Multiplexed All-Optical Permutation Operations Using a Reconfigurable Diffractive Optical Network

Large-scale and high-dimensional permutation operations are important for various applications in, for example, telecommunications and encryption. Here, all-optical diffractive computing is used to execute a set of high-dimensional permutation operations between an input and output field-of-view through layer rotations in a diffractive optical network. In this reconfigurable multiplexed design , every diffractive layer has four orientations: $0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$. Each unique combination of these layers represents a distinct rotation state, tailored for a specific permutation operation. Therefore, a K-layer rotatable diffractive design can all-optically perform up to $4^K$ independent permutation operations. The original input information can be decrypted by applying the specific inverse permutation matrix to output patterns. The feasibility of this reconfigurable multiplexed diffractive design is demonstrated by approximating 256 randomly selected permutation matrices using $K$= 4 rotatable diffractive layers. To further enhance its multiplexing capability, input polarization diversity is also utilized. Additionally, this reconfigurable diffractive design is experimentally validated using terahertz radiation and 3D-printed diffractive layers, providing a decent match to numerical results. The presented rotation-multiplexed diffractive processor is particularly useful due to its mechanical reconfigurability, offering multifunctional representation through a single fabrication process.