Fluorescence profile of a nitrogen-vacancy center in a nanodiamond

Nanodiamonds containing luminescent point defects are widely explored for applications in quantum biosensing such as nanoscale magnetometry, thermometry, and electrometry. A key challenge in the development of such applications is the large variation in fluorescence properties observed between particles, even when obtained from the same batch or nominally identical fabrication processes. By theoretically modeling the emission of nitrogen-vacancy color centers in spherical nanoparticles, we are able to show that the fluorescence spectrum varies with the exact position of the emitter within the nanoparticle, with noticeable effects seen when the diamond radius, $a$, is larger than around 100 nm, and significantly modified fluorescence profiles found for larger particles when $a=200$ and 300 nm, with negligible effects below $a=100$ nm. These results show that the reproducible geometry of point defect position within a narrowly sized batch of diamond crystals is necessary for controlling the emission properties. Our results are useful for understanding the extent to which nanodiamonds can be optimized for biosensing applications.

Figure 1

Four cases under consideration for the photon collections by a circular optical objective with NA=0.9 emitted from a single NV center, which is represented by an electric dipole with moment $\mathit{p}$, implemented in a spherical nanodiamond when the NV center is located at different position along the $x$ axis: (a) case A, $\mathit{p}=(p,0,0)$ and side view; (b) case B, $\mathit{p}=(p,0,0)$ and top view; (c) case C, $\mathit{p}=(0,0,p)$ and side view; and (d) case D, $\mathit{p}=(0,0,p)$ and side view.

Figure 2

The normalized photon counts at $x_d/a=0$ for (a) case A and (b) case D, which almost fully represent the relative intensities of a NV center in bulk diamond at the low-temperature condition listed in Table 1.

Figure 3

The overall photon counts emitted from a NV center embedded in a nanodiamond with radius of $a=100$ nm at selected NV center locations for (a) case A, (b) case B, (c) case C, and (d) case D. For the $x$-oriented dipole [(a) side view and (b) top view] the emission is higher when $x_d/a\approx 0$. For the $z$-oriented dipole, the emission is higher when the dipole is close to the diamond particle surface on the left for the side view (case C) while for the top view (case D), the emission is weaker when $x_d/a\approx 0$.

Figure 4

The overall photon counts emitted from a NV center embedded in a nanodiamond with radius of $a=200$ nm at selected NV color center locations for (a) case A, (b) case B, (c) case C, and (d) case D. From the side view (case A and C), the emission is stronger as $x_d/a<0$ with both $x$- and $z$-oriented dipoles. From the top view, the emission is much enhanced when $x_d/a\approx 0$ for the $x$-oriented dipole (case B).

Figure 5

The normalized photon counts emitted from a NV center embedded in a nanodiamond with radius of $a=200$ nm at selected NV color center location for (a) case A, (b) case B, (c) case C, and (d) case D. For the $x$-oriented dipole from the side view (case A), when $x_d/a=0.6$, the original emission peak at 709 nm disappears while two peaks appear at 659 and 765 nm.

Figure 6

The overall photon counts emitted from a NV center embedded in a nanodiamond with radius of $a=300$ nm at selected NV color center locations for (a) case A, (b) case B, (c) case C, and (d) case D. For the $x$-oriented dipole, the emission is strongly enhanced when $x_d/a=-0.5$ from the side view (case A) and when $x_d/a=0.55$ from the top view (case B). For the $z$-oriented dipole, the emission is highly enhanced when $x_d/a=-0.4$ from the side view (case C) and when $x_d/a=0.4$ from the top view (case D). Also, the emission spectrum profiles are changed significantly when $x_d/a=-0.75$ from the side view and when $x_d/a=0.85$ from the top view.

Figure 7

The normalized photon counts emitted from a NV center embedded in a nanodiamond with radius of $a=300$ nm at selected NV color center locations for (a) case A, (b) case B, (c) case C, and (d) case D. For the $z$-oriented dipole, the emission spectrum profiles are changed significantly relative to that of a NV center in a bulk diamond, for example when $x_d/a=-0.75$ from the side view (case C) and when $x_d/a=0.85$ from the top view (case D).

Figure 8

Comparisons of the normalized emission spectra of a NV center in diamond particles to that in a bulk diamond: (a) the mean value and (b) the standard derivation of $D$ defined in Eq. (3). As the diamond particle size increases, the overall trend of the mean value of $D$ grows indicating that the normalized emission spectra of a NV center are more likely different in larger particles than smaller ones relative to the emission spectrum of a NV center in bulk.

Figure 9

Sketch of the calculation model for the internal and external electromagnetic fields driven by (a) a vertical or (b) a horizontal electric dipole embedded in a dielectric sphere.

Figure 10

Good agreement has been found for the electromagnetic fields between the results obtained by the asymptotic approximations shown in Appendix pp2 (solid lines), by the in-house built field only surface integral method [43] (symbols) when $a=200$ nm, $d=50$ nm, $n_1=1$, $n_2=2.4$, $E_0=p/\left(4\pi {\epsilon }_0{a}^3\right)$, and $\lambda =708$ nm: (a) a vertical electric dipole and (b) a horizontal electric dipole. The curves plotted are the magnitudes of the electromagnetic fields along the circle concentric with the spherical particle with radius as $4a$ on the $xz$ plane [as shown in the inset of Fig. 10].