Inverse-Designed Metastructures Operate with Light to Perform ‘Photonic Calculus’

A research team at the University of Pennsylvania has demonstrated a metamaterial device that can function as an analog computer. Such processing typically requires complex systems of bulky optical elements like lenses, filters, and mirrors. The researchers demonstrated that specially designed nanophotonic structures can take input waveforms encoded as complex mathematical functions, manipulate them, and provide an output that is the integral of the functions.

University of Pennsylvania engineers designed a metamaterial device that can solve integral equations. The device works by encoding parameters into the properties of an incoming electromagnetic wave; once inside, the device’s unique structure manipulates the wave in such a way that it exits encoded with the solution to a preset integral equation for that arbitrary input. Courtesy of Eric Sucar.

The researchers encoded parameters into the properties of an electromagnetic wave and sent the wave through a device made from metamaterial and structured using inverse design. The team theorized that once the wave was inside the device, the device’s structure could manipulate the wave in such a way that the wave would exit encoded with the solution to a preset equation.

The ‘Swiss cheese’ pattern is milled out of a type of polystyrene plastic. Its complicated shape represents part of a specific integral equation that can be solved for different variables, which are encoded in the microwaves sent into the device. Courtesy of Eric Sucar.

The device used for the proof-of-concept experiment has a block of dielectric material with precisely distributed air holes. “Our team likes to call it Swiss cheese,” said professor Nader Engheta. The intricate shape of the material is carved by a CNC milling machine.

“Controlling the interactions of electromagnetic waves with this ‘Swiss cheese’ metastructure is the key to solving the equation,” researcher Nasim Mohammadi Estakhri said. “Once the system is properly assembled, what you get out of the system is the solution to an integral equation.”

The pattern of hollow regions in the “Swiss cheese” material is set to solve an integral equation with a kernel (the kernel is the part of the equation that describes the relationship between two variables). The preset equation can be solved for any arbitrary inputs, which are represented by the phases and magnitudes of the waves that are introduced into the device. The kernel is represented physically through the arrangement of the air holes in the metamaterial.

Researchers Brian Edwards, Nader H. Engheta, and Nasim Mohammadi Estakhri (left to right) with their device. Courtesy of Eric Sucar.

“For example, if you were trying to plan the acoustics of a concert hall, you could write an integral equation where the inputs represent the sources of the sound, such as the position of speakers or instruments, as well as how loudly they play. Other parts of the equation would represent the geometry of the room and the material its walls are made of,” Engheta said. “Our system allows you to change the inputs that represent the locations of the sound sources by changing the properties of the wave you send into the system, but if you want to change the shape of the room, for example, you will have to make a new kernel.”

The experiment was conducted with microwaves, because longer wavelengths make the macroscale device easier to construct. The researchers say that the principles behind their findings can be scaled down to lightwaves, eventually fitting onto a microchip. Such metamaterial devices could function as analog computers that operate with light rather than electricity. They could be used to solve integral equations orders of magnitude faster than their digital counterparts, while using less power.

“Even at this proof-of-concept stage, our device is extremely fast compared to electronics,” Engheta said. “With microwaves, our analysis has shown that a solution can be obtained in hundreds of nanoseconds, and once we take it to optics, the speed would be in picoseconds.”

Scaling down the concept to the scale where it could operate on lightwaves and on a microchip could not only make the device more practical for computing; it could also open the doors to other technologies that would enable the device to be more like the multipurpose digital computers that first made analog computing obsolete decades ago.

“We could use the technology behind rewritable CDs to make new ‘Swiss cheese’ patterns as they’re needed,” Engheta said. “Someday you may be able to print your own reconfigurable analog computer at home!”

The research was published in Science (https://doi.org/10.1126/science.aaw2498).