Our recently developed ability to structure materials at nanometer scales has led to a variety of applications, but few of them have made geeks as excited as they are about cloaking devices. Although still fairly limited, these cloaking devices rely on what are termed metamaterials—devices that are structured so that they can manipulate light, bending it in unusual directions. Now, researchers have determined that it should be possible to create metamaterials that can take lightwaves and perform calculus using them.

Although the paper is entirely theoretical—no actual devices were constructed, nor were any light waves bent—simulations using the properties of materials we know how to work with, like silicon, indicate that real-world devices should perform almost as well as virtual ones.

The authors of the paper describing these metamaterials say they were inspired by analog computers. Earlier mechanical computers could do things like continuously update as the values they worked with changed—examples include the geared fire control computers that gave the US Navy a huge advantage in World War II. But compared to digital computers, the analog forms tended to be bulky and overly specialized, so they were quickly dropped as advances were made on the digital versions.

But the authors were intrigued by the prospect that they could create an analog computer that operates on light. Such a computer would still be very specialized, but it might have some potential utility, as it would do the equivalent of image manipulation without needing to actually capture an image first. So the authors built a couple of model devices to see if it would work based on materials we already know how to make.

Their first go is rather complicated, in that it involves a lens that performs the equivalent of a Fourier transform on the incoming light. The light then passes through a thin layer of metamaterial, which manipulates the light's wavefront. A second lens then reverses the Fourier transform. The output is a modified light wave, one that behaves as if it had been processed. Put another way, digitizing the light after it had passed through the device would be the equivalent of digitizing it first and then performing a calculation with the results.

Because the first device was so complex, the authors tried an alternate approach: multiple layers of metamaterials. These were not especially exotic—they modeled them with aluminum-doped zinc oxide and silicon—they just had to have the appropriate structure and thickness.

What can you do with these? The authors demonstrated that it should be possible to construct devices that take the derivative and the second-order derivative of the light wave's curve. Those could be used to perform edge detection on the image. It was also possible to perform convolutions, merging the function that describes the light's wavefront with one encoded by the metamaterial. As with other analog computers, regardless of what math was being performed, the output would update instantly as the light would change.

These aren't especially useful at the moment, but the authors haven't demonstrated that they can build a working device yet, either. Once they do, it's possible that they and others will put some serious thought into how to get something useful out of it.

Science, 2014. DOI: 10.1126/science.1242818 (About DOIs).