Surface Plasmons on Metal Nanoparticles - UNAM

More documents

Recommendations

Info

Feature Article J. Phys. Chem. C, Vol. 111, No. 10, 2007 3817Figure 11. Model of the induced local field for an applied field (a)parallel and (b) transversal to the NPs chain.quasistatic limit, and we perform a systematic study for differenttypes of disorder and for filling fractions covering the wholerange, from the extreme-dilute to the closed-packed limits. Ourobjective is twofold, (i) we want to study the properties of an1D system due to the intrinsic interest that exists in the behaviorof low-dimensional systems and (ii) we want to shed some lightinto the possible dependence of the effective dielectric responseon the type of disorder. This allows us to analyze fluctuationsinduced in the local field by the positional disorder of the NPs.We employed the spectral representation to calculate the modes,and the details can be found elsewhere. 102,103When spherical NPs are aligned along a particular direction,the symmetry of the system is broken, and different propermodes can be found for light polarized parallel and perpendicularto the chain. When the external field is parallel, it polarizes theparticles, such that, the induced local field is in the samedirection as the applied field, see Figure 11a, and against therestoring forces, thus decreasing the frequency of the SPRs.When the field is perpendicular to the chain, shown in Figure11b, it polarizes the induced local field against the applied field,but in the same direction of the restoring forces, thus increasingthe frequency of the SPRs.To understand the influence of the physical environment,results are presented for the extinction efficiency Q ext as afunction of wavelength, for the ordered case and two differentkinds of disorder (A and B), and for different filling fractions.In disorder A, we randomly move the NPs within an interval2δ from the positions of a periodic chain. The parameter 0 eδ e 1/2 serves as a measure of the disorder, for example, δ )0 corresponds to the ordered case and δ ) 1/2 to the maximumallowed disorder of this type. The disorder type B correspondsto random positions with the only restriction that NPs do notoverlap. The choice of these types of disorder has nothing inparticular; the idea is simply to illustrate the sensitivity of theoptical response to a specific type of disorder algorithm,although some similar behaviors can be found. For example,(i) when a periodic 1D crystal is heated up, such that, the atomsmove randomly around their ordered positions, or (ii) when thesystem is heated up and suddenly cooled down, such that,random positions without any correlation can be found.In Figure 12, the influence of disorder is shown at differentfilling fractions. The nanospheres of 20 nm of radii are madeof silver and embedded in air, and we have set δ ) 1/2 fordisorder A. We consider an external field parallel to the chain.The case when the external field lies transversal to the chainwill not be reported in this work; nevertheless, our study showedthat in this case the corresponding disorder and multipolar effectsare similar but less pronounced. In Figure 12a, the extinctionfor an ordered NP chain for three different filling fractions isshown. In the ordered case and dilute limit (f f 0), the propermodes of the system become equal to the multipolar resonancesof the isolated sphere, where for small and medium fillingfractions the dipolar mode is dominant. For a finite f, theeigenmodes are shifted due to the coupling of the spheresthrough fields of the same multipolar order. Upon interaction,the individual multipolar character is lost. One should noticethat, due to the symmetry of the ordered chain, the interactingfields of multipoles of even order are canceled. Therefore, at f) 0.8 also the octupolar fields are important. As f increases,the proper modes have a monotonic red (blue) shift when thefield is parallel (transversal) to the chain. In Figure 12, weappreciate that the larger the disorder, the larger the shift, andthe multipolar fluctuations, instead of few resonances, excite acontinuum distribution of them. This makes the multipolarcoupling more efficient. In Figure 12b for disorder A moreFigure 12. Extinction efficiency of a 1D chain of metal NPs at different filling fractions, for an external field parallel to the chain axis. The upperpanels a-c correspond to the ordered chain and disorders A and B, respectively. The lower panels d-f corresponds to filling fractions f ) 0.3, 0.5,and 0.8, respectively.
3818 J. Phys. Chem. C, Vol. 111, No. 10, 2007 Noguezresonances are observed only at f ) 0.8, whereas for disorderB, shown in Figure 12c, the multipolar character is evident atany filling fraction. Notice that for larger filling fractions andgreater disorder the dipolar character of the resonant mode islost.In conclusion, we found that as the filling fraction increases,more multipolar interactions are present, for all the positionalarrangements. As the positional disorder increases, it alsoinduces the excitation of new multipolar contributions. It seemsthat the spectrum becomes wider as there is more “room’’ fordisorder. As a consequence, the inclusion of these multipolarmodes shifts the main peak to higher (lower) wavelengths andincreases the extension of the tail in the low (high)-wavelengthside, for an external field parallel (transversal) to the chain. Butthe most interesting thing is that there is not only a red shift ofthe peaks but also a drastic change in the profile. Furthermore,it was found that, due to the symmetry of the system, there isno coupling between the directions parallel and transversal tothe chain. This means that an external field parallel to the chainwill induce multipoles in each sphere, with an axis of symmetryalso parallel to the chain, but they will fluctuate in magnitudeand phase. These fluctuations cause the existence of a manifoldof collective modes with a continue range of resonant frequencies.VII. Summary and Future TrendsWe have studied the general behavior of the surface plasmonresonances on small metal NPs in terms of their shape andphysical environment. For instance, the location of theseresonances on NPs of different shapes has been studied andhas been found that NPs with fewer faces and sharper verticesshow resonances in a wider range of wavelengths. We alsoshowed that, when a NP is truncated, the main resonance isblue-shifted, overlapping secondary resonances and, therefore,increasing the full width at half-maximum. However, fordecahedral particles, the truncation to Marks and roundeddecahedra shows the same blue shift effect, but the full widthat half-maximum decreases, perhaps because the secondaryresonances no longer exist as the number of faces increases.We also explained in detail the optical anisotropy of elongatedNPs, such as, ellipsoids, decahedra, etc., where the dependenceof the position of the resonances is analytically explained interms of their aspect ratio.We have analyzed the case where noninteracting elongatedNPs are aligned in a given direction, such that, the opticalresponse can be tuned using polarized light and changing theaspect ratio. We also studied the case of a linear chain ofinteracting NPs, where again, the surface plasmon resonancesare sensitive to the light polarization, and their dependence withthe positional disorder of the particles. This 1D nanostructurescan be the starting point for more complex structures. Finally,the case of supported NPs was also studied. In this case, theline-shape of the spectra, and its relation with high-multipolarexcitation, is studied in detailed for ellipsoidal NPs. The opticalresponse is studied for different physical situations: as a functionof the distance between the particle and substrate, as well as interms of the anisotropy of the particle.This information would be useful to motivate the developmentof more complex nanostructures with tunable surface plasmonresonances. For this, it would be desirable to develop a simpletheory capable of predicting the position and strength of theSPRs of an ample variety of NPs shapes and physical environments.We have already mentioned that the spectral representationformalism completes with these characteristics, because itseparates the contribution of the dielectric properties from thegeometrical ones. We have shown the potentiality of this theory,that allows us to perform a systematic study of the opticalresponse of NPs, once a shape is chosen. However, explicitexpressions of the spectral representation are difficult to obtain,but alternative forms could be found.Acknowledgment. I am in debt to my many colleagues andstudents that have contributed along these years to the study ofthe optical response on nanoparticles. In particular, I would liketo acknowledge Professor Rubén G. Barrera and Dr. Carlos E.Román for their illuminating contributions in spectral representationformalism and substrate effects. I also want toacknowledge the contribution of Ana Lilia González in the studyof the polyhedral particles. Partial financial support fromCONACyT Grant Nos. 48521-F and 44306-F and DGAPA-UNAM Grant No. IN101605 is also acknowledged.References and Notes(1) Noguez, C.; Román-Velázquez, C. E. Phys. ReV. B 2004, 70,195412.(2) Intravaia, F.; Lambrecht, A. Phys. ReV. Lett. 2005, 94, 110404.(3) Xu, H.; Käll, M. Phys. ReV. Lett. 2002, 89, 2468021.(4) Ozbay, E. Science 2006, 331, 189.(5) Maier, S. A.; Kik, P. G.; Atwater, H. A.; Meltzer, S.; Harel, E.;Koel, B. E.; Requicha, A. A. G. Nat. Mat. 2003, 2, 229.(6) Maier, S. A.; Atwater, H. A. J. Appl. Phys. 2005, 98, 011101.(7) Zhang, Y.; Gu, C.; Schwartzberg, A.; Chen, S.; Zhang, J. Z. Phys.ReV. B2006, 73, 1654051.(8) Haynes, C. L.; McFarland, A. D.; Van Duyne, R. P. Anal. Chem.2005, 77, 338A.(9) Jin, R.; Cao, Y.; Mirkin, C. A.; Kelly, K. L.; Schatz, G. C.; Zheng,J.-G. Science 2001, 294, 1901.(10) Jin, R.; Cao, Y. C.; Hao, E.; Métraux, G. S.; Schatz, G. C.; Mirkin,C. A. Nature 2003, 425, 487.(11) Sönnichsen, C.; Reinhard, B. M.; Liphardt, J.; Alivisatos, A. P.Nat. Biotechnol. 2005, 33, 741.(12) Hibbins, A. P.; Evans, B. R.; Sambles, J. R. Science 2005, 308,670.(13) Liz-Marzán,L.M.Langmuir 2006, 22, 32.(14) Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Nature 2003, 424, 824.(15) Huang, X.; El-Sayed, I. H.; Qian, W.; El-Sayed, M. A. J. Am. Chem.Soc. 2006, 128, 2115.(16) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. J. Phys.Chem. B 2003, 107, 668.(17) Sosa, I. O.; Noguez, C.; Barrera, R. G. J. Phys. Chem. B 2003,107, 6269.(18) Noguez, C. Opt. Mat. 2005, 27, 1204.(19) Payne, E. K.; Shuford, K. L.; Park, S.; Schatz, G. C.; Mirkin, C.A. J. Phys. Chem. B 2006, 110, 2150.(20) Lee, K.-S.; El-Sayed, M. A. J. Phys. Chem. B 2005, 109, 20331.(21) Wang, Z. L. J. Phys. Chem. B 2000, 104, 1153.(22) Yacamán, M. J.; Ascencio, J. A.; Liu, H. B.; Gardea-Torresdey, J.J. Vac. Sci. Technol. B 2001, 19, 1091.(23) Yang, C. Y. J. Cryst. Growth 1979, 47, 274.(24) Kuo, C.-H.; Chiang, T.-F.; Chen, L.-J.; Huang, M. H. Langmuir2004, 20, 7820.(25) Wei, G.; Zhou, H.; Liu, Z.; Song, Y.; Wang, L.; Sun, L.; Li, Z. J.Phys. Chem. B 2005, 109, 8738.(26) Nilius, N.; Ernst, N.; Freund, H.-J. Phys. ReV. Lett. 2000, 84, 3994.(27) Gonzalez, A. L.; Noguez, C.; Ortiz, G. P.; Rodriguez-Gattorno, G.J. Phys. Chem. B 2005, 109, 17512.(28) Tao, A.; Sinsermsuksakul, P.; Yang, P. Angew. Chem., Int. Ed.2006, 45, 4597.(29) Baletto, F.; Ferrando, R. ReV. Mod. Phys. 2005, 77, 371.(30) Barnard, A. S.; Lin, X. M.; Curtiss, L. A. J. Phys. Chem. B 2005,109, 24465.(31) Román-Velázquez, C. E.; Noguez, C.; Garzón,I.L.J. Phys. Chem.B 2003, 107, 12035.(32) Sánchez-Castillo, A.; Román, Velázquez, C. E.; Noguez, C. Phys.ReV. B2006, 73, 045401.(33) Yao, H.; Miki, K.; Nishida, N.; Sasaki, A.; Kimura, K. J. Am. Chem.Soc. 2005, 127, 15536.(34) Negishi, Y.; Nobusada, K.; Tsukuda, T. J. Am. Chem. Soc. 2005,127, 5261.(35) Nobusada, K. J. Phys. Chem. B 2004, 108, 11904.
Page 3 and 4: 3808 J. Phys. Chem. C, Vol. 111, No
Page 11: 3816 J. Phys. Chem. C, Vol. 111, No

Surface Plasmons on Metal Nanoparticles - UNAM

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?