Recently, Prof. Huang Lingling from the team of Prof. Wang Yongtian from Beijing Institute of Technology (BIT) and others, in collaboration with Prof. Zhang Shuang from the University of Hong Kong (HKU), proposed a beam differential operation method based on the Dammam vortex metasurface, which realizes the all-optical expression of differential addition and subtraction of mathematical functions. The research results were published in the internationally renowned journalScience Advanceswith the title Basis function approach for diffractive pattern generation with Dammann Vortex Metasurfaces.

Optical computing is a hot topic in current scientific research development. Unlike electronic computing, which originates from the control of logic gates, light has various physical properties and high-speed parallel computing capabilities. As the core basis of mathematical theory, functional differentiation and four arithmetic operations are also important means to improve the computing power of modern photons. As a basic physical property of light, orbital angular momentum has the characteristics of an infinite number of orthogonal channels. Therefore, multiplexing/demultiplexing of orbital angular momentum can realize the multiplexing of optical information. The generalized vortex beam can correlate different orbital angular momentums with the density changes around the optical singularity phase differential, realizing the combination of functional phase differential and beam profile shape, thus breaking the limitation of the traditional vortex beam phase differential being a constant. Usually, the Damman vortex grating is the basic carrier of orbital angular momentum multiplexing and demultiplexing. It can orderly present vortex beams carrying different topological charges on different diffraction orders of the grating. There is a typical multiplication and addition and subtraction operation relationship related to the diffraction order.

In order to use the all-optical method to realize the combination of function differentiation and four arithmetic functions, the team of Prof. Huang Lingling applied the design method of generalized vortex beam, combined with Dammam vortex optimization, and realized the intuitive optical display of addition and subtraction of various differential functions of different diffraction orders by setting a custom phase differential basic function. Taking the trigonometric function as an example, analogous to the Fourier order method for the expansion expression of any periodic function, using the combination of the phase differential of the central basic topological charge and the changes of the lateral and vertical phase differential functions, different functions on different diffraction orders are realized. distribution of features. Moreover, according to the relationship between the phase differential of the generalized vortex beam and the beam shape, the variation of the anomalous functions at different diffraction orders presents different beam profiles, forming a rich and diverse array pattern. The array of various vortex beams can be up to 7×7. Compared with traditional optical calculation, this method realizes the intuitive graphical expression of functional differential addition and subtraction, and this new functional differential addition and subtraction calculation function break through the limitation of traditional optical calculation to analyze the numerical value of specific trigonometric functions. In addition, the closed circle covering a continuous range of independent variables for a single beam and the correlation of differential addition and subtraction between multiple beams make optical computing more flexible and functional.

This newly proposed beam differential operation method realizes high-speed and large-capacity parallel calculation and visual display, and uses beam forms such as generalized vortex light, structured light, and spatial mode as the display of mathematical operations, breaking the traditional optical calculation graphics display difficulties, which further enriches the form and function of optical computing. And this optical differential computing metasurface supports complex-form beam input operations, so it can introduce more degrees of freedom for orbital angular momentum information transmission and storage encryption. This method can be used for exploring vortex information encryption, optical manipulation and optical communication, and quantum entanglement. And so various applications open new doors.

Link：https://www.science.org/doi/10.1126/sciadv.abp8073