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In mathematics, general functions can be decomposed into a linear combination of basis functions. This principle can be used for creating an infinite number of distinct geometric patterns based on a finite number of basis patterns. Here, we propose a Dammann vortex metasurface (DVM) for optically generating an array of diverse, diffraction -multiplexed vortex patterns, based on three custom-defined basis patterns. The proposed DVM, with its capabil-ity of quantitatively correlating phase and intensity distribution in different diffraction orders, opens up doors for various applications including orbital angular momentum encryptions and quantum entanglement.

Automated summary

In this paper, the principle of generating diverse geometric patterns using a linear combination of basis functions is introduced. A new type of Dammann vortex metasurface (DVM) is proposed to create an array of diffraction-multiplexed vortex patterns based on three custom-defined basis patterns. This research has important implications for applications such as orbital angular momentum encryption and quantum entanglement.