Exploring the potential of light to perform mathematical operations

Shown in the image is a simulation of mathematical calculations with a metamaterial; the results of this international study were published in Science.

By Elton Alisson

Agência FAPESP – The telecommunications, optics and aerospace industries, among others, are beginning to place their chips on metamaterials in efforts to develop structures with unprecedented capacities, such as flat lenses, structures that curve light and optical devices capable of manipulating light, such as electronic circuits that control the flow of electrons.

A study published in Science at the beginning of January demonstrated that these compound structures of common materials, made specifically to modify electromagnetic properties and create behaviors not found in nature, can also be projected to conduct advanced mathematical calculations with electromagnetic waves, such as light.

Photonic calculations are obtained by manipulating the profiles of electromagnetic waves as they propagate over a metamaterial block – much like the operations conducted in old analog computers.

These discoveries create the prospect of smaller computer devices with faster processing speeds than those on the market today, highlight the authors of the study. The research team, led by a Brazilian, involves participants from the University of Pennsylvania, the University of Texas at Austin and the University of Sannio (Italy).

“Until now, there has not been a study like this one, in which we conducted mathematical calculations with electromagnetic waves using a spatial profile rather than in a solely temporal manner,” commented Alexandre Manoel Pereira Alves da Silva, lead author of the article.

“When I began my post-doctoral research at the University of Pennsylvania under the mentorship of Professor Nader Engheta, he posed this challenge to me,” said Silva, who holds a doctorate in Electrical Engineering and Computing (FEEC) from the Universidade Estadual de Campinas (Unicamp), which is linked to the National Institute of Science and Technology in Photonics (Fotonicom), one of the national science institutes (INCTs) funded by FAPESP in São Paulo.

During his doctorate studies, Silva’s adviser was Professor Hugo Enrique Hernandez-Figueroa, a researcher at the Campinas Optics and Photonics Research Center of the Research, Innovation and Dissemination Centers (RIDCs) funded by FAPESP.

According to Silva, a light wave has a profile like a curve on a Cartesian plane when described in terms of space and time.

The researcher and his collaborators projected and simulated metamaterials with the ability to modify the profile of an incident light wave.

As the light wave propagates inside the metamaterial, which measures less than the wavelength of the light, its profile is naturally altered.

In this manner, as the light passes through the metamaterial block, it bends to a profile that is equivalent to the result of a specific mathematical operation, like the first and second derivative of the function described by the profile of the input wave.

“When a light wave propagates through these metamaterial blocks, as it exits, it adopts the shape of the result of the calculation, such as a derivative, integral or convolution of the profile of the input wave,” explains Silva.

Applications

According to the researcher, one of the possible applications of this metamaterial is in image processing.

Today, images are processed by capturing light waves, which are converted into electronic signals in the form of digital information and only then processed in accordance with the desired operation.

The metamaterials proposed by researchers could conduct these operations almost instantaneously and directly on the original incident light wave that enters through the camera lens, “eliminating the need to convert it into digital signals,” explained Silva.

“This type of material would considerably reduce the processing time for electromagnetic waves in medical imaging equipment, for example,” affirmed Silva.

According to the researcher, metamaterials can be used for edge detection – a very common image processing technique that helps software to identify people and objects in diagnostic imaging exams, for example.

The image processing techniques available today carry out edge detection pixel by pixel, comparing each pixel with nearby pixels in a computationally costly process, explained Silva.

With a camera made with the metamaterial, however, edge detection could be possible instantaneously, estimates the researcher.

“The concept of metamaterials is relatively new in science, but the technology is mature enough to be used in industry,” pondered Silva.

Currently, the researcher and other participants in the study are attempting to build the metamaterials for testing in the laboratory.

If the tests are successful, they intend to develop metamaterials that can conduct other mathematical operations and even resolve differential and integral equations.

Based on these metamaterials, according to the researchers, it will be possible to develop devices that are orders of magnitude smaller than those based on conventional lenses.

“If we manage to show in the laboratory that these metamaterials work on the real plane, this will pave the way for much smaller computing devices on the scale of just a few wavelengths, with greater processing speed and lower energy consumption than those used today,” added Silva.

The article Performing mathematical operations with metamaterials (doi: 10.1126/science.1242818), by Silva et al., can be read at www.sciencemag.org/content/343/6167/160.