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

Nature Photonics (2024)Cite this article

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Abstract

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.

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Fig. 1: Schematic of our inverse-designed structures in a SiPh platform.
Fig. 2: Inverse-designed metastructures based on silicon photonics for performing 2 × 2 and 3 × 3 vector–matrix multiplications.
Fig. 3: Comparison between simulations and experimental results.
Fig. 4: Inverse design of a SiPh metastructure for performing a 10 × 10 vector–matrix multiplication.

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Data availability

Data for Figs. 2–4 are available via Zenodo at https://doi.org/10.5281/zenodo.10083901 (ref. 39).

Code availability

All codes produced during this research are available from the corresponding author upon reasonable request.

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Acknowledgements

This work is supported in part by the US Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI) grant no. FA9550-21-1-0312 (to N.E.) and in part by the US Office of Naval Research (ONR) grant no. N00014-19-1-2248 (to F. Aflatouni.).

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Authors and Affiliations

  1. Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA

    Vahid Nikkhah, Ali Pirmoradi, Farshid Ashtiani, Brian Edwards, Firooz Aflatouni & Nader Engheta

  2. Nokia Bell Labs, Murray Hill, NJ, USA

    Farshid Ashtiani

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  1. Vahid Nikkhah
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Contributions

N.E., F. Aflatouni. and B.E. conceived the idea, envisioned the experiments and supervised the project. V.N. conducted theoretical analysis, numerical simulations and inverse-design of the structures. A.P., F. Ashtiani. and B.E. prepared the designs for nanofabrication by the Advanced Micro Foundry (AMF) and designed the experiments. A.P. performed the experiments and collected data. All authors reviewed, studied and discussed the experimental and numerical simulation results, and discussed the main outcomes of the project. V.N. prepared the first draft of the main text and the Supplementary Information. All authors subsequently worked on the manuscript up to its completion for submission.

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Correspondence to Nader Engheta.

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Nature Photonics thanks Yannick Salamin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–6, Discussion and Table 1.

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Nikkhah, V., Pirmoradi, A., Ashtiani, F. et al. Inverse-designed low-index-contrast structures on a silicon photonics platform for vector–matrix multiplication. Nat. Photon. (2024). https://doi.org/10.1038/s41566-024-01394-2

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