Computer simulations suggest that etching a repeating array of holes through a metal-and-dielectric optical stack could help a single-photon emitter send more light into a collection path. The researchers call their measure the radiative Purcell factor: power crossing a simulated collection plane divided by the same emitter’s power in vacuum. Their best modeled value is about 10 to 15 on a plane equivalent to a high-NA objective.
The conventional Purcell factor measures how quickly an emitter loses energy near a material, counting both energy radiated as light and energy absorbed. In the modeled flat titanium-dioxide-and-silver stack, this score exceeds 100 in the hyperbolic range, yet external quantum efficiency—the share of emission that escapes as light—falls below 1%. The radiative Purcell factor, which compares radiated power with the same emitter in vacuum, is only 1 to 2.
The proposed fix is a photonic crystal: holes etched through the alternating layers. Like a diffraction grating, the pattern changes the momentum of light waves that would otherwise stay trapped in the stack, allowing them to escape into free space. The researchers estimate radiative output on a plane equivalent to a collection cone with a numerical aperture of about 0.8, similar to a high-NA objective. In their model, the patterned stack raises the radiative Purcell factor above 10, compared with 1 to 2 for the flat design.
A second design pairs silver with antimony trisulfide (Sb2S3), a material whose optical response changes between amorphous and crystalline phases. For the optimized geometry, the simulations predict a radiative Purcell factor of about 10 to 15 in the near-infrared amorphous state. Around 1,230 nanometers, the modeled radiative Purcell factor in the amorphous state is more than 15 times its crystalline-state value.
These are predictions, not measurements from a fabricated source. The optimized model places a horizontally oriented emitter 1 nanometer above the stack at the edge between holes; the authors say random emitter orientations would likely reduce performance, while precise placement at the strongest optical fields may be difficult. An experiment must establish whether the patterned layers can deliver the modeled gain with realistic emitters and positioning.
Sources
- Karmakar et al., “Tunable hyperbolic metamaterials for brightening single-photon emission,” arXiv:2609.30179v1 (submitted September 24, 2026); full text and simulation methods.
- Illustrative image: National Institute of Standards and Technology, “Single Photons; Quantum Dots”, public domain in the United States. The image depicts a separate quantum-dot experiment, not the design in the paper.
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