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Surface Plasmon Enhanced Third-Order Nonlinear Optical Effects in Ag-Fe3O4 Nanocomposites Venkatesh Mamidala, Guichuan Xing, and Wei Ji* Department of Physics, National UniVersity of Singapore, Singapore 117542 ReceiVed: August 26, 2010; ReVised Manuscript ReceiVed: NoVember 17, 2010
We report an approach to enhance the third-order nonlinear optical properties of a nanocrystal through the attachment of another metallic nanoparticle. Both two-photon absorption (TPA) cross section and nonlinear refractive (NR) cross section of a Fe3O4 nanocube with and without the attachment of an Ag nanoparticle are characterized by using the Z-scan technique. As compared to pristine Fe3O4 nanocube, the TPA and NR cross section of Ag-particle-attached Fe3O4 nanocube is increased by several folds at light frequencies far below the surface plasmon resonance of Ag particle, with precise values depending on the size of the Ag particle. These enhanced values are in agreement with the theoretically calculated enhancement by discrete dipole approximation modeling, which reveals that the local electric field induced by the metal nanoparticle should play an essential role in the enhancement. Introduction Nanomaterials with strong nonlinear optical properties have been the focus of research interest for many years because they are a good candidate for a great number of photonic applications such as optical data storage,1 micro fabrication,2 optical limiting,3 and biophotonics applications.4 There have been many approaches to increase their nonlinear optical properties, in particular, third-order nonlinear optical processes like two-photon absorption and optical Kerr nonlinearity. One of them is to apply a local electric field to a nanocrystal.5 In this approach, a metallic nanoparticle, especially gold (Au) and silver (Ag) particles that are nanometers in diameter, generates a giant local electric field at and near its surface through its surface plasmon resonance (SPR). If such a metallic particle is attached to another nanocrystal, as shown in Figure 1, the great optical polarization associated with the SPR should significantly alter the nanocrystal’s linear optical responses as well as nonlinear optical responses.6,7 Theoretical calculations of electric-field intensity enhancement through thin metal films predict a maximum enhancement of approximately 350-fold in Ag and 50-fold in Au.8 Similar effects can also be induced by metallic particles. For instance, silver and gold spherical particles possess a SPR with maxima at ∼410 and ∼530 nm, respectively.8 The peak position of SPR depends not only on the metal particle itself but also on its size and shape.6,9 In addition, it is also influenced by both the dielectric constant of the surrounding medium10,11 and interparticle coupling interactions.12 The enhancement in the nonlinear optical responses of composite systems in which nanocrystals are attached with metallic particles have been demonstrated, such as surfaceenhanced Raman scattering (SERS) and second-harmonic generation (SHG), due in part to large local field effects.13,14 Dielectric films embedded with nanometer-sized metallic particles have been studied for years because they possess large * To whom correspondence should be addressed. E-mail: phyjiwei@ nus.edu.sg.
optical nonlinearity,15,16 which is essential for applications in optical switching17 and optical limiting.18 The greatest enhancement in the nonlinear optical properties of nanocrystals is predictably attainable at the peak position of SPR. At this position, however, the linear (or background) light absorption also reaches maximum, which is extremely undesirable in the above-said applications. To avoid this situation, the SPR peak position should be far away from the light frequency used; at least doubling the light frequency where the linear absorption under nonresonant conditions is practically acceptable yet a considerable enhancement manifests itself in both nonlinear absorption and refraction of nanocrystals. To realize the above concept, we focus our attention on a composite system in which an iron oxide nanocrystal is attached with a noble metallic particle. Iron oxide nanoparticles have recently received great attention because of its variety of applications such as environmental and energy applications,19 material nanocomposites,20 drug delivery,21 magnetic resonance imaging,22 and various other biomedical applications.21,23 Iron oxide magnetic nanoparticles tend to be either paramagnetic or superparamagnetic, with particle sizes of approximately 20 nm being classified as the latter. And they are known for giant two-photon absorption24,25 and other nonlinear optical phenomena.26,27 It has also been reported that the magneto-optical responses of iron oxide nanoparticles can be enhanced when each of them is in physical contact with a silver particle28 or coated with a gold layer.29 Here we report the effects of attached silver particles on the nonlinear optical properties of Fe3O4 nanocubes. In particular, the silver-size dependence of both a two-photon absorption (TPA) cross section and a nonlinear refractive (NR) cross section of Fe3O4 nanocubes is measured experimentally by using femtosecond Z-scan technique and compared with the theoretical calculated enhancement factor through discrete dipole approximation (DDA) modeling. Experimental Section The details of synthesis for Ag-Fe3O4 nanocomposites (NCs) can be found elsewhere.30 Structure and size of the NCs were
10.1021/jp1080912 2010 American Chemical Society Published on Web 12/09/2010
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Figure 1. (A) Low-resolution and (B) high-resolution TEM images of Ag-Fe3O4 nanocomposites. (C) Schematic of an Ag-Fe3O4 nanocomposite with capping layer.
investigated with high-resolution transmission electron microscopy (HRTEM). As shown in Figure 1A,B, Ag nanoparticles and Fe3O4 nanocubes formed are nearly monodisperse with size dispersions less than 20%. The average length of Fe3O4 nanocubes and the average diameter of Ag particles are 13 and 7 nm, respectively. In Figure 1, 7-nm Ag particle attached Fe3O4 nanocubes are displayed as an example. The NCs are capped with a hydrophobic layer (composed of oleic acid and oleylamine), as illustrated by Figure 1C. With a UV-visible spectrophotometer (Shimadzu, UV-1700), the one-photon absorption spectra of Ag-Fe3O4 NCs and pristine Fe3O4 nanocubes in toluene solution were recorded and are shown in Figure 2. In the spectral range from 650 to 1000 nm, the similarity between the spectra suggests that the absorption should be predominated by Fe3O4 nanocubes. The difference between the spectra in the range from 300 to 650 nm is indicative of the presence of Ag particles, increasing with the size of Ag particles. The third-order nonlinear optical properties of Ag-Fe3O4 NCs were characterized with femtosecond open- and closed-aperture Z-scan measurements.31 The Z-scan technique was employed as it provides separate characterization on the imaginary or real part of third-order nonlinear susceptibility, which corresponds to the TPA coefficient or NR index, respectively. In this technique, a nonlinear sample is scanned along a focused laser beam and gives rise to a different transmission. In particular, a dip in the transmission appears at the focus (as shown in Figure 3), signaling the occurrence of TPA. If an aperture is placed in the front of the detector, a peak-to-valley signal (as shown in Figure 4) is observed if the sample exhibits a negative NR index. To obtain the magnitude of the TPA coefficient or NR index, the Z-scan data have to fit with the Z-scan theory. The details
Figure 2. Absorption spectra of Ag-Fe3O4 nanocomposites and Fe3O4 nanocubes (black) in toluene solution.
of the Z-scan theory can be found elsewhere.31 In the fitting, the TPA coefficient or NR index is treated as a free parameter. The best fit to the measured open-aperture (or close-aperture) Z-scans generates the TPA coefficient (or NR index). Laser pulses of 330-fs duration, 780-nm wavelength, and 1-kHz repetition rate were provided by a Ti:Sapphire regenerative amplifier (Titan, Quantronix). After a spatial filter, the spatial profiles of the pulses were of near Gaussian distribution. The pulses were also divided into two parts: one part was used as the reference and the other part was focused onto a 1-mmthick quartz cuvette that contained the sample solution with a focus lens (f ) 10 cm) in the Z-scans. The beam radius was measured to be 30 ( 2 µm. The linear transmittance of all the sample solutions was adjusted to 60% at 780 nm. The incident and transmitted laser pulses were measured simultaneously with two energy detectors (Laser Probe RKP 465). In an openaperture (OA) configuration, the total transmitted pulse energy was measured in the far field as a function of the sample position, while only the central part of the transmitted pulse energy was recorded for a closed-aperture (CA) Z-scan. The typical OA and CA Z-scan curves are depicted in Figures 3 and 4, respectively. From Figure 4, we observe that a peak is followed by a valley in the Z-scan curve and it is due to selfdefocusing effect, which confirms the negative nonlinearity. By assuming spatially and temporally Gaussian profiles for the input laser pulse, all the Z-scan curves can be fit by the Z-scan theory.32 In the Z-scan simulations, the TPA coefficient and NR index are treated as free parameters. The best fits between the theory and experimentally measured Z-scans generate the values for TPA coefficients (R2) and NR index (n2). The effective TPA cross section (σ2) is derived from σ2 ) (pω)R2/N and the effective NR cross section is derived from σn ) n2/N, where N is the nanocomposite density. The obtained σ2 and σn values are tabulated in Table (1). Note that the large experimental errors result from both uncertainties in the determination of NC density in solution and fluctuation in the measurement of laser pulse energy. The insets of Figures 3 and 4 show that the measured effective TPA coefficients and NR indexes slightly depend on the light irradiance, which implies that these values include the contributions from higher order nonlinear processes like TPAinduced free-carrier absorption and refraction. As such, what we measured are the effective TPA and NR cross sections. But, in the case of Ag-Fe3O4 NCs, these higher order nonlinear processes are diminished as the excited electrons might relax quickly through extra relaxation channels available in the Ag-Fe3O4 dimer, such as charge and/or energy transfer between Fe3O4 and Ag nanoparticle. Therefore, such high-order nonlinear
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Figure 3. Open-aperture Z-scans of (A) Fe3O4 nanocubes and (B) Fe3O4-Ag (7 nm) nanocomposites in toluene with the theoretical fittings (black solid lines). The insets show the measured effective TPA coefficients as a function of the input light irradiance.
Figure 4. Closed-aperture Z-scans of (A) Fe3O4 nanocubes and (B) Fe3O4-Ag (7 nm) nanocomposites in toluene with the theoretical fittings (red solid lines). The insets show the measured effective NR index as a function of the input light irradiance.
TABLE 1: Effective NR and TPA Cross Sections Measured at a Wavelength of 780 nm and Light Irradiance of 100 GW/cm2a Fe3O4 length (nm)
Ag diameter (nm)
σn (cm5/GW)
σ2 (GM)
13 13 13 13
0 3.5 7 10
-4.2 × 10-20 -5.8 × 10-20 -6.5 × 10-20 -8.1 × 10-20
0.3 × 107 0.9 × 107 1.3 × 107 1.8 × 107
a
Experiment uncertainty: (40% and 1 GM ) 10-50 cm4 · s.
processes become insignificant as the induced changes in the measurements are less than 15% in the light intensity range of interest. From Table (1), we can observe that the TPA cross section of Fe3O4 nanocube is comparable to (at least on the same order of magnitude) materials known to exhibit very large TPA cross sections, and several orders of magnitude greater than frequently reported nanomaterials.33 With the field enhancement effect caused by 7- and 10-nm Ag particles, Fe3O4 nanocubes can offer TPA cross section of 1 order higher, as compared to pristine Fe3O4 nanocubes. Similarly, the enhancement due to Ag particles can also be extended to the nonlinear refraction of Fe3O4 nanocubes. Theoretical Section The theoretical calculations were carried out to give insightful information on the above experimental finding. The DDA calculation is one of the numerical approximation methods that are often used to compute the scattering and absorption of metal particles.34 To model the enhancement through the DDA method, we employed DDSCAT 7.0, the open FORTRAN
source code, which is provided by Draine and Flatau.35 And it approximates the target by a finite array of polarizable points (or point dipoles). The points acquire dipole moments in response to the local electric field, which then interact with each nother via their electric field. The effect of Ag particle on Fe3O4 nanocube was calculated in the following manner: first, the enhanced scattered electric field by an Ag particle (outside Ag sphere) was simulated, and second the effect of enhanced scattered electric field (Eeff) on the Fe3O4 nanocube was calculated. In the calculation, the Ag particle was assumed to have no influence on the physical properties and electronic band structures of Fe3O4 nanocubes except by inserting Eeff into the Fe3O4 nanocube for altering its optical nonlinearities. The dielectric functions used in our calculations were the experimental values reported by Palik and co-workers36 for the bulk metal εb, modified to include the additional damping mechanism in the particles introduced by collision of the conduction electrons with the particle surface37
ε ) εb +
ωp2 ωp2 ω(ω + i/τ) ω(ω + i/τ + i/τa)
(1)
In the above equation, εb, ωp, and 1/τ are the experimental bulk metal values of the dielectric function, plasma angular frequency, and damping constant, respectively. The quantity 1/τa ≈ VF/r is the surface damping term, VF is the Fermi velocity, and r is the particle radius. The values of the different parameters used were ωp ) 1.46 × 1016 rad/s, τ ) 2.74 × 10-13 s, and VF ) 1.4 × 106 m/s. The refractive index of toluene used was 1.485.38 The Ag particle was assumed to be an isotropic and homogeneous sphere.
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Figure 5. Comparison of normalized absorption efficiency factor (Qabs, black lines) and normalized linear absorption coefficient (R, red lines) of Ag particles with diameter (A) 3.5 nm, (B) 7 nm, and (C) 10 nm.
Figure 6. (a) 〈Eeff3〉 for Ag particle diameter of 3.5 nm, 7 nm, and 10 nm in toluene is plotted as a function of distance from the particle surface at wavelength of 780 nm. (b) 〈Eeff3〉 on the surface of the Ag particle with a diameter of 7 nm in toluene is plotted as a function of wavelength.
Figure 5 displays the calculated absorption efficiency factor (Qabs) and the linear absorption coefficient (R) of three sizes of Ag particles using the DDA method. And it also shows the comparison with the results calculated from the MaxwellGarnet theory (MGT).39 As the MGT is a simple yet effective method for calculating SPR positions of spherical metal nanoparticles, we use it to double check our DDA calculation. The good agreements on the SPR positions simulated by both MGT and DDA method validate the DDA calculation reported here. Figure 5 also shows that the MGT underestimates the field in the off-resonant spectral region, as compared to the DDA result. From the Qabs values, we can conclude that the Ag particle with larger diameter possesses a greater absorption efficiency factor. Figure 6 shows the enhanced scattered electric field (Eeff) profiles of three differently sized Ag particles in toluene on the XY plane with a light wavelength of 780 nm. In Figure 6, R is the radial distance from the center of the Ag nanoparticle. Because the Fe3O4 nanocube is located outside the Ag nanoparticle, it is exposed to the electric field whose strength is determined by the size of the Ag nanoparticle. The larger the Ag particle size, the greater the field. Therefore, we expect the enhancement on the nonlinear refraction and nonlinear absorption is greater for the Fe3O4 nanocube attached with a larger size of Ag particle. The magnitude of Eeff at a given point outside the Ag particle also depends on the radial distance between the point and the center of the Ag particle. In other words, different points within the Fe3O4 nanocube experience different enhancements because of the different Eeff. Therefore, an integral over volume was performed to calculate the averaged enhancement over the whole cube of Fe3O4, as shown below.
In the experiment, each Fe3O4 nanocube had no fixed orientation. Therefore, it was the first step to average up the Eeff at a radius from the center of the Ag particle over orientation or angles. After the average over orientation was determined, 〈Eeff(R)〉 is a function of R, where R is the radius from the center of the Ag particle. Because of the symmetry of the |Eeff|2 contours in the XY plane and XZ plane, averaging over only one plane was numerically conducted in the calculation. The effective third-order nonlinear polarization is given by P ) ε0 χeff(3) Eeff3, where χeff(3)is the effective third-order nonlinear susceptibility. The real part and imaginary part of χeff(3) give rise to the NR and TPA cross section, respectively. Figure 6 shows 〈Eeff3〉 for three different diameters of Ag particle in toluene at a given distance away from a Ag nanoparticle surface. Clearly, 〈Eeff3〉 becomes weaker the greater the distance from the Ag particle surface. By making use of all the calculated 〈Eeff3〉 values, one can obtain the effective TPA cross section and effective NR cross section over the nanocube by
σeff 2
)
∫ σ2〈Eeff3(R)〉 dV ∫ σn〈Eeff3(R)〉 dV eff and σn ) ∫ Einc3 dV ∫ Einc3 dV (2)
where 〈Eeff3(R)〉 is the average of Eeff3 over orientation at a distance away from the center of the Ag sphere. Einc refers to the incident electric field and σ2 and σn are denoted as the TPA and NR cross section of a pure Fe3O4 nanocube, respectively. Both σ2 and σn are measured experimentally, as shown in the
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TABLE 2: Enhancement Factor in the Effective TPA Cross Section (σ2) at 780 nm enhancement
Fe3O4-Ag (3.5 nm)
Fe3O4-Ag (7 nm)
Fe3O4-Ag (10 nm)
experiment theory (in toluene) theory (in vacuum)
3 1.3 1.25
4.3 2.9 2.6
6 4.3 3.8
TABLE 3: Enhancement Factor in the Effective NR Cross Section (σn) at 780 nm enhancement
Fe3O4-Ag (3.5 nm)
Fe3O4-Ag (7 nm)
Fe3O4-Ag (10 nm)
experiment theory (in toluene) theory (in vacuum)
1.4 1.3 1.25
1.55 2.9 2.6
1.9 4.3 3.8
Experimental Section. The calculated result divided by σ2 or σn results in the enhancement factor in the TPA or NR cross section, respectively.
Figure 7. Experimental and theoretical enhancement factors of TPA and NR cross sections at 780-nm wavelength.
However, these two factors should not be too large to result in significant discrepancy. Conclusion
Discussion The nonlinear optical responses of Fe3O4 nanocube are enhanced by the attachment of Ag particle, as shown by Tables 2 and 3. The observed effect qualifies as a nonresonant enhancement because the wavelength (780 nm) used is far from the SPR. Its doubled frequency is close to the SPR, and hence, the second-harmonic generation (SHG) is expected. Taking into consideration the randomness of NC orientations (as they are in toluene solution) in this experiment, however, the SHG output is too small to be detected with the energy detectors (Laser Probe RKP 465). Our theoretically calculated enhancement factors are in agreement with the experimental results, within 1 order of magnitude. The larger the size of the Ag particle, the greater the enhancement factor. In principle, a greater enhancement is achievable with a larger size of Ag nanoparticle. However, the larger the nanoparticle, the more unstable the Fe3O4-Ag dimer becomes, which imposes a maximum size that practically permits for Ag nanoparticle. In addition, our DDA simulation predicts a 26-fold enhancement for the attachment of 10-nm Ag particle as the light wavelength approaches the SPR resonance. In the calculation, the enhancement is also computed as the surrounding medium of toluene is replaced by vacuum. As demonstrated by Tables 2 and 3, the surrounding medium plays an insignificant role in the enhancement. This can be anticipated because the light frequency interested in this experiment is far from the peak position of SPR wherein the difference in the dielectric constant of the surrounding medium is of paramount importance, as demonstrated by considerable changes in Figure 5. Furthermore, the bulk part of the Fe3O4 nanocube experiences no sizable difference in the field between the two different surrounding media. Although there is a difference very near the surface, as displayed by Figure 7, it results in an unobservable difference in the enhancement. Despite the agreement within the same order of magnitude between experiment and theory, the discrepancy still manifests itself in Tables 2 and 3, in particular, for the NR cross sections. We attribute the discrepancy to the following two reasons. First, the calculation excludes the interaction between the metal nanoparticle and Fe3O4 nanocube, which may alter the electronic band structures of the Fe3O4 nanocube. Second, the theoretical calculation is carried out with an assumption that the nanocubes have the same size, which was not the case in the experiment.
In conclusion, we have demonstrated an approach to enhance the third-order nonlinear optical properties of a nanocrystal through the attachment of another metallic nanoparticle. Both TPA cross section and NR cross section of a Fe3O4 nanocube with and without an Ag particle of diameter in the range from 3 to 10 nm are characterized by using the Z-scan technique. As compared to pristine Fe3O4 nanocube, the TPA and NR cross section of Ag-particle-attached Fe3O4 nanocube are increased by several folds at light frequencies far below the surface plasmon resonance of Ag particle, with precise values depending on the size of Ag particle. These enhanced values are in agreement with the theoretically calculated enhancement by discrete dipole approximation modeling, which reveals that the local electric field induced by the metal nanoparticle should play an essential role in the enhancement. Acknowledgment. The authors are grateful for the financial support from the National University of Singapore through both Research Grant R-144-000-213-112 and research scholarships. It is also acknowledged that the samples were synthesized by Jiang J. and J. Y. Ying of A*Star Institute of Bioengineering and Nanotechnology, Singapore. References and Notes (1) Parthenopoulos, D. A.; Rentzepis, P. M. Science 1989, 245, 843. (2) Cumpston, B. H.; Ananthavel, S. P.; Barlow, S.; Dyer, D. L.; Ehrlich, J. E.; Erskine, L. L.; Heikal, A. A.; Kuebler, S. M.; Lee, I. Y. S.; McCord-Maughon, D.; Qin, J. Q.; Rockel, H.; Rumi, M.; Wu, X. L.; Marder, S. R.; Perry, J. W. Nature 1999, 398, 51. (3) Bhawalkar, J. D.; He, G. S.; Prasad, P. N. Rep. Prog. Phys. 1996, 59, 1041. (4) Prasad, P. N. Introduction to Biophotonics; Wiley-Interscience: Hoboken, NJ, 2003. (5) Shen, Y. R. The Principles of Nonlinear Optics;: J. Wiley: Singapore, 1991. (6) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. J. Phys. Chem. B 2003, 107, 668. (7) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer: Berlin, 1995. (8) Raether, H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings;: Springer-Verlag: Berlin, 1988. (9) Jain, P. K.; Lee, K. S.; El-Sayed, I. H.; El-Sayed, M. A. J. Phys. Chem. B 2006, 110, 7238. (10) Ghosh, S. K.; Nath, S.; Kundu, S.; Esumi, K.; Pal, T. J. Phys. Chem. B 2004, 108, 13963. (11) Underwood, S.; Mulvaney, P. Langmuir 1994, 10, 3427. (12) Su, K. H.; Wei, Q. H.; Zhang, X.; Mock, J. J.; Smith, D. R.; Schultz, S. Nano Lett. 2003, 3, 1087.
Optical Effects in Ag-Fe3O4 Nanocomposites (13) Kneipp, K.; Kneipp, H.; Itzkan, I.; Dasari, R. R.; Feld, M. S. Chem. ReV. 1999, 99, 2957. (14) Boyd, G. T.; Rasing, T.; Leite, J. R. R.; Shen, Y. R. Phys. ReV. B 1984, 30, 519. (15) Liao, H. B.; Xiao, R. F.; Wang, H.; Wong, K. S.; Wong, G. K. L. Appl. Phys. Lett. 1998, 72, 1817. (16) JoseYacaman, M.; Perez, R.; Santiago, P.; Benaissa, M.; Gonsalves, K.; Carlson, G. Appl. Phys. Lett. 1996, 69, 913. (17) Sasaki, K.; Nagamura, T. J. Appl. Phys. 1998, 83, 2894. (18) Doyle, J. J.; O’Flaherty, S. M.; Chen, Y.; Hegarty, T.; Hanack, M.; Blau, W. J. Polymer-phthalocyanine composite systems as solid-state passive optical limiters. Presented at the Conference on Organic Optoelectronics and Photonics, Strasbourg, France, 2004. (19) Zhang, W. X.; Wang, C. B.; Lien, H. L. Catal. Today 1998, 40, 387. (20) Novakova, A. A.; Lanchinskaya, V. Y.; Volkov, A. V.; Gendler, T. S.; Kiseleva, T. Y.; Moskvina, M. A.; Zezin, S. B. Magnetic properties of polymer nanocomposites containing iron oxide nanoparticles. Presented at the 2nd Moscow International Symposium on Magnetism (MISM 2001), Moscow, Russia, 2001. (21) Gupta, A. K.; Gupta, M. Biomaterials 2005, 26, 3995. (22) Babes, L.; Denizot, B.; Tanguy, G.; Le Jeune, J. J.; Jallet, P. J. Colloid Interface Sci. 1999, 212, 474. (23) Curtis, A.; Wilkinson, C. Trends Biotechnol. 2001, 19, 97. (24) Ando, M.; Kadono, K.; Haruta, M.; Sakaguchi, T.; Miya, M. Nature 1995, 374, 625. (25) Soga, D.; Alves, S.; Campos, A.; Tourinho, F. A.; Depeyrot, J.; Figueiredo, A. M. J. Opt. Soc. Am. B 2007, 24, 49.
J. Phys. Chem. C, Vol. 114, No. 51, 2010 22471 (26) Yu, B. L.; Zhu, C. S.; Gan, F. X.; Wu, X. C.; Zhang, G. L.; Tang, G. Q.; Chen, W. J. Opt. Mater. 1997, 8, 249. (27) Yu, B. L.; Zhu, C. S.; Gan, F. X. Physica E 2000, 8, 360. (28) Li, Y. Q.; Zhang, G.; Nurmikko, A. V.; Sun, S. H. Nano Lett. 2005, 5, 1689. (29) Jain, P. K.; Xiao, Y. H.; Walsworth, R.; Cohen, A. E. Nano Lett. 2009, 9, 1644. (30) Xing, G. C.; Jiang, J.; Ying, J. Y.; Ji, W. Opt. Express 2010, 18, 6183. (31) Sheik-Bahae, M.; Said, A. A.; Wei, T. H.; Hagan, D. J.; Vanstryland, E. W. IEEE J. Quantum Electron. 1990, 26, 760. (32) He, J.; Qu, Y. L.; Li, H. P.; Mi, J.; Ji, W. Opt. Express 2005, 13, 9235. (33) He, G. S.; Tan, L. S.; Zheng, Q.; Prasad, P. N. Chem. ReV. 2008, 108, 1245. (34) Draine, B. T.; Flatau, P. J. J. Opt. Soc. Am. A 1994, 11, 1491. (35) Draine, B. T.; Flatau, P. J. DDSCAT 7.0, available online at http:// www.astro.princeton.edu/∼draine/DDSCAT.html, 2008. (36) Ghosh, G.; Prucha, E. J.; Palik, E. D. Handbook of Optical Constants of Solids; Academic Press Handbook Series; Academic Press: Orlando, FL, 1985. (37) Ungureanu, C.; Rayavarapu, R. G.; Manohar, S.; van Leeuwen, T. G. J. Appl. Phys. 2009, 105, 7. (38) Rheims, J.; Koser, J.; Wriedt, T. Meas. Sci. Technol. 1997, 8, 601. (39) Stockman, M. I.; Kurlayev, K. B.; George, T. F. Phys. ReV. B 1999, 60, 17071.
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