# 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](https://github.com/invrs-io/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](https://arxiv.org/abs/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](https://doi.org/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](https://doi.org/10.1364/OE.503481)
4. invrs.io. Bayer sorter leaderboard (final state, archived October 2025). [Leaderboard page](https://invrs-io.github.io/leaderboard/notebooks/leaderboards/bayer_sorter.html)

## Source

Imported from [invrs-gym bayer_sorter](https://invrs-io.github.io/gym/notebooks/challenges/bayer_sorter.html), 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.