[Paper Review] Inverse-designed low-index-contrast structures on silicon photonics platform for vector-matrix multiplication

Vahid Nikkhah, Ali Pirmoradi+4 more|arXiv (Cornell University)|Feb 1, 2023

Photonic Crystals and Applications4 citations

TL;DR

This paper proposes a 2D inverse-design method using effective index approximation with low-index-contrast silicon photonics to enable scalable, broadband, and fabrication-tolerant vector-matrix multiplication. By leveraging a reduced-order model, it designs compact, non-resonant, feed-forward metastructures that achieve high accuracy in 2×2, 3×3, and 10×10 matrix operations, validated through simulation and experiment.

ABSTRACT

Inverse-designed Silicon photonic metastructures offer an efficient platform to perform analog 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 utilizes 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 2D inverse-design method based on the effective index approximation with a low-index contrast constraint. This results in compact amorphous lens systems which are generally feed-forward and low-resonance. We designed and experimentally demonstrated a vector-matrix product for a 2 x 2 and a 3 x 3 matrix. We also designed a 10 x 10 matrix using the proposed 2D computational method. These examples demonstrate that these techniques have the potential to enable larger-scale wave-based analog computing platforms.

Motivation & Objective

• Address the challenge of scaling inverse-designed photonic metastructures for large-scale vector-matrix multiplication in silicon photonics.
• Overcome the computational burden of full 3D simulations for large optical structures by introducing a reduced-order approximation.
• Develop a low-index-contrast design constraint to minimize resonances, improve bandwidth, and enhance fabrication tolerance.
• Enable scalable inverse design for large matrix operations (e.g., 10×10) using a computationally efficient 2D model.
• Demonstrate experimental validation of 2×2 and 3×3 vector-matrix multiplication with high fidelity.

Proposed method

• Employ a propagation-based 2D effective index approximation (p2DEIA) to model 3D planar silicon photonic structures with low-index contrast.
• Use density-based topology optimization with the adjoint method to compute gradients efficiently, enabling large-scale design optimization.
• Apply low-index contrast (small variation in silicon thickness) to suppress out-of-plane scattering and reduce resonant behavior.
• Design a 2D computational domain where silicon thickness is parameterized across a region, enabling feed-forward, low-resonance response.
• Validate designs via full-wave 3D simulations and experimental fabrication, comparing target, p2DEIA, and 3D simulation results.
• Use complex amplitude mapping of spatial modes to represent input/output vectors and define the transmission matrix as the core design objective.

Experimental results

Research questions

• RQ1 Can a 2D effective index approximation accurately model large-scale 3D planar silicon photonic structures for inverse design?
• RQ2 How does low-index contrast improve bandwidth and reduce fabrication sensitivity in inverse-designed photonic metastructures?
• RQ3 To what extent can the p2DEIA model enable scalable inverse design for large matrix operations (e.g., 10×10) without full 3D simulation?
• RQ4 What is the agreement between target transmission matrices, p2DEIA predictions, and full 3D simulations in large-scale designs?
• RQ5 Can experimentally fabricated 2×2 and 3×3 structures achieve high-fidelity vector-matrix multiplication with minimal error?

Key findings

• The p2DEIA model achieved excellent agreement between target transmission matrices and simulated results for 2×2 and 3×3 designs, with complex-valued transmission parameters closely matching across target, p2DEIA, and 3D simulations.
• The 10×10 vector-matrix multiplication structure was successfully designed using p2DEIA within a 35.4 μm × 29.4 μm region, spanning 66λg × 55λg, demonstrating scalability.
• Experimental results for 2×2 and 3×3 structures confirmed high accuracy, with transmission fidelity validated through measured and simulated field distributions.
• The low-index-contrast design resulted in feed-forward, low-resonant behavior, enabling broadband operation and reduced sensitivity to fabrication errors.
• Despite coarser meshing and simplified boundary conditions, 3D simulations of the 10×10 structure showed acceptable agreement with p2DEIA predictions, confirming design robustness.
• The method reduced computational cost significantly compared to full 3D simulations, enabling hundreds of optimization iterations for large-scale structures.