Controlled multimode wave propagation can enable more space-efficient photonic processors than architectures based on discrete components connected by single-mode waveguides. Instead of defining discrete elements, one can sculpt the continuous substrate of a photonic processor to perform computations through multimode interference in two dimensions. Here we designed and demonstrated a device with a refractive index that can be rapidly reprogrammed across space, allowing arbitrary control of wave propagation. The device, a two-dimensional programmable waveguide, uses parallel electro-optic modulation of the refractive index of a slab waveguide with about $10^4$ programmable spatial degrees of freedom. We implemented neural network inference on benchmark tasks with up to $49$-dimensional vectors in a single pass, without digital pre-processing or post-processing. Theoretical and numerical analyses further indicated that two-dimensional programmable waveguides may offer not only a constant-factor reduction in device area but also a scaling benefit, with the area required growing as $N^{1.5}$ rather than $N^2$.

翻译：受控的多模波传播能够实现比基于单模波导连接分立元件架构更具空间效率的光子处理器。无需定义分立元件，可通过在二维空间中利用多模干涉对光子处理器的连续基底进行塑形以执行计算。本研究设计并展示了一种折射率可在空间中快速重编程的器件，实现了对波传播的任意控制。该器件为二维可编程波导，通过约$10^4$个可编程空间自由度的平行电光调制对平板波导的折射率进行调控。我们以单次传播方式实现了基准任务中最高49维向量的神经网络推理，无需数字预处理或后处理。理论与数值分析进一步表明，二维可编程波导不仅可能带来器件面积的常数因子缩减，更可提供扩展性优势——其所需面积按$N^{1.5}$而非$N^2$的规模增长。