Scientists managed to make 2D-material (meta-surface), capable of performing mathematical operations of differentiation and integration. That is, the material finds the derivatives and integrals of the function. A kind of "analog computer" changes the characteristics (amplitude and phase) of the laser beam, which is directed to the meta-surface.
The work of specialists from the University of Southern Denmark was
published in the journal Nano Letters.

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The meta-surface consists of an array of tiny metal diffusers, each of which is less than the wavelength of light passing through them. The photo above was taken with a scanning tunneling microscope. The 50 x 50 nm differentiator is shown on the left, and an integrator of the same size on the right. The first meta-surface calculates the derivatives, and the second the integrals.
Danish scientists have manufactured material from gold nanoparticles as diffusers. They are fixed on a lining of silicon dioxide and on a gold film. When the metamaterial is illuminated by a laser beam with a wavelength of 800 nm, light excites surface plasmons; they go into the intermediate layer of silicon dioxide. For the first time, scientists were able to simultaneously control both the amplitude and phase of the light waves of reflected light.
The advantage of metamaterials is that they are several orders of magnitude thinner than ordinary optical elements, like lenses or wave plates. Such a small thickness potentially allows for the development of miniature, compact optical circuits in which analog mathematical calculations will become one of the applications.