Inverse-designed low-index-contrast structures on a silicon photonics platform for vector–matrix multiplication

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.