Non-blinking quantum dot with a plasmonic nanoshell resonator

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1 SUPPLEMENTARY INFORMATION DOI: /NNANO Non-blinking quantum dot with a plasmonic nanoshell resonator Botao Ji, Emerson Giovanelli, Benjamin Habert, Piernicola Spinicelli, Michel Nasilowski, Xiangzhen Xu, Nicolas Lequeux, Jean-Paul Hugonin, Francois Marquier, Jean-Jacques Greffet, Benoit Dubertret Detailed protocol for QD/SiO 2 /Au hybrid synthesis The synthesis of QD/SiO 2 /Au hybrids (golden QDs) is a three-step process which consists in the synthesis of CdSe/CdS core/shell quantum dots (QDs), the encapsulation of these QDs in a silica shell, and the formation of a gold nanoshell. 1. Synthesis of CdSe/CdS core/shell quantum dots 1.1. Precursors preparation S-ODE: Sulfur stock solution in ODE (S-ODE 0.1 M) was prepared by heating 320 mg of sulfur in 100 ml of degassed ODE at 120 C until complete dissolution. Cadmium oleate: 0.5 M Cd(oleate) 2 in oleic acid was synthesized by heating 3.2 g of CdO in 50 ml of oleic acid at 160 C under Ar for 1 h until all the CdO was dissolved. Then this solution was degassed under vacuum at 70 C for 30 min. Cadmium myristate was prepared by a procedure published previously 1. Se-ODE: Selenium stock solution in ODE (Se-ODE 0.1 M) was prepared by first suspending 790 mg of selenium in 10 ml of ODE. This mixture was injected by small portions in 90 ml of degassed ODE at 170 C, so that it becomes limpid again after each injection, while the temperature was raised progressively to 205 C. The solution was then kept at 205 C for 30 min. NATURE NANOTECHNOLOGY 1

2 1.2. Synthesis of CdSe cores CdSe cores were synthesized using a protocol adapted by Mahler 2 from Yang et al. 1 with slight modifications. A dispersion of selenium powder (12 mg) in ODE (8 ml) was added in a three-neck flask to cadmium myristate (174 mg), and additional ODE (8 ml) was introduced. The mixture was degassed for 30 min under vaccum, and then the flask was filled with argon and heated up to 240 C. After 25 min, 570-nm-emitting cores were obtained. Oleic acid (200 µl) was injected at this temperature and the solution was heated up to 260 C. At this temperature, oleylamine (2 ml) was injected and the reaction was further stirred for 20 min. The temperature was raised to 280 C, and 4 ml of a mixture of Se-ODE (0.1 M, 5 ml) and cadmium oleate (0.5 M, 1 ml) were injected dropwise (36 ml/h), while the temperature was raised progressively to 305 C. Once the addition of the precursors has been completed, the solution was rapidly cooled down to room temperature. The 630-nm-emitting QDs (6 nm in diameter) were washed with ethanol, and then taken up in hexane (10 ml) Formation of a CdS shell on CdSe cores In a three-neck flask, a mixture of freshly-made CdSe cores (40 nmol) 3,4, ODE (5 ml) and cadmium myristate (10 mg) was degassed for 30 min at 70 C under vaccum. The flask was then filled with argon and heated up to 260 C. At this temperature, oleylamine (2 ml) was injected and the reaction was further stirred for 20 min. 4.5 ml of a mixture of S-ODE (0.1 M, 16.5 ml) and cadmium oleate (0.5 M, 3.5 ml) were added dropwise (2.25 ml/h). After injection, the temperature was raised to 310 C. Then, the remaining 15.5 ml of the precursors mixture were added dropwise (7 ml/h). After injection, 22 ml of the reaction medium were withdrawn, and another 20 ml of a mixture of S-ODE (0.1 M, 16.5 ml) and cadmium oleate (0.5 M, 3.5 ml) were added dropwise (7 ml/h) to the QDs remaining in the flask. The solution was then cooled down to room temperature. The core/shell CdSe/CdS QDs were finally washed with ethanol and redispersed in hexane (C = 1.42 µm) 3,4. The CdSe/CdS QDs were characterized optically and by electronic microscopy (Figure 1a in main text). Their final diameter was 30 nm, corresponding to a CdS shell thickness of 12 nm. 6 nm 12 nm Absorption and photoluminescence spectra of 15-nm-in-radius CdSe/CdS core/shell QDs. 2

3 2. Encapsulation of CdSe/CdS core/shell QDs in a silica shell Previously synthesized CdSe/CdS core/shell QDs were encapsulated in silica using a reverseemulsion method µl (0.08 nmol) 3,4 of a CdSe/CdS solution were added to a solution of g of Triton X-100 (poly(ethylene glycol) p-(1,1,3,3-tetramethylbutyl)-phenyl ether, C 14 H 22 O(C 2 H 4 O) n (n = 9-10)) and g of hexanol in 5 ml cyclohexane. After 15 min, 0.19 ml of water and 30 µl of NH 4 OH (29 wt.% NH 3 in water) were added successively, then 30 µl of tetraethoxysilane (TEOS) were added to start the encapsulation. The mixture was stirred for 12 h at room temperature. Another 170 µl of TEOS were added and the solution was further stirred for 24 h to achieve the encapsulation process. 7.5 ml of acetone were added to break the emulsion. The suspension was centrifuged (4,000 g, 10 min) to separate the nanoparticles (NPs), which were washed successively with 20 ml of a butanol/hexane mixture (1/1 v/v), 20 ml of an isopropanol/hexane mixture (1/1 v/v), 20 ml of an ethanol/hexane mixture (1/1 v/v), and 20 ml of ethanol. CdSe/CdS/SiO 2 NPs were dispersed in 10 ml of water, further washed 3 times with water and finally redispersed in 10 ml of methanol. From the TEM images (Figure 1b in main text), the size of CdSe/CdS/SiO 2 NPs was evaluated at 99 nm, corresponding to a silica shell thickness of 35 nm. Below, we will take these QD/SiO 2 NPs as an example for the deposition of the gold shell; but the silica shell thickness could be tuned between 5 and 55 nm by varying the amount of TEOS with respect to the quantity of QDs. 3. Formation of a gold nanoshell on QD/SiO 2 NPs The growth of a gold nanoshell was performed using a protocol derived from the method invented by Halas and coll. 6, with slight modifications. First, QD/SiO 2 NPs were functionalized with a polymer, the poly(1-vinylimidazole-co-vinyltrimethoxysilane) (PVIS); then small gold seeds (~ 2 nm in diameter) were adsorbed onto the surface of SiO 2 at a high density thanks to PVIS; and finally, gold(iii) ions were added to the NPs and reduced to gold(0) on adsorbed gold seeds, so that the seeds grow and merge to form a continuous gold nanoshell around QD/SiO 2 NPs. 3

4 3.1. Functionalization of QD/SiO 2 NPs with PVIS Synthesis of PVIS 1-vinylimidazole (4.38 g, 46.5 mmol) and vinyltrimethoxysilane (0.519 g, 3.5 mmol) in 10 ml of ethanol were degassed under argon for 30 min and then heated at 75 C. A solution of recrystallized AIBN (25 mg, 0.15 mmol) in 5 ml of ethanol was injected into the reaction medium. After 24 h, the polymer was precipitated into diethyl ether (500 ml), washed with diethyl ether and finally dried under vacuum. Thermogravimetric analysis confirmed the silane incorporation into the polymer was in agreement with the starting ratio in monomers (93/7) Functionalization of QD/SiO 2 NPs with PVIS 2 ml from the previous 10-mL methanol dispersion of QD/SiO 2 NPs were washed 4 times with methanol to remove all of the water, and redispersed in 4 ml of methanol. A solution of 1.5 mg of PVIS in 2 ml EtOH was added and the mixture was heated up to 65 C for 1.5 h. The solution was cooled down to room temperature, the QD/SiO 2 /PVIS NPs were washed 4 times with methanol, to get rid of all unreacted PVIS, and redispersed in 2 ml of methanol Adsorption of gold seeds onto the surface of QD/SiO 2 /PVIS NPs Synthesis of gold seeds 0.45 ml of a 0.2 M aqueous NaOH solution and 0.3 ml of an aqueous THPC solution (tetrakis(hydroxymethyl)phosphonium chloride, (HOCH 2 ) 4 PCl; prepared by diluting 1.2 ml of 80 wt.% THPC aqueous solution into 100 ml with water) were successively added to ml of water, and the mixture was stirred for 5 min. 0.6 ml of a solution of HAuCl 4 (1 wt.% in water) was added dropwise and the solution was stirred for 15 min. This gold seeds solution was aged at 4 o C for at least 2 weeks before use Adsorption of the gold seeds on functionalized NPs 100 µl from the preceding 2-mL methanol dispersion of QD/SiO 2 /PVIS NPs were dispersed in 3 ml of the THPC-coated gold seeds solution under sonication and the mixture was stirred for 1 h at room temperature. QD/SiO 2 /PVIS/Au seeds NPs were separated by centrifugation (9,000 g, 3 min) and redispersed in 1 ml of pure water. This washing procedure was repeated twice to make sure that all free (unadsorbed) gold seeds were removed. All of the QD/SiO 2 /Au seeds NPs were finally redispersed in 1 ml of water. The corresponding TEM image (Figure 1c in main text) show that the silica surface is densely covered by the Au seeds. These freshly-made QD/SiO 2 /PVIS/Au seeds NPs were then used readily to grow the gold nanoshell. 4

5 3.3. Formation of a continuous gold nanoshell around QD/SiO 2 /PVIS/Au seeds NPs Preparation of a gold plating solution A gold plating solution was prepared by addition of 0.75 ml of a 1 wt.% aqueous solution of HAuCl 4 to 50 ml of a 1.8 mm aqueous solution of K 2 CO 3, and stirring for 30 min, during which the solution turned from light yellow to colorless. The plating solution was stored at room temperature for a minimum of 24 h, and used between 24 h and 72 h after the preparation Growth of a continuous gold nanoshell 100 µl from the 1-mL aqueous dispersion of QD/SiO 2 /PVIS/Au seeds NPs were dispersed in 3 ml of the previously made gold plating solution, followed by the addition of 120 µl of a 0.35 wt.% PVP (K12, MW: 3,500 g/mol) aqueous solution, and the mixture was stirred for 2 min. 15 µl of a formaldehyde solution (37 wt.% CH 2 O in water) were added to grow adsorbed gold seeds by reduction of the gold(iii) ions of the plating solution, and the mixture was stirred for 40 min. The NPs were separated by centrifugation (450 g, 3 min), washed with 2 ml of water and finally redispersed in 2 ml of water. Golden QDs were stored at 4 C. In this case, the thickness of the gold nanoshell was 20 nm (see Figure 1d in main text and the SEM image below); but it could be tuned easily by adjusting the molar ratio between the QD/SiO 2 /PVIS/Au seeds NPs and the gold plating solution. SEM image (for a gold thickness of 20 nm, left) and photoluminescence spectrum (right) of the golden QDs. 5

6 4. Optical characterization 4.1. Intensity decays We report the evolution of the ensemble fluorescence lifetime acquired for each important step of the golden QDs synthesis (see Table 1a in main text). Figure S1 Evolution of the fluorescence lifetime of an ensemble of nanoparticles during golden QDs synthesis Photostability of QD/SiO 2 and QD/SiO 2 /Au seeds hybrids vs the gold plating solution Figure S2 Photoluminescence evolution over time of QD/SiO 2 (black squares) and QD/SiO 2 /Au seeds hybrids (red circles) incubated with the gold(iii) salt solution in the conditions used for the synthesis (PL normalized at t = 0). 6

7 4.3. Additional time traces of CdSe/CdS and golden QDs with anti-bunching and intensity distribution Figure S3 Additional time traces of 5 single QDs chosen arbitrarily. The traces also show anti-bunching and the distribution of the occurences. Top: CdSe/CdS QDs; bottom: golden QDs. In the case of golden QDs, the distributions of the intensities are fit with a Poisson distribution (black curve). 7

8 4.4. SEM/fluorescence co-localization In order to ensure the optical study at single molecule level, all the studied golden QDs solutions have been dispersed over home-made gridded glass coverslips. Hybrid nanocrystals are first observed on a confocal microscope (raster scan in Figure S4a) and analyzed individually. Afterwards, a study on a scanning electron microscope (SEM) allows us to clearly distinguish individual nanoparticles from aggregates (Figure S4b). The sample is finally analyzed again on the confocal microscope. Figure S4c shows that almost all of the nanoparticles withstanded the electron beam excitation. A deeper study on single nanocrystals demonstrates that their optical properties (both average intensity and lifetime) have been perfectly preserved after the SEM study. Figure S4 SEM/fluorescence correlation image for a typical sample of golden QDs. a. Fluorescence image of a square containing golden QDs spread on a TEM grid. b. SEM of the same region. c. Same as a. after SEM imaging. 8

9 4.5. Photostability of golden QDs over time Golden QDs show an extremely good resistance to photobleaching. In Figure S5 we report the fluorescence time trace of an individual golden QD subjected to CW ultraviolet light (~1 mw) before and after 24 h of continuous excitation. On an ensemble of nanoparticles, we observe an average loss of intensity limited to 20% of the initial signal. Figure S5 Fluorescence intensity of a typical single golden QD as a function of time under continuous UV excitation Comparison of the anti-bunching properties of CdSe/CdS and golden QDs Figure S6 Histograms of coincidence counts of a typical golden QD (top) and of a typical CdSe/CdS QD (bottom). 9

10 The histograms of the coincidence counts can be extracted from the respective time traces of CdSe/CdS and golden QDs. They are reported on Figure S6. A strong anti-bunching is clearly visible for the CdSe/CdS QDs, while for the golden QDs, single photon emission is not observed. In addition, the difference in the lifetime emission between golden QDs and CdSe/CdS QDs appears clearly in the histograms: the peaks are much sharper for golden QDs than for CdSe/CdS QDs. 5. Numerical model 5.1. Calculation of the extinction spectrum We use a multilayer spherical system to describe numerically the QD/SiO 2 /Au NP (golden QD) nanostructure. The respective diameters of the QD and the silica bead, as well as the total thickness of the gold shell (H shell = 18 nm), were measured on TEM images. Using these experimental parameters and a bulk dielectric function for the gold shell, we observed a mismatch between the experimental and theoretical resonance of the structure (model 1 in Figure S7, dashed blue line). We consequently implemented a more accurate numerical model (model 2 in Figure S7, solid black line) to account for two effects: i) losses are increased for gold in very thin and polycrystalline layers 7, ii) the gold layer has a significant roughness. Following a standard procedure used in ellipsometry 8, we model the roughness layer by a homogeneous porous layer with a mean dielectric constant 1 2 (ε Au(ω, C Γ ) + ε ext ) and a thickness (1 r) H shell. The successive layers of this model are: the QD (refractive index n = 2.8, diameter D QD = 30 nm), the silica core (refractive index n = , diameter D core = 99 nm), the continuous gold layer (ε Au (ω, C Γ ), thickness = r H shell ), and the porous gold layer ( 1 2 (ε Au(ω, C Γ ) + ε ext ), thickness = (1 r) H shell ). The model has two free parameters: C Γ and r. C Γ takes into account the surface scattering of electrons in the gold shell 10,11 and introduces homogeneous broadening of the plasmonic resonance. Using this parameter, the dielectric function for gold is the sum of an interband contribution and a modified Drude model dielectric function: ε u(ω, C Γ ) ε inter (ω) + (1 ω p 2 ω 2 + iγ ul C Γ ), where ε inter (ω) and the Drude model parameters (ω p, Γ bulk ) are extracted from experimental data

11 Figure S7 Measured (yellow disks) and calculated extinction spectra for the golden QD structure. For model 1 (dashed blue line), we used the bulk dielectric function of gold and obtained a mismatch for the position and width of the resonance. Model 2 (black line) is the two-parameter model used in the article, where surface scattering of electrons and shell roughness are taken into account. The calculated extinction spectrum for a dimer (magenta) shows a second resonance around 1200 nm. Mie theory calculations were used to compute the extinction spectrum of the multilayer system. A fit against an experimental extinction spectrum allowed us to extract the value of the two parameters: C Γ = 5.4 and r = 0.65 (see Figure S7). We used these adjusted parameters in the calculation of the Purcell factor. The experimental extinction spectrum shows a second resonance around λ 1200 nm that we attri ute to the presence of dimers in the solution. This model was applied to several hybrid core/shell systems with D core ranging from 86 nm to 125 nm, and H shell from 13 nm to 30 nm, and was found to reproduce accurately the extinction spectra measured experimentally (see Figure S8). It is important to note that the absorption peak is not a Lorentzian and presents a second resonance peak at 600 nm that is well reproduced by the model. Additionally, the width of the plasmonic resonance could not be attributed to inhomogeneous broadening caused by size polydispersity. 11

12 Figure S8 Results of our 2-parameter model fit against experimental extinction spectra. The model accurately reproduces the position and width of dipolar (λ = 800 nm) and quadrupolar (λ = 600 nm) resonances as well as the interband contribution of gold around 400 nm. a. Silica core diameter: 99 nm; b. Silica core diameter: 124 nm Purcell factor for a golden QD on a glass slide We use a classical electromagnetic simulation to compute how the multilayer spherical structure can modify the lifetime η of the QD. In such a simulation, the two-level system is represented by a point dipole placed at the center of the multilayered spherical system and the power P emitted by this dipole is calculated (including losses in the metal). We use the equivalence F Purcell = η 0 /η = P/P 0 to deduce the modification of lifetime from the calculation. In the previous equation, the subscript 0 corresponds to the reference: a QD without the gold shell. Using Mie theory, it is straightforward to compute the power emitted by the dipole in the multilayer spherical system in a homogeneous environment. However, the lifetime measurements were performed in a fluorescence microscopy setup: the emitter is deposited on a glass slide. Accounting for the interface is important as it modifies significantly the local density of states. We used the method described in previous works 13,14 to account for the interface. The basic idea of the method is to replace the nanoshell by an ensemble of effective dipolar scatterers located on a sphere of 3 nm in radius. The polarizability of these dipoles is adjusted in order to reproduce the field scattered by the nanoshell in a homogeneous environment. The advantage of the technique is that the influence of the interface on dipoles can then be included easily. In our case, we found that 20 dipolar scatterers were enough to compute accurately the emitted power. 12

13 5.3. Influence of gold seeds on QD lifetime The decay rate of the QD/SiO 2 system in water is Γ 0 = 1/123 ns 1. When gold seeds are deposited on the silica surface, the decay rates increases to Γ* 1/84 ns 1. This can be interpreted by the presence of a non-radiative decay channel characterized y the rate Γ NR Γ* Γ 0 = 1/265 ns 1. We show here that this additional decay rate can be attributed to the light absorption by the seeds, thus proving that the QD is not chemically altered during this step. Let us consider a dipole emitter (λ 670 nm) at the center of the QD/SiO 2 structure. We first compute the power radiated by this dipole P rad. We now consider a gold nanoparticle (radius r seed = 1.5 nm) deposited on the silica bead and we compute the electric field E 0 at its position. The power absorbed by this nanoparticle is given by: a s 1 2 ω e{. }, where the dipole moment induced in the nanoparticle is given y its polarisa ility α: α ε 0 ε ext α 3 ε u ε ext 4 r seed, ε u + 2ε ext where ε ext = 1.77 and ε Au = i are the dielectric functions of the surrounding medium (water) and the gold nanoparticle (we use the same dielectric functions as in section 5.1.). The power scattered by this small nanoparticle is negligible 15 : ζ scatt ζ a s 4 6 r seed r seed We can now compare the power absorbed by the gold nanoparticle to the total power radiated by the source dipole: a s rad We estimate the amount N of gold nanoparticles required to explain the experimental modification of the decay rate: This yields. a s rad Γ Γ nanoparticles, which would cover 62% of the silica surface and represent a volume of μm 3 of gold. This is consistent with what is observed on TEM images of the QD/SiO 2 /Au seeds structures. The shortening of fluorescence lifetime from 123 ns to 84 ns can consequently be attributed to the absorption of light by the gold nanoparticles. 13

14 5.4. Fluorescence signal in a pulsed excitation regime We derive in this section a model for the fluorescence signal under a pulsed excitation. This will be applied to the low-excitation regime used in the article (Figure 2 of the main text). Considering an ensemble of N tot emitters, we first derive the number of emitters in the excited state as a function of time N e (t). We consider periodic pulses with a repetition rate R of small duration δt that excite the emitters in the ground state with a pro a ility. Let N e (0 ) be the number of excited emitters before the pulse; the number of excited emitters after the pulse is thus N e (0 + ) = N e (0 ) + (N tot N e (0 )). This populations decay with a rate Γ and the num er of excited emitters at the end of a cycle is N e (t = 1/R) = N e (0 + ) e Γ. Because the excitation is periodic, we have N e (t = 1/R) = N e (0 ). We consequently derive the number of excited emitters as a function of time: e(t) e(0 + )e Γt, e(0 + ) tot 1 (1 )e Γ We can now use the population to derive the emitted intensity. The radiative decay rate of the emitter is Γ r and the collection efficiency of the system is f coll. During an excitation cycle, the mean intensity collected (in photons.s 1 ) is: which yields: 1 0+ Γ r f coll e (t) dt, Γ r Γ f Γ coll tot Γ (1 e ) (1) 1 (1 )e Possible saturation effects are included in the dependence of the excitation probability on the pump irradiance. We introduce this effect using rate equations for populations of an ensemble of QDs. The excitation is assumed to be proportional to the product of the absorption cross-section ζ abs, the pump irradiance and the population of QDs in the ground state. In this simple model, we have assumed that internal relaxation processes after excitation are faster than the electron-hole recombination rate. During the excitation (duration δt), the population equation is: d e dt ζ a s inc ω inc ( tot e(t)) Γ tot e (t) 14

15 We solve this equation for N e (0) = 0. The transition probability ground state can then be cast in the form: for an emitter initially in its ( inc ) e(δt) tot 1 δt ζ a s 1+ Γ ω ω (1 e inc inc e Γδt ) inc ζ a s inc This expression can be simplified when the duration of the pulse is short compared to the lifetime of the emitter (Γδt << 1), which is often verified during measurements. The probability becomes: ( inc ) (1 e inc ω inc 0), with (2) 0 δt ζ a s Equations (1) and (2) give us a model for the fluorescence collected in a pulsed excitation regime, regardless of the relative magnitude of the repetition rate R and decay rate Γ. In the case of a low-excitation regime ( inc 0 1, and consequently 1), we get: Γ r Γ f coll tot, which corresponds to the formula used in the article for a single emitter (note that we obtain the same expression in the case of a small repetition rate ( Γ 1), regardless of the pump irradiance). As explained in the article, we can take into account the presence of the gold shell by modifying the values of Γ and Γ r. The gold shell also changes the excitation pro a ility ; in the low-excitation regime, the probability is simply multiplied by a constant shell ζ a s QD ζ a s as is proportional to the absorption cross-section of the emitter. Although it is not the case for this structure, an antenna can also modify the emission pattern and thus increase the collection rate f coll. References 1. Yang, Y. A.; Wu, H. M.; Williams, K. R.; Cao, Y. C. Angew. Chem. Int. Ed. 44, 6712 (2005). 2. Mahler, B.; Lequeux, N.; Dubertret, B. J. Am. Chem. Soc. 132, 953 (2010). 3. Leatherdale, C. A.; Woo, W.-K.; Mikulec, F. V.; Bawendi, M. G. J. Phys. Chem. B 106, 7619 (2002). 4. Yu, W. W.; Qu, L. H.; Guo, W. Z.; Peng, X. G. Chem. Mater. 15, 2854 (2003). 5. Yang, Y. H.; Jing, L. H.; Yu, X. L.; Yan D. D.; Gao, M. Y. Chem. Mater. 19, 4123 (2007). 15

16 6. Oldenburg, S. J.; Averitt, R. D.; Westcott, S. L.; Halas, N. J. Chem. Phys. Lett. 288, 243 (1998). 7. Thèye, M.-L. Phys. Rev. B 2, 3060 (1970). 8. Fujiwara, H. Spectroscopic Ellipsometry, John Wiley & Sons (2007). 9. Khlebtsov, B. N.; Khanadeev, V. A.; Khlebtsov, N. G. Langmuir 24, 8964 (2008). 10. Averitt, R. D.; Westcott, S. L.; Halas, N. J. J. Opt. Soc. Am. B 16,1824 (1999). 11. Westcott, S. L.; Jackson, J. B.; Radloff, C.; Halas, N. J. Phys. Rev. B 66, (2002). 12. Johnson, P. B.; Christy, R. W. Phys. Rev. B 6, 4370 (1972). 13. Stout, B.; Auger, J. C.; Devilez, A. J. Opt. Soc. Am. A 25, 2549 (2008). 14. Castanié, E.;Vincent, R.;Pierrat, R.; Carminati, R. AIP Conf. Proc. 1475, 116 (2012). 15. Bohren, C. F.; Huffman, D. R. Absorption and scattering of light by small particles, John Wiley & Sons (2008). 16

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