Inverse-designed silicon photonic metastructures offer an efficient platform to perform analogue computations with electromagnetic waves. However, due to computational difficulties, scaling up these metastructures to handle a large number of data channels is not trivial. Furthermore, a typical inverse-design procedure is limited to a small computational domain and therefore tends to employ resonant features to achieve its objectives. This results in structures that are narrow-bandwidth and highly sensitive to fabrication errors. Here we employ a two-dimensional (2D) inverse-design method based on the effective index approximation with a low-index contrast constraint. This results in compact amorphous lens systems that are generally feed-forward and low-resonance. We designed and experimentally demonstrated a vector–matrix product for a 2 × 2 matrix and a 3 × 3 matrix. We also designed a 10 × 10 matrix using the proposed 2D computational method. These examples demonstrate that these techniques have the potential to enable larger-scale wave-based analogue computing platforms.

逆向设计的硅光子元结构提供了一个利用电磁波执行模拟计算的有效平台。然而，由于计算困难，扩展这些元结构以处理大量数据通道并非易事。此外，典型的逆向设计过程仅限于较小的计算域，因此倾向于采用共振特征来实现其目标。这导致结构带宽窄且对制造误差高度敏感。在这里，我们采用基于具有低指数对比度约束的有效指数近似的二维（2D）逆设计方法。这导致紧凑的非晶透镜系统通常是前馈和低谐振的。我们设计并通过实验演示了 2 × 2 矩阵和 3 × 3 矩阵的向量矩阵乘积。我们还使用所提出的 2D 计算方法设计了一个 10 × 10 矩阵。这些例子表明这些技术有潜力实现更大规模的基于波的模拟计算平台。