Metamaterials Perform 'Photonic Calculus'

The discovery that metamaterials can be designed to perform "photonic calculus" as lightwaves pass through them could give rebirth to analog computers.

The theoretical metamaterial could perform a specific mathematical operation on a lightwave’s profile, such as finding its first or second derivative, as that lightwave passes through it, says a team from the University of Pennsylvania, University of Texas at Austin and University of Sannio.

Computational metamaterials could almost instantly perform operations on the original wave, such as the light coming in through the lens of a camera, without conversion to electronic signals. Essentially, mechanical gears and electrical circuits used in original analog computers are replaced with optical materials that operate on lightwaves.

Shining a lightwave on one side of a metamaterial would result in that wave profile's derivative exiting the other side. These metamaterials could be put to use doing specific computational tasks that are best suited to an analog approach. Metamaterials capable of other calculus operations, such as integration and convolution, could also be produced.

This theoretical metamaterial, working like an analog computer, produces the derivative of the incoming lightwave's profile. Courtesy of University of Pennsylvania.

“By applying the concepts behind [analog computers] to optical metamaterials, one day we might be able to make them at micro- and nanoscale sizes, and operate them at nearly the speed of light using little power," said Nader Engheta, a professor of electrical and systems engineering at Penn’s School of Engineering and Applied Science.

In applications such as image processing, it is commonplace to view and manipulate this type of lightwave, although these functions are typically performed after the signals have been converted to electronic ones in the form of digital information.

The research began with the creation of a computer simulation of an ideal metamaterial that could change the shape of the incoming wave profile into that of its derivative. Using this as a guide, the researchers constrained the simulations to specific materials suitable for existing fabrication techniques, such as silicon and aluminum-doped zinc oxide.

Analog-suited metamaterials applications that could benefit include edge detection, an increasingly common image processing technique that helps software find faces and identify objects in pictures.

"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."

Future research will entail constructing and testing these computational metamaterials in laboratory settings. If successful, plans for metamaterials that can perform other mathematical operations, such as solve equations, could be made. By encoding the input wave with a mathematical function, then feeding the outgoing wave back to the input, the intervening metamaterial would ultimately produce a wave that would reveal the desired variables within that function.

The research was supported by the U.S. Office of Naval Research's Multidisciplinary University Research Initiative and is published in Science.

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