Nitrogen-Vacancy Emission from Nanodiamond: Size, Depth, and Surroundings

TL;DR

This work addresses the variability of nitrogen-vacancy (NV) emission in nanodiamonds by introducing a hybrid framework that couples full-wave Maxwell electrodynamics with a quantum-optical model of the NV center, including phonon sidebands, across subwavelength to wavelength-scale regimes. By modeling a spherical ND of radius $R$ with an NV at depth $D$ in a background of permittivity $oldsymbol{\\epsilon_b}$, the authors quantify how the local excitation field $E_{NV}$, the LDOS-driven decay rates, and both near-field and far-field spectra depend on ND size, NV position, and surrounding refractive index $n_b$. Key findings show strong LDOS suppression that grows at longer emission wavelengths, excitation and near-field brightness that increase with ND size and high-index surroundings (PMMA $>\$ water $>\$ air), and a wavelength-dependent shift in far-field escape efficiency (near-field peak around $682$ nm vs. far-field around $663$ nm). The framework explains variability observed in NV brightness in realistic environments and provides design guidelines for efficient NV-based sensors and quantum devices, while remaining valid across scales and adaptable to more complex geometries and surface effects in future work.

Abstract

The negatively charged nitrogen-vacancy (NV) center in diamond is a leading solid-state quantum emitter, offering spin-photon interfaces over a wide temperature range with applications from electromagnetic sensing to bioimaging. While NV centers in bulk diamond are well understood, embedding them in nanodiamond (ND) introduces complexities from size, NV location, and NV polarizations. NVs in ND show altered fluorescence properties including longer lifetimes, lower quantum efficiency, and higher sensitivity to dielectric surroundings, which arise from radiative suppression, surface-induced non-radiative decay, and escape inefficiency at the diamond-background interface. Prior models typically addressed isolated aspects, such as dielectric contrast or surface quenching, without integrating full quantum-optical NV behavior with classical electrodynamics. We present a hybrid framework coupling rigorous electromagnetic simulations with a quantum-optical NV model including phonon sideband dynamics. NV emission is found to depend strongly on ND size, NV position, and surrounding refractive index. Our results explain observations such as shallow NVs in water-coated ND appearing brighter than deeper ones in air. This integrated model provides a unified framework for realistic NV in ND emission scenarios and informs the design of efficient NV-based sensors and quantum devices, advancing understanding of quantum emitter photophysics in nanoscale crystals.

Figures (5)

• Figure 1: (Colour online) (a) Host nanodiamond (ND) in the medium of relative permittivity $\epsilon_b$ (b) Atomic structure and the orientation of the negatively charged nitrogen-vacancy (NV) centre embedded in the ND (c) Optical abstraction of the NV level structure.
• Figure 2: (Colour online) Fraction of $x$-polarised electric field amplitude at the NV location relative to the incident green light, $|\tilde{E}_x^+|$. (a) $|\tilde{E}_x^+|$ as a function of nanodiamond diameter ($2R$), with the NV center fixed at the origin ($D=0$), showing the effect of a different infinitely extending background dielectric media (air with refractive index of $n=1$, water $n=1.33$, PMMA $n=1.5$). (b) $|\tilde{E}_x^+|$ as a function of the radial distance to the NV location from the origin along the $x$-axis, for a $100nm$ diameter nanodiamond, for the same background media.
• Figure 3: (Colour online) Numerically computed decay rate modifications, $\gamma_u(\lambda_k)/\gamma^\text{ref}_u(\lambda_k)$, for unit dipoles emitting at NV transition wavelengths $\lambda_k\in\lbrace 639, 649, 663, 682, 699, 721, 744, 764 \rbrace\;nm$ within a spherical nanodiamond, relative to a unit dipole in infinitely extending bulk diamond (reference). The first row depicts $\gamma_u(\lambda_k)/\gamma^\text{ref}_u(\lambda_k)$ as a function of nanodiamond size ($2R$) for a unit dipole located at the origin of the spherical nanodiamond ($D=0$) when the infinitely extending background medium is (a) air, (b) water and (c) PMMA. The second row depicts decay rate modification as a function of the unit dipole location along the $x-$axis in a $100nm$ diameter nanodiamond in background media (d) air (e) water and (f) PMMA. The legend in (a) is common for all subplots and colors of the lines progressively darken with increasing emission wavelength (from $639nm$ to $764nm$).
• Figure 4: (Colour online) Numerically computed near-field emission spectra for an NV center within a spherical nanodiamond, radiated inside the nanodiamond, as described in Section \ref{['Sec:Quantum_Model']}. The first row depicts the variation of emission intensity spectra of an NV center located at the origin ($D=0$) as a function of nanodiamond diameter ($2R$), ranging from $10nm$ to $100nm$ (line colors darken with increasing diameter). Each column corresponds to a different infinitely extending background medium, (a) air, (b) water, and (c) PMMA. The second row depicts the variation of emission intensity spectra for different NV distances from the origin along the $x-$axis (ranging from $0nm$ to $45nm$, with line colors darkening with decreasing distance) in a $100nm$ diameter nanodiamond. All plots are normalised by the maximum intensity of the emission spectrum of an NV centre in an infinitely extending bulk diamond as the reference.
• Figure 5: (Colour online) Numerically computed far-field emission intensity spectra for an NV center hosted within a spherical nanodiamond. The first row shows the variation of far-field spectra with nanodiamond diameter ($2R$, where darker lines correspond to increasing diameters), for an NV centre located at the origin of the nanodiamond host submerged in background media (a) air, (b) water, and (c) PMMA. The second row shows the variation of far-field spectra with the distance to the NV location from the origin along the $x-$axis (ranging from $0nm$ to $45nm$, with darker lines corresponding to decreasing distance) in a $100nm$ diameter nanodiamond in (d) air, (e) water, and (f) PMMA. Insets in (a) and (d) provide an enlarged view of the y-axis to highlight details of the significantly suppressed emission in air. All plots are normalised by the maximum intensity of the emission spectrum of an NV centre in an infinitely extending bulk diamond as the reference.