'Metasurfaces' manipulating light on a small scale could find applications in consumer technology

Most of us know optical lenses in the form of curved and transparent pieces of plastic or glass, designed to focus light for microscopes, glasses, cameras, and so on. For the most part, the curved shape of a lens has not changed much since its invention several centuries ago.

Over the last decade, however, engineers have created flat, ultra-thin materials called "metasurfaces" that can light far beyond what traditional curved lenses can do. Engineers engrave individual features, hundreds of times smaller than the width of a single hair, on these metasurfaces in order to create patterns allowing the surface as a whole to disperse light very accurately. But the challenge is knowing exactly what pattern is needed to produce the desired optical effect.

It is here that mathematicians at MIT have found a solution. In a study published this week in Optics Express, a team describes a new computer technique that quickly determines the ideal composition and disposition of millions of individual microscopic features on a metasurface, in order to generate a flat lens that manipulates the light in a specified manner.

Earlier work had solved the problem by limiting the possible patterns to combinations of predetermined shapes, such as circular holes of different radii, but this approach only explores a tiny fraction of the patterns that can be created.

This new technique is the first to efficiently design completely arbitrary patterns for large-scale optical metasurfaces, measuring about 1 square centimeter – a relatively large area, considering that each individual line is no more than 20 nanometers wide. Steven Johnson, professor of mathematics at MIT, explains that the calculation technique can quickly draw patterns for a range of desired optical effects.

"Suppose you want a lens that works well for many different colors, or you want to capture the light instead of focusing it on a spot, beam, hologram, or optical trap," says Johnson. . "You can tell us what you want to do, and this technique can give the model you should do."

Johnson's co-authors on paper are lead author Zin Lin, Raphael Pestourie and Victor Liu.

Pixel by pixel

A single metasurface is usually divided into tiny nano-sized pixels. Each pixel can be engraved or left intact. Those that are engraved can be assembled to form any number of different patterns.

To date, researchers have developed computer programs to search for any possible pixel pattern for small optical devices measuring tens of microns. These tiny, accurate structures can be used, for example, to trap and direct light in an ultra-thin laser. The programs that determine the exact patterns of these small devices do so by solving Maxwell's equations, a set of fundamental equations describing the scattering of light, according to each pixel of a device, then adjusting the pixel pattern by Pixel structure produces the desired optical effect.

But Johnson says that this pixel-by-pixel simulation task becomes almost impossible for large areas measuring millimeters or centimeters. A computer should not only work with a much larger surface, with orders of magnitude more pixels, but should also run multiple simulations of many possible pixel arrangements to ultimately achieve an optimal model.

"You have to simulate on a scale large enough to capture the entire structure, but small enough to capture the finer details," says Johnson. "The combination is really a huge computational problem if you attack it directly.If you launched the biggest supercomputer on Earth, and you had a lot of time, you could possibly simulate one of these models But it would be a turn to Obligate. "

Rising research

The Johnson team has now come up with a shortcut that effectively simulates the desired pixel pattern for large-scale metasurfaces. Instead of having to solve Maxwell's equations for each nano-sized pixel in a square centimeter of material, the researchers solved these equations for pixel "patches".

The computer simulation that they developed begins with a square centimeter of nano-sized pixels randomly etched. They divided the surface into groups of pixels, or patches, and used Maxwell's equations to predict how each patch was scattering light. They then found a way to "sew" approximately the patch solutions to determine the dispersion of light over the entire randomly etched surface.

From this starting schema, the researchers then adapted a mathematical technique known as topology optimization, in order to essentially adjust the pattern of each patch over many iterations, up to the end of the process. the end surface, or topology, diffuses the light in a preferred manner.

Johnson compares the approach to trying to find your way up a hill, blindfolded. To produce a desired optical effect, each pixel of a patch must have an optimal etched pattern to achieve, which one might think metaphorically as a peak. The search for this peak, for each pixel of a fix, is considered a problem of topology optimization.

"For each simulation, we find a way to modify each pixel," says Johnson. "You then have a new structure that you can resimate, and you continue this process, going up each time until you reach a peak or an optimized pattern."

The team's technique makes it possible to identify an optimal pattern in just a few hours, compared to traditional pixel-by-pixel approaches, which, if applied directly to large metasurfaces, would be virtually impossible to solve.

Using their technique, researchers quickly developed optical models for several "metadevices", or lenses with varied optical properties, including a solar concentrator that captures incoming light in any direction and focuses it on a single point, and an achromatic lens. diffuses the light of different lengths of waves, or colors, at the same point, with an equal focus.

"If you have a lens in a camera, if it's centered on you, you have to do it for all colors simultaneously," Johnson said. "The red must not be sharp, but the blue is blurry, so you have to create a pattern that scatters all the colors in the same way, so that they are in the same place, and our technique is able to go back up with a crazy motive that does that. "

In the future, researchers are working with engineers, who can create the intricate patterns their technique traces, to produce large metasurfaces, potentially for more accurate mobile phone lenses and other optical applications.

"These surfaces could be produced as sensors for cars that drive themselves, or in augmented reality, where you need good optics," says Pestourie. "This technique allows you to tackle much more difficult optical designs."

This story is republished with the permission of MIT News (web.mit.edu/newsoffice/), a popular site that covers the news of MIT's research, innovation, and teaching. .