Effect of the Dielectric Core and Embedding Medium on the Second

Article pubs.acs.org/JPCC

Effect of the Dielectric Core and Embedding Medium on the Second Harmonic Generation from Plasmonic Nanoshells: Tunability and Sensing Jérémy Butet, Isabelle Russier-Antoine, Christian Jonin, Noel̈ le Lascoux, Emmanuel Benichou, and Pierre-François Brevet* Laboratoire de Spectrométrie Ionique et Moléculaire, UMR CNRS 5579, Université Claude Bernard Lyon 1, 43 Boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France ABSTRACT: Using Mie theory extended to the second harmonic generation from gold nanoshells, we have investigated the effect of the dielectric constant of the dielectric core and embedding medium. As the linear extinction, the SHG cross section is found to be tunable through a change of the core dielectric constant. The impact of the dielectric constant of the embedding medium is also addressed, and practical applications like sensing are discussed. Finally, we show that sensing properties can be optimized by modifying the core dielectric constant.

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INTRODUCTION Metallic nanoparticles support surface plasmon resonances (SPR), i.e., the collective excitation of the conduction electrons, leading to unique optical properties.1 These resonances lead to strong electric field enhancements close to metallic nanostructures and nonlinear optical processes therefore can be easily observed. As an example, one can consider second harmonic generation (SHG), the nonlinear optical process whereby two photons at the fundamental frequency are converted into one at the second harmonic (SH) frequency. SHG from metallic nanoparticles or metamaterials has been reported in several works.2−14 For instance, SHG from homogeneous metallic spheres,3 hollow gold spheres,4 nanocups,5 nanotriangles,6 Lshaped and G-shaped lithographed nanoparticles,7−9 nanotips,10 dimers and nanoantennae,11−13 and curved gold nanowires14 has been observed. Recently, it has been shown that SHG can be more sensitive to defects in metallic nanostructures than linear optics,15 and the efficiency of plasmonic sensors can be increased using nonlinear optics.16 The case of spherical metallic nanoparticles is here of particular interest.17,18 Indeed, Mie theory can be extended to SHG from a homogeneous sphere, therefore providing an interesting framework for understanding the SPR enhancement of SHG.19,20 Nevertheless, tunability can be required for practical applications, and the optical response of metallic homogeneous spheres is only weakly adjustable, particularly in the nearinfrared region. This limitation can be overcome by including a dielectric core inside metallic nanospheres. These composite nanostructures formed by a dielectric core embedded in a thin metallic shell are called nanoshells.21−23 Their optical response is dominated by SPR as in the case of homogeneous metallic spheres. A very useful tool for the description of the nanoshell optical response is the hybridization model in which the © 2012 American Chemical Society

plasmon modes of a complex nanostructure are obtained by combination of the plasmon resonances of its elementary components.24,25 The SPRs in metallic nanoshells arise from the interaction of the plasmon modes sustained by the outer and the inner shell surfaces and can therefore be described as the hybridization of the plasmon modes of a metallic sphere and that of a nanocavity. The impact of the embedding medium and nanocore dielectric constants on the linear optical response of metallic nanoshells has already been investigated in several works.26,27 To our knowledge, this impact on the nonlinear optical response, and that of SHG in particular, has not been reported yet. In this article, we use the extended Mie theory to investigate the effect of the dielectric constants of the dielectric core and embedding medium on the SHG from gold nanoshells with an inner radius a = 40 nm and an outer radius b = 50 nm, standard dimensions of chemically synthesized nanoshells.22 The extended Mie theory has been previously used to investigate the impact of silver and gold nanoshell dimensions on the SH emission spectra,28 but it is briefly described in this article for clarity. The impact of the dielectric constant of the dielectric core is addressed first, and the tunability in the SH response of metallic nanoshells is highlighted. We also discuss the impact of the embedding medium and practical applications like sensing are emphasized. Finally, we show that sensing properties can be optimized with a modification of the core dielectric constant. Received: October 15, 2012 Revised: December 19, 2012 Published: December 21, 2012 1172

dx.doi.org/10.1021/jp310169u | J. Phys. Chem. C 2013, 117, 1172−1177

The Journal of Physical Chemistry C

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THEORETICAL METHODS Mie theory extended to the case of the SHG from metallic nanoshells is used to calculate the SH scattering cross section.28 This model is briefly described in this article, but all calculation details can be found in ref 28. First, the fundamental electric field is calculated in the nanoshell assuming an incident plane wave and applying the boundary conditions at both the core− shell and shell−embedding medium interfaces. The dielectric constant for gold is taken from the literature.29 All involved electromagnetic fields are expanded in vector spherical harmonics. The nonlinear polarization oscillating at the SH frequency is then calculated considering a pure surface contribution. Indeed, SHG is forbidden in centrosymmetric media in the dipolar approximation. Nevertheless, the centrosymmetry is locally broken at the interface between centrosymmetric media allowing SHG. We retain the χ⊥⊥⊥ component only, where the symbol ⊥ denotes the direction normal to the interface. This tensor element is known to be the largest element of the surface susceptibility tensor in the case of metallic interfaces.30 The frequency dependence of the χ⊥⊥⊥ component is calculated using the equation31 a eε χ⊥⊥⊥ = − RS [εr(ω) − 1] 02 (1) 4 mω where e and m denote the charge and the mass of the electron, respectively, and ε0εr(ω) = ε2(ω) is the dielectric constant of the metallic shell. Also, aRS is the so-called Rudnick-and-Stern parameter.32 In the present work, aRS is chosen equal to one for the sake of simplicity for both interfaces, but surface properties (surface roughness, capping layer, etc.) could result in different values of aRS for the inner and outer interfaces. The introduction of different values of aRS in our model is straightforward, but the determination of the impact of surface quality on the aRS Rudnick-and-Stern parameter is beyond the scope of the present article. The scattered SH electric field is then obtained by applying the boundary conditions at both interfaces. The total SH scattering cross section is then given by Csca(2ω) =

c 8πk 2(2ω)

Figure 1. Extinction cross section (a) and total SH scattering cross section (b) calculated for a (40, 50) nm gold nanoshell with core dielectric constants equal to 2 (dotted lines), 4 (dashed lines), and 6 (full lines). Gold nanoshells are considered in water (n = 1.33).

dielectric cores calculated for (40, 50) nm nanoshells in water (n = 1.33).33 The optical properties of the embedding medium are described by its refractive index instead of its dielectric constant in order to make the comparison with previous works easier.27 All extinction spectra reveal a huge peak corresponding to the dipolar bonding resonance mode (between 680 and 900 nm) and a smaller peak corresponding to the quadrupolar bonding resonance mode (between 580 and 700 nm), where the word “bonding” refers to the symmetric coupling between the sphere and cavity plasmons in the hybridization model.24 As the dielectric constant of the core increases, both resonances shift to longer wavelength. This behavior is easily understood using the hybridization model framework in which the plasmon modes of a nanoshell are described as the interaction of the SPR of the inner and outer interfaces.24,25 As the dielectric constant of the core increases, the core plasmon energy decreases, resulting in a decreasing energy of the final hybridized modes. This behavior has been already observed in the linear optical response of metallic nanoshells.27 Now, we consider the impact of the dielectric core on the SHG from metallic nanoshells. Figure 1b depicts the total SH scattering cross sections as functions of the fundamental wavelength for gold nanoshells with identical dimensions but with different dielectric constants (dielectric constant still ranging from 2 to 6). As in the case of the linear extinction, the calculated spectra are composed of two resonances. The resonances occur at wavelengths equal to twice the wavelengths of the resonances observed in extinction spectra. Indeed, it is well-known that the SH scattering from metallic nanoparticles is enhanced by surface plasmon resonances, and this enhancement can occur either at the fundamental or at the SH frequency.19 For this reason, the tunability of SHG purely

∞

∑ |AlE,m,sca(2ω)|2 l ,m

(2)

AE,sca l,m (2ω)

where the coefficients are the scattering coefficients weighting the contribution of the modes (l, m) to the total scattered wave. In this framework, the contribution of each emission mode can be easily determined. For example, the weight of the dipolar and quadrupolar modes can be calculated separately fixing l = 1 and l = 2, respectively. One can note that the analysis presented in this article is performed considering perfectly spherical gold nanoshells (as in the case of the Mie theory) and is not expected to be accurate for the smallest nanoshells. Indeed, it was demonstrated experimentally that SHG from compact gold nanoparticles larger than 80 nm arises from retardation effects and is not induced by symmetry breaking.18 In the next sections, we will consider (40, 50) nm gold nanoshells. For such dimensions, our model is expected to be in good agreement with the SH response of well-synthesized nanoshells.

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RESULTS AND DISCUSSION Impact of the Dielectric Core. The impact of the dielectric core on both the linear and nonlinear optical properties of gold nanoshells is investigated in this part. Figure 1a shows the linear extinction of gold nanoshells with different 1173



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stems from the tunability of the linear SPR of gold nanoshells. One can note that the band observed between 1000 and 1200 nm in the case of a core dielectric constant εc = 6 is due to the enhancement of the fundamental electric field (see Figure 1a). Contrary to the case of linear extinction, the quadrupolar bonding resonance mode is easily observed in SH scattering cross section. This behavior, surprising at first sight, can be easily explained, similarly to the case of SHG from homogeneous metallic sphere. Indeed, SHG is forbidden in centrosymmetric media in the dipolar approximation. The plasmonic nanoshells considered in this work are spherical, i.e., centrosymmetric, and retardation effects are required to allow SHG. Retardation effects can arise either at the fundamental frequency or at the SH frequency. If the spatial variation of the incident wave is neglected, then the dipolar SH emission mode is forbidden and the leading order emission mode is a quadrupolar one. If the spatial variation of the incident wave is taken into account, then the dipolar SH emission mode is allowed. Since the SH quadrupolar emission mode does not require retardation effects at the fundamental frequency, its contribution to the SH scattering cross section can be equivalent to (and even higher than) the contribution of the dipolar emission mode. For this reason, SHG makes the observation of higher multipolar (quadrupolar, octupolar) resonance modes much easier.17,18 Moreover, the impact of the core dielectric constant on SHG varies with the emission mode order. For example, it is obvious that the impact of the core dielectric constant on the position of the dipolar resonance is higher than the position on the amplitude of the quadrupolar resonance (see Figure 1). In the section below, we will see that the impact of the surrounding medium on SHG from plasmonic nanoshells also depends of the emission mode order. Impact of the Embedding Medium. In this section, we address the impact of the embedding medium on the linear and nonlinear optical properties of metallic nanoshells. Figure 2a shows the extinction cross sections calculated for a (40, 50) nm gold nanoshell with a core dielectric constant εc equal to 4 and considering embedding media with different refractive index: n = 1.33 (full lines), n = 1.41 (dashed lines), and n = 1.49 (dotted lines). The spectra are composed of two resonances corresponding to the dipolar bonding resonance (close to 800 nm) and the quadrupolar bonding resonance (close to 650 nm) modes even if the quadrupolar bonding resonance mode is barely observed in the extinction spectra. As the refractive index of the embedding medium increases, both resonances are shifted to longer wavelength. Indeed, the energy of the plasmon modes initially sustained by the outer surface decreases. This results in a decreasing energy of the final hybridized modes. This behavior explains why the optical properties of metallic nanoshells are sensitive to the embedding medium. Nevertheless, the impact of the surrounding medium on the position of the maxima depends on the surface plasmon resonance order. For example, Figure 2b shows the maxima of the dipolar mode (squares) and the quadrupolar mode (circles) as functions of the refractive index calculated for a (40, 50) nm gold nanoshell. It is easily observed that the dipolar SPR shift faster than the quadrupolar SPR to longer wavelengths with increasing index. Linear fitting procedure leads to sensitivities equal to 275 nm/refractive index unit (RIU) in the case of the dipolar mode and 125 nm/RIU in the case of the quadrupolar mode. It was recently shown that the intrinsic properties of nonlinear optical processes increase the plasmonic sensor

Figure 2. (a) Extinction cross section calculated for a (40, 50) nm gold nanoshell with a core dielectric constant εc equal to 4 considering different embedding media: n = 1.33 (full lines), n = 1.41 (dashed lines), and n = 1.49 (dotted lines). (b) Maxima of the dipolar mode (square) and the quadrupolar mode (circle) as functions of the refractive index calculated for the same (40, 50) nm gold nanoshell. The lines correspond to fit by linear functions.

sensitivity.16 The SH cross sections calculated for a (40, 50) nm gold nanoshell with a core dielectric constant εc equal to 4 considering embedding media with different refractive index: n = 1.33 (full lines), n = 1.41 (dashed lines), and n = 1.49 (dotted lines) are depicted in Figure 3a. As in the case of the linear extinction, the maxima of the SH dipolar and quadrupolar emission modes are shifted to longer wavelengths as the refractive index of the surrounding medium increases. Figure 3b shows the maxima of the dipolar mode (squares) and the quadrupolar mode (circles) as functions of the refractive index calculated for the same gold nanoshell. Linear fitting procedure leads to sensitivities equal to 550 nm/RIU in the case of the dipolar mode and 250 nm/RIU in the case of the quadrupolar mode. These values are exactly twice the ones obtained in the case of the linear extinction case. The resonances correspond to an enhancement of the SH dipolar and quadrupolar emission modes at the harmonic frequency (compare Figure 3a with Figure 2a). The fundamental wavelength has to be increased by 2 nm to increase the harmonic wavelength by 1 nm. For this reason, the sensitivity is increased by a factor 2 due to the SHG intrinsic properties.16 In the next section, we will show that sensing properties of metallic nanoshells depend on the core dielectric constant and that the sensitivity can be optimized selecting the appropriated core dielectric constant. Sensing Optimization. In the above sections, we have separately discussed the impact of the dielectric core and of the embedding medium on the SHG response from metallic nanoshells. In this part, we discuss calculations performed by 1174



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Figure 3. (a) SH cross section calculated for a (40, 50) nm gold nanoshell with a core dielectric constant εc equal to 4 considering different embedding media: n = 1.33 (full lines), n = 1.41 (dashed lines), and n = 1.49 (dotted lines). (b) Maxima of the SH dipolar emission mode (square) and the SH quadrupolar emission mode (circle) as functions of the refractive index calculated for the same (40, 50) nm gold nanoshell. The lines correspond to fit by linear functions.

Figure 4. SH cross section calculated for a (40, 50) nm gold nanoshell with core dielectric constant from 2 to 6 considering embedding media with refractive index n = 1.33 (full lines), n = 1.41 (dashed lines), and n = 1.49 (dotted lines).

sensitivities decrease as the core dielectric constant increases. In other words, the longer are the wavelengths of the primitive cavity plasmon resonances, the smaller are the wavelength shifts induced by a given variation of the refractive index of the surrounding medium. Nevertheless, the sensitivity is not the only relevant parameter to characterize a plasmonic sensor. The width of the resonance is also important. A figure-of-merit (FOM) has been introduced as the ratio between the sensitivity and the full width at half-maximum (fwhm) of a given resonance, making the comparison between plasmonic sensors straightforward.34 FOMs of the SH quadrupolar and dipolar emission modes are shown as functions of the core dielectric constant in Figures 5a and 5b, respectively. Contrary to sensitivities, FOMs are the maximum for core dielectric constant close to 6. This observation is explained by the evolution of SPR line widths which are directly related to surface plasmon lifetimes. Higher are the losses broader are SPRs. As the core dielectric constant increases, the dipolar and quadrupolar bonding resonance modes are shifted to longer wavelength, without modifying the nanoshell dimensions, leading to a decreasing nanoshell diameter/resonance wavelength ratio. As a result, the radiative losses decrease and, therefore, SPR line widths tend to be narrower.27 Intrinsic losses, i.e., energy dissipation in the gold shell, are also responsible for plasmonic damping. The impact of the core dielectric constant on the intrinsic losses is more complicated than on radiative losses. The smaller the core dielectric constant is, the closer to the interband transition threshold (617 nm in gold) the SPRs are, resulting in an extra plasmon damping by

modifying simultaneously the core dielectric constant and the refractive index of the surrounding medium. Figure 4 shows the SH cross section calculated for (40, 50) nm gold nanoshells with a core dielectric constant ranging from 2 to 6 and considering an embedding media with a refractive index n = 1.33 (full lines), n = 1.41 (dashed lines), and n = 1.49 (dotted lines). For all core dielectric constants, resonances are shifted to longer wavelengths as the refractive index of the embedding medium increases. As discussed in the Theroretical Methods section, variation of the core dielectric constant leads to a change in the optical properties of metallic nanoshells (see Figure 1). In other words, a variation of the core dielectric constant modifies the properties of the primitive nanocore SPRs and, then, the properties of the nanoshell SPRs as predicted by the hybridization model.24,25 More precisely, as the core dielectric constant increases, the primitive cavity plasmon resonances shift to longer wavelength, leading to a red-shift of the dipolar and quadrupolar bonding resonance modes.27 Since the SPR properties are different, the impact of the surrounding medium is expected to vary with the core dielectric constant. In order to quantify this impact, sensitivities of the SH dipolar and quadrupolar emission modes have been determined and are shown as functions of the core dielectric constant in Figure 5. One can note that sensitivity quantifies the impact of the refractive index of the surrounding medium on the SPR position and are expressed in nm shift/refractive index unit. It is observed that, whatever the emission mode, 1175



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surrounding medium on the SH emission spectra have also been addressed showing that the sensitivity is multiplied by 2 due to the intrinsic properties of the SHG process. Finally, we have demonstrated that the sensing properties of SHG from metallic nanoshells can also be improved by modifying the core dielectric constant. This work paves the way for further experimental investigations of the SHG from metallic nanoshells, for instance, using polarization resolved hyper-Rayleigh scattering experiments17,18 or angle-resolved SH scattering.37,38

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AUTHOR INFORMATION

Corresponding Author

*Fax +33(0)4 72 43 15 07, Tel +33(0)4 72 44 58 73, e-mail [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Maier, S. A. In Plasmonics: Fundamentals and Applications; Springer: New York, 2007. (2) Sandrock, M. L.; Pibel, C. D.; Geiger, F. M.; Foss, C. A. J. Phys. Chem. B 1999, 103, 2668−2675. (3) Butet, J.; Duboisset, J.; Bachelier, G.; Russier-Antoine, I.; Benichou, E.; Jonin, C.; Brevet, P.-F. Nano Lett. 2010, 10, 1717−1721. (4) Chandra, M.; Dowgiallo, A.-M.; Knappenberger, K. L., Jr. J. Phys. Chem. C 2010, 114, 119971−19978. (5) Zhang, Y.; Grady, N. K.; Ayala-Orozco, C.; Halas, N. J. Nano Lett. 2011, 11, 5519−5523. (6) Singh, A. K.; Senapati, D.; Neely, A.; Kolawole, G.; Hawker, C.; Ray, P. C. Chem. Phys. Lett. 2009, 481, 94−98. (7) Valev, V. K.; Silhanek, A. V.; Verellen, N.; Gillijns, W.; Van Dorpe, P.; Aktsipetrov, O. A.; Vandenbosch, G. A. E.; Moshchalkov, V. V.; Verbiest, T. Phys. Rev. Lett. 2010, 104, 127401. (8) Valev, V. K.; Smisdom, N.; Silhanek, A. V.; De Clercq, B.; Gillijns, W.; Ameloot, M.; Moshchalkov, V. V.; Verbiest, T. Nano Lett. 2009, 9, 3945−3948. (9) Husu, H.; Siikanen, R.; Mäkitalo, J.; Lehtolahti, J.; Laukkanen, J.; Kuittinen, M.; Kauranen, M. Nano Lett. 2012, 12, 673−677. (10) Bouhelier, A.; Beversluis, M.; Hartschuch, A.; Novotny, L. Phys. Rev. Lett. 2003, 90, 013903. (11) Slablab, A.; Le Xuan, L.; Zielinski, M.; de Wilde, Y.; Jacques, V.; Chauvat, D.; Roch, J.-F. Opt. Express 2012, 20, 220−227. (12) Aouani, H.; Navarro-Cia, M.; Rahmani, M.; Sidiropoulos, T. P. H.; Hong, M.; Oulton, R. F.; Maier, S. A. Nano Lett. 2012, 12, 4997− 5002. (13) Thyagarajan, K.; Rivier, S.; Lovera, A.; Martin, O. J. F. Opt. Express 2012, 20, 12860−12865. (14) Belardini, A.; Larciprete, M. C.; Centini, M.; Fazio, E.; Sibilia, C.; Chiappe, D.; Martella, C.; Toma, A.; Giordano, M.; Buatier de Mongeot, F. Phys. Rev. Lett. 2011, 107, 257401. (15) Bautista, G.; Huttunen, M. J.; Mäkitalo, J.; Kontio, J. M.; Simonen, J.; Kauranen, M. Nano Lett. 2012, 12, 3207−3212. (16) Butet, J.; Russier-Antoine, I.; Jonin, C.; Lascoux, N.; Benichou, E.; Brevet, P.-F. Nano Lett. 2012, 12, 1697−1701. (17) Butet, J.; Bachelier, G.; Russier-Antoine, I.; Jonin, C.; Benichou, E.; Brevet, P.-F. Phys. Rev. Lett. 2010, 105, 077401. (18) Russier-Antoine, I.; Benichou, E.; Bachelier, G.; Jonin, C.; Brevet, P.-F. J. Phys. Chem. C 2007, 111, 9044−9048. (19) Dadap, J. I.; Shan, J.; Eisenthal, K. B.; Heinz, T. F. Phys. Rev. Lett. 1999, 83, 4045−4048. (20) Pavlyukh, Y.; Hübner, W. Phys. Rev. B 2004, 70, 245434. (21) Averitt, R. D.; Sarkar, D.; Halas, N. J. Phys. Rev. Lett. 1997, 78, 4217−4220. (22) Jankiewicz, B. J.; Jamiola, D.; Choma, J.; Jarioniec, M. Adv. Colloid Interface Sci. 2012, 170, 28−47. (23) Averitt, R. D.; Westcott, S. L.; Halas, N. J. J. Opt. Soc. Am. B 1999, 16, 1824−1832.

Figure 5. FOM (right axis) and sensitivity (left axis) of the quadrupolar mode (a) and the dipolar mode (b) as functions of the core dielectric constant calculated for a (40, 50) nm gold nanoshell (lines are guides for the eyes).

excitation of electron−hole pairs between the d-band and conduction band.35 As core dielectric constant increases, the energy confinement in the nanoshell increases, resulting in an intrinsic losses enhancement.27 As a result of these effects, the narrowest SPRs are obtained for core dielectric constants comprised between 6 and 8. Finally, the highest FOM is obtained for the dipolar SPR with a value of 3.15. This value is below the ones obtained for the best plasmonic sensors but can be improved using a silver shell although the chemical synthesis is probably more challenging.36 Furthermore, the dielectric functions of realistic core materials could be dispersive, as the Cu2O core discussed in ref 27, and the impact on SPR properties is expected to be more complicated than the one discussed in this article. Nevertheless, the introduction of dispersive core dielectric functions in our model is straightforward, and the impact of realistic dielectric cores on the SH emission spectra is easily calculated.

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CONCLUSIONS In conclusion, the impact of the core dielectric constant and the refractive index of the surrounding medium on the SHG from (40, 50) nm gold nanoshells has been investigated using the nonlinear Mie theory. Two resonances, corresponding to the enhancement of the SH dipolar and quadrupolar emission modes, have been observed in the SH emission spectra. The properties of these resonances have been found tunable by modifying the core dielectric constant. The impact of the 1176



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(24) Prodan, E.; Radloff, C.; Halas, N. J.; Nordlander, P. Science 2003, 302, 419−422. (25) Prodan, E.; Nordlander, P. J. Chem. Phys. 2004, 120, 5444− 5454. (26) Prodan, E.; Lee, A.; Nordlander, P. Chem. Phys. Lett. 2002, 360, 325−332. (27) Bardhan, R.; Grady, N. K.; Ali, T.; Halas, N. J. ACS Nano 2010, 4, 6169−6179. (28) Butet, J.; Russier-Antoine, I.; Jonin, C.; Lascoux, N.; Benichou, E.; Brevet, P.-F. J. Opt. Soc. Am. B 2012, 29, 2213−2221. (29) Johnson, P. B.; Christy, R. W. Phys. Rev. B 1972, 6, 4370−4379. (30) Wang, F. X.; Rodriguez, F. J.; Albers, W. M.; Ahorinta, R.; Sipe, J. E.; Kauranen, M. Phys. Rev. B 2009, 80, 233402. (31) Bachelier, G.; Butet, J.; Russier-Antoine, I.; Jonin, C.; Benichou, E.; Brevet, P.-F. Phys. Rev. B 2010, 82, 235403. (32) Rudnick, J.; Stern, E. A. Phys. Rev. B 1971, 4, 4274−4290. (33) Aden, A. L.; Kerker, M. J. Appl. Phys. 1951, 22, 1242−1246. (34) Sherry, L. J.; Chang, S. H.; Schatz, G. C.; van Duyne, R. P.; Wiley, B. J.; Xia, Y. Nano Lett. 2005, 5, 2034−2038. (35) Sönnischen, C.; Franzl, T.; Wilk, T.; von Plessen, G.; Feldmann, J.; Wilson, O.; Mulvaney, P. Phys. Rev. Lett. 2002, 88, 077402. (36) Mayer, K. M.; Hafner, J. F. Chem. Rev. 2011, 111, 3828−3857. (37) Gonella, G.; Gan, W.; Dai, H.-L. J. Phys. Chem. Lett. 2012, 3, 2877−2881. (38) Schürer, B.; Wunderlich, S.; Sauerbeck, C.; Peschel, U.; Peukert, W. Phys. Rev. B 2010, 82, 241404.

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Effect of the Dielectric Core and Embedding Medium on the Second

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