Adjoint-optimized nanoscale light extractor for nitrogen-vacancy centers in diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-11-16 |
| Journal | Nanophotonics |
| Authors | Raymond Wambold, Zhaoning Yu, Yuzhe Xiao, Benjamin F. Bachman, Gabriel R. Jaffe |
| Institutions | University of WisconsinâMadison |
| Citations | 18 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThe research details the design and optimization of a silicon-based Nanoscale Light Extractor (NLE) engineered to maximize the outcoupling of broadband fluorescence from shallow Nitrogen-Vacancy (NV-) centers in diamond.
- Performance Achievement: The NLE enhances the optical output of an NV center positioned 10 nm below the diamond surface by a factor of >35x compared to unpatterned diamond.
- Collection Efficiency: The device beams the extracted light into a narrow far-field cone (±30°), enabling high collection efficiency (~40% for NA 0.75) using low-Numerical Aperture (NA) optics.
- Fabrication Advantage: The NLE consists of a patterned silicon layer placed directly on a flat, unpatterned diamond surface, eliminating the need for complex and potentially damaging diamond etching.
- Design Methodology: The structure was designed using adjoint optimization combined with broadband Finite-Difference Time-Domain (FDTD) simulations, focusing on maximizing the Figure of Merit (FoM) across the entire NV emission spectrum (635-800 nm).
- Robustness: The optimized design exhibits strong tolerance to fabrication errors (±20 nm edge deviation) and alignment errors (±20° angular misalignment), crucial for real-world implementation.
- Material Compatibility: The optimal NLE thickness is 300 nm, compatible with standard Silicon-on-Insulator (SOI) technology and membrane transfer techniques for integration onto diamond.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Target Emitter | NV- Center | - | Negatively charged Nitrogen-Vacancy in [100] diamond. |
| NV Center Depth (Optimized) | 10 | nm | Below diamond surface. |
| NLE Material | Silicon (Si) | - | Patterned layer on diamond substrate. |
| NLE Thickness (Optimized) | 300 | nm | Determined via 2D optimization sweep. |
| Figure of Merit (FoM) | ~35 | x | Broadband enhancement factor (10 nm depth). |
| Purcell Enhancement (Average) | ~3 | x | Averaged across the 635-800 nm emission spectrum. |
| Collection Efficiency (Peak) | ~40 | % | For NA 0.75 objective (635-670 nm range). |
| Beaming Angle | ±30 | ° | Cone angle for directed light output. |
| Emission Wavelength Range | 635 to 800 | nm | Covers zero-phonon line (ZPL) and phonon sideband. |
| Robustness (Edge Deviation) | ±20 | nm | Tolerance to fabrication under/over-etching. |
| Robustness (Angular) | ±20 | ° | Tolerance to rotational misalignment of the NLE. |
| Robustness (Depth Tolerance) | 3 | x | Minimum FoM enhancement maintained at 300 nm NV depth. |
| Minimum Feature Size | 40 | nm | Set by conical blurring function radius (R). |
Key Methodologies
Section titled âKey MethodologiesâThe NLE structure was developed using an inverse design approach based on adjoint optimization and FDTD simulations, focusing on broadband performance and fabrication constraints.
- Simulation Environment: Finite-Difference Time-Domain (FDTD) simulations (Lumerical FDTD) were used to calculate the forward and adjoint electromagnetic fields across the target spectrum (635-800 nm).
- Optimization Target: The optimization maximized the Figure of Merit (FoM), defined as the spectrum-averaged extraction efficiency ($\eta(\lambda)$) weighted by the NV emission spectrum ($I_{NV}(\lambda)$).
- NV Emission Modeling: The unpolarized, room-temperature NV emission was modeled by incoherently summing the results from two orthogonal linear dipoles, both orthogonal to the NV axis (tilted 54.7° from the surface normal).
- Adjoint Source Definition: The adjoint simulation used two orthogonally polarized Gaussian beams (diffraction angle ±30°) injected from free space toward the structure, defining the desired collection cone.
- Topological Constraints: To ensure fabricability via top-down techniques:
- The refractive index profile was constrained to be constant in the vertical (Z) direction.
- The optimization was performed in 3D using a fixed, optimal height of 300 nm (determined by prior 2D sweeps).
- Binarization and Smoothing:
- A conical blurring function (radius R = 40 nm) was applied iteratively to smooth the index distribution and enforce a minimum feature size suitable for electron-beam lithography.
- A binary push function was applied iteratively to force the continuous index profile into a final binary structure (Air or Silicon).
- Phase Relaxation: Multiple optimization runs were performed, varying the relative phases of the forward and adjoint sources (0 to 2Ï in steps of Ï/2) to relax the phase degree of freedom and find the optimal structure.
Commercial Applications
Section titled âCommercial ApplicationsâThis technology significantly enhances the efficiency of collecting photons from near-surface NV centers, directly benefiting applications where signal-to-noise ratio is limited by photon count.
- Quantum Sensing: Provides a critical boost in sensitivity for high-spatial-resolution sensing of magnetic fields, electric fields, and temperature, especially when using shallow NV centers where extraction is typically poor due to surface proximity.
- Quantum Communication and Computing: Improves the coupling efficiency of single photons from NV qubits into external optical systems, essential for quantum network nodes and entanglement generation.
- Solid-State Emitter Integration: The inverse design methodology and silicon-on-diamond platform can be readily adapted to optimize light extraction for other solid-state color centers (e.g., in SiC or hexagonal boron-nitride).
- Simplified Microscopy Systems: By directing light into a narrow cone, the NLE allows high collection efficiency using low-NA objectives, reducing the complexity, cost, and size of the required optical setup compared to high-NA oil immersion systems.
- Diamond Material Preservation: The design avoids etching the diamond substrate, which is crucial for maintaining the high spin coherence and quantum properties of near-surface NV centers that can be degraded by surface roughness or chemical modification resulting from etching.
View Original Abstract
Abstract We designed a nanoscale light extractor (NLE) for the efficient outcoupling and beaming of broadband light emitted by shallow, negatively charged nitrogen-vacancy (NV) centers in bulk diamond. The NLE consists of a patterned silicon layer on diamond and requires no etching of the diamond surface. Our design process is based on adjoint optimization using broadband time-domain simulations and yields structures that are inherently robust to positioning and fabrication errors. Our NLE functions like a transmission antenna for the NV center, enhancing the optical power extracted from an NV center positioned 10 nm below the diamond surface by a factor of more than 35, and beaming the light into a ±30° cone in the far field. This approach to light extraction can be readily adapted to other solid-state color centers.