Probing individual quantum emitters in bulk semiconductors via photonic nanojets

Sci. Adv. 12, eaea5936 (2026) · DOI: 10.1126/sciadv.aea5936

License: CC BY 4.0.

Abstract

Solid-state quantum emitters serve as fundamental building blocks for quantum information processing, quantum telecommunication, and quantum-enhanced sensing, particularly at the nanoscale. However, the high refractive index of the emitters’ host materials often result in low-efficiency collection of the photons generated by the emitters. In addition, isolating individual quantum emitters generally requires high-purity samples and precise defect implantation, adding to the fabrication complexity. In this work, we use free-form topology optimization to design broadband monolithic photonic structures within high–refractive index materials hosting a relatively dense ensemble of randomly distributed quantum emitters. Fabricated via standard top-down patterning techniques, these inverse-designed nanostructures generate tightly confined photonic nanojets, which in turn enable selective excitation of individual emitters and improve photon extraction efficiency. The optimized geometries also substantially suppress background photoluminescence from near-surface optically active defects and from randomly distributed emitters in the bulk, boosting the signal-to-noise ratio. We demonstrate this paradigm using negatively charged nitrogen vacancy (NV⁻) centers in a low-cost diamond sample at room temperature as a case study, achieving selective single emitter excitation with a 10-fold power enhancement and more than 15-fold improvement in the photon extraction efficiency of photoluminescence collection in confocal microscopy. Beyond NV centers and other diamond-embedded quantum emitters, the use of inverse-designed structures generating subwavelength photonic nanojets is applicable to other semiconductor materials containing emitters and can be seamlessly generalized to fiber-integrated platforms.

Figures

33 panels with data across 5 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

• panel (e): Inverse-design convergence profile: enhancement of the power coupled to the selected Gaussian profile against iteration number, through the grayscale and binarization stages. The insets of intermediate patterns ($N = 30$ to 430) are not reproduced. data.csv

Fig. 2

• panel (b-2): Simulated intensity profile $I$ [a.u.] of the photonic nanojet along $z$ [$\mu$m], the line cut beside the vertical ($xz$) plane field map of panel (B); hosted with $I$ on the horizontal axis as printed. data.csv
• panel (b-4): Simulated intensity profile $I$ [a.u.] of the photonic nanojet along $y$ [$\mu$m], the line cut beside the transverse ($xy$) plane field map of panel (B); hosted with $I$ on the horizontal axis as printed. data.csv
• panel (e-1): Simulated directivity pattern (radiated power, a.u.) against angle from the surface normal for the nanojet structure and bare diamond. The lower half-plane is the diamond substrate, shaded in print and not here; the print labels the angles 0 to 180 degrees on both sides, here they run clockwise from the top. data.csv
• panel (e-2): Simulated directivity pattern (radiated power, a.u.) against angle from the surface normal for the bare diamond alone, on an expanded radial scale. The lower half-plane is the diamond substrate, shaded in print and not here; the print labels the angles 0 to 180 degrees on both sides, here they run clockwise from the top. data.csv

Fig. 3

• panel (c): Confocal photoluminescence map, counts [KC/s], of a square array of inverse-design structures imaged at a 2 $\mu$m height offset, against $x$ and $y$ [$\mu$m]. data.csv
• panel (d-1): Photoluminescence scan, counts [KC/s], around the brightest structure at height offset $z = 0$ $\mu$m, slice 1 of the 8 stacked in 3D in print; hosted flat, with pixel axes (the print shows no $x$, $y$ scale). data.csv
• panel (d-2): Photoluminescence scan, counts [KC/s], around the brightest structure at height offset $z = 0.7$ $\mu$m, slice 1 of the 7 stacked in 3D in print, coloured from its own minimum to maximum as printed; hosted flat, with pixel axes (the print shows no $x$, $y$ scale). data.csv
• panel (d-3): Photoluminescence scan, counts [KC/s], around the brightest structure at height offset $z = 1.5$ $\mu$m, slice 2 of the 7 stacked in 3D in print, coloured from its own minimum to maximum as printed; hosted flat, with pixel axes (the print shows no $x$, $y$ scale). data.csv
• panel (d-4): Photoluminescence scan, counts [KC/s], around the brightest structure at height offset $z = 2.3$ $\mu$m, slice 3 of the 7 stacked in 3D in print, coloured from its own minimum to maximum as printed; hosted flat, with pixel axes (the print shows no $x$, $y$ scale). data.csv
• panel (d-5): Photoluminescence scan, counts [KC/s], around the brightest structure at height offset $z = 3.1$ $\mu$m, slice 4 of the 7 stacked in 3D in print, coloured from its own minimum to maximum as printed; hosted flat, with pixel axes (the print shows no $x$, $y$ scale). data.csv
• panel (d-6): Photoluminescence scan, counts [KC/s], around the brightest structure at height offset $z = 3.9$ $\mu$m, slice 5 of the 7 stacked in 3D in print, coloured from its own minimum to maximum as printed; hosted flat, with pixel axes (the print shows no $x$, $y$ scale). data.csv
• panel (d-7): Photoluminescence scan, counts [KC/s], around the brightest structure at height offset $z = 4.7$ $\mu$m, slice 6 of the 7 stacked in 3D in print, coloured from its own minimum to maximum as printed; hosted flat, with pixel axes (the print shows no $x$, $y$ scale). data.csv
• panel (d-8): Photoluminescence scan, counts [KC/s], around the brightest structure at height offset $z = 5.5$ $\mu$m, slice 7 of the 7 stacked in 3D in print, coloured from its own minimum to maximum as printed; hosted flat, with pixel axes (the print shows no $x$, $y$ scale). data.csv
• panel (e): Photoluminescence spectrum, intensity [a.u.], of photons collected from a nanojet-excited NV center against wavelength [nm], showing the zero-phonon line at 637 nm and the phonon sideband. The zoom on the zero-phonon line is hosted as panel e-inset. data.csv
• panel (e-inset): Inset of panel (E): zoom on the NV zero-phonon line, spectrum intensity [a.u.] against wavelength [nm] (632 to 642 nm labelled); the print gives the inset no intensity scale. data.csv
• panel (f): ODMR signal, normalized count [a.u.] against microwave frequency [MHz], for the $m_s = 0$ to $m_s = \pm 1$ transition without external magnetic field: measured points and the fitted curve. data.csv

Fig. 4

• panel (a-1): Power-normalized photoluminescence map PL/$P_{\mathrm{exc}}$ [K counts/S$\cdot$mW] around an extractor with an embedded NV center, at 0.24 mW pump power, against the two scan voltages [mV]. The print shows a central crop with no axes; hosted whole, displayed at that crop. data.csv
• panel (a-2): Power-normalized photoluminescence map PL/$P_{\mathrm{exc}}$ [K counts/S$\cdot$mW] around an extractor with an embedded NV center, at 0.60 mW pump power, against the two scan voltages [mV]. The print shows a central crop with no axes; hosted whole, displayed at that crop. data.csv
• panel (a-3): Power-normalized photoluminescence map PL/$P_{\mathrm{exc}}$ [K counts/S$\cdot$mW] around an extractor with an embedded NV center, at 1.50 mW pump power, against the two scan voltages [mV]. The print shows a central crop with no axes; hosted whole, displayed at that crop. data.csv
• panel (a-4): Power-normalized photoluminescence map PL/$P_{\mathrm{exc}}$ [K counts/S$\cdot$mW] around an extractor with an embedded NV center, at 3.00 mW pump power, against the two scan voltages [mV]. The print shows a central crop with no axes; hosted whole, displayed at that crop. data.csv
• panel (a-5): Power-normalized photoluminescence map PL/$P_{\mathrm{exc}}$ [K counts/S$\cdot$mW] around an extractor with an embedded NV center, at 6.00 mW pump power, against the two scan voltages [mV]. The print shows a central crop with no axes; hosted whole, displayed at that crop. data.csv
• panel (b): Saturation curve of the nanojet photon extractor with an embedded NV: count rate [M counts/S] against input power [mW], measured (purple) and background subtracted (green), each with its dashed fitted curve. data.csv
• panel (c): Count rate [M counts/S] against input power [mW]: background on bare diamond (red points) and the linear background of the nanojet (blue points), each with its dashed linear fit; the area under each line is shaded as printed. data.csv
• panel (d): Fluorescence lifetime measurement with pulsed excitation: counts [a.u.] against time [ns], the measured decay and its fitted curve. data.csv
• panel (e): Second-order autocorrelation $g^{(2)}(\tau)$ against time delay [ns] at excitation power $P = 0.3$ mW: measured points (purple) and the theory prediction (blue, drawn as a shaded region under the curve as printed). data.csv
• panel (f): Second-order autocorrelation $g^{(2)}(\tau)$ against time delay [ns] at excitation power $P = 0.6$ mW: measured points (purple) and the theory prediction (blue, drawn as a shaded region under the curve as printed). data.csv
• panel (g): Second-order autocorrelation $g^{(2)}(\tau)$ against time delay [ns] at excitation power $P = 1.8$ mW: measured points (purple) and the theory prediction (blue, drawn as a shaded region under the curve as printed). data.csv

Fig. 5

• panel (a): Histogram of fluorescence brightness [MC/S, million counts per second] of nanojet devices on one patterned type IIb diamond sample at about 0.9 mW excitation: occurrence against brightness in 20 bins. The print colours the bars by brightness; one colour here. data.csv
• panel (b): Background-corrected second-order autocorrelation $g^{(2)}(\tau = 0)$ for the eight brightest nanojet devices, by device number, with error bars. The print draws horizontal bars with device # on the vertical axis; hosted as vertical bars. data.csv
• panel (c): Extracted saturation count rate [MC/S] for the eight selected nanojet devices, by device number, with error bars. The print draws horizontal bars with device # on the vertical axis; hosted as vertical bars. data.csv
• panel (d): Background suppression factor $B^{\mathrm{Bare}}/B^{\mathrm{Nanojet}}$ (ratio) for the eight selected devices, by device number, with error bars. The print draws horizontal bars with device # on the vertical axis; hosted as vertical bars. data.csv
• panel (e): Excitation enhancement factor $\mathcal{E}_{\mathrm{eff}}$ (ratio) for the eight selected devices, by device number, with error bars. The print draws horizontal bars with device # on the vertical axis; hosted as vertical bars. data.csv

Cite

Behrooz Semnani, Sai Sreesh Venuturumilli, Mohammad Soltani, Pratik Adhikary, Abdolreza Pasharavesh, Nikolay Videnov, Paul Anderson, Supratik Sarkar, Vinodh Raj Rajagopal Muthu, Michal Bajcsy. Probing individual quantum emitters in bulk semiconductors via photonic nanojets. Sci. Adv. 12, eaea5936 (2026). https://doi.org/10.1126/sciadv.aea5936

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