Large-scale and high-dimensional permutation operations are important for various applications in e.g., telecommunications and encryption. Here, we demonstrate the use of all-optical diffractive computing 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 material designed by deep learning, every diffractive layer has four orientations: 0, 90, 180, and 270 degrees. Each unique combination of these rotatable layers represents a distinct rotation state of the diffractive design tailored for a specific permutation operation. Therefore, a K-layer rotatable diffractive material is capable of all-optically performing up to 4^K independent permutation operations. The original input information can be decrypted by applying the specific inverse permutation matrix to output patterns, while applying other inverse operations will lead to loss of information. We demonstrated the feasibility of this reconfigurable multiplexed diffractive design by approximating 256 randomly selected permutation matrices using K=4 rotatable diffractive layers. We also experimentally validated this reconfigurable diffractive network using terahertz radiation and 3D-printed diffractive layers, providing a decent match to our numerical results. The presented rotation-multiplexed diffractive processor design is particularly useful due to its mechanical reconfigurability, offering multifunctional representation through a single fabrication process.

翻译：大规模和高维置换操作在电信、加密等多种应用中具有重要意义。本文通过衍射光网络中的层旋转，展示了利用全光衍射计算在输入与输出视场之间执行一组高维置换操作的方法。在这种由深度学习设计的可重构多路复用材料中，每个衍射层具有四个方向：0°、90°、180°和270°。这些可旋转层的每种独特组合均对应一种专用于特定置换操作的衍射设计旋转状态。因此，一个K层可旋转衍射材料能够全光地执行多达4^K种独立的置换操作。通过将特定的逆置换矩阵应用于输出模式，可解密原始输入信息，而应用其他逆操作则会导致信息丢失。我们利用K=4的可旋转衍射层逼近256个随机选择的置换矩阵，验证了这种可重构多路复用衍射设计的可行性。同时，通过太赫兹辐射和3D打印衍射层对该可重构衍射网络进行了实验验证，实验结果与数值结果高度吻合。所提出的旋转多路复用衍射处理器设计因其机械可重构性而尤为实用，能够通过单一制造过程实现多功能表示。