Optical diffractive neural network-based orbital angular momentum mode fixed-base multiplication/division

Optical digital computing, leveraging optical signals for high-speed, efficient, and high-precision discretized digital computations and information processing, is widely applied in artificial intelligence, communication, and network. However, the development of multiplication/division, pivotal components within digital optical computing systems, has been constrained by the absence of effective computational physical dimensions conducive to manipulating optical signals and the stringent requirement for precise operational control. We propose a fixed-base multiplication and division scheme based on orbital angular momentum (OAM) modes using optical diffractive neural networks (ODNNs). Utilizing the OAM mode as the computational physical dimension, and employing ODNN to perform mode-parallel and independent transformations on it for achieving numerical equivalent shifts, it is feasible to realize 2ⁿ-fold multiplication and division operations. Using this mechanism, we have constructed a 3-layer ODNN to realize OAM mode fixed-base multiplication and division for n = 1, 2, and 3, with mode purities of the operation outputs reaching 99%. Furthermore, a dynamic switching between multiplication and division operations has been achieved within the same system through rotation of the phase matrix. Our design suggests a feasible pathway for fixed-base optical multiplication and division, and may offer useful insights for future research on optical digital computing architectures.