Optical Magnetism and Fundamental Modes of Nanodiamonds: Supporting Information

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1 Optical Magnetism and Fundamental Modes of Nanodiamonds: Supporting Information Daniil A. Shilkin, 1, 2 Maxim R. Shcherbakov, 1 Evgeny V. Lyubin, 1 1, 3, 4 Konstantin G. Katamadze, Oleg S. Kudryavtsev, 5 Vadim S. Sedov, 5 Igor I. Vlasov, 5, 3 and Andrey A. Fedyanin 1, 1 Faculty of Physics, Lomonosov Moscow State University, Moscow , Russia 2 Center for Functionalized Magnetic Materials, Immanuel Kant Baltic Federal University, Kaliningrad , Russia 3 National Research Nuclear University MEPhI, Moscow , Russia 4 Institute of Physics and Technology, Russian Academy of Sciences, Moscow , Russia 5 Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow , Russia I. FABRICATION OF THE NANODIAMONDS II. EXPERIMENTAL SETUP The particles were grown by chemical vapor deposition (CVD) in methane hydrogen gas mixtures. The purities of the gases were % for CH 4 and % for H 2. Five-nanometer detonation diamonds from Adamas Nanotechnologies were used as precursors for the CVD diamond production. They were seeded on a sapphire substrate from a water suspension using an ultrasonic technique. The resulted concentration of the particles varied among the substrate; this allowed us to find a region where the concentration is low enough to resolve the particles in the optical scheme and collect the scattering signal from single nanoparticles. The synthesis was performed in a microwave (MW) plasma reactor ARDIS-100 (2.45 GHz, 5 kw) according to the following algorithm: (1) The ignition of the plasma was performed at a MW power of 1.9 kw and a gas pressure of 10 Torr in pure hydrogen (200 sccm); (2) The intensity of the plasma was slowly increased to reach 2.8 kw and 60 Torr. (3) CH 4 gas was added (H 2 : 475 sccm, CH 4 : 25 sccm), giving 5% CH 4 in the feeding gas mixture. The substrate temperature was as low as C (lower than the detection range of a Williamson C pyrometer), so there was no intensive diamond growth at this stage. The time for the initial gas admixture was 1 min. (4) The MW power was increased to 3 kw, and the gas pressure was increased to 75 Torr, which resulted in an increase in the substrate temperature to 850 C. Isolated diamond crystallites were formed on the sapphire substrate at this stage. The size of the particles was controlled by the deposition time at this stage (6 min). (5) The gas feed was changed to pure hydrogen (500 sccm), the plasma conditions were set to 2.8 kw and 80 Torr, and the substrate temperature was 800 C. The surfaces of the particles were etched by atomic hydrogen to remove the sp2 phase. (6) The MW power and the gas pressure were slowly reduced, and the termination of the process was performed. Electronic address: fedyanin@nanolab.phys.msu.ru The experimental setup for measuring the scattering by single nanodiamonds is shown in Fig. S1. It is based on a standard transmitted light microscopy scheme with Köhler illumination. White light from a 50 W halogen lamp is directed into the setup by a multimode optical fiber F1 with a core diameter of 0.6 mm and a numerical aperture (NA) of The lamp is imaged on the fiber input face in a 2f-2f configuration by a biconvex lens L1 with a focal distance of 25 mm. The fiber output is collimated by an aspheric condenser lens L2 with a focal distance of 10.5 mm. The field diaphragm FD is placed in the focal plane of a biconvex lens L3 with a focal distance of 250 mm. An image of the field diaphragm FD is formed on the sample by a strain-free plan achromat objective lens O1 with a focal distance of 16 mm and an NA of The polarization of the illumination light is controlled by a Glan prism GP, which was removed for the measurements of the unpolarized scattering spectra. The sample is placed on a two-dimensional transla- FIG. S1: Experimental setup. L1 6, lenses; F1,2, multimode optical fibers; FD, field diaphragm; GP, Glan prism; O1,2, objective lenses; CS, central stop; M, mirror. Elements enclosed by dotted lines are removable.

2 2 tion stage, which allows manipulation in the horizontal plane, with nanoparticles facing upwards. A waterimmersion plan apochromat objective lens O2 (Olympus UPlanSApo 60XW) with a focal distance of 3 mm and an NA of 1.2 is mounted on a vertical translation stage for precise focusing on the surface of the sample. A pair of achromatic doublets L4, each with a focal distance of 200 mm, is used to form an image of the back focal plane of the lens O2 in a 2f-2f configuration. A central stop CS with a diameter of 2 mm is mounted on a flip mount and placed in the plane of this image, which enables blocking unscattered illumination to obtain dark-field images of the sample and measuring the scattering spectra of single nanodiamonds. Further, depending on the position of the mirror M on another flip mount, light can be directed either into a video camera or into a spectroscopic arm. In the camera, an image of the sample is formed by an achromatic doublet L5 with a focal distance of 60 mm on a CMOS imaging sensor Thorlabs DCC1545M. In the spectroscopic arm, an achromatic doublet L6 with a focal distance of 150 mm forms a 33-fold magnified image of the sample in the plane, where the face of a multimode optical fiber F2 is mounted on a translation mount. The fiber is connected to an Ocean Optics USB4000 spectrometer with a resolution of 1 nm and a grating set to the registration range of nm (the actual range is limited by the sensitivity of the silicon matrix). Scattering spectra of a few small particles were also measured by a Solar LS S100 spectrometer with a resolution of 2 nm and a lower sensitivity but a registration range of nm (again, the actual range is limited by the sensitivity of the silicon matrix). Because of the higher noise level, it was inferior to the other spectrometer at larger wavelengths and was not used in all the measurements. To minimize the mode coupling effects, a servo motor is used to vibrate the fiber F2 at about the middle of its length. During the measurements, the position of the fiber facet on the translation mount is manipulated to maximize the collected light power. The core diameter of the fiber F2 is 105 µm, which corresponds to an area of approximately 3 µm on the sample. The fact that the light analyzed by the spectrometer is collected from such a small area on the sample ensures that this light is scattered by a single nanodiamond. III. CHARACTERIZATION OF THE NANODIAMONDS The measurements were performed with particles localized around characteristic features on the sapphire substrate that allowed us to find the analyzed particles with a scanning electron microscope (SEM). The images of the working regions on the sample obtained with the SEM and in the setup described above are shown in Fig. S2. The optical microscope images were obtained with the default gain values. The particles are labelled for further reference. In the dark field photos, one can see a non-uniform background, which is caused by a ripple on the operated side of the sapphire substrate that is clearly seen in the SEM images. The background was taken into account during the measurements, see Section IV. All of the analyzed particles were characterized by SEM. The obtained SEM images were analyzed using ImageJ software. For every particle, its contour was manually identified, as shown in Fig. S3(a) using particle d as an example. The area A and perimeter P of the selected area were determined. The histograms of the calculated effective sizes d = 2 A/π and circularities f = 4πA/P 2 are shown in Fig. S3(b,c). IV. PROCESSING THE SPECTRA The operated side of the sapphire substrate has ripples that are clearly seen in the SEM images. As one can see in the dark field photographs, these ripples cause a noticeable non-uniform background, which should be taken into account when measuring the spectra of the scattering by the nanodiamonds. For this reason, the background spectra were measured at different places on the sample where there are no diamonds. The normalized spectrum of the background scattering is shown in Fig. S4(a). The average background spectrum was subtracted from the one measured at a nanodiamond, and the difference was normalized by the lamp spectrum, which was measured at the open position of the stop CS and averaged for different places on the sample where no diamonds were present. Examples of the obtained spectra are shown in Fig. S4(b d) by the gray and pink lines. The two different experimental spectra shown in Fig. S4(b) were obtained using the two spectrometers. To determine the resonance peak positions, the spectra were fitted with two Lorentzian peaks. Only peaks identified inside the registration regions were shown in the dependence in Fig. 3 in the main manuscript. The examples of the approximation curves are indicated in Fig. S4(b d) by black lines. The individual peaks are denoted by the purple lines. The spectra shown in the main manuscript were additionally normalized by the maximum value and smoothed by the Savitzky-Golay filter with a 10-point window. In Fig. 1(b) in the main manuscript, a scattering spectrum for particle d is shown. Fig. 2 presents scattering spectra from particles s, t, v, d, i (referred to from the bottom to the top). All of the analyzed particles were used for Fig. 3, although only the peaks identified inside the registration regions are shown. The same dependence with the points labelled as the corresponding particles is shown in Fig. S5. Fig. 4 in the main manuscript presents polarized scattering spectra from particle x.

3 3 FIG. S2: Images of the analyzed particles. (a,d) SEM. (b,e) Bright field microscope photographs. (c,f) Dark field microscope photographs. The non-uniform background in the dark field photographs is due to the ripples on the substrate, which can clearly be seen in the SEM images. The background was taken into account during the measurements, see Section IV. FIG. S3: Shape analysis. (a) Typical identification of the contour of a nanodiamond. Particle d, which had a size of 386 nm and a circularity of 0.81, is shown. (b) Histogram of the effective sizes of the analyzed particles. (c) Histogram of the particle circularities. V. NUMERICAL CALCULATIONS The numerical calculations were performed with Lumerical FDTD Solutions. The dispersion of diamond from [1] and the dispersion of sapphire from [2] were used. The same dispersion of diamond was used in the analytical calculations. The model used to calculate the scattering spectra is shown in Fig. S6(a). A plane wave (Total Field Scattered Field source) was used as the radiation source. A short pulse propagation was simulated, and the Fourier components at different wavelengths were calculated to obtain the result for the continuous wave radiation. Po- larized radiation was used in the simulations. In the case of spherical particles, the symmetry of the model guarantees that the same spectra will be obtained for unpolarized illumination. To simulate the experimental conditions, only light scattered into the experimental angles of registration was analyzed. For this purpose, far field scattering was calculated, and the flux of the radiation scattered between 11 and 43.3 was integrated. The total scattered radiation was found as well. Fig. S6(b) presents the calculated spectra of scattering at the experimental collection angles with the substrate enabled and disabled for a 320-nm diamond sphere. The peaks are more clearly identified without

4 4 FIG. S4: Processing the spectra. (a) Normalized background signal caused by scattering by the ripples on the sapphire substrate. (b d) Scattering spectra from single nanodiamonds. The particles j (b), b (c) and i (d) are shown. The gray lines represent spectra obtained using an Ocean Optics USB4000 spectrometer, and the pink line shows a spectrum obtained using a Solar S100 spectrometer. Two-Lorentzian peak fits are indicated by black lines. The purple lines denote the individual peaks obtained by two-peak fitting. FIG. S5: Dependences of the resonance peak positions on the effective particle diameter with the points labelled according to the corresponding particles shown in Fig. S2. The dashed lines show linear fits to the results for sphere-like particles (f > 0.9, indicated by filled circles). the substrate, although their positions do not change significantly. The difference between the absolute values is explained by the higher directivity of the scattered radiation in the presence of the substrate. The model was additionally verified by comparison with the results obtained from Mie theory. For this purpose, the total scattering was analyzed. The result of the simulation with the substrate disabled is shown in Fig. S6(c) and indicated by the purple line. The same spectrum obtained analytically is shown in black. The insignificant differences may be caused by the different interpolation methods used for the dispersion data. The Purcell factor was calculated for a single sphere without the substrate. A dipole source oscillating for a short time was simulated, and the Fourier components of the radiated light at different wavelengths were calculated to obtain the result for the continuous dipole oscillation. The Purcell factor was calculated as the energy of the radiation emitted in the scheme with a particle normalized by the one emitted in bulk diamond. The method of calculating the Purcell enhancement was verified by applying it to a non-resonant particle. In this simulation, a dipole was located in the center of a 30-nm diamond sphere. The obtained Purcell factor of varies by less than 20% over the entire visible spectrum. This result was compared to the analytical prediction for a sphere in the Rayleigh limit F P = 1/n (3/(n 2 + 2)) 2 [3]. At a refractive index of n = 2.41, this expression gives F P = 0.061, which is in excellent agreement with the results of the simulation. VI. PURCELL ENHANCEMENT IN SPHEROIDAL PARTICLES In the main manuscript, the Purcell enhancement in a spherical diamond particle is analyzed. To clarify how anisotropy affects the Purcell factor, we have performed

5 5 FIG. S6: (a) FDTD model geometry. The yellow disk denotes the light collection region in the experiment. (b) FDTD calculated scattering spectra at the experimental collection angles with the substrate enabled (blue) and disabled (purple). The spectra are normalized by the maximum value with the substrate enabled. (c) FDTD calculated total scattering efficiency with the substrate enabled (blue) and disabled (purple) and analytical solution for a free standing sphere. The results are for a 320-nm sphere. additional calculations that are presented below. The calculations were carried out by the same method as described in the previous section with an exception that the particle had a spheroidal shape. Its semi-axes a and b are related as a 2 b = (160 nm) 3. In this case, the volume of the particle is fixed and is equal to the volume of the sphere analyzed in the main manuscript. An arbitrarily oriented dipole in a spherical particle can be considered as the superposition of radially and tangentially oriented dipoles. It means that the results shown in the main manuscript fully describe the case of an arbitrary dipole in a spherical nanodiamond. In the case of a spheroidal shape, a higher number of non-identical geometries are possible. Here we consider the five main cases shown in the insets of Fig. S7. For each of the geometries, spheroids with ratios a/b in the range from 0.5 to 2 are analyzed. For each of the ratios, 20 evenly spaced displacements of the dipole from the center are considered. For every wavelength we independently set the maximal value of the Purcell factor among the ones obtained for different displacements from the center as the maximized Purcell enhancement. The results shown in Fig. S7 demonstrate how the maximal Purcell enhancement depends on the shape of the particle and the wavelength corresponding to the dipole emission frequency. Varying the shape of the particle leads to the shift of the resonances; however, the values of the Purcell enhancement do not change dramatically that allows us to expect that the effect can be observed in realistic particles. [1] H. R. Phillip and E. A. Taft, Kramers-Kronig analysis of reflectance data for diamond, Phys. Rev., vol. 136, no. 5A, pp. A1445 A1448, [2] E. D. Palik, Handbook of optical constants of solids, Academic Press, [3] H. Chew, Radiation and lifetimes of atoms inside dielectric particles, Phys. Rev. A, vol. 38, no. 7, pp , 1988.

6 6 FIG. S7: Purcell effect in a free standing diamond spheroid. (a e) The Purcell enhancement factor maximized by the distance between the dipole and the particle center z as a function of the wavelength in vacuum and the shape factor a/b calculated for the five general geometries shown in the insets. The volume of the particle is fixed and is equal to the volume of the sphere analyzed in the main manuscript. (f,g) Dependence of the Purcell factor on the wavelength in vacuum and the distance z between the particle center and the dipole in the case of a spherical shape.