Basis function approach for diffractive pattern generation with Dammann vortex metasurfaces

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 capability 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.