High-order nonlinearity of silia-gold nanoells in hloroform at 1560 nm E. L. Falão-Filho, 1 R. Barbosa-Silva, R. G. Sobral-Filho, A. M. Brito-Silva, A. Galembek, 3 and Cid B. de Araújo, 1,* 1 Departamento de Físia, Universidade Federal de Pernambuo, 50670-901, Reife, Pernambuo, Brazil Programa de Pós-Graduação em Ciênia de Materiais, Universidade Federal de Pernambuo, 50670-901, Reife, Pernambuo, Brazil 3 Departamento de Químia Fundamental, Universidade Federal de Pernambuo, 50670-901, Reife, Pernambuo, Brazil *id@df.ufpe.br Abstrat: The nonlinear response of silia - gold nanoells (SGNs) in hloroform was studied using laser pulses of 65 fs at 1560 nm. The experiments were performed using the thermally managed Z - san tehnique that allows measurements of the eletroni ontribution for the nonlinear response, free from thermal influene. The results were analyzed using an analytial approah based on the quasi - stati approximation that allowed extration of the nonlinear suseptibility of a SGN from the data. High third - order suseptibility, χ (3) = - 1.5 x 10 11 m /V, approximately four orders of magnitude larger than for gold nanospheres in the visible, and large fifth - order suseptibility, χ (5) = - 1.4 x 10 4 m 4 /V 4, were obtained. The present results offers new perspetives for nonlinear plasmonis in the near - infrared. 010 Optial Soiety of Ameria OCIS odes: (160.4330) Nonlinear optial materials; (190.3970) Miropartile nonlinear optis; (190.4710) Optial nonlinearities in organi materials; (40.6680) Surfae plasmons. Referenes and links 1. R. D. Averitt, S. L. Westott, and N. J. Halas, Linear optial properties of gold nanoells, J. Opt. So. Am. B 16(10), 184 183 (1999).. Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, Nanophotoni resent moon strutures with arp edge for ultrasensitive biomoleular detetion by loal eletromagneti field enhanement effet, Nano Lett. 5(1), 119 14 (005). 3. M.-R. Choi, K. J. Stanton-Maxey, J. K. Stanley, C. S. Levin, R. Bardhan, D. Akin, S. Badve, J. Sturgis, J. P. Robinson, R. Bair, N. J. Halas, and S. E. Clare, A ellular Trojan Horse for delivery of therapeuti nanopartiles into tumors, Nano Lett. 7(1), 3759 3765 (007) (and referenes therein). 4. D. Zhang, O. Neumann, H. Wang, V. M. Yuwono, A. Barhoumi, M. Perham, J. D. Hartgerink, P. Wittung- Stafede, and N. J. Halas, Gold nanopartiles an indue the formation of protein-based aggregates at physiologial ph, Nano Lett. 9(), 666 671 (009). 5. J. J. Penninkhof, L. A. Sweatlok, A. Moroz, H. A. Atwater, A. van Blaaderen, and A. Polman, Optial avity modes in gold ell olloids, J. Appl. Phys. 103(1), 13105 (008). 6. J. T. Seo, Q. Yang, W. J. Kim, J. Heo, S. M. Ma, J. Austin, W. S. Yun, S. S. Jung, S. W. Han, B. Tabibi, and D. Temple, Optial nonlinearities of Au nanopartiles and Au/Ag oreells, Opt. Lett. 34(3), 307 309 (009). 7. J. F. Li, Y. F. Huang, Y. Ding, Z. L. Yang, S. B. Li, X. S. Zhou, F. R. Fan, W. Zhang, Z. Y. Zhou, Y. Wu, B. Ren, Z. L. Wang, and Z. Q. Tian, Shell-isolated nanopartile-enhaned Raman spetrosopy, Nature 464(787), 39 395 (010). 8. T. Pham, J. B. Jakson, N. J. Halas, and T. R. Lee, Preparation and haraterization of gold nanoells oated with self-assembled monolayers, Langmuir 18(1), 4915 490 (00). 9. W. Stöber, A. Fink, and E. Bohn, Controlled growth of monodisperse silia spheres in the miron size range, J. Colloid Interfae Si. 6(1), 6 69 (1968). 10. C. A. R. Costa, C. A. P. Leite, and F. Galembek, Size dependene of Stöber silia nanopartile mirohemistry, J. Phys. Chem. B 107(0), 4747 4755 (003). 11. P. C. Lee, and D. Meisel, Adsorption and surfae-enhaned Raman of dyes on silver and gold sols, J. Phys. Chem. 86(17), 3391 3395 (198). 1. S. J. Oldenburg, S. L. Westott, R. D. Averitt, and N. J. Halas, Surfae enhaned Raman sattering in the near infrared using metal nanoell substrates, J. Chem. Phys. 111(10), 479 4735 (1999). (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 1636
13. A. Gnoli, L. Razzari, and M. Righini, Z-san measurements using high repetition rate lasers: how to manage thermal effets, Opt. Express 13(0), 7976 7981 (005). 14. L. A. Gómez, C. B. de Araújo, R. Putvinskis, Jr., S. H. Messaddeq, Y. Ledemi, and Y. Messaddeq, Nonlinear optial properties of antimony germanium sulfur glasses at 1560 nm, Appl. Phys. B 94(3), 499 50 (009). 15. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. van Stryland, Sensitive measurement of optial nonlinearities using a single beam, IEEE J. Quantum Eletron. 6(4), 760 769 (1990). 16. E. L. Falão-Filho, and C. B. de Araújo, and J. J. Rodrigues, High-order nonlinearities of aqueous olloids ontaining silver nanopartiles, J. Opt. So. Am. B 4(1), 948 956 (007). 17. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, Determination of bound-eletroni and free-arrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe, J. Opt. So. Am. B 9(3), 405 414 (199). 18. See for example: J. D. Jakson, Classial eletrodynamis (Wiley, New York, 1998). 19. A. E. Neeves, and M. H. Birnboim, Composite strutures for the enhanement of nonlinear-optial suseptibility, J. Opt. So. Am. B 6(4), 787 796 (1989). 0. Corning produt information data eet for standard silia (http://www.orning.om/dos/speialtymaterials/pieets/h0607_hpfs_standard_produtsheet.pdf). 1. A. Samo, Dispersion of refrative properties of solvents: Chloroform, toluene, benzene, and arbon disulfide in ultraviolet, visible, and near-infrared, J. Appl. Phys. 94(9), 6167 6174 (003).. R. W. Boyd, Nonlinear optis (Aademi, San Diego, 003). 3. H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, Origin of third-order optial nonlinearity in Au:SiO( ) omposite films on femtoseond and pioseond time sales, Opt. Lett. 3(5), 388 390 (1998). 4. N. E. Christensen, and B. O. Seraphin, Relativisti band alulation and the optial properties of gold, Phys. Rev. B 4(10), 331 3344 (1971). 5. F. Hahe, D. Riard, and C. Flytzanis, Optial nonlinearities of small metal partiles: surfae-mediated resonane and quantum size effets, J. Opt. So. Am. B 3(1), 1647 1655 (1986). 6. B. B. Baizakov, A. Bouketir, A. Messikh, and B. A. Umarov, Modulational instability in two-omponent disrete media with ubi-quinti nonlinearity, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 046605 (009). 7. M. Lewenstein, and B. A. Malomed, Spatiotemporal solitons in the Ginzburg Landau model with a twodimensional transverse grating, N. J. Phys. 11, 113014 (009). 8. D. Mihalahe, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, Spatiotemporal solitons in the Ginzburg Landau model with a two-dimensional transverse grating, Phys. Rev. A 81(), 05801 (010). 9. G. I. Stegeman, in Nonlinear optis of organi moleules and polymers, p.799, edited by H. S. Nalva and S. Miyata (CRC, Boa Raton, Fl., 1997). 30. K. Wang, H. Long, M. Fu, G. Yang, and P. Lu, Intensity-dependent reversal of nonlinearity sign in a gold nanopartile array, Opt. Lett. 35(10), 1560 156 (010). Loalized Surfae Plasmon (LSP) is the quanta of olletive eletron harge osillations in metalli nanopartiles. The LSP resonane frequeny depends on the nanopartile s ape as well as the dieletri funtions of the metal and the dieletri host. As a onsequene of the disontinuity of the dieletri funtion on the metal - dieletri interfae (MDI), the loal eletromagneti field on the interfae may be very large. Hene, the strong field may enhane the optial response of atoms or moleules loated near a MDI. This is one of the reasons that make omposite systems ontaining metalli nanopartiles attrative for tehnologial appliations. Indeed, the optial properties of suh systems an be engineered by new fabriation tehniques that allow a large variety of partile geometries with an exellent size - and - ape homogeneous distribution. For instane, silia - gold nanoell deserves partiular attention beause their LSP resonane is tunable from the visible towards the near - infrared as the ratio between the ell thikness and the ore diameter is redued [1]. Although the usefulness of SGNs in biophotonis has been well establied, relevane of the SGNs for nonlinear (NL) optis has not been fully reognized [ 7]. In this paper we report on the NL response of olloids ontaining silia - gold nanoells (SGNs) suspended in hloroform, using a laser operating at 1560 nm. A new synthesis proedure that allows fabriation of SGNs with narrow size distribution was developed and experiments were performed to determine the NL suseptibility of a single SGN. Large values for the SGN suseptibility were measured and the results herein reported indiate possible suessful uses of SGNs for appliations in teleom devies. The syntheti route was based on the method desribed by Pham et al [8] with modifiations. The method omprises (i) Stöber silia preparation; (ii) Stöber silia funtionalization with 3-aminopropyl-trimethoxysilane (APTMS); (iii) gold nanopartiles (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 1637
preparation; (iv) gold nanopartiles attahment to silia (to obtain nanoislands) and, (v) gold nanoells growth. Stöber silia nanopartiles [9] were synthesized by alkaline hydrolysis of tetraethylorthosiliate (TEOS) with aqueous ammonia solution, in ethanol under soniation [10] to give 10 ± 1 nm silia nanopartiles, whih were waed thoroughly to remove the ammonia exess and dried. The resulting powder (0.7 g) was dispersed in toluene (100 ml) together with APTMS (00 µl), stirred at room temperature for 3 hours and refluxed for 9 hours. Gold nanopartiles were synthesized starting from a 0 mm HAuCl4 aqueous solution. Sodium borohydride was used as reduing agent and poly(vinyl-pyrrolidone) (PVP, ~55000 g.mol 1 ) as the stabilizing agent. The synthesis was performed at room temperature under strong stirring to give the.0 ± 0.3 nm nanopartiles [11]. Nanoislands were formed by mixing the gold olloid (30 ml) and APTMS-funtionalized Stöber silia olloids (3.0 ml) at room temperature under stirring for hours. The nanoislands were separated from unattahed gold nanopartiles by entrifugation. TEM images of the nanoislands are presented in Figs. 1 (b); the gold nanopartiles are very well dispersed in the silia surfae. In order to obtain gold nanoells, 1 µl of the nanoisland olloid (5.0 10 11 partiles/ml) was added to 8 ml of a K-gold solution [1]. Formaldehyde (70 µl) was then added under vigorous stirring for 4 minutes and the olloid left under rest for two hours. The resulting nanoells are presented in Fig. 1 () and 1 (d). The average partile size is 160 ± 16 nm, whih means that the ell thikness is 0 nm. For the NL experiments the samples were entrifuged several times in order to eliminate residual water and the partiles were re-suspended in hloroform (CHCl 3 ), whih presents small absorption at 1560 nm. Fig. 1. Eletron mirosope images of the nanopartiles. (a) Silia ore (average diameter: ~10 nm). (b) Silia - APTMS - gold nanopartiles (average diameter: ~160 nm). () and (d) Silia - gold nanoells (average diameter: ~160 nm). Figures 1(a) to 1() were obtained using a 100 kv transmission eletron mirosope. Figure 1(d) was obtained using a 00 kv sanning eletron mirosope. The absorption spetrum of pure hloroform is own in Fig. (red line) and the extintion spetrum of the SGNs, obtained for a olloid with filling fration f = 3 10 5, using the CHCl 3 spetrum as blank, is represented by the blue line in Fig.. The LSP resonane, entered at 830 nm, is in agreement with the relative sizes of ore and ell thikness [1]. (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 1638
Fig.. Absorption oeffiient of CHCl 3 in a 10 mm uvette (red line) and extintion oeffiient of SGNs - CHCl 3 olloid (blue line) using CHCl 3 as blank. The SGNs filling fration is 3 10 5. For the NL experiments we used a fiber laser (1560 nm; 65 fs; 50 MHz) operating in the TEM 00 mode (M =1.08). The SGNs - CHCl 3 olloid presents a linear absorption oeffiient of 0.49 m 1 at 1560 nm. Due to the large laser repetition rate thermal lensing may be indued; then, in order to obtain results not influened by thermal effets and to determine the atual eletroni NL response, we applied the Thermally Managed Z-san (TM - Z san) tehnique [13, 14]. The TM - Z san tehnique is a variation of the well known Z-san tehnique [15] and onsists in aquiring the time evolution of the NL transmittane signal when the sample is plaed in pre-foal and post-foal positions with respet to the inident beam fous (usually in the positions orresponding to the peak and valley of the Z-san profile). The light indued refrative index is determined from measurements of T PV, the peak - to - valley differene in the samples transmittane. As in the onventional Z-san tehnique, using an iris plaed in front of the photodetetor, in the far - field, it is possible to infer sign and magnitude of the NL refrative index. The experiments made without an iris, olleting all light transmitted by the sample, allow measurements of the NL absorption oeffiient [13 15]. The time evolution of T PV is obtained by introdution of a hopper in the onventional Z - san setup as in refs [13, 14]. Then, the time resolution is determined by the hopper opening time, whih depends on the finite size of the beam waist on the hopper wheel. The time behavior of the NL signal is determined by delaying the signal aquisition time with respet to the instant t = 0, whih is determined by the opening time of the hopper. An exponential urve is used to fit the experimental data and to determine the normalized transmittane free of thermal effets at t = 0 [13,14]. The TM - Z san results were obtained using a 1 mm thik glass uvette. The laser was foused using a 7 m foal - length lens and the beam waist was 3 µm. The opening time of the hopper was 10 µs and the iris plaed in front of the far - field detetor orresponds to light transmittane S = 0.00. Figures 3(a) and 3(b) ow the TM - Z san urves obtained at different times for pure CHCl 3 and for the SGNs - CHCl 3 olloid, respetively. Negative NL refrative index is observed in both ases but the signal in the presene of the SGNs is larger at all times. Figures 3() and 3(d) ow the time evolution of the transmittane signal with the sample at positions orresponding to the minimum and maximum transmittane for pure hloroform and for the SGNs - CHCl 3 olloid, respetively. The red and the blue lines orrespond to the experimental data and the blak line represents the best numerial fit using a single exponential funtion. The data were taken using the maximum laser intensity, I, equal to 1. and 1.0 GW/m for pure hloroform and for the SGNs - CHCl 3 olloid, respetively. It was observed that for pure hloroform the ratio T PV / I is onstant in the range 0.1 < I < 1.0 GW/m, as is expeted for a third - order NL material. Extrapolating the urves of Fig. 3() to t = 0, we get T PV = 0.016 and using Eq. (13) of ref [15]. we obtain n = 0.8 10 18 (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 1639
m /W, whih orresponds to χ h (3) = 0.6 10 0 m /V, for pure hloroform. However, T PV / I for the SGNs - CHCl 3 olloid, for very ort times, depends on the laser intensity indiating that higher order eletroni nonlinearities may be ontributing for the results. The extrapolated results for t = 0 are given in Fig. 4 owing a linear dependene of T PV / I versus I. Indeed, in ases where the third- and the fifth - order ontributions are present it is expeted a straight line with nonzero angular oeffiient for T PV / I as a funtion of I [16, 17]. Figure 4 also ows the dependene of T PV / I versus I for t = 0.95 ms. In this ase, a onstant ratio T PV / I versus I is observed beause the thermal ontribution is dominant. Spetra of linear absorption were obtained before and after eah Z-San measurement and no hanges were observed in the results. This indiates that no relevant hanges due to indued photohemial proess are ourring in our samples. The experiments made without an iris in front of the detetor indiate that the NL absorption oeffiient is smaller than the minimum that our apparatus an measure (0.1 m/gw). Fig. 3. Thermally Managed Z-san results. Figures 3(a) and 3(b) ow Z-san profiles obtained at t = 0.10, 0.40, 0.65, 0.95 ms; for pure hloroform and for the olloid, respetively. Figures 3() and 3(d) ow the time evolution of the transmittane signal with the sample at positions orresponding to the minimum and maximum transmittane for pure hloroform and for the SGNs - CHCl 3 olloid, respetively. The data were obtained using a 1 mm thik uvette and intensities at the fous of 1. and 1.0 GW/m for pure hloroform and SGNs - CHCl 3 olloid, respetively. Considering small NL phase distortions, small iris transmittane (S << 1), and the peak - to - valley separation, Z PV, given by 1.4 times the Rayleigh length, the dependene of T PV / I an be desribed by [16, 17]: TPV (1) () k0[0.396 nleff + 0.198 n4 Leff I], (1) I where L eff (m) = [1 exp( m α 0 L)]/(m α 0 ) with m = 1,; n (m /W) = 3Re[χ eff (3) ]/(4ε 0 n 0 ); and n 4 (m 4 /W ) = 5Re[χ eff (5) ]/(4ε 0 n 0 3 ), with χ eff (3) and χ eff (5) being the effetive third- and fifth - order suseptibility, respetively. The results obtained for the SGNs - CHCl 3 olloid with f = (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 1640
3 10 5 were n = 6.0 10 18 m /W and n 4 = + 8.6 10 31 m 4 /W whih orrespond to χ eff (3) = 4.4 10 0 m /V and χ eff (5) = + 1.4 10 35 m 4 /V 4. Fig. 4. Intensity dependene of T PV / I as a funtion of I for t = 0.95 ms (blak irles) and for t = 0 ms (blue squares). Red lines represent numerial fits to the data. In order to determine the nonlinearity of a single SGN we onsidered the quasistati approximation [18] and developed an extension of the previous theories for metalli nanoells [1,19], inluding the ontribution of the fifth - order suseptibility. Considering the ore - ell geometry, the filling fration f << 1, and an external eletri field, E 0, the sample polarization an be written as N 1 P P= Ph + pi, V i = 1 where N P is the total number of partiles in a volume V, P h is the host polarization and p i is the indued dipole moment of eah SGN that an be written as p = ( ε α ) E, (3) i h i where ε h is the dieletri funtion of the host medium and α i is the partile polarizability given by [19]: ε [ ε (3 R) + ε R] ε h[ ε R+ ε (3 R)] αi = 3 υi, ε [ ε (3 R) + ε R] + ε h[ ε R+ ε (3 R) where υ i is the volume oupied by eah SGN and R = 1 (r /r ) 3, where r and r represent the ore and the external ell radius, respetively. ε (ε ) is the ell (ore) dieletri funtion. Due to the metalli ielding effet whih redues the magnitude of the eletri field in the ore and to the fat that silia presents small nonlinearity, the dominant NL ontribution omes from the gold ell. Thus, negleting the ore nonlinear response, the NL ontribution for the dieletri funtion of the SGN may be written as 0 ( NL) 3 (3) 5 (5) ε = χ E + χ E, (5) 4 8 () (4) (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 1641
with E representing the mean modulus squared of the eletri field inside the ell, that is given by E = E 0 g(r, r ) / β, where and ε + d ε h β =, 3a ε h (6) 3 6 r 1 1 ( a b+ ab ) r 1 1 b 5 5 r r r a r r r a g( r, r ) = 1 + +, 4( r r ) ( r r ) with a = ε + ε ; b = ε ε ; = (3 R)ε + Rε ; and d = Rε + (3 R)ε. Introduing Eq. (5) in Eq. (4) and expanding Eq. (4) up to seond order in E, we obtain and χ (3) (3) R g( r, r ) ε + d ε (3) χeff = χh + f χ, (8) β β a R [ g( r, r )] ε + d ε (5) (5) eff = f χ 4 β β a (9) 3 ( ε + d ε ) + 18 ε ( R 1)( ε + ε ε h ) (3) [ χ ], 10 a ( ε + d ε h ) where χ h (3) is the host third - order NL response. The SGN suseptibilities an be determined from Eqs. (8) and (9) onsidering ε =.085 [0], ε h =.055 [1], ε = 115.74 + i 19.48 [1], and χ h (3) = 0.6 10 0 m /V. The results are χ (3) = 1.5 10 11 m /V and χ (5) = 1.4 10 4 m 4 /V 4. An interesting point to notie is the magnitude of χ (3) whih is 9 orders of magnitude larger than χ h (3). This giant nonlinearity is attributed to the high polarizability of gold at 1560 nm whose dieletri funtion, ε = 117, is one order of magnitude higher than in the visible range. Hene, onsidering Miller s rule [], χ (3) χ (1) 4, it is expeted a suseptibility enhanement of 10 4 in omparison to the gold NL suseptibility in the visible. Indeed, from experiments in the visible range with 00 fs laser pulses [3], values of χ (3) =.1 10 15 m /V were obtained for gold nanospheres and this result is 10 4 times smaller than the value of χ (3) determined in the present work. For a quik disussion about the different eletroni ontributions to the nonlinear response of the gold nanoells, it is well know, from the band alulations, that the outermost d and s eletrons of gold atoms originate the d-bands, 5 bands fairly flat whih lie a few ev below the Fermi level, and the ondution band or s-p band whih presents roughly a paraboli dispersion relation and exhibits almost a free-eletron-like behavior. Thus, the optial properties of bulk gold are mainly assoiated to s-p intraband transitions and also to interband transitions between the d and s-p bands [4, 5]. Aordingly, in general, the experimental dieletri permittivity of gold is deomposed into the interband and the Drude ontributions, where this last is related to the s-p intraband transitions. Due to the thikness of the gold ell (0 nm) and the fat that the eletron has a mean free path of about 4 nm in gold at room temperature, the damping rate Γ in the Drude model has to be orreted by a fator proportional to d /V F, where d is the ell thikness and V F is the Fermi veloity (1.4 10 6 m/s) [1]. This orretion introdues, for free eletrons, a relaxation mehanism assoiated to the eletron-interfae sattering at the inner and outer interfaes of the metal (7) (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 164
layer. However, the major aspets related to the eletroni transitions still mainly determined by the bulk band-struture of gold. Another mehanism whih may ontribute to the ell nonlinearities is the hot eletron ontribution. The hot eletron ontribution is assoiated to the heating of the free eletron gas due to the fration of the laser light absorbed by the metal. This ontribution exhibits strong dependene with pulse duration, photon energy and laser intensity. In general the hot eletron ontribution is more pronouned for wavelengths lose to the Plasmon resonane. Beause the exitation of the samples was made with photons of 0.795 ev, we disregard the interband ontributions. Indeed, in order to indue the eletroni transition between the d- bands and the ondution band, the photon energy has to be larger than 1.7 ev, whih orresponds to the bandgap at the X point of the first Brillouin zone in gold [4]. However, due to the density of states of gold whih exhibits a large number of unoupied states for energies above.38 ev, the interband transitions aount signifiantly to the dieletri permittivity of gold typially for photon energies higher than ~.4 ev. Thus, we attribute the NL optial response of the olloid in this experiment to ontributions of intraband transitions and the hot-eletrons. In partiular, sine that it is possible to explain the magnitude of χ (3) in terms of the gold polarizability, i.e., by the free eletron response, the dominant ontribution for the nonlinear proess probably is the intraband transitions. Indeed the intraband ontribution ould exhibits a dependene with λ 8 [5], then onsidering a fator of 3 relative to the differene of wavelength from the visible to the infrared, one more, we obtain a fator of ~10 4 of gain in magnitude for χ (3). Conerning the fifth order nonlinearity we reall that in olloidal systems, the presene of relevant χ (5) eff was already demonstrated in silver olloids exited at 53 nm [16]. In that ase the role played by the asade proess orresponding to the [χ (3) ] term in Eq. (9), was not relevant and the fifth - order response was dominated by the intrinsi fifth - order suseptibility, χ (5). In the present ase, although χ (5) has large negative value the value of χ (5) (5) eff, obtained from Eq. (9), have opposite sign to χ being dominated by the term assoiated to the loal field fator, i.e., the term ontaining [χ (3) ]. The presene of relevant effetive fifth - order nonlinearity in the SGN - CHCl 3 olloid deserves further omments. In general, materials exhibiting ubi - quinti nonlinearity are attrative due to ompetitive proesses assoiated to different NL orders that an play an important role on light propagation effets. For example, the ombined ontribution of the ubi - quinti nonlinearity may indue modulational instability in some regions of the parameters spae, whereas the individual ation of the ubi or quinti nonlinearity does not lead to instabilities [6]. Also, based on studies of soliton propagation in suh media, the reation of entanglement states between solitons an be onsidered [7]. Another interesting subjet is the formation of robust D arrays of solitons and vorties built in materials featuring the ubi - quinti nonlinearity [8]. With basis on the NL parameters reported here, we evaluate the SGNs - CHCl 3 olloid as promising system for suh studies. Besides the high NL response of the SGN, one important point to understand is that at 1560 nm the eletri field inside the ell is muh smaller than for silver and gold nanospheres in the visible range, for frequenies near the LSP resonane. This is beause for the infrared light the free eletrons in the SGN sreen more effiiently the infrared light eletri field than the visible light field. As a onsequene, the enhanement of the SGN suseptibility is ompensated by the small eletri field inside the partile providing an effetive NL suseptibility for the SGNs - CHCl 3 olloid, at the infrared, that is omparable to the result obtained for gold nanospheres olloids in the visible. However, we reall that the LSP resonane of a SGN an be tuned from the visible towards the near - infrared (inluding the teleommuniation wavelength range) and the drawbak of a small eletri field inside the metalli ell an be overome when performing experiments in the infrared. This may allow fabriation of omposite materials with large effetive nonlinearity that may be very attrative for all - optial swithing appliations. In this sense we onsider that the present results may open new doors for appliations of SGNs omposites in teleom devies. For example, in order to evaluate the performane of the SGNs omposites in all-optial swithing devies we (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 1643
reall that suitable materials for suh appliation must have n values large enough to ahieve swithing for a sample thikness omparable to the absorption length. Aordingly, a good material for all-optial swithing using the NL Fabry-Perot onfiguration ould satisfy W = n I 0 / (λ α 0 ) > 0.7 [9, 30]. The figure-of-merit to evaluate the material performane with respet to the two-photon absorption is T = α λ / n whih has to be smaller than 1, irrespetive of the devie [9, 30]. Assuming I 0 = 0.1 GW/m and α = 0.1 m/gw we obtain W = 8.8 10 3 and T = 0.05 whih are exellent values. These numbers ows that SGNs omposites an be as ompetitive for photoni appliations as Ge-As-Se-based glasses or systems ontaining arbon nanotubes, but it has the great apability of tuning the LSP resonane whih turns SGNs omposites in a very versatile system suited for different kinds of photoni appliations. Aknowledgments We aknowledge the partial support reeived from the Brazilian agenies Conselho Naional de Desenvolvimento Científio e Tenológio (CNPq) and Fundação de Amparo à Ciênia e Tenologia do Estado de Pernambuo (FACEPE). The work was performed under the Photonis National Institute of Siene and Tehnology Projet (INCT de Fotônia) and the Nanophotonis Network, supported by the Brazilian Ministry of Siene and Tehnology. (C) 010 OSA 11 Otober 010 / Vol. 18, No. 1 / OPTICS EXPRESS 1644