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Home Material Science & Technology

Mathematics and the speed of light

by Nano Digest
January 17, 2023
in Material Science & Technology
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Mathematics and the speed of light. Nano Digest.

A tailored silicon nanopattern coupled to a semitransparent gold mirror can solve a complex mathematic equation with light. Image credit: Ella Maru studio. Courtesy: AMOLF.

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Researchers from AMOLF, the University of Pennsylvania and the City University of New York (CUNY) have created a nanostructured surface that can use light to solve (Mathematics and the speed of light) equations. This research opens up exciting new opportunities in the field of optical metasurface-based analog processing. AMOLF PhD student Andrea Cordaro and his team publish their findings in Nature Nanotechnology on January 12, 2023.

The increasing need for efficient computing worldwide has driven researchers from various research fields to explore different approaches to the current digital computing system. “The processing speed and power efficiency of off-the-shelf electronics has become a barrier to disruptive innovations that are rapidly entering our daily lives, such as artificial intelligence, machine learning, computer vision and others. ” Andrea Cordaro says. “In this context, analog computing has already begun and has regained much attention as a means of support for traditional architecture.”

Calculate the speed of light

Optical analog design refers to the use of light to perform analog calculations, as opposed to traditional electronic systems that use electricity. One of the main advantages of using light to perform specific computing tasks is that it can operate at much higher speeds than electronic methods because the computation is performed at the speed of light passing through surfaces. very fine nanostructured structures called metasurfaces. Additionally, optical analog processing can be more energy efficient than electronic methods because it does not generate heat in the same way electronic circuits do. This makes it well suited for use in high-end computing applications where speed and power are important.

“In self-driving cars, for example, image recognition and processing takes a lot of time,” Cordaro explains. “In the previous paper, we showed that it is possible to use the optical metasurface for fast face detection in input images. Identify parts of objects – such as cars, people, etc. – is the first step in image processing in many applications. Doing this process visually can save planning time and energy.

The Matrix has changed dramatically

Cordaro and his colleagues realized that they could also use metasurfaces to perform other mathematical tasks. “One of the most common problems that arise in many fields, including engineering, science, and economics, are “transformational problems.” These involve matrix transformations, which not fast math,” he says. The research team created a thin dielectric nanostructure, called a meta-lattice, and placed a transparent mirror inside the sample to reflect the signal back to the nanostructures, each time amplified by the matrix. the meta-lattice expands.

“We use a unique optimization process to design a nanostructured cell array unit, or meta-array, that can perform any number of desired functions,” explains Cordaro. “Each mathematical problem requires a specific arrangement for the metallattice, but in theory, one could design its surface with many parallel lattices to solve many equations one by one.”

Mathematics and the speed of light. Nano Digest.
(Left) A light signal sent to a metagrating is diffracted and subsequently interacts repeatedly with the grating because it bounces back from a partially reflecting mirror, each time multiplied by the metagrating scattering matrix. In this way, a metagrating is capable to perform mathematical operations in the form of matrix equations. (Right) Scanning electron microscopy (SEM) image of the patterned metagrating used by the research team. Courtesy: AMOLF.

These results demonstrate the ability to solve complex mathematical problems and generic matrix transformations at a higher speed than conventional arithmetic methods. In fact, the solution converges in about 349 fs (ie less than a billionth of a second), an order of magnitude faster than the clock speed of the processor. Cordaro: “We have demonstrated a powerful new alliance between nanotechnology and analog computing that could pave the way for hybrid circuits and computers. By opening up our minds, we will be able to solve problems of previously unanticipated complexity with speed and efficiency.

Tags: analogcalculationsdielectric nanostructuredigital computingequationsMathsMatrixMetasurfacesnanostructured surfaceOptical analogoptical metasurfaceself-driving carsspeed of light
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