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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17697–17712
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Wavelength-dependent emission enhancement through the design of active plasmonic nanoantennas

Mélanie Ferrié, Nicola Pinna, Serge Ravaine, and Renaud A. L. Vallée  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17697-17712 (2011)
http://dx.doi.org/10.1364/OE.19.017697


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Abstract

Owing to the competition between the radiative and non-radiative decay channels occurring in plasmonic assemblies, we show here how to conceive a long pass emission filter and actually design it. We report the synthesis of gold@silica nanoparticles grafted with dye molecules. The control of the thickness of the silica shell allows us to tune the distance between the metal core and the dye molecules. Assemblies of small number (1 to 7) of these core-shell (CS) particles, considered as multimers, have also been produced for the first time. We show that the shaping of the emission spectra of the multimers is drastically enhanced by comparison with the corresponding monomers. We also show a strong enhancement of the decay rates at the LSP resonance, dominated by the non-radiative energy tranfer from the active medium to the metal. The decay rates decrease as the detuning between the long wavelength emission and the LSP resonance increases.

© 2011 OSA

1. Introduction

The interaction between light and metal nanoparticles (NPs) is dominated by localized surface plasmon (LSP) resonances, or charge-density oscillations on the closed surfaces of the particles. These LSP resonances cause confinement of the electromagnetic field near the surface and lead to strong extinction in the visible and near infrared, depending on the geometry, size, and shape of the NP [1

1. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

, 2

2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

]. The large local enhancements of the electromagnetic fields can be used to exalt the fluorescence emission [3

3. J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman scattering by molecules adsorbed on rough surfaces,” J. Chem. Phys. 73, 3023 (1980). [CrossRef]

6

6. F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7, 496–501 (2007). [CrossRef] [PubMed]

] or the photostability of dye molecules (atoms, molecules, quantum dots) close to the metal surface by shortening the excited-state lifetime [7

7. A. Parfenov, I. Gryczynski, J. Malicka, C. D. Geddes, and J. R. Lakowicz, “Enhanced fluorescence from fluorophores on fractal silver surfaces,” J. Phys. Chem. B 107, 8829–8833 (2003). [CrossRef] [PubMed]

9

9. J. Enderlein, “Theoretical study of single molecule fluorescence in a metallic nanocavity,” Appl. Phys. Lett. 80, 315–317 (2002). [CrossRef]

], possibly leading to new intense and stable light sources confined to the nanometer scale.

Understanding the interaction between light, NPs and dye molecules is a real challenge since at least three competing phenomena occur simultaneously. In the absence of metal NPs, the optical excitation is absorbed directly by the molecules. With a metal NP located in the vicinity of the molecules, the excitation beam can firstly be coupled into the tighly confined LSP mode, which then enhances the optical energy density near the molecule field and so the absorption rate. The same LSP mode (generally at slightly longer wavelength [10

10. M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Aria-Gonzales, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004). [CrossRef]

]) also enhances the energy-emission efficiency of the excited molecules and so the radiative emission rate through the Purcell [11

11. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37 (1946). [CrossRef]

] effect. Finally, an extra non-radiative decay channel is opened which allows the energy transfer from the molecule to the metal [12

12. R. Carminati, J.-J. Greffet, C. Henkel, and J. Vigoureux, “Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle,” Opt. Commun. 261, 368 (2006). [CrossRef]

]. While the first two effects combine to enhance the overall emission rate, the third quenches it. As a matter of fact, all three effects depend strongly and differently on the separation between the metal NP and the molecule [8

8. O. G. Tovmachenko, C. Graf, D. J. van den Heuvel, A. van Blaaderen, and H. C. Gerritsen, “Fluorescence enhancement by metal-core/silica-shell nanoparticles,” Adv. Mater. 18, 91–95 (2006). [CrossRef]

, 13

13. E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, “Fluorescence quenching of dye molecules near gold nanoparticles: radiative and nonradiative effects,” Phys. Rev. Lett. 89, 203002 (2002). [CrossRef] [PubMed]

19

19. G. Schneider, G. Decher, N. Nerambourg, R. Praho, M. H. V. Werts, and M. Blanchard-Desce, “Distance-dependent fluorescence quenching on gold nanoparticles ensheathed with layer-by-layer assembled polyelectrolytes,” Nano Lett. 6, 530–536 (2006). [CrossRef] [PubMed]

], as well as the detuning between the LSP resonance and the absorption and luminescence wavelengths of the molecule [6

6. F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7, 496–501 (2007). [CrossRef] [PubMed]

, 8

8. O. G. Tovmachenko, C. Graf, D. J. van den Heuvel, A. van Blaaderen, and H. C. Gerritsen, “Fluorescence enhancement by metal-core/silica-shell nanoparticles,” Adv. Mater. 18, 91–95 (2006). [CrossRef]

, 20

20. S. Kuehn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef]

23

23. Y. Chen, K. Munechika, and D. Ginger, “Dependence of fluorescence intensity on the spectral overlap between fluorophores and plasmon resonant single silver nanoparticles,” Nano Lett. 7, 690–696 (2007). [CrossRef] [PubMed]

], the shape of the NP, and the orientation of the molecules dipole moment [10

10. M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Aria-Gonzales, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004). [CrossRef]

,24

24. J. B. Khurgin, G. Sun, and R. A. Soref, “Electroluminescence efficiency enhancement using metal nanoparticles,” Appl. Phys. Lett. 93, 021120 (2008). [CrossRef]

27

27. G. Sun, J. B. Khurgin, and R. A. Soref, “Practical enhancement of photoluminescence by metal nanoparticles,” Appl. Phys. Lett. 94, 101103 (2009). [CrossRef]

]. In addition, the molecules eventually might interact between themselves if appropriately located and oriented [28

28. T. Förster, “Transfer mechanisms of electronic excitation,” Discuss. Faraday Soc. 27, 7–17 (1959).

], and a new mechanism for cooperative emission of light by an ensemble of N dipoles near a metal NP, dubbed as plasmonic Dicke effect, has been reported recently [29

29. V. N. Pustovit and T. V. Shahbazyan, “Cooperative emission of light by an ensemble of dipoles near a metal nanoparticle: the plasmonic Dicke effect,” Phys. Rev. Lett. 102, 077401 (2009). [CrossRef] [PubMed]

, 30

30. V. N. Pustovit and T. V. Shahbazyan, “Plasmon-mediated superradiance near metal nanostructures,” Phys. Rev. B 82, 075429 (2010). [CrossRef]

]. Finally, inside nanoparticle dimer resonators, strong enhancement of the fluorescence intensity and of the overall decay rates haven been reported [31

31. J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005). [CrossRef] [PubMed]

34

34. A. Bek, R. Jansen, M. Ringler, S. Mayilo, T. A. Klar, and J. Feldmann, “Fluorescence enhancement in hot spots of AFM-designed gold nanoparticle sandwiches,” Nano Lett. 8, 485–490 (2008). [CrossRef] [PubMed]

] as well as shaping of the fluorescence emission spectra due to the selective, resonant enhancement, of radiative transitions [35

35. M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. A. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent molecules with single plasmonic nanoresonators,” Phys. Rev. Lett. 100, 203002 (2008). [CrossRef] [PubMed]

].

In this paper, owing to the competition between the radiative and non-radiative parts of the overall relaxation process, we show how to and actually design a long pass emission filter. We designed several types of size controlled, spherical monomer and multimer nanoantennas. We show shaping of the emission spectra and modification of the radiative decay rates as a function of wavelength and spacing between the metal cores and the dye molecules. The decay rates are shown to decrease as the distance from the molecules to the NP increases and as the detuning between the long wavelength emission and the LSP resonance increases.

The experimental situations concern two types of nanostructures: passive and active ones. For the first series, the particles consist of a gold NP core of 60 nm diameter, with a silica shell thickness varying from 10 to 20 and 30nm, here after labeled as Core-Shell (CS) particles CS1, CS2 and CS3, respectively. The second series is built from the first one, by firstly grafting a rhodamine B derivative with ethoxy-silano group on the silica shell and then covering this layer by a second protective silica shell of 10 nm (see scheme in Fig. 1(j)). The NPs of the second series are called active since they comprise an active gain material (dye molecules). Depending on the NPs used from the first series, the samples of the second category are labeled as CS1+, CS2+ and CS3+, respectively. The good uniformity in shape and size of the CS+ particles can be observed in the TEM pictures shown in Figs. 1(a), 1(c) and 1(e). Finally, multimers were formed (mixtures of dimers, trimers, quadrimers, heptamers, ...) from both seriess CS and CS+ and are labeled as CS1M, CS2M, CS3M, CS1+M, CS2+M and CS3+M, respectively (TEM and AFM pictures for the last three species are displayed in Figs. 1(b), 1(d), 1(f) and 1(g)–1(i), respectively; see Materials for details). The various nanostructures are investigated on the ensemble level in ethanol solution in order to determine their UV-visible absorption spectra, fluorescence emission spectra and decay rates (see Methods for details).

Fig. 1 TEM pictures of the various CS+ (a,c,e) monomers and CS+M (b,d,f) multimers with shell thicknesses ranging from 10 (a,b) to 20 (c,d) and 30nm (e,f). AFM phase images of CS1 CS2+ CS3+ (g, h, i) multimers. Scale bar: 200 nm (both for TEM and AFM). (j) Schemes of the active monomer, dimer, trimer, quadrimer in line, tetramer and heptamer NPs.

2. Results and Discussion

We predicted the optical properties of various experimental situations owing to finite-difference time-domain (FDTD) simulations (see Methods for details). In all simulations, the polarization direction of the excitation has been chosen along the x axis, i.e. along the line joining the particles in the multimers in line (Fig. 1(j)). Figure 2(a) shows the simulated reflexion spectra of the monomers, trimers and heptamers corresponding to silica shells of 10 to 20 and 30 nm, respectively. Clearly, for each type of monomers and multimers, a shift of the LSP resonance to long wavelengths is observed as the shell thickness is increased. This effect is well-known for CS monomers and simply results from an increase of the local refractive index around the gold particles, since amorphous silica has a higher refractive index (n = 1.45) than that of the solvent (ethanol, n = 1.36) [36

36. J. Rodríguez-Fernández, I. Pastoriza-Santos, J. Pérez-Juste, F. J. García de Abajo, and L. M. Liz-Marzán, “The effect of silica coating on the optical response of sub-micrometer gold spheres,” J. Phys. Chem. C 111, 13361–13366 (2007). [CrossRef]

]. For shell ticknesses above the core radius, light scattering from the shell dominates and the shift of the LSP resonances saturates, since the metal cores are no longer sensitive to the solvent outside [36

36. J. Rodríguez-Fernández, I. Pastoriza-Santos, J. Pérez-Juste, F. J. García de Abajo, and L. M. Liz-Marzán, “The effect of silica coating on the optical response of sub-micrometer gold spheres,” J. Phys. Chem. C 111, 13361–13366 (2007). [CrossRef]

, 37

37. Y. Lu, Y. Yin, Z.-Y. Li, and Y. Xia, “Synthesis and self-assembly of Au@SiO2 core-shell colloids,” Nano Lett. 2, 785–788 (2002). [CrossRef]

]. A red-shift of the the LSP resonances is also observed as the number of coupled monomers in a multimer increases. This is nicely illustrated in Fig. 2(b) showing the dependance of the near field coupling between resonance modes of adjacent particles as a function of shell thickness: the LSP resonance strongly shifts to longer wavelengths when considering monomer, dimer, trimer, quadrimer as the distance between neighbouring cores is reduced from 30 to 10 nm. This effect is also noticeable for the tetramers and heptamers but to a lesser extent, due to the fact that, in the latter cases, the plasmonic dipole interactions can interfere constructively and destructively while, for multimers in line, only constructive interferences give rise to the enhanced near field coupling.

Fig. 2 (a) Simulated reflectivity spectra of monomers, trimers in line and heptamers with gold core diameter of 60 nm and silica shell thickness of 10, 20 and 30 nm, respectively. (b) LSP resonance as a function of the number of monomers coupled in a multimer for a silica shell thickness ranging from 10, 20 to 30 nm, respectively. Solid lines are linear fits of the LSP resonances as a function of the number of monomers coupled in a multimer. Non-radiative, radiative and total enhancement rates (c) as well as the apparent quantum yield (d) as a function of wavelength for dimers with a shell varying from 10 to 20 and 30 nm, respectively.

Fig. 3 (a) Absorption and emission spectra of RITC molecules, absorption spectra of CS monomers and CSM multimers in ethanol. (b) Absorption and emission spectra of RITC molecules, absorption spectra of CS+ and CS+M NPs in ethanol.

Figures 4(a)–4(c) exhibit the spectro-temporal intensity plots of RITC, CS3+ and CS3+M particles in ethanol. Projecting the intensity on the x axis provides us with the emission spectra, showing a shift of the maximum emission to longer wavelengths as the sample investigated switches from pure RITC (a) to CS3+ monomers (b) and CS3+M multimers (c). By projecting the intensity on the y axis, one alternatively obtains decay rates profiles with shortened decay times as the sample investigated switches from pure RITC to CS3+ and CS3+M samples (note that, on the graph (a), the y-axis extends over 20 ns while, on the graphs (b) and (c), it extends over 2 ns). Figure 5 further exemplifies these results for all samples investigated in this study. The emission spectra of RITC in ethanol and RITC grafted on 100 nm diameter silica beads in ethanol are almost indistinguishable and show an emission maximum at λ = 577nm, indicating that the energy levels of the RITC molecules are not affected by grafting and that there is no self-quenching by non-radiative energy transfer between molecules. A similar behaviour is expected for RITC molecules incorporated in the CS+ and CS+M NPs. The emission maximum is shifted to a longer wavelength λ = 586 nm and a broadening of the spectra is observed for RITC molecules in the active monomer CS+ NPs. Further red-shift of the emission maximum to λ = 594nm and broadening / complete reshaping to the long wavelength range of the spectra are observed for RITC molecules in the active multimer CS+M NPs. The reshaping of the emission spectra in the case of CS+M multimers is in complete agreement with the predictions made already at the level of the dimer (Fig. 2(d)).

Fig. 4 Time and spectrally resolved spontaneous emission intensities of RITC molecules (a), CS+3 (b) and CS+3M in ethanol (c).
Fig. 5 Emission spectra of RITC molecules, RITC molecules grafted to 100 nm diameter silica beads, CS+ active monomer and CS+M active multimer NPs in ethanol solutions.

To investigate further the emission properties as a function of wavelength, we built the decay profiles for all active samples by dividing the wavelength range in 10 regions of 8nm width and proceeded to fitting of these decay profiles. Figures 6(a)–6(c) show the 6 more intense decay profiles (at least 104 counts at maximum) for three different samples, namely RITC molecules, CS3+ and CS3+M NPs in ethanol. On the one side, the decay profiles of RITC in ethanol (a) show a clear single exponential decay profile with a decay rate independent of wavelength. According to the spectrum shown in Fig. 5, the absolute intensity increases from the region at 565 nm to the one at 580 nm, prior to decrease to the one at 604 nm. On the other side, the decay profiles of the CS3+ (b) and CS3+M (c) in solutions strongly deviates from a single exponential decay profile. In order to fit such decay profiles adequately, we used a stretched exponential function
I(t)=I0exp((t/τK)β),
(3)
i.e., introducing a stretching parameter 0 < β <= 1 in the logarithmic time [42

42. R. Zorn, “Logarithmic moments of relaxation time distributions,” J. Chem. Phys. 116, 3204–3209 (2002). [CrossRef]

], convoluted to the instrumental response function (IRF), instead of directly fitting with the convolution product of a linear superposition of simple exponential decays [42

42. R. Zorn, “Logarithmic moments of relaxation time distributions,” J. Chem. Phys. 116, 3204–3209 (2002). [CrossRef]

, 43

43. R. A. L. Vallée, K. Baert, B. Kolaric, M. Van der Auweraer, and K. Clays, “Nonexponential decay of spontaneous emission from an ensemble of molecules in photonic crystals,” Phys. Rev. B 76, 045113 (2007). [CrossRef]

] and the IRF. The decay time (mean relaxation time) is then obtained from the relation
τ=τKβΓ(1β),
(4)
where Γ is the gamma function.

Fig. 6 Decay profiles as a function of wavelength for RITC molecules (a), CS+3 monomers (b) and CS+3M multimers in ethanol (c). The solid lines are convoluted stretched exponentials fits with the instrumental response function of the setup of the various decay profiles.

For β = 1, the exponential decay 〈τ〉 = τK is recovered and the larger departure of β from 1, the more exponential relaxations are involved in the superposition. Figures 6(b) and 6(c) clearly reveal that the τK and β (degree of nonexponentiality) values are increasing as the wavelength is increased. To quantitatively trace these features, the τK, β and τ values are reported in Table 1 for the 18 curves fitted in Fig. 6.

Table 1. τK, β and τ Values as a Function of Wavelength and Sample (RITC, CS3+ and CS3+M) for the 18 Fits of the Experimental Data Curves shown in Fig. 6

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We reported in Fig. 7 the decay times 〈τ(λ)〉 as a function of wavelength for all samples CS+ and CS+M taken pair by pair. For comparison, the wavelength-independent fluorescent lifetime τ 0 = 3 ns of RITC molecules in ethanol is also shown. As such, the decay times of monomers and multimers in which the fluorescent molecules are separated from the core metal NPs by the same silica shell thickness show the same linear increase as a function of wavelength. The slope of this linear relationship is further enhanced as the spacer size increases, as further indicated in Table 2.

Fig. 7 Decay times as a function of silica shell thickness, 10 (a), 20 (b) and 30 nm (c) and as a function of the emission wavelength for the monomers CS+ and multimers CS+M. Also shown for comparison are the wavelength-independent decay times of pure RITC molecules in ethanol.The solid lines are linear fits of the decay times as a function of wavelength.

Table 2. Slopes of the Linear Relationships Fitting the Experimental Curves Shown in Fig. 7

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In terms of the decay rate enhancement defined as gt=τ0τ(λ), Fig. 8 equivalently shows the gt1λ proportionaly law. Remarquably, the decay rate enhancement reaches values up to 120 and 60 for spacings of 10 and 30nm between the RITC molecules and the gold NPs and go down to 40 and 20 as the detuning between the long wavelength emission and the LSP resonance increases.

Fig. 8 Decay rate enhancement gt (λ) as a function of silica shell thickness (10, 20 and 30nm) and as a function of the emission wavelength for the multimers CS+1M, CS+2M and CS+3M. The solid lines are fits gt(λ)1λ of the decay times as a function of wavelength.

3. Conclusion

In conclusion, we have synthesized several types of size controlled, spherical monomer and multimer plasmonic nanoantennas with well defined silica shell thicknesses used as spacers between the active dye molecules and the gold core. We show shaping of the absorbance and emission spectra and modification of the decay rates as a function of wavelength and spacing between the metal NPs and the dye molecules. The decay rate enhancement is shown to decrease as the distance from the molecules to the NP increases and as the detuning between the long wavelength emission and the LSP resonance increases. The experimental and simulated results are in agreement. The shaping of the emission spectra and the origin of the nonexponential decay profiles of the various samples are explained as a result of both imperfections in the morphology of the NPs in both monomer and multimer samples and near field couplings bewteen neighbouring particles in the case of multimer samples. The strong reshaping of the spectra in the latter case make these nanostructures good candidates for long pass emission filters.

4. Materials and Methods

60±5nm gold nanoparticles were synthesized through the reduction of hydrogen tetrachloroaurate (III) (HAuCl 4) in the presence of sodium citrate (Na 3 C 6 H 5 O 7.2H 2 O) and sodium borohydride (NaBH 4) according to the procedure published by Brown et al. [44

44. K. R. Brown, D. G. Walter, and M. J. Natan, “Seeding of colloidal Au nanoparticle solutions. 2. improved control of particle size and shape,” Chem. Mater. 12, 306–313 (2000). [CrossRef]

] The gold particles were coated with a silica shell (CS NPs) according to the procedure published by Graf et al. [45

45. C. Graf and A. van Blaaderen, “Metallodielectric colloidal core-shell particles for photonic applications,” Langmuir 18, 524–534 (2002). [CrossRef]

] The thickness of the shell was controlled by changing the amount of silica precursor (tetraethyl orthosilicate, TEOS). The active particles (CS+) were obtained from the CS ones by firstly grafting a rhodamine B derivative with ethoxy-silano group, which was previously prepared by reacting rhodamine B isothiocyanate (RITC) with aminopropyltriethoxysilane in absolute ethanol [46

46. X. Gao, J. He, L. Deng, and H. Cao, “Synthesis and characterization of functionalized rhodamine B-doped silica nanoparticles,” Opt. Mater. 31, 1715–1719 (2009). [CrossRef]

], on the silica shell. To do so, an amount corresponding to 15 RITC molecules / nm 2 of silica surface was added in an ammonia (6 % v/v) / ethanol suspension of CS particles. The reactive medium was heated at 800 C during 1h. The CS+ particles were collecvted by centrifugation and washed three times with absolute ethanol. A second protective silica shell of 10 nm diameter was then grown by dropwise addition of an ethanolic solution of TEOS [47

47. S. Kang, S. I. Hong, C. R. Choe, M. Park, S. Rim, and J. Kim, “Preparation and characterization of epoxy composites filled with functionalized nanosilica particles obtained via sol-gel process,” Polymer 42, 879–887 (2001). [CrossRef]

]. The increase of the concentration of the CS or CS+ particles during the addition of the TEOS solution lead to the formation of multimers (mixture of dimers, trimers, quadrimers, heptamers, ...). These mulitmers are formed as a result of collisions between CS or CS+ particles and are permanently fixed via the hydrolysis and condensation of TEOS molecules on their surface [48

48. M. Ibisate, Z. Zou, and Y. Xia, “Arresting, fixing, and separating dimers composed of uniform silica colloidal spheres,” Adv. Funct. Mater. 16, 1627–1632 (2006). [CrossRef]

].

Various experimental situations have been simulated by solving Maxwell equations using the three-dimensional finite-difference time-domain (FDTD method) [49

49. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House Inc., 2005).

], as implemented in the freely available MEEP software package [50

50. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010). [CrossRef]

]. The dielectric permittivity of gold was specified by using the Drude-Lorentz model with parameters determined by Vial et al. [51

51. A. Vial, A.-S. Grimault, D. Macas, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion : application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005). [CrossRef]

], based on the best fits, following a FDTD approach, to the relative permittivity of gold as tabulated by Johnson and Christy [52

52. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

]. By Fourier-transforming the response to a short, broadband, spatially extended gaussian pulse in the far field of the passive structures and normalizing with the response in vacuum for the same excitation conditions, a single simulation yielded the reflexion spectra over a wide spectrum of frequencies. Similarly, in order to compute the emission properties gr(λ), gnr(λ) and η(λ) for the active nanostructures, we performed Fourier-transforms of the response to a short, broadband, point dipole (electric current) gaussian pulse polarized along the axis joining the monomers in the dimer and located in the gap of the dimer. We then normalized this response with the one obtained in vacuum for the same excitation conditions.

Atomic Force Microscopy images were recorded by a commercial ICON AFM (from Brucker, Santa Barbara, CA) equipped with a 90μm scanner (EV-scanner). The samples were imaged using tapping-mode phase imaging and a standard silicon cantilever (50N/m, 300kHz) to provide topographic and corresponding phase images. The particles were cast on a glass substrate by leaving a drop of a dilute suspension evaporating. TEM observations were performed with a Hitachi H-600 microscope operating at 75 kV. The UV-visible spectra have been recorded with a UNICAM UV/Vis spectrometer (UV4). The spontaneous emission properties of RITC molecules and the various active samples CS+ and CS+M in ethanol solutions were recorded with a spectral- and time- resolved setup consisting of a streak camera (HAMA-MATSU Streak Scope C10627) pre-fitted with a spectrograph (Princeton Instruments) with a 100 gr/mm choice of the grating. The excitation light was the frequency doubled output of the λ = 1030 nm wavelength, 10 MHz repetition rate, 300 fs line width pulses delivered by a diode-pumped Ytterbium femtosecond oscillator from Amplitude systems (t-Pulse 200). The beam was collimated to a 3 mW, 5 mm diameter spot to excite the particles in a quartz cuvette prior to focus the 530 nm long-pass filtered emission intensity on the entrance slit of the spectrograph.

Acknowledgments

The authors acknowledge le Conseil Régional d’Aquitaine and the European Research Network FAME for the Ph.D scholarship of Mélanie Ferrié. Hassan Saadaoui is thanked for AFM measurements.

References and links

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2.

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7.

A. Parfenov, I. Gryczynski, J. Malicka, C. D. Geddes, and J. R. Lakowicz, “Enhanced fluorescence from fluorophores on fractal silver surfaces,” J. Phys. Chem. B 107, 8829–8833 (2003). [CrossRef] [PubMed]

8.

O. G. Tovmachenko, C. Graf, D. J. van den Heuvel, A. van Blaaderen, and H. C. Gerritsen, “Fluorescence enhancement by metal-core/silica-shell nanoparticles,” Adv. Mater. 18, 91–95 (2006). [CrossRef]

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J. Enderlein, “Theoretical study of single molecule fluorescence in a metallic nanocavity,” Appl. Phys. Lett. 80, 315–317 (2002). [CrossRef]

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M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Aria-Gonzales, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004). [CrossRef]

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R. Carminati, J.-J. Greffet, C. Henkel, and J. Vigoureux, “Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle,” Opt. Commun. 261, 368 (2006). [CrossRef]

13.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, “Fluorescence quenching of dye molecules near gold nanoparticles: radiative and nonradiative effects,” Phys. Rev. Lett. 89, 203002 (2002). [CrossRef] [PubMed]

14.

B. Dubertret, M. Calame, and A. J. Libchaber, “Single-mismatch detection using gold-quenched fluorescent oligonucleotides,” Nat. Biotechnol. 19, 365–370 (2001). [CrossRef] [PubMed]

15.

D. J. Maxwell, J. R. Taylor, and S. Nie, “Self-assembled nanoparticle probes for recognition and detection of biomolecules,” J. Am. Chem. Soc. 124, 9606–9612 (2002). [CrossRef] [PubMed]

16.

C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, and G. F. Strouse, “Nanometal surface energy transfer in optical rulers, breaking the FRET barrier,” J. Am. Chem. Soc. 127, 3115–3119 (2005). [CrossRef] [PubMed]

17.

E. Dulkeith, M. Ringler, T. A. Klar, J. Feldmann, A. M. Javier, and W. J. Parak, “Gold nanoparticles quench fluorescence by phase induced radiative rate suppression,” Nano Lett. 5, 585–589 (2005). [CrossRef] [PubMed]

18.

N. Liu, B. S. Prall, and V. I. Klimov, “Hybrid gold/silica/nanocrystal-quantum-dot superstructures: synthesis and analysis of semiconductor-metal interactions,” J. Am. Chem. Soc. 128, 15362 (2006). [CrossRef] [PubMed]

19.

G. Schneider, G. Decher, N. Nerambourg, R. Praho, M. H. V. Werts, and M. Blanchard-Desce, “Distance-dependent fluorescence quenching on gold nanoparticles ensheathed with layer-by-layer assembled polyelectrolytes,” Nano Lett. 6, 530–536 (2006). [CrossRef] [PubMed]

20.

S. Kuehn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef]

21.

O. Kulakovich, N. Strekal, A. Yaroshevich, S. Maskevich, S. Gaponenko, I. Nabiev, U. Woggon, and M. Artemyev, “Enhanced luminescence of CdSe quantum dots on gold colloids,” Nano Lett. 2, 1449–1452 (2002). [CrossRef]

22.

J. Song, T. Atay, S. Shi, H. Urabe, and A. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5, 1557–1561 (2005). [CrossRef] [PubMed]

23.

Y. Chen, K. Munechika, and D. Ginger, “Dependence of fluorescence intensity on the spectral overlap between fluorophores and plasmon resonant single silver nanoparticles,” Nano Lett. 7, 690–696 (2007). [CrossRef] [PubMed]

24.

J. B. Khurgin, G. Sun, and R. A. Soref, “Electroluminescence efficiency enhancement using metal nanoparticles,” Appl. Phys. Lett. 93, 021120 (2008). [CrossRef]

25.

G. Sun, J. B. Khurgin, and R. A. Soref, “Plasmonic light-emission enhancement with isolated metal nanoparticles and their coupled arrays,” J. Opt. Soc. Am. B 25, 1748–1755 (2008). [CrossRef]

26.

J.B. Khurgin, G. Sun, and R. A. Soref, “Practical limits of absorption enhancement near metal nanoparticles,” Appl. Phys. Lett. 94, 071103 (2009). [CrossRef]

27.

G. Sun, J. B. Khurgin, and R. A. Soref, “Practical enhancement of photoluminescence by metal nanoparticles,” Appl. Phys. Lett. 94, 101103 (2009). [CrossRef]

28.

T. Förster, “Transfer mechanisms of electronic excitation,” Discuss. Faraday Soc. 27, 7–17 (1959).

29.

V. N. Pustovit and T. V. Shahbazyan, “Cooperative emission of light by an ensemble of dipoles near a metal nanoparticle: the plasmonic Dicke effect,” Phys. Rev. Lett. 102, 077401 (2009). [CrossRef] [PubMed]

30.

V. N. Pustovit and T. V. Shahbazyan, “Plasmon-mediated superradiance near metal nanostructures,” Phys. Rev. B 82, 075429 (2010). [CrossRef]

31.

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005). [CrossRef] [PubMed]

32.

J. Zhang, Y. Fu, M. H. Chowdhury, and J. R. Lakowicz, “Metal-enhanced single-molecule fluorescence on silver particle monomer and dimer: coupling effect between metal particles,” Nano Lett. 7, 2101–2107 (2007). [CrossRef] [PubMed]

33.

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007). [CrossRef] [PubMed]

34.

A. Bek, R. Jansen, M. Ringler, S. Mayilo, T. A. Klar, and J. Feldmann, “Fluorescence enhancement in hot spots of AFM-designed gold nanoparticle sandwiches,” Nano Lett. 8, 485–490 (2008). [CrossRef] [PubMed]

35.

M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. A. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent molecules with single plasmonic nanoresonators,” Phys. Rev. Lett. 100, 203002 (2008). [CrossRef] [PubMed]

36.

J. Rodríguez-Fernández, I. Pastoriza-Santos, J. Pérez-Juste, F. J. García de Abajo, and L. M. Liz-Marzán, “The effect of silica coating on the optical response of sub-micrometer gold spheres,” J. Phys. Chem. C 111, 13361–13366 (2007). [CrossRef]

37.

Y. Lu, Y. Yin, Z.-Y. Li, and Y. Xia, “Synthesis and self-assembly of Au@SiO2 core-shell colloids,” Nano Lett. 2, 785–788 (2002). [CrossRef]

38.

L. Novotny and N. F. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011). [CrossRef]

39.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef] [PubMed]

40.

P. Viste, J. Plain, R. Jaffiol, A. Vial, P. M. Adam, and P. Royer, “Enhancement and quenching regimes in metal-semiconductor hybrid optical nanosources,” ACS Nano 4, 759–764 (2010). [CrossRef] [PubMed]

41.

Manuscript in preparation.

42.

R. Zorn, “Logarithmic moments of relaxation time distributions,” J. Chem. Phys. 116, 3204–3209 (2002). [CrossRef]

43.

R. A. L. Vallée, K. Baert, B. Kolaric, M. Van der Auweraer, and K. Clays, “Nonexponential decay of spontaneous emission from an ensemble of molecules in photonic crystals,” Phys. Rev. B 76, 045113 (2007). [CrossRef]

44.

K. R. Brown, D. G. Walter, and M. J. Natan, “Seeding of colloidal Au nanoparticle solutions. 2. improved control of particle size and shape,” Chem. Mater. 12, 306–313 (2000). [CrossRef]

45.

C. Graf and A. van Blaaderen, “Metallodielectric colloidal core-shell particles for photonic applications,” Langmuir 18, 524–534 (2002). [CrossRef]

46.

X. Gao, J. He, L. Deng, and H. Cao, “Synthesis and characterization of functionalized rhodamine B-doped silica nanoparticles,” Opt. Mater. 31, 1715–1719 (2009). [CrossRef]

47.

S. Kang, S. I. Hong, C. R. Choe, M. Park, S. Rim, and J. Kim, “Preparation and characterization of epoxy composites filled with functionalized nanosilica particles obtained via sol-gel process,” Polymer 42, 879–887 (2001). [CrossRef]

48.

M. Ibisate, Z. Zou, and Y. Xia, “Arresting, fixing, and separating dimers composed of uniform silica colloidal spheres,” Adv. Funct. Mater. 16, 1627–1632 (2006). [CrossRef]

49.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House Inc., 2005).

50.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010). [CrossRef]

51.

A. Vial, A.-S. Grimault, D. Macas, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion : application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005). [CrossRef]

52.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

OCIS Codes
(160.2540) Materials : Fluorescent and luminescent materials
(160.4236) Materials : Nanomaterials
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 27, 2011
Revised Manuscript: July 26, 2011
Manuscript Accepted: July 27, 2011
Published: August 24, 2011

Citation
Mélanie Ferrié, Nicola Pinna, Serge Ravaine, and Renaud A. L. Vallée, "Wavelength-dependent emission enhancement through the design of active plasmonic nanoantennas," Opt. Express 19, 17697-17712 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17697


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References

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  4. J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett.88, 131109 (2006). [CrossRef]
  5. T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “Lambda/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett.7, 28–33 (2007). [CrossRef] [PubMed]
  6. F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett.7, 496–501 (2007). [CrossRef] [PubMed]
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  9. J. Enderlein, “Theoretical study of single molecule fluorescence in a metallic nanocavity,” Appl. Phys. Lett.80, 315–317 (2002). [CrossRef]
  10. M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Aria-Gonzales, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett.85, 3863–3865 (2004). [CrossRef]
  11. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev.69, 37 (1946). [CrossRef]
  12. R. Carminati, J.-J. Greffet, C. Henkel, and J. Vigoureux, “Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle,” Opt. Commun.261, 368 (2006). [CrossRef]
  13. E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, “Fluorescence quenching of dye molecules near gold nanoparticles: radiative and nonradiative effects,” Phys. Rev. Lett.89, 203002 (2002). [CrossRef] [PubMed]
  14. B. Dubertret, M. Calame, and A. J. Libchaber, “Single-mismatch detection using gold-quenched fluorescent oligonucleotides,” Nat. Biotechnol.19, 365–370 (2001). [CrossRef] [PubMed]
  15. D. J. Maxwell, J. R. Taylor, and S. Nie, “Self-assembled nanoparticle probes for recognition and detection of biomolecules,” J. Am. Chem. Soc.124, 9606–9612 (2002). [CrossRef] [PubMed]
  16. C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, and G. F. Strouse, “Nanometal surface energy transfer in optical rulers, breaking the FRET barrier,” J. Am. Chem. Soc.127, 3115–3119 (2005). [CrossRef] [PubMed]
  17. E. Dulkeith, M. Ringler, T. A. Klar, J. Feldmann, A. M. Javier, and W. J. Parak, “Gold nanoparticles quench fluorescence by phase induced radiative rate suppression,” Nano Lett.5, 585–589 (2005). [CrossRef] [PubMed]
  18. N. Liu, B. S. Prall, and V. I. Klimov, “Hybrid gold/silica/nanocrystal-quantum-dot superstructures: synthesis and analysis of semiconductor-metal interactions,” J. Am. Chem. Soc.128, 15362 (2006). [CrossRef] [PubMed]
  19. G. Schneider, G. Decher, N. Nerambourg, R. Praho, M. H. V. Werts, and M. Blanchard-Desce, “Distance-dependent fluorescence quenching on gold nanoparticles ensheathed with layer-by-layer assembled polyelectrolytes,” Nano Lett.6, 530–536 (2006). [CrossRef] [PubMed]
  20. S. Kuehn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett.97, 017402 (2006). [CrossRef]
  21. O. Kulakovich, N. Strekal, A. Yaroshevich, S. Maskevich, S. Gaponenko, I. Nabiev, U. Woggon, and M. Artemyev, “Enhanced luminescence of CdSe quantum dots on gold colloids,” Nano Lett.2, 1449–1452 (2002). [CrossRef]
  22. J. Song, T. Atay, S. Shi, H. Urabe, and A. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett.5, 1557–1561 (2005). [CrossRef] [PubMed]
  23. Y. Chen, K. Munechika, and D. Ginger, “Dependence of fluorescence intensity on the spectral overlap between fluorophores and plasmon resonant single silver nanoparticles,” Nano Lett.7, 690–696 (2007). [CrossRef] [PubMed]
  24. J. B. Khurgin, G. Sun, and R. A. Soref, “Electroluminescence efficiency enhancement using metal nanoparticles,” Appl. Phys. Lett.93, 021120 (2008). [CrossRef]
  25. G. Sun, J. B. Khurgin, and R. A. Soref, “Plasmonic light-emission enhancement with isolated metal nanoparticles and their coupled arrays,” J. Opt. Soc. Am. B25, 1748–1755 (2008). [CrossRef]
  26. J.B. Khurgin, G. Sun, and R. A. Soref, “Practical limits of absorption enhancement near metal nanoparticles,” Appl. Phys. Lett.94, 071103 (2009). [CrossRef]
  27. G. Sun, J. B. Khurgin, and R. A. Soref, “Practical enhancement of photoluminescence by metal nanoparticles,” Appl. Phys. Lett.94, 101103 (2009). [CrossRef]
  28. T. Förster, “Transfer mechanisms of electronic excitation,” Discuss. Faraday Soc.27, 7–17 (1959).
  29. V. N. Pustovit and T. V. Shahbazyan, “Cooperative emission of light by an ensemble of dipoles near a metal nanoparticle: the plasmonic Dicke effect,” Phys. Rev. Lett.102, 077401 (2009). [CrossRef] [PubMed]
  30. V. N. Pustovit and T. V. Shahbazyan, “Plasmon-mediated superradiance near metal nanostructures,” Phys. Rev. B82, 075429 (2010). [CrossRef]
  31. J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett.95, 017402 (2005). [CrossRef] [PubMed]
  32. J. Zhang, Y. Fu, M. H. Chowdhury, and J. R. Lakowicz, “Metal-enhanced single-molecule fluorescence on silver particle monomer and dimer: coupling effect between metal particles,” Nano Lett.7, 2101–2107 (2007). [CrossRef] [PubMed]
  33. O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett.7, 2871–2875 (2007). [CrossRef] [PubMed]
  34. A. Bek, R. Jansen, M. Ringler, S. Mayilo, T. A. Klar, and J. Feldmann, “Fluorescence enhancement in hot spots of AFM-designed gold nanoparticle sandwiches,” Nano Lett.8, 485–490 (2008). [CrossRef] [PubMed]
  35. M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. A. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent molecules with single plasmonic nanoresonators,” Phys. Rev. Lett.100, 203002 (2008). [CrossRef] [PubMed]
  36. J. Rodríguez-Fernández, I. Pastoriza-Santos, J. Pérez-Juste, F. J. García de Abajo, and L. M. Liz-Marzán, “The effect of silica coating on the optical response of sub-micrometer gold spheres,” J. Phys. Chem. C111, 13361–13366 (2007). [CrossRef]
  37. Y. Lu, Y. Yin, Z.-Y. Li, and Y. Xia, “Synthesis and self-assembly of Au@SiO2 core-shell colloids,” Nano Lett.2, 785–788 (2002). [CrossRef]
  38. L. Novotny and N. F. van Hulst, “Antennas for light,” Nat. Photonics5, 83–90 (2011). [CrossRef]
  39. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett.96, 113002 (2006). [CrossRef] [PubMed]
  40. P. Viste, J. Plain, R. Jaffiol, A. Vial, P. M. Adam, and P. Royer, “Enhancement and quenching regimes in metal-semiconductor hybrid optical nanosources,” ACS Nano4, 759–764 (2010). [CrossRef] [PubMed]
  41. Manuscript in preparation.
  42. R. Zorn, “Logarithmic moments of relaxation time distributions,” J. Chem. Phys.116, 3204–3209 (2002). [CrossRef]
  43. R. A. L. Vallée, K. Baert, B. Kolaric, M. Van der Auweraer, and K. Clays, “Nonexponential decay of spontaneous emission from an ensemble of molecules in photonic crystals,” Phys. Rev. B76, 045113 (2007). [CrossRef]
  44. K. R. Brown, D. G. Walter, and M. J. Natan, “Seeding of colloidal Au nanoparticle solutions. 2. improved control of particle size and shape,” Chem. Mater.12, 306–313 (2000). [CrossRef]
  45. C. Graf and A. van Blaaderen, “Metallodielectric colloidal core-shell particles for photonic applications,” Langmuir18, 524–534 (2002). [CrossRef]
  46. X. Gao, J. He, L. Deng, and H. Cao, “Synthesis and characterization of functionalized rhodamine B-doped silica nanoparticles,” Opt. Mater.31, 1715–1719 (2009). [CrossRef]
  47. S. Kang, S. I. Hong, C. R. Choe, M. Park, S. Rim, and J. Kim, “Preparation and characterization of epoxy composites filled with functionalized nanosilica particles obtained via sol-gel process,” Polymer42, 879–887 (2001). [CrossRef]
  48. M. Ibisate, Z. Zou, and Y. Xia, “Arresting, fixing, and separating dimers composed of uniform silica colloidal spheres,” Adv. Funct. Mater.16, 1627–1632 (2006). [CrossRef]
  49. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House Inc., 2005).
  50. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181, 687–702 (2010). [CrossRef]
  51. A. Vial, A.-S. Grimault, D. Macas, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion : application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B71, 085416 (2005). [CrossRef]
  52. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972). [CrossRef]

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