# Metamaterials solve equations with microwaves

A holey piece of swiss-cheese plastic can do complex maths in a millionth of a second
22 March 2019

## MATHS-BOARD-FOURIER

Material that instantly solves complex maths developed by scientists...

Have you ever moved your Wi-Fi router and the various boosters at home to get a good connection, only to find certain spots of the house still have bad signal? Or been to a concert and wondered how they make sure the sound from the speakers reaches every part of the audience, without quiet spots?

A new material can calculate the answer to these and all kinds of other problems, without using a computer. And because it relies only on its special shape to do it, each answer comes out in less than a millionth of a second - so it’s extremely fast!

This speed is not the only benefit. Nader Engheta, who designed the system at the University of Pennsylvania explains “it is also low power, so may require much less energy”. This means many tricky real world problems could become more easily solved.

Because such problems can be modelled by mathematical equations, working out how to sort the WiFi or the concert speakers can be made to look like a complex sum, that if you worked through logically, would give you the best answer. Engheta highlights the current downside to this, that “computers of course can solve these types of equations but they usually do it by simulation and that usually takes time.”

Instead of computers, the system Engheta has designed is an example of a metamaterial (meta-, from the Greek, meaning beyond), which uses the structure of the material to give it properties beyond what the material alone could do. In this case, interact with and change electromagnetic waves.

These waves are part of a spectrum that includes the radio waves used to broadcast music to your car, microwaves like you’d use to heat up food, the visible light we see and even x-rays and gamma radiation - those two you want to limit your exposure to.

As you move along that spectrum from radio, you start with the waves with the distance between their peaks (their wavelength) being biggest, gradually decreasing to the very small wavelengths of gamma waves. To prove his concept, Engeta uses microwaves, at the larger end, fired into the metamaterial structure.

The system is made of plastic, with holes drilled through, to give it a unique structure. It reminds Engheta’s team of something more edible, “We like to call it a swiss cheese! The location, the size and the shape of these air holes in this piece of plastic swiss cheese is the thing that relates directly to the equation we would like to solve.”

Solving the equation is simply a case of putting in microwaves made to match the equation’s input, by modifying their properties such as strength and phase”,  and as Engheta explains “when the microwave propagates through this material and hits some of the air holes, that’s what actually does the magic in order to solve the equation. The waves interact with the plastic and the holes and when the wave comes out, the shape and intensity and the phase of the wave that is coming out will be the solution.” Essentially the microwaves are solving the mathematical problems.

And because it uses microwaves, the system is about 30cm x 60cm in size. This translates to about four wavelengths by eight wavelengths, which would be the same no matter what wave type is used. So it would also work with light waves, which have a smaller wavelength, where things get really exciting. “The system would scale down to a very small size, becoming in the order of a few microns, a fraction the thickness of a human hair”, Engheta suggests.

This small size is where the real potential of the discovery lies. Engheta explains “You can imagine many of these plastic swiss cheeses next to each other in a very small area, each one of them can solve different equations and these can be coupled together”, effectively forming an analog computer chip that requires no digital computation.

And especially interesting for the future, Engheta dreams “to actually have these things reconfigurable, so using technologies like re-writable CDs that we used to have. That technology could be used for making these plastic swiss cheese in the future, on the micron scale.” If they pull this off, in the future you could actually print and modify your own super-fast, low power, analog computer.