Metamaterials has been used to create fascinating devices in the past including flat lenses and invisibility cloaks; new research suggests they could also be key in bringing back analog computing.

The team found metamaterials can perform "photonic calculus" when run through with a light wave, a University of Pennsylvania news release reported.

Metamaterials are "composites of natural materials" that have the ability to manipulate light waves.

"A light wave, when described in terms of space and time, has a profile in space that can be thought of as a curve on a Cartesian plane. The researchers' theoretical material can perform a specific mathematical operation on that wave's profile, such as finding its first or second derivative, as the light wave passes through the material," the news release reported.

When light is shone through one side of the material the wave profile's derivative exits out the other; the material could also be used to perform operations like integration and convolution.

This technique is often used in functions such as image processing, but in these cases the light tends to have been converted into "electronic signals in the form of digital information" before the process takes place. The team found this conversion was not necessary with computational metamaterials.

Before there were modern-day computers humans relied on mechanical calculators, which employed mechanisms such as "sliding rulers to complex arrays of gears and drive shafts" to create and store numerical information. In the mid-20th century these mechanical devices were replaced with electronic analog computers that used "series of resistors, capacitors, inductors and amplifiers" instead.

"Starting values were represented by electric voltage and current, and the results could be read out from the changes in voltage and current after passing through these dedicated circuits," the news release reported.

These devices helped to make calculations less tedious and eliminated the chance of human error.

The first "all-purpose, digital computer" was Penn's ENIAC abstracted data allowing digital computers to multi-task. These devices showed a strong advantage over analog computers.

Now analog computers may be ready to make a comeback using light-run metamaterials; especially for use on the micro- and nanoscale.

"Compared to digital computers, these analog computers were bulky, power hungry, and slow," Nader Engheta, the H. Nedwill Ramsey professor of Electrical and Systems Engineering in Penn's School of Engineering and Applied Science said. "But by applying the concepts behind them to optical metamaterials, one day we might be able to make them at micro- and nanoscale sizes, and operate them at nearly speed of light using little power."

"The thickness of our structures can be comparable with the optical wave length or even smaller," Vincenzo Galdi of the University of Sannio, said. "Implementing similar operations with conventional optical systems, such as lenses and filters, would require much thicker structures."

The metamaterials achieve their electromagnetic properties through special arrangements of atoms and molecules that are "dictated" by the laws of chemistry and physics. Researchers can use these materials to alter waves by making these micro-patterns smaller than the waves passing through them.

The researchers used an example of a pen sticking out of a glass of water to explain the phenomenon; this happens because the liquid surface refracts (bends) the light. The angle of the light from the pen to the viewer's eyes is at a different angle from the one above. Metamaterials can be manipulated to create "negative angles of refraction," which in this scenario would cause the pen's reflection to appear to be "flipped."

The team used a computer simulation of a metamaterial that could "perfectly change the shape of the incoming wave profile into that of its derivative." They also tested simulations of materials such as silicon and aluminum-doped zinc oxide.

"The simulation results of the two were almost identical, so we're hopeful we'll be able to do photonic calculus in a physical experiment in the future," Engheta said.

In reality these materials could be used to perform functions such as taking derivatives of algebraic functions almost "instantaneously" as opposed to digital computers that would take much longer. It could also be effective in certain imaging techniques such as edge detection.

"When we do edge detection on an image now with currently available image processing techniques, we do it digitally, pixel by pixel," Engheta said. "We scan an image and compare all of the neighboring pixels, and where there is a big difference between two, we label it an edge. With this computational metamaterial in the future, hopefully we will be able to do it all at once. The light from the image itself could go in and the edge-detected profile could come out the other side."

"Thanks to recent advances in nanotechnology," Andrea Alù, Associate Professor and David & Doris Lybarger Endowed Faculty Fellow at The University of Texas at Austin, said. "Today we are able to control light propagation through a material in unprecedented ways, and realize material functionalities that would have been unthinkable only a few years ago. In this paper, we set the stage to have metamaterials realize a broad set of mathematical operations for us on-the-fly, as light propagates through them."