Photonic Systolic Array for All‐Optical Matrix–Matrix Multiplication

ABSTRACT Systolic arrays have proven to be highly efficient for parallelized matrix–matrix multiplication (MMM), utilizing synchronized, heartbeat‐like data flows across an array of processing elements. While optical structures, such as waveguide crossbar arrays and Mach‐Zehnder interferometer‐based meshes, serve as photonic equivalents to the systolic arrays, the disparity between the two input matrices for multiplication—one using optical signals and the other with system‐defined parameters—gives rise to a bottleneck in modern machine‐learning tasks, such as evaluating attention scores in large language models. Here, a photonic systolic array that performs MMM entirely with optical signals is proposed, utilizing homodyne detection at each array cell. Adjoint‐based design of compact on‐chip freeform optical modules enables precise control of light flow without bulky waveguide coupling schemes. The operation of 4×4 and 2×2 photonic systolic arrays are numerically verified, achieving a theoretical computation density of 4.4 PMACs/mm 2 /s. This design marks a significant step toward practical photonic computing hardware for modern AI workloads.