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Inverse-designed Silicon photonic metastructures offer an efficient platformto perform analog computations with electromagnetic waves. However, due tocomputational difficulties, scaling up these metastructures to handle a largenumber of data channels is not trivial. Furthermore, a typical inverse-designprocedure utilizes a small computational domain and therefore tends to employresonant features to achieve its objectives. This results in structures thatare narrow-bandwidth and highly sensitive to fabrication errors. Here, weemploy a 2D inverse-design method based on the effective index approximationwith a low-index contrast constraint. This results in compact amorphous lenssystems which are generally feed-forward and low-resonance. We designed andexperimentally demonstrated a vector-matrix product for a 2 x 2 and a 3 x 3matrix. We also designed a 10 x 10 matrix using the proposed 2D computationalmethod. These examples demonstrate that these techniques have the potential toenable larger-scale wave-based analog computing platforms.

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