Photon extractor for a diamond nitrogen-vacancy center

Design a patterned gallium-phosphide layer on diamond that pulls light out of a nitrogen-vacancy (NV) center buried just below the surface and sends it up into a collection region. Collecting more of this light matters for quantum-information applications that read out single defects.

Task

An NV center sits 100 nm below the surface of a diamond substrate (refractive index 2.4102) and emits at its 637 nm zero-phonon line. On the surface lies a 250 nm gallium-phosphide layer (index 3.31) capped by a 130 nm SiO₂ hard mask (index 1.46) that is left in place after etching. The design variable is the binary GaP pattern in a 1.5 µm × 1.5 µm region centred over the defect, on a 5 nm grid (300 × 300 pixels), with mirror symmetry about both axes and both diagonals. Emission is modelled by $x$-, $y$- and $z$-oriented dipoles $d$. Let $\Phi_d$ be the power that passes through a 1.5 µm × 1.5 µm monitor 0.4 µm above the oxide, and $\Phi^0_d$ the same quantity for bare diamond. The score is the orientation-averaged enhancement of collected power,

$$\mathcal{M}=\frac{\Phi_x+\Phi_y+\Phi_z}{\Phi^0_x+\Phi^0_y+\Phi^0_z},$$

higher is better. A valid design is fully binary, with minimum feature width and minimum gap of at least 10 pixels (50 nm), measured with the imageruler package, the challenge's default target.

Background

The challenge is based on the inverse-designed photon extractors of Chakravarthi et al. (2020), produced by topology optimization with a custom finite-difference frequency-domain solver and checked with FDTD. Maximizing collected power combines two effects: extracting light that would otherwise be trapped, and enhancing the local density of optical states at the emitter, which is very sensitive to small features. Schubert (2024) implemented the problem in the invrs-gym with the FMMAX Fourier modal method; a Fourier basis models point dipoles only approximately, but its enhancements approach the published values as the number of Fourier orders grows.

Data and evaluation

• Instance: one fixed device, invrs_gym.challenges.photon_extractor() with default arguments.
• Evaluation code: the invrs leaderboard scorer (invrs_leaderboard.utils.evaluate_solutions_to_challenge), on CPU in 64-bit precision with the challenge's default simulation settings (about 1200 Fourier terms). It also reports the minimum width and spacing in pixels. Designs can be submitted as a CSV density array or a totypes JSON file.
• Hardware: none assumed; the score does not depend on run time.

What is known

• Schubert (2024) reports that a design from Chakravarthi et al. (2020), whose sharp features measure below 20 nm, and a gym design with 80 nm minimum features reach similar scores, 11.3 and 12.1.
• Best on the final leaderboard: 13.93, a design by M. F. Schubert (January 2024) with exactly 50 nm width and spacing; it raises the local density of states by a factor of only 1.24, so most of the gain comes from extraction.
• The leaderboard holds nine designs, all from the gym's author.

What would count as progress

• A binary design meeting the 50 nm target with $\mathcal{M}>13.93$, re-scored with the leaderboard code.
• A design with features of 80 nm or more scoring above 12.1, the best published value at that size.
• An independent FDTD check of a top design, confirming the FMMAX enhancement for a true point dipole.

References

1. S. Chakravarthi, P. Chao, C. Pederson, et al. Inverse-designed photon extractors for optically addressable defect qubits. Optica 7, 1805–1811 (2020). doi:10.1364/OPTICA.408611
2. M. F. Schubert. invrs-gym: a toolkit for nanophotonic inverse design research. 2024. arXiv:2410.24132
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. Photon extractor leaderboard (final state, archived October 2025). Leaderboard page

Source

Imported from invrs-gym photon_extractor, 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.