Exotic materials that bend light in extreme ways could be used to perform complex mathematical operations, creating a new kind of analogue computer.

Tools for manipulating light waves have taken off in recent years thanks to the development of metamaterials. These materials have complex internal structures on scales smaller than the wavelength of the light they interact with, and so they produce unusual effects. Most famously, metamaterials promise to deliver “invisibility cloaks” that can route light around an object, making it seem to disappear.

Nader Engheta at the University of Pennsylvania, Philadelphia, and his colleagues decided to explore a different use for metamaterials, one that adapts the old idea of analogue computing. Today’s digital computers are based on electrical switches that are either on or off. But before these machines were analogue computers based on varying electrical or mechanical properties. The slide rule is one example of such an analogue calculator.

Analogue computers were limited in precision by the materials available at the time – for example, anything requiring moving parts for computation was limited by how small those parts could be made. But metamaterials, which rely mainly on light, have no such constraints. Engheta’s team has simulated a metamaterial capable of calculus functions like differentiation and integration, and other fundamental mathematical tools.


Imaginative application

The metamaterial computer works because light waves can draw mathematical curves in space, akin to a graph. In calculus, differentiation describes the slope of that curve at various points, while integration gives the area under the curve.

The team’s metamaterial block can perform these calculations by modifying the light wave’s profile. For example, if you shine a light wave describing a parabola (which corresponds to the equation y = x2) into a metamaterial that computes differentiation, it will come out the other side looking like a straight line described by y = 2x.

“As the wave goes through this block, its profile changes such that by the time it comes out it has the profile expected from the given mathematical operation,” says Engheta.

Camera angle

So far the team had only simulated these metamaterials, as both an ideal theoretical material and a more realistic one made from precisely alternating layers of silicon and aluminium-doped zinc oxide. “As our near-future action item, we are planning to build our proposed blocks in order to test the proof of the concept,” says Engheta.

If it works, the new metamaterial could in theory be included in camera lenses to perform image processing tasks like edge-detection or pattern recognition, which is useful for identifying faces and other objects in pictures. At the moment such tasks are done pixel-by-pixel using an ordinary computer chip, but a metamaterial computer could process the entire image at once.

“It’s a very imaginative application of metamaterials – it takes things off in a completely new direction,” says John Pendry of Imperial College London, who pioneered the field of metamaterials. Although image-processing is the obvious application, the basic mathematical tools could also be used to solve equations, he says. “These techniques could be adapted to do that.”

Journal reference: Science, DOI: 10.1126/science.1242818