Metasurface color sorter for a Bayer image sensor

Design a patterned silicon-nitride layer that sits above a 2×2 block of camera pixels and steers blue, green and red light into their own pixels, instead of throwing the other colors away in a filter. The benchmark asks for the best worst-color efficiency that can be reached with features no smaller than 80 nm.

Task

The unit cell is 2 µm × 2 µm: four 1 µm subpixels in a Bayer arrangement, one blue, two green and one red. Unpolarized light arrives at normal incidence from air. The design variables are

• a binary pattern of Si₃N₄ and air on a 10 nm grid (200 × 200 pixels), mirror-symmetric about a diagonal;
• the metasurface thickness $t\in[0.4,0.8]$ µm;
• the distance from the metasurface to the pixel plane, in $[2.0,2.5]$ µm, through an SiO₂ spacer.

For each color $c$, let $\eta_c$ be the fraction of incident power transmitted into the subpixel(s) of that color (both green subpixels for green), averaged over the two polarizations and over two wavelengths per color: 433 and 467 nm for blue, 533 and 567 nm for green, 633 and 667 nm for red. The score is

$$\mathcal{M}=\min(\eta_B,\eta_G,\eta_R),$$

higher is better. A valid design is fully binary and its minimum feature width and minimum gap, measured with the imageruler package, are both at least 8 pixels (80 nm), the challenge's default target.

Background

Image sensors usually put an absorbing color filter over each pixel, so each pixel discards the light of the other colors. Zou et al. (2022) reported a pixel-level metasurface color router with the same materials and dimensions, designed with a genetic algorithm and a commercial FDTD solver. Schubert (2024) made it one of the challenges of the invrs-gym, a JAX toolkit for photonic inverse design, with a differentiable FMMAX (Fourier modal method) model that agrees closely with the commercial solver.

Data and evaluation

• Instance: one fixed device, invrs_gym.challenges.bayer_sorter() with default arguments.
• Evaluation code: the invrs leaderboard scorer (invrs_leaderboard.utils.evaluate_solutions_to_challenge), which runs on CPU in 64-bit precision with stricter simulation settings than the optimization default: the six wavelengths above and about 1000 Fourier terms. It also reports the minimum width and spacing in pixels. Submissions are parameter files in the totypes JSON format.
• Hardware: none assumed; the score does not depend on run time.

What is known

• Best on the final leaderboard: 0.5511, a design by M. F. Schubert (March 2024) with 80 nm minimum width and spacing; its per-color efficiencies are 0.656 (blue), 0.594 (green) and 0.551 (red).
• Larger features cost efficiency: the best leaderboard designs with 100 nm and 120 nm minimum features reach 0.5105 and 0.4927.
• The leaderboard holds 13 designs in all, every one by the gym's author; it has no independent entries.

What would count as progress

• A binary design meeting the 80 nm width and spacing target with $\mathcal{M}>0.5511$, re-scored with the leaderboard code.
• A higher score at 100 nm or 120 nm minimum features, which are easier to fabricate.
• A design whose score holds up under small edge erosion or dilation, reported with the scores of the perturbed patterns.

References

1. M. F. Schubert. invrs-gym: a toolkit for nanophotonic inverse design research. 2024. arXiv:2410.24132
2. X. Zou, Y. Zhang, R. Lin, et al. Pixel-level Bayer-type colour router based on metasurfaces. Nature Communications 13, 3288 (2022). doi:10.1038/s41467-022-31019-7
3. M. F. Schubert, A. M. Hammond. Fourier modal method for inverse design of metasurface-enhanced micro-LEDs. Optics Express 31, 42945 (2023). doi:10.1364/OE.503481
4. invrs.io. Bayer sorter leaderboard (final state, archived October 2025). Leaderboard page

Source

Imported from invrs-gym bayer_sorter, curated by Martin F. Schubert (invrs.io). The gym and its leaderboard were archived in October 2025 and no longer take submissions; the scores above are the leaderboard's final state. The statement above is written in our own words; see the source for the original wording, history and discussion.