• *Physical* 17, 52

New architectures based on metamaterials offer a promising platform for building reprogrammable and mass-producible schemes that perform computing tasks with light.

The idea of an analog computer – a device that uses continuous variables instead of zeros and ones – may evoke obsolete machinery, from mechanical clocks to bomb-aiming devices used in World War II. But emerging technologies, including AI, can reap major benefits from this computational approach. One promising direction involves analog computers that process information with light rather than electrical currents. As reported at the March 2024 APS meeting by Nader Engheta of the University of Pennsylvania, composite media known as metamaterials offer a powerful platform for building analog optical computers. In recent work, his team demonstrated a metamaterial platform that could be mass-produced and integrated into silicon electronics. [1]as well as an approach to building architectures that can be reprogrammed on the fly to perform different computational tasks [2]. Analog optical computers based on metamaterials could one day perform certain tasks much faster and with less power than conventional computers, says Engheta.

Metamaterials are synthetic materials made by assembling many units, each smaller than the wavelength of light they were designed to manipulate. They can be adapted to exhibit properties not found in natural materials, most famously, a near-zero or negative index of refraction. These exotic properties could enable unique applications, from wavelength imaging to invisibility camouflage.

The design flexibility of metamaterials has inspired several groups to explore strategies for turning them into computational machines. In 2014, Engheta and collaborators presented a first set of proposals. Their simulations suggested that metamaterials could perform a set of mathematical operations, including differentiation, integration and convolution. The approach involves taking an electromagnetic wave as the input function and manipulating it through interaction with the metamaterial so that the output wave corresponds to a desired mathematical transformation of the input.

Five years later, Engheta’s group implemented this proposal experimentally. Working at microwave wavelengths, their scheme involved a block of metamaterial with multiple input and output ports connected by waveguides in a feedback circuit. The experiments demonstrated that for a given input, the device’s output was the solution to the so-called Fredholm integral equation, which is used in fields as diverse as fluid mechanics, antenna design, and quantum mechanical perturbation theory. To choose the metamaterial structure performing the desired mathematics, the researchers used “inverse design” – an iterative approach to solving optimization problems. The resulting metamaterial had a non-trivial “Swiss cheese” structure, with an inhomogeneous distribution of small islands with different dielectric properties – air holes, polystyrene and microwave-absorbing materials.

Because microwaves imply bulky and impractical setups, several research groups have decided to extend similar concepts to optical frequencies, demonstrating a variety of computing schemes. Most of these demonstrations have used thin sheets of metamaterials with lower wavelengths, known as metasurfaces, to manipulate the propagation of light in free space and transmitted through the sheet. Metasurface schemes, however, require sophisticated and customized manufacturing processes, which limits the potential for mass production, says Engheta.

Engheta and his colleagues have now developed an on-chip platform that can overcome such limitations [1]. Unlike metasurface schemes with light propagation in free space, the team’s metamaterial design channels light through structured waveguides on a silicon chip. The researchers reverse-designed and built a micron-sized chip with a structure reminiscent of the 2019 microwave design: an array of waveguides that feed light into and out of a flat cavity containing a metamaterial similar to Swiss cheese. This structure can simply be ordered from commercial foundries, says Engheta. Compared to its microwave cousin, the optical chip does simpler math: it multiplies a vector by a matrix, an operation useful for AI tools like neural networks. To solve equations, the scheme will need to incorporate feedback waveguides connecting outputs to inputs, as was done in microwaves, an engineering challenge the team plans to tackle in next-generation chips.

In parallel with the optical work, Engheta is improving the mathematical abilities of analog computers using proof-of-principle devices at lower frequencies. The group’s latest output added an important new feature: reconfigurability – the ability for an equation solver to be reprogrammed to perform different mathematical operations. The scheme consisted of a 5×5 module of radio frequency (45 MHz) elements such as amplifiers and phase shifters. The device can be reconfigured by controlling the parameters of each of the elements. As a demonstration, the researchers made their machine solve two different problems: finding the roots of a system of polynomials and carrying out the inverse design of a metastructure. Both problems are non-stationary, that is, they require a sequence of steps with different mathematical operations in each step.

Engheta predicts that this reconfigurability capability could ultimately be transferred to silicon photonic chips. One approach to doing this would involve depositing a patterned layer of “phase change” material on top of the device’s waveguides. When heated, such a material changes its refractive index, affecting the propagation of light in the waveguides and, therefore, the mathematical operator that such propagation encodes.

The programmable metamaterial silicon photonic chip would be a boon for analog optical computing, Engheta says, processing information at the speed of light with a fraction of the energy needed to power the millions of operations a conventional digital processor needs to perform to solve the same tasks. “Here, the light goes through a waveguide maze, and when it comes out, you get the answer all at once,” he says. And because photons, unlike electrons, do not interact with each other, parallel operations could be performed simultaneously simply by shining light at different wavelengths through the device. What’s more, such a device would bring privacy benefits because it doesn’t require intermediate steps that store information in potentially hackable memory, says Engheta.

–Matteo Rini

Matteo Rini is the editor of *Physics Magazine*.

## References

- V. Nikkhah
*and others.*“Low Contrast Index Structures with Inverse Design on a Silicon Photonic Platform for Vector Matrix Multiplication,” Nat. Fóton. (2024). - DC Tzarouchis
*and others.*“Programmable wave-based analog computing machine: a metastructure that designs metastructures”, arXiv:2301.02850.

## Thematic areas