Curved Grating Emitters in Quantum Photonics

• Curved grating emitters are nanoscale photonic and plasmonic structures with concentric or sector-shaped patterns that reshape emission for controlled mode confinement.
• They enhance emission directionality and extraction efficiency by converting rotational symmetry into focused free-space or surface-wave modes.
• Precise fabrication using lithography and etching optimizes quality factors and mode volumes, enabling deterministic integration for single-photon generation.

Searching arXiv for recent and foundational papers on curved grating emitters, including circular Bragg grating and bullseye cavity implementations. First search: circular Bragg grating / bullseye emitters in quantum photonics. Curved grating emitters are photonic or plasmonic structures in which concentric or sector-shaped gratings reshape the radiation of guided, localized, or embedded emitters into controlled free-space or surface-wave modes. In nanophotonics, the term commonly refers to circular Bragg grating (CBG) or “bullseye” cavities, where concentric rings surrounding a central disk provide radial Bragg feedback, small effective mode volume, and highly directional out-of-plane emission. Across semiconductor, silicon, van der Waals, plasmonic, and x-ray implementations, the defining function of the curved geometry is to convert rotational or cylindrical symmetry into mode confinement, wavefront engineering, and efficient extraction or focusing (Iff et al., 2021).

1. Definition and architectural scope

In integrated quantum photonics, curved grating emitters are most often realized as circular Bragg grating cavities consisting of a central disk surrounded by concentric etched grooves. In the AlGaAs/WSe$_2$ implementation, the structure comprises a 230 nm-thick Al$_{0.31}$Ga$_{0.69}$As membrane bonded to 430 nm SiO$_2$ and a 150 nm Au mirror, with 5 concentric air-etched grooves, grating period $\Lambda = 350$ nm, groove width $w = 100$ nm, slab width $s = 250$ nm, and nominal inner disk radius $R_0 \approx 800$ nm (Iff et al., 2021). In silicon-on-insulator, the analogous platform uses a 220 nm-thick silicon layer on 2 $\mu$m buried oxide, a central disk of diameter $D \simeq 970$ nm, and $_{0.31}$0 grating periods with period $_{0.31}$1 nm and groove width $_{0.31}$2 nm (Lefaucher et al., 2023).

Related van der Waals implementations in hBN also adopt the same radial-grating motif. One design uses 6 concentric high-index rings around a central disk of radius 360 nm, with ring width 117 nm, gap 63 nm, period $_{0.31}$3 nm, and hBN thickness in the range $_{0.31}$4–220 nm (Liddle-Wesolowski et al., 7 Jan 2026). Another hBN bullseye geometry employs a central disk diameter $_{0.31}$5 nm, ring width $_{0.31}$6 nm, trench width $_{0.31}$7 nm, radial period $_{0.31}$8 nm, and approximately 6–8 rings in a flake of thickness $_{0.31}$9 nm (Spencer et al., 2023).

Outside dielectric cavity QED, curved gratings also appear as plasmonic lenses and ring gratings. Sector-shaped concentric grooves etched into thin gold films couple linearly polarized free-space light into focused surface plasmon polaritons (SPPs), while ring gratings integrated with nanoantennas feed localized plasmonic hotspots via SPP–LSP coupling (Maleki et al., 2015). In x-ray interferometry, cylindrical gratings are bent to conform to a divergent cone beam, enabling normal incidence over a large field of view and supporting Talbot self-imaging on concentric cylindrical surfaces (Cong et al., 2015).

This distribution of platforms suggests that “curved grating emitter” is best understood as a geometric class rather than a single device family: the same curved periodicity can serve extraction, Purcell enhancement, near-field focusing, or self-imaging, depending on the underlying wave physics.

2. Electromagnetic principles and figures of merit

For circular Bragg grating cavities used with quantum emitters, the central metric is the Purcell factor,

$_{0.69}$0

or, equivalently in the WSe$_{0.69}$1 study,

$_{0.69}$2

with

$_{0.69}$3

The governing design objective is therefore simultaneous control of quality factor $_{0.69}$4, effective mode volume $_{0.69}$5 or $_{0.69}$6, and emitter placement at an electric-field antinode (Iff et al., 2021).

In the silicon W-center platform, the ideal single-dipole maximum Purcell factor is written as

$_{0.69}$7

and for position-, orientation-, and detuning-dependent coupling the cavity enhancement becomes

$_{0.69}$8

For ensembles, the total decay rate must include radiative emission into the zero-phonon line (ZPL), phonon sidebands, leaky modes, and non-radiative channels:

$_{0.69}$9

The same work also defines the Debye–Waller factor $_2$0 and extracts a bulk internal quantum yield $_2$1 by matching intensity and lifetime data to the ensemble Purcell model (Lefaucher et al., 2023).

For radial Bragg gratings in hBN, the basic resonance condition is

$_2$2

with $_2$3 used in one deterministic hBN implementation and $_2$4 for an hBN slab on SiO$_2$5 (Liddle-Wesolowski et al., 7 Jan 2026). In the 436 nm hBN bullseye design, the same radial Bragg condition is written as

$_2$6

and for first-order radial Bragg reflection gives $_2$7, consistent with a fabricated trench width $_2$8 nm for $_2$9 nm and $\Lambda = 350$0 (Spencer et al., 2023).

In plasmonic curved gratings, the operative principle is grating-mediated momentum matching:

$\Lambda = 350$1

with $\Lambda = 350$2. The sector angle controls an effective numerical aperture,

$\Lambda = 350$3

with $\Lambda = 350$4, and the lateral focal width scales approximately as

$\Lambda = 350$5

This expresses a direct geometric route from curved-grating aperture to focal confinement (Maleki et al., 2015).

For out-of-plane focusing emitters on neural probes, the grating is designed holographically to impose a spherical-wave phase profile

$\Lambda = 350$6

or, more generally,

$\Lambda = 350$7

thereby defining curved grating teeth as $\Lambda = 350$8 phase contours that focus at a prescribed point above the chip (Xue et al., 2024).

3. Dielectric circular Bragg gratings for quantum emitters

The WSe$\Lambda = 350$9/AlGaAs circular Bragg grating cavity is a representative dielectric bullseye emitter in which a strain-localized monolayer quantum dot is placed at the center of the cavity. Finite-difference time-domain simulations identify a best-coupled mode at $w = 100$0 nm with $w = 100$1 and simulated maximum $w = 100$2, while a second mode at $w = 100$3 nm has $w = 100$4 and weaker Purcell enhancement. The side-view field profile shows confinement in the central disk with evanescent extension into air, enabled by choosing a TE$w = 100$5 slab mode whose second-order vertical profile maximizes the field at the surface where the two-dimensional quantum dot sits. The top-view field hotspot lies at the disk center, and the far-field projection has angular full-width below $w = 100$6, with NA $w = 100$7 collecting more than 70% of the emitted photons (Iff et al., 2021).

Experimentally, the same platform shows a consistent increase of spontaneous emission rate for WSe$w = 100$8 emitters located in the center of the grating. Time-correlated single-photon counting with 448 nm, 2 ps pump pulses and 350 ps Si-APD resolution yields an average lifetime $w = 100$9 ns for emitters in the cavity center and $s = 250$0 ns for off-cavity emitters, corresponding to an experimental Purcell factor up to $s = 250$1. The source retains clear single-photon character with $s = 250$2 under CW 532 nm excitation, and cavity-center emitters saturate at higher count rates than off-cavity emitters, typically a few $s = 250$3 counts/s under NA = 0.65 (Iff et al., 2021).

The silicon W-center CBG realizes the same design logic in a CMOS-compatible material system. Here the resonant wavelength is $s = 250$4 nm, the designed $s = 250$5 is 100–200 with simulated $s = 250$6, and the mode volume is $s = 250$7. The cavity supports a fundamental in-plane dipole mode concentrated in the central disk with two orthogonal linear polarizations and an antinode at the cavity center. Simulations give an on-resonance Purcell factor $s = 250$8 for a single dipole at the antinode and a collection efficiency $s = 250$9 into NA = 0.26, while experiments show up to 20-fold enhancement of ZPL intensity and a lifetime reduction from 39 ns off resonance to 19 ns on resonance under 1 MHz pulsed excitation (Lefaucher et al., 2023).

These two systems illustrate a recurring distinction within dielectric curved grating emitters. In the WSe$R_0 \approx 800$0 platform, the cavity is broadband enough to cover the inhomogeneous spread of 2D quantum-dot energies, with $R_0 \approx 800$1–40 and $R_0 \approx 800$2–30 nm, while still producing measurable lifetime acceleration and highly directional collection. In the silicon platform, higher $R_0 \approx 800$3 and explicit ensemble modeling of ZPL, phonon sidebands, and non-radiative channels enable more detailed cQED analysis, but with similar emphasis on free-space extraction (Iff et al., 2021).

4. Deterministic integration in van der Waals materials

A central development in curved grating emitters is the move from stochastic coupling to deterministic emitter–cavity registration. In the WSe$R_0 \approx 800$4 bullseye device, electron-beam lithography defines the grating in resist, reactive-ion etching with Ar/Cl$R_0 \approx 800$5 transfers the pattern to the semiconductor, and a single 200 nm-tall SiO$R_0 \approx 800$6 nanopillar is grown by focused-ion-beam–assisted deposition of Si(C$R_0 \approx 800$7H$R_0 \approx 800$8O)$R_0 \approx 800$9 at the center of each cavity. Exfoliated WSe$\mu$0 monolayers are then all-dry transferred at $\mu$1C, and capillary and van der Waals forces conform the monolayer over the nanopillar “tent,” inducing a local strain-defined quantum dot exactly at the field antinode. The reported design guideline is that deterministic nanopillar-strain alignment ensures greater than 90% yield of quantum dots placed exactly at the field antinode (Iff et al., 2021).

In hBN, deterministic integration is achieved by a different route: pre-selecting emitters before cavity fabrication. The 2026 hBN study uses a Si wafer with 285 nm thermal SiO$\mu$2, CSAR.09 resist, and etched alignment markers produced by ICP-RIE at 300 W with Ar 60 sccm, SF$\mu$3 5 sccm, 11 mTorr, and approximately 100 nm depth into SiO$\mu$4. After Scotch-tape exfoliation of approximately 200 nm thick hBN and defect activation by annealing at $\mu$5C in 1000 sccm O$\mu$6 for 4 h followed by UV-ozone for 4 h, two confocal microscopes are used: a “spectral” setup to identify zero-phonon-line wavelengths and count rates, and a “spatial” setup to map marker edges and emitter photoluminescence. Reflected 532 nm leakage delineates marker edges with FWHM uncertainty of approximately 7 nm, while 2 $\mu$7 2 $\mu$8m emitter scans show FWHM of approximately 240 nm. A custom Python distortion-correction routine maps measured marker coordinates to the lithographic grid to obtain sub-$\mu$9m emitter coordinates, after which aligned electron-beam lithography defines a 6-ring CBG scaled to the target emitter wavelength (Liddle-Wesolowski et al., 7 Jan 2026).

The deterministic hBN devices show that spatial and spectral registration can be separated into two design loops: coordinate alignment to place the emitter in the cavity center and global scaling factor $D \simeq 970$0 to tune the cavity mode into the 550–700 nm ZPL range. Using a calibration curve $D \simeq 970$1, the cavity geometry is scaled so that $D \simeq 970$2, with measured cavity modes matching simulations to within approximately 2 nm and static scaling delivering less than 2 nm detuning on average. Out of 10 deterministically integrated emitters, 5 showed clear enhancement; a representative single-photon emitter increased from approximately 81 kcps pristine ZPL saturation counts to approximately 188 kcps in the CBG, i.e. a 2.3-fold increase, while ODMR contrast remained preserved under $D \simeq 970$3 mT with spin-1 transitions at approximately 0.95 GHz and 2.95 GHz and spin-1/2 at approximately 1.9 GHz (Liddle-Wesolowski et al., 7 Jan 2026).

A complementary hBN approach is monolithic integration with site-specific electron-beam irradiation. In that system, B-centers are created at predefined locations using 5 kV, 1.6 nA irradiation with dwell time around 1 s, achieving positioning accuracy relative to cavity center of at most 50 nm, limited by SEM stage and beam drift. The rotational symmetry of the cavity is explicitly noted to render coupling independent of azimuth despite random in-plane dipole orientation (Spencer et al., 2023).

5. Directionality, collection efficiency, and focusing behavior

A defining advantage of curved grating emitters is directional far-field control. In the WSe$D \simeq 970$4 AlGaAs cavity, far-field projection reveals a highly collimated beam with angular full-width below $D \simeq 970$5, and the narrow far-field lobe implies that more than 70% of the photons are collected into NA = 0.6 (Iff et al., 2021). The hBN deterministic CBG gives a similar result in simulation, with approximately 80% of the power emitted into a half-angle cone of $D \simeq 970$6 and more than 60% collection into NA = 0.9 (Liddle-Wesolowski et al., 7 Jan 2026). In the silicon W-center cavity, the curvature yields a near-Gaussian far field suited for free-space collection, and the measured extraction efficiency is approximately 40% at NA = 0.26, in excellent agreement with FDTD (Lefaucher et al., 2023).

The 436 nm hBN bullseye emphasizes collection enhancement over large Purcell enhancement. FDTD gives a near-normal emission lobe with half-angle at most $D \simeq 970$7, low simulated $D \simeq 970$8, and $D \simeq 970$9, so that in practice $_{0.31}$00. Experimentally, room-temperature saturation measurements give an uncoupled saturation intensity of 0.4 Mcps at 0.82 mW and a CBG-coupled saturation intensity of 2.3 Mcps at 1.23 mW, corresponding to net collection enhancement of approximately $_{0.31}$01 with $_{0.31}$02. At 5 K the device exhibits a ZPL at 432.5 nm, spectrometer-limited ZPL FWHM of 0.10 nm, phonon sideband FWHM of 5 nm, no measurable spectral diffusion within spectrometer resolution over 2 min, and $_{0.31}$03 (Spencer et al., 2023).

Curved gratings also serve as focusing optics rather than resonant cavities. Sector-shaped gold gratings couple p-polarized light into SPPs whose wavelets interfere constructively at a focal spot. Increasing sector angle reduces lateral spot size: for 7 grooves and inner radius around 3 $_{0.31}$04m, reported values are $_{0.31}$05m at $_{0.31}$06, $_{0.31}$07m at $_{0.31}$08, $_{0.31}$09m at $_{0.31}$10, $_{0.31}$11m at $_{0.31}$12, and about 300 nm for $_{0.31}$13 (Maleki et al., 2015). A two-faced asymmetric configuration with groove-radius offset $_{0.31}$14 leaves lateral width essentially unchanged but reduces longitudinal extent from $_{0.31}$15 to $_{0.31}$16 and increases peak intensity to approximately $_{0.31}$17 (Maleki et al., 2015).

The out-of-plane focusing emitters used in implantable neural probes generalize this concept to guided-wave holography. Designed for 488 and 594 nm, with grating apertures of $_{0.31}$18m $_{0.31}$19 $_{0.31}$20m on 100 $_{0.31}$21m-wide shanks and local periods ranging approximately 300–450 nm for blue and 350–550 nm for red, these emitters generate focused spots about 50 $_{0.31}$22m above the chip. Simulated free-space beam waists are approximately $_{0.31}$23m $_{0.31}$24 $_{0.31}$25m at 488 nm and $_{0.31}$26m $_{0.31}$27 $_{0.31}$28m at 594 nm, while measured values are $_{0.31}$29m $_{0.31}$30 $_{0.31}$31m and $_{0.31}$32m $_{0.31}$33 $_{0.31}$34m, respectively. In brain tissue, measured side-view FWHM broadens to 8.4 $_{0.31}$35m for blue and 9.1 $_{0.31}$36m for red, with the authors attributing much of this broadening to scattered fluorescence rather than the underlying beam waist (Xue et al., 2024).

6. Fabrication regimes, trade-offs, and optimization rules

Several design heuristics recur across dielectric curved gratings. In the WSe$_{0.31}$37 platform, a membrane thickness is chosen to support a higher-order slab mode such as TE$_{0.31}$38 so that the cavity field peaks at the air interface. The reported recommendation is to use 5–7 rings to provide sufficient radial Bragg feedback while maintaining a small diffraction-limited divergence, and to select duty cycle $_{0.31}$39–0.35 to trade off $_{0.31}$40 against bandwidth; specifically, $_{0.31}$41 nm and $_{0.31}$42 nm yield $_{0.31}$43–40 and $_{0.31}$44–30 nm (Iff et al., 2021). The silicon W-center study similarly notes that increasing the number of rings beyond 4 raises $_{0.31}$45 but reduces bandwidth and extraction, and that varying period or groove width by $_{0.31}$46 shifts resonance by a few nanometers and modulates $_{0.31}$47 by $_{0.31}$48 (Lefaucher et al., 2023).

In hBN, fabrication sensitivity is especially pronounced. The monolithic 436 nm bullseye study compares several etch processes: argon ion-beam etching gives rough surfaces and slanted sidewalls, chemically assisted ion-beam etching improves smoothness but causes polymer mask cracking and lateral undercut, chlorine-based RIE yields very smooth sidewalls but shallow etch, and fluorine-based RIE provides full 275 nm flake through-etch in 37 s with slight microtrenching and was therefore chosen for final devices. Fabrication tolerance on ring width and spacing is stated as $_{0.31}$49 nm achievable by electron-beam lithography, and maximum collection occurs at nominal dimensions, with $_{0.31}$50 deviations reducing coupling by at least 30% (Spencer et al., 2023).

For plasmonic ring gratings integrated with nanoantennas, optimization takes a different form. A five-groove ring of period 519 nm, chosen for $_{0.31}$51 nm and $_{0.31}$52, launches SPPs toward a central nanoprism or bowtie antenna. Simulated near-field enhancement in a 100 nm gap reaches approximately $_{0.31}$53 for a nanoprism, $_{0.31}$54 for a single bowtie, and $_{0.31}$55 for a double bowtie. Experimentally, for a 100 nm gap the PL enhancement factor $_{0.31}$56 is 13.7 for the single-cavity structure and 31.3 for the double-cavity structure, while for 50 nm gaps in the double-cavity double-bowtie geometry the radiative-rate enhancement rises to approximately 6.8 and $_{0.31}$57 to about $_{0.31}$58 (Rahbany et al., 2018). The corresponding design trade-off is explicit: smaller gaps increase field enhancement and Purcell factor but are harder to fabricate and can quench emitters (Rahbany et al., 2018).

In x-ray cylindrical gratings, the relevant fabrication and alignment trade-off is macroscopic rather than nanometric. Curving the grating so that its radius matches the source–grating distance ensures normal incidence throughout the illuminated sector, increasing flux and usable field of view relative to flat gratings. The self-imaging condition,

$_{0.31}$59

defines the downstream observation radius $_{0.31}$60 for Talbot reconstruction, with approximate Talbot distance

$_{0.31}$61

when $_{0.31}$62 (Cong et al., 2015). This is a distinct curved-grating design space, but it highlights the same geometric theme: curvature is used to maintain phase-matched propagation over a divergent angular aperture.

7. Applications, limitations, and research directions

The most mature application of dielectric curved grating emitters is single-photon generation with improved extraction. In WSe$_{0.31}$63, the cavity-enhanced source combines deterministic strain localization, Purcell enhancement, and antibunched emission with $_{0.31}$64, while maintaining simple and low-cost production and intrinsic scalability (Iff et al., 2021). In silicon, circular Bragg gratings enable cavity quantum electrodynamics with W centers on a silicon-on-insulator platform, yielding ZPL enhancement, lifetime control, and a route toward on-demand sources of single photons in silicon photonic chips (Lefaucher et al., 2023). In hBN, both monolithic bullseye cavities and deterministic post-selection workflows indicate that curved gratings can be combined with visible emitters and, in the 2026 study, with optically addressable spin states while preserving ODMR contrast (Liddle-Wesolowski et al., 7 Jan 2026).

A recurrent misconception is that all bullseye cavities are primarily Purcell devices. The data show a more differentiated picture. The hBN 436 nm bullseye explicitly operates in a low-$_{0.31}$65, relatively large-$_{0.31}$66 regime where collection efficiency is prioritized over lifetime shortening (Spencer et al., 2023). By contrast, the WSe$_{0.31}$67 and silicon devices are designed to obtain moderate Purcell enhancement together with directional extraction (Iff et al., 2021). A plausible implication is that curved grating emitters should be classified by objective function—extraction-dominant, Purcell-balanced, or strongly cavity-enhanced—rather than by geometry alone.

Another important limitation is fabrication sensitivity. In hBN, $_{0.31}$68 deviations in ring spacing can reduce coupling by at least 30%, and deterministic integration currently shows enhancement in 5 out of 10 devices rather than universal success (Spencer et al., 2023). In silicon, the same work points to improvement paths including additional rings or buried Bragg mirrors to raise $_{0.31}$69 toward 50–100 at the cost of bandwidth, site-selective focused-ion-beam implantation for single-emitter placement, and waveguide-coupled collection exceeding 80% with adiabatic tapers (Lefaucher et al., 2023). In hBN, geometric scaling already provides sub-2 nm spectral matching without active tuning, suggesting a route to scalable cavity–spin platforms if emitter yield and spectral reproducibility continue to improve (Liddle-Wesolowski et al., 7 Jan 2026).

Beyond quantum light sources, curved gratings support plasmonic sensing, spectroscopy, nonlinear plasmonics, and optical routing through subwavelength SPP focusing (Maleki et al., 2015), as well as implantable optogenetic stimulation through out-of-plane focusing spots with dimensions on the scale of neuron somata (Xue et al., 2024). These parallel developments indicate that the broader significance of curved grating emitters lies in their ability to convert local geometry into a prescribed radiation phase space: moderate-$_{0.31}$70 cavity emission, narrow-cone extraction, sub-diffraction plasmonic hotspots, or finite-distance free-space focusing all emerge from the same curved periodicity principle.