaging performance, but, nope, not a chance. Instead, the researchers presented calculations on how a more complete—but still unrealistic—mirror might perform.

Fault tolerant

They used calculations to examine the quality of the electromagnetic waves reflected from the beads. Even though the beads give the mirror a surface that, by ordinary standards, is very rough, the mirror seemed to focus nearly as well as a perfect mirror. Note that this requires a nice, regular array of beads. That phrase—"regular array"—should sound familiar to any electrical engineers in the audience, since it should remind them of a phased array antenna commonly used in antenna systems. What the researchers seem to show is that the beads act like an array of light antennas. Which they should, because that is what they are.

More interesting was an analysis of how fault tolerant the mirror would be. In these calculations, they allowed the beads to move off the perfect parabolic shape and examined how imaging performance was degraded (it will never improve). To do this, they considered two light waves impinging on the mirror from slightly different angles (as if from different objects). These focus into two blobs at slightly different locations, and, as long as the blobs don't overlap, you can see the two objects that emitted the light. They showed that the beads in the mirror could move off a perfect array by about 80 percent of their width before it was impossible to distinguish the two blobs.

In the calculations, unlike their experiment, the beads were smaller than the wavelength, and they were touching, so the "roughness" of the mirror surface was much smaller than the wavelength. So, hey, they showed that a relatively smooth surface gives good imaging performance. That also means that the 80 percent displacement should be interpreted as an absolute number, rather than a percentage. In the end, it means that the beads need to be positioned with 200nm accuracy. That seems rather challenging to achieve in an optical trap.

The last calculation showed that the mirror could have big gaps in it and still produce a reasonable focus. This is also entirely expected given the conditions they used to simulate it. It is exactly the same as taking a perfect mirror and breaking it up into a set of smaller mirrors that are physically separated. This is known to work, so it is hardly surprising that it still works.

Now, we get to the good part: taking a look at some numbers associated to get an idea of just how awesomely ridiculous this all is. According to their calculations, a 35m telescope mirror, made up from 100nm beads would weigh 100g. That is pretty cool. Even if we go to micron sized beads, the weight is still going to be negligible compared to a solid mirror. That is the ultimate justification, and I like it.

Captain, we need more power

The mirror is held together by a laser, though. In the researcher's experiment, they used a 5W laser to create a trap that was 40 micrometers in diameter. Okay, they don't say how much of the 5W they used, but trapping requires high intensities, so, let's assume 50mW—you will see later that I could be out by a factor of 100, and it wouldn't make much difference in practical terms. But, the critical number is the intensity, which is 4kW/cm². A mirror with a radius of 35m would require a laser power of 38GW. A good laser has an efficiency of around one-third, so the required electrical power is around 100GW, which is several times the output from a very large power station.

And, since we are looking at an advanced idea, let's use advanced solar cells with an efficiency of 45 percent. That means we are required to capture 220GW of solar energy, requiring a whopping 170km² of solar panels. So, even if the mirror weighs 100g, the supporting solar cells will weigh about 18,000kg. So much for saving on launch costs.

Speaking of mass and volume, a good laser diode with the right quality beam amplified nicely will produce 10W and takes up about 3cm³, so we are talking about launching 4 billion lasers (with a volume of 12 billion cm³) into space and combining their output. All-in-all, this seems like a challenging project.

From this you might get the idea that I think a laser-trapped space mirror is ridiculous. And it is—at least for now. Yet I still love the idea. It will certainly find uses in other areas—imagine assembling and manipulating lenses in places that are physically difficult to access, like inside a vacuum chamber. And, with work, someone far cleverer than I am will think of ways to overcome all the problems (and there are a lot of them; I only outlined a few of the obvious ones).

No matter what comes out of this, I was thoroughly entertained reading that paper, and I hope the authors continue this work.

Physical Review Letters, 2014, DOI: 10.1103/PhysRevLett.112.023902