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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 17 — Aug. 17, 2009
  • pp: 15032–15042
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Structural control of nonlinear optical absorption and refraction in dense metal nanoparticle arrays

Dana C. Kohlgraf-Owens and Pieter G. Kik  »View Author Affiliations


Optics Express, Vol. 17, Issue 17, pp. 15032-15042 (2009)
http://dx.doi.org/10.1364/OE.17.015032


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Abstract

The linear and nonlinear optical properties of a composite containing interacting spherical silver nanoparticles embedded in a dielectric host are studied as a function of interparticle separation using three dimensional frequency domain simulations. It is shown that for a fixed amount of metal, the effective third-order nonlinear susceptibility of the composite χ(3)(ω) can be significantly enhanced with respect to the linear optical properties, due to a combination of resonant surface plasmon excitation and local field redistribution. It is shown that this geometry-dependent susceptibility enhancement can lead to an improved figure of merit for nonlinear absorption. Enhancement factors for the nonlinear susceptibility of the composite are calculated, and the complex nature of the enhancement factors is discussed.

© 2009 OSA

1. Introduction

Recently a surge of interest has occurred in the theory, fabrication and characterization of metamaterials: micro- and nano-structured materials with properties significantly different from their constituents, for example negative index materials [1

1. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]

3

3. H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007). [CrossRef] [PubMed]

] and cloaking devices [4

4. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

,5

5. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

]. One specific thrust focuses on the design of highly nonlinear optical materials [6

6. K. Tsuchiya, S. Nagayasu, S. Okamoto, T. Hayakawa, T. Hihara, K. Yamamoto, I. Takumi, S. Hara, H. Hasegawa, S. Akasaka, and N. Kosikawa, “Nonlinear optical properties of gold nanoparticles selectively introduced into the periodic microdomains of block copolymers,” Opt. Express 16(8), 5362–5371 (2008). [CrossRef] [PubMed]

] based on nanocomposites. A possible approach to obtaining a large nonlinear optical response involves taking advantage of the strong local electric fields that can be achieved in and around plasmon resonant metal nanoparticles. Since the enhancement of the third-order nonlinear susceptibility scales with the fourth power of the electric field [7

7. J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46(3), 1614–1629 (1992). [CrossRef] [PubMed]

9

9. D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988). [CrossRef]

], these resonantly enhanced local fields can dramatically increase the nonlinear response of a composite compared to that of its constituent materials. Such plasmon enhanced metal-dielectric composites have many potential optical applications; for example for enhanced two-photon fluorescence [10

10. H. Ditlbacher, N. Felidj, J. R. Krenn, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Electromagnetic interaction of fluorophores with designed two-dimensional silver nanoparticle arrays,” Appl. Phys. B 73(4), 373–377 (2001). [CrossRef]

12

12. W. Wenseleers, F. Stellacci, T. Meyer-Friedrichsen, T. Mangel, C. A. Bauer, S. J. K. Pond, S. R. Marder, and J. W. Perry, “Five Orders-of-Magnitude Enhancement of Two-Photon Absorption for Dyes on Silver Nanoparticle Fractal Clusters,” J. Phys. Chem. B 106(27), 6853–6863 (2002). [CrossRef]

] or as optical switches [13

13. X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008). [CrossRef]

15

15. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73(10), 1368–1371 (1994). [CrossRef] [PubMed]

], and nonlinear optical absorption [16

16. D. C. Kohlgraf-Owens and P. G. Kik, “Numerical study of surface plasmon enhanced nonlinear absorption and refraction,” Opt. Express 16(14), 10823–10834 (2008). [CrossRef] [PubMed]

,17

17. G. Piredda, D. D. Smith, B. Wendling, and R. W. Boyd, “Nonlinear optical properties of a gold-silica composite with high gold fill fraction and the sign change of its nonlinear absorption coefficient,” J. Opt. Soc. Am. B 25(6), 945–950 (2008). [CrossRef]

]. The latter application in particular requires materials that provide significant linear transmission, while exhibiting large optical absorption under high incident irradiance. Several studies have considered the nonlinear effective medium properties of such metal-dielectric composites either experimentally or theoretically. Reports indicate that while the addition of metal leads to significant linear absorption, the composite nonlinear response can be increased with respect to the linear absorption, for example, by increasing the volume filling fraction of the nanoparticles [18

18. H. B. Liao, W. Wen, and G. K. L. Wong, “Preparation and characterization of Au/SiO2 multilayer composite films with nonspherical Au particles,” Appl. Phys., A Mater. Sci. Process. 80(4), 861–864 (2005). [CrossRef]

,19

19. N. Pinçon, B. Palpant, D. Prot, E. Charron, and S. Debrus, “Third-order nonlinear optical response of Au:SiO2 thin films: Influence of gold nanoparticle concentration and morphologic parameters,” Eur. Phys. J. D 19, 395–402 (2002). [CrossRef]

], by increasing host refractive index [20

20. O. Maruyama, Y. Senda, and S. Omi, “Non-linear optical properties of titanium dioxide films containing dispersed gold particles,” J. Non-Cryst. Solids 259(1-3), 100–106 (1999). [CrossRef]

,21

21. G. Ma, W. Sun, S.-H. Tang, H. Zhang, Z. Shen, and S. Qian, “Size and dielectric dependence of the third-order nonlinear optical response of Au nanocrystals embedded in matrices,” Opt. Lett. 27(12), 1043–1045 (2002). [CrossRef]

], and by increasing the aspect ratio of spheroidal metal particles [22

22. J. Jayabalan, A. Singh, R. Chari, and S. M. Oak, “Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs,” Nanotechnology 18(31), 315704 (2007). [CrossRef]

]. However, no systematic studies appear to exist on the effect of interparticle interactions in metal dielectric composites.

In the present study we investigate the nonlinear optical properties of a nanocomposite consisting of spherical silver nanoparticles arranged in a regular lattice, with a lattice spacing that is sufficiently small to prevent diffractive effects. The linear and nonlinear optical properties of these composites are studied as a function of interparticle interaction, which is varied by changing the lattice spacing while maintaining a fixed metal volume fraction. The effective optical properties are determined using numerical simulations of the three dimensional electric field distribution in the composite under plane wave excitation. We show that changing the nanoparticle arrangement significantly increases the complex nonlinear refractive index with respect to the linear absorption. The feasibility of experiments demonstrating the presence of a surface plasmon enhanced host nonlinear optical response is discussed.

2. Theory

The composite linear dielectric function εc of an isotropic composite with a position dependent isotropic dielectric function ε(ω,r) can be obtained based on a known linear electric field distribution of the form E(ω,r)eiωt within a volume V using the following relation [23

23. O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers,” Phys. Rev. B 56(13), 8035–8046 (1997). [CrossRef]

]:

εc(ω)=ε(ω,r)E(ω,r)2VE(ω,r)V2.
(1)

Here E(ω,r) is the position dependent complex electric field in the composite, the notation ...V represents spatial averaging over volume V, and the notation E2 represents taking the dot product EE. Note that this dot product yields a complex number with a phase angle that is twice that of the original electric field vector, which will become important in this study. For simplicity of notation, frequency and position arguments are omitted in the remainder of this manuscript. The definition of the effective dielectric function given in Eq. (1) follows from the requirement of equal energy density in the effective medium and the composite. Note that identical results can be obtained by using the more common assumption of equal electric displacement in the effective medium and in the composite, as was confirmed in numerical evaluation of simulated electric field data using both approaches (data not shown). In the case of a dilute random distribution of isolated isotropic spherical nanoparticles in an isotropic host, Eq. (1) leads to the well-known Maxwell Garnett result [24

24. J. C. M. Garnett, ““Colours in Metal Glasses and in Metallic Films,” Philos. Trans. R. Soc. London Ser. A 203(1), 385–420 (1904). [CrossRef]

]. Here we consider binary composites containing spherical inclusions of a material with an isotropic dielectric function εin embedded in a host material with an isotropic dielectric function εh. We limit our study to composites in which the inclusions are arranged in a rectangular lattice, and consider optical excitation with electric fields aligned with one of the principal axes of the lattice. In this specific case, Eq. (1) provides only a single diagonal element of the dielectric tensor of the anisotropic effective medium.

Analogous to the approach shown for the composite dielectric function, the effective complex third order nonlinear susceptibility of an isotropic composite χc (3)(ω) can be determined based on a known linear electric field distribution for the composite using the following relation [9

9. D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988). [CrossRef]

,23

23. O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers,” Phys. Rev. B 56(13), 8035–8046 (1997). [CrossRef]

,25

25. H. R. Ma, R. F. Xiao, and P. Sheng, “Third-order optical nonlinearity enhancement through composite microstructures,” J. Opt. Soc. Am. B 15(3), 1022–1029 (1998). [CrossRef]

]:
χc(3)(ω)=χ(3)(ω,r)|E|2E2V|EV|2EV2
(2)
where χ(3)(ω,r) represents a position-dependent isotropic Kerr-type third order nonlinear susceptibility at the fundamental frequency. Equation (2) was derived based on the assumption that the nonlinear polarization response is sufficiently small to be considered a perturbation on the linear response. In this study we focus on the effect of local electric field enhancement on the nonlinear refractive and absorptive properties of the composite, and ignore higher harmonic effects such as third harmonic generation. For the more general case of an anisotropic composite under monochromatic excitation, χc (3)(ω) must be represented by a complex fourth rank tensor. In this study we derive the effective χc (3) only for excitation along one of the principal axes of the simulated structure, here the x-direction. In this specific case Eq. (2) provides only the tensor component χc,xxxx (3), which in the following will be denoted χc (3). Given this simplified notation, it is important to keep in mind that the calculated susceptibilities do not represent an effective isotropic nonlinear susceptibility, but instead represent the calculated χc (3) for excitation with a specific electric field direction with respect to a highly symmetric structure.

For a binary composite in which the inclusion and host materials have an isotropic Kerr-type third order nonlinear susceptibility χin (3) and χh (3) respectively, it can easily be shown that Eq. (2) can be written in the following form:
χ(3)=fingin(3)χin(3)+fhgh(3)χh(3)
(3)
where fin is the volume fraction of the inclusion in the composite, fh is the volume fraction of the host material given by fh = 1 - fin, and the factors gj(3) represent susceptibility enhancement factors that satisfy the following relation:
gj(3)=E2|E|2VjEV2|EV|2.
(4)
The subscript j represents either the inclusion (‘in’) or the host (‘h’). It is important to note that the numerator is averaged over a limited volume Vj indicating the volume of the inclusion or the host respectively. From Eq. (3) the factors gj(3) can be seen to represent the enhancement of the third order susceptibility contribution from host and inclusion, relative to the value expected based on a homogeneous electric field distribution throughout the volume. Note that another common definition of the enhancement factor considers the volume fraction f as part of the enhancement factor, see e.g. Ref [8

8. M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: Dipolar spectral theory,” Phys. Rev. B 60(24), 17071–17083 (1999). [CrossRef]

]. Although the latter approach certainly provides valid results, we favor the definition shown in Eq. (3) as it more clearly highlights the contribution of the electric field redistribution to the χ(3) enhancement, even for components with a small fill-fraction.

Based on the calculated composite nonlinear susceptibility χc (3) one can obtain the composite nonlinear refractive index η2,c = n2,c + 2,c where n2,c and κ2,c represent the real and imaginary parts of the nonlinear refractive index. In highly absorptive composites the conversion from χc (3) to the nonlinear refractive index η2 must take into account linear loss in the composite [26

26. R. del Coso and J. Solis, “Relation between nonlinear refractive index and third-order susceptibility in absorbing media,” J. Opt. Soc. Am. B 21(3), 640–644 (2004). [CrossRef]

] which has been shown to lead to the relation η2,c=(3/(4ε0c|ηc|2))(1i(κc/nc))χc(3) where ε0 is the permittivity of vacuum, c is the speed of light in vacuum, ηc is the complex linear refractive index of the composite, and nc and κc are the real and imaginary parts of ηc. The thus obtained nonlinear refractive index can be used to determine the nonlinear absorption coefficient of the composite βc according to βc = (4π/λ) κ2,c with λ the free space wavelength. Finally, using the calculated linear and nonlinear optical properties one can obtain the frequency dependent figure of merit for nonlinear absorption given by β/α. This figure of merit reflects the fact that high nonlinear absorption requires both a high β value as well as a low linear absorption to enable a long interaction length. This figure of merit is especially relevant in metal dielectric composites, where plasmon enhanced linear absorption will significantly affect the figure of merit.

3. Simulation geometry

For all simulations, we consider arrays of spherical silver nanoparticles embedded in a host with a frequency independent real refractive index of 1.5. This index is chosen as a typical value of commonly used host materials at visible frequencies, similar to that of for example SiO2 (n = 1.45), many organic polymers (n ~1.4-1.6), and soda lime glass (n = 1.52). For the linear silver dielectric properties we use a surface scattering corrected Drude model fit of available literature values [27

27. P. B. Johnson and R. W. Christy, “Optical-Constants Of Noble-Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

] given by εin = ε - ωp2/(ω2 + iω(Γ0 + Γs)) where ε = 5.451, ωp = 1.474 × 1016 rad/s, and the bulk electron scattering rate Γ0 = 8.354 × 1013 s−1. The surface scattering rate Γs is given by Γs = Aυf/r = 2.8 × 1014 s−1, where A is set to 1, υf = 1.39 × 106 m/s is the Fermi velocity in silver, and r = 5 nm is the radius of the particle. This particle radius allows the use of sufficiently small interparticle separations to consider the composite as an effective medium in the wavelength range of interest. Note that this choice makes surface scattering the dominant contribution to the total electron damping.

4. Results and discussion

Figure 2
Fig. 2 Linear absorption of rectangular arrays of interacting spherical Ag particles. Symbols represent numerically computed values and are connected by a spline fit. The unit cells and the corresponding incident field polarization are shown schematically in the x-y plane.
shows the linear absorption coefficient as calculated using Eq. (1) based on the simulated three-dimensional electric field data, evaluated for several frequencies of the incident plane wave. Each of the curves in Fig. 2 corresponds to one of the five interparticle spacings considered. The locations of the symbols indicate the frequency samples at which the field distribution and the corresponding optical properties were evaluated. For comparison, the dashed line labeled ‘MG limit’ shows the analytical result obtained using Maxwell Garnett (MG) theory for this fill fraction. The observed absorption peaks are due to the resonant excitation of approximately dipolar plasmon modes on the metal nanoparticles, leading to resonantly enhanced energy dissipation. As the longitudinal interparticle separation is reduced, a red-shift is observed in the location of the plasmon resonance compared to the Maxwell Garnett result. Conversely, at large longitudinal interparticle spacing (and small transverse interparticle spacing) a blue-shift is observed. These are well known effects that can be understood in terms of near-field interactions between neighboring metal nanoparticles [29

29. S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss,” Appl. Phys. Lett. 81(9), 1714–1716 (2002). [CrossRef]

]. Consequently these resonance must be interpreted as collective plasmon resonances of the lattice, rather than as individual nanoparticle plasmon resonances. The maximum linear absorption coefficient is seen to increase slightly as the longitudinal interparticle spacing is reduced. Finally, the analytical Maxwell Garnett result is seen to lie close to the numerically computed absorption coefficient for Lx = 24 nm (square arrangement), indicating that interparticle interactions are minimal in this specific geometry.

Figure 3
Fig. 3 Complex geometry-dependent nonlinear susceptibility enhancement factor gh (3) for different frequencies of the incident plane wave, showing (a) the phase angle of the complex enhancement factor, and (b) the magnitude of the enhancement on a logarithmic scale. The dashed curves show the corresponding analytically obtained results for non-interacting particles (MG limit). The inset shows the real (solid line) and imaginary (dotted line) enhancement factors on a linear scale for the case of non-interacting particles.
shows the complex geometry-dependent nonlinear susceptibility enhancement factor gh (3) calculated based on the simulated three-dimensional electric field data using Eq. (4), for different frequencies of the incident plane wave. Figure 3(a) shows the phase angle of the complex enhancement factor, and Fig. 3(b) shows the magnitude of the enhancement on a logarithmic scale. The dashed curve shows the corresponding results calculated using an analytic expression for the third order nonlinear susceptibility of composites consisting of non-interacting particles [8

8. M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: Dipolar spectral theory,” Phys. Rev. B 60(24), 17071–17083 (1999). [CrossRef]

]. The inset in Fig. 3(b) shows the real and imaginary part of the enhancement factor on a linear scale for the non-interacting particles. Note that the analytical curve closely resembles our numerically obtained results for Lx = 24 nm in terms of magnitude, shape, and resonance frequency, showing that inter-particle interactions only weakly affect the nonlinear response in this particular geometry. For all geometries a significant nonlinear susceptibility enhancement (g (3) > 1) is observed across a large frequency bandwidth near the plasmon resonance, with maximum enhancement occurring near the surface plasmon resonance of the structure. As the longitudinal interparticle spacing is reduced, the magnitude of the enhancement is seen to increase by more than an order of magnitude. Apparently the field enhancement obtained at small interparticle spacing results in a net increase of g (3), despite the fact that the enhancement occurs only within a small volume. While interparticle interaction does contribute to the enhancement, the field enhancement obtained due to the plasmon resonance provides the main contribution to the observed enhancement factors. The resonant nature of the enhancement has an important consequence: as can be seen in Fig. 3(a), the phase angle of the enhancement factor increases from approximately 0° to 360° as the frequency is increased from below the plasmon resonance frequency to well above the resonance frequency. This behavior can be understood by realizing that near resonance the local electric fields inside and just outside the nanoparticles occur with respectively a −90° and + 90° phase delay with respect to the incident field. As can be seen in Eq. (4), the phase of the numerator of the enhancement factor scales with E2, and consequently the 90° phase difference of the linear fields on resonance lead to a 180° phase difference of the numerator in Eq. (4) compared to the phase of the average field. The complex nature of the enhancement indicates that in the presence of metal nanoparticles, a Kerr-type positive nonlinear refractive host can act as a nonlinear absorber, a negative nonlinear refractive medium, or a saturable absorber, depending on the frequency used [16

16. D. C. Kohlgraf-Owens and P. G. Kik, “Numerical study of surface plasmon enhanced nonlinear absorption and refraction,” Opt. Express 16(14), 10823–10834 (2008). [CrossRef] [PubMed]

,17

17. G. Piredda, D. D. Smith, B. Wendling, and R. W. Boyd, “Nonlinear optical properties of a gold-silica composite with high gold fill fraction and the sign change of its nonlinear absorption coefficient,” J. Opt. Soc. Am. B 25(6), 945–950 (2008). [CrossRef]

]. Note that in experiments on metal-dielectric composites these effects may be overshadowed by nonlinearities introduced by the metal nanoparticles.

Figure 4
Fig. 4 Complex geometry-dependent nonlinear susceptibility enhancement factor gin (3) for different frequencies of the incident plane wave, showing (a) the phase angle of the complex enhancement factor, and (b) the magnitude of the enhancement on a logarithmic scale. The dashed curves show the corresponding results for non-interacting particles (MG limit).
shows the phase (Fig. 4(a)) and magnitude (Fig. 4(b)) of the geometry-dependent nonlinear susceptibility enhancement factor gin (3) of the inclusion, based on the same simulated three-dimensional electric field data used to generate Fig. 3. Note that while the phase dependence on frequency appears virtually identical to that observed in Fig. 3(a), the curves shown in Fig. 4(a) are in fact independently calculated values based on the internal electric fields, as opposed to the external electric fields that were used to generate Fig. 3(a). The dashed curves represent the corresponding analytical result for this fill fraction. This analytical result relies on a different equation than the one used in Fig. 3, since it also considers the internal fields [8

8. M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: Dipolar spectral theory,” Phys. Rev. B 60(24), 17071–17083 (1999). [CrossRef]

]. In the limit of weak interparticle interaction (Lx = 24 nm), the magnitude of the enhancement gin (3) is seen to be significantly larger than that of gh (3) observed in Fig. 3. This is due to fact that the internal field enhancement that contributes to gin (3) occurs throughout the entire volume of the particle, while the external field enhancement that contributes to gh (3) occurs only in a small fraction of the host volume. In stark contrast with the observations made in Fig. 3, the magnitude of the nonlinear susceptibility enhancement of the inclusion is found to be nearly independent of interparticle separation. This very different behavior is due to the fact that the internal field distribution is relatively unaffected by changes in the interparticle separation.

The total figure of merit for nonlinear absorption can be shown to be separable into a host contribution and an inclusion contribution. Figure 5(a)
Fig. 5 Contributions to the figure of merit of the composite as a function of geometry considering separately (a) a nonlinear host, and (b) a nonlinear inclusion.
shows the host contribution to the figure of merit of the composite as a function of geometry. Despite the fact that a nonlinear refractive host is assumed, a positive figure of merit for nonlinear absorption is observed across a significant frequency range due to the complex nature of the susceptibility enhancement factor near the plasmon resonance of the structure. As the longitudinal interparticle spacing is decreased from 46 nm to 12.5 nm, the peak figure of merit is seen to increase by more than an order of magnitude. This increase follows from the observed large increase in the effective nonlinear susceptibility (Fig. 3) due to near-field coupling between adjacent particles accompanied by additional field enhancement and confinement (Fig. 1), combined with the relatively small change in peak absorption coefficient as the interparticle spacing is modified (Fig. 2). These results demonstrate that while the presence of the metal nanoparticles does introduce significant absorption, the nonlinear optical absorption performance of a thin metal-dielectric composite can be improved significantly by modifying the spatial distribution of the metal. Figure 5(b) shows the contribution of the inclusion to the overall figure of merit of the composite as for the same geometries. The entirely imaginary χin (3) assumed for the metal is seen to lead to a negative figure of merit for nonlinear absorption, indicative of a composite that exhibits saturable absorption. Experimental studies of metal-dielectric composites indeed show saturable absorption near the plasmon resonance [17

17. G. Piredda, D. D. Smith, B. Wendling, and R. W. Boyd, “Nonlinear optical properties of a gold-silica composite with high gold fill fraction and the sign change of its nonlinear absorption coefficient,” J. Opt. Soc. Am. B 25(6), 945–950 (2008). [CrossRef]

,30

30. D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects,” J. Opt. Soc. Am. B 14(7), 1625–1631 (1997). [CrossRef]

]. As the longitudinal interparticle spacing is decreased, the magnitude of the figure of merit is seen to decrease slightly due to the observed weak increase in linear absorption as the longitudinal interparticle spacing is decreased (Fig. 2), and partly due to an additional frequency dependence introduced by the factor 1/λ in the conversion from χ (3) to β.

5. Summary and conclusions

The effect of interparticle spacing on the linear and nonlinear optical properties of periodic metal-dielectric nanocomposites was discussed. Under the assumption that the materials exhibit a third-order Kerr type nonlinearity, it is shown that a reduced interparticle spacing along the incident field direction can lead to a significantly increased composite nonlinear optical response at frequencies near the plasmon resonance, while leaving the maximum linear optical absorption largely unaffected. These two findings lead to the observation of an enhanced figure of merit for nonlinear absorption by a nonlinear refractive host.

Acknowledgements

We would like to thank Prof. David G. Stroud for helpful discussions. This material is based upon work supported by the U. S. Army Research Office under contract/grant number 50372-CH-MUR.

References and links

1.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]

2.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

3.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007). [CrossRef] [PubMed]

4.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

5.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

6.

K. Tsuchiya, S. Nagayasu, S. Okamoto, T. Hayakawa, T. Hihara, K. Yamamoto, I. Takumi, S. Hara, H. Hasegawa, S. Akasaka, and N. Kosikawa, “Nonlinear optical properties of gold nanoparticles selectively introduced into the periodic microdomains of block copolymers,” Opt. Express 16(8), 5362–5371 (2008). [CrossRef] [PubMed]

7.

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46(3), 1614–1629 (1992). [CrossRef] [PubMed]

8.

M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: Dipolar spectral theory,” Phys. Rev. B 60(24), 17071–17083 (1999). [CrossRef]

9.

D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988). [CrossRef]

10.

H. Ditlbacher, N. Felidj, J. R. Krenn, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Electromagnetic interaction of fluorophores with designed two-dimensional silver nanoparticle arrays,” Appl. Phys. B 73(4), 373–377 (2001). [CrossRef]

11.

A. M. Glass, A. Wokaun, J. P. Heritage, J. G. Bergman, P. F. Liao, and D. H. Olson, “Enhanced two-photon fluorescence of molecules adsorbed on silver particle films,” Phys. Rev. B 24(8), 4906–4909 (1981). [CrossRef]

12.

W. Wenseleers, F. Stellacci, T. Meyer-Friedrichsen, T. Mangel, C. A. Bauer, S. J. K. Pond, S. R. Marder, and J. W. Perry, “Five Orders-of-Magnitude Enhancement of Two-Photon Absorption for Dyes on Silver Nanoparticle Fractal Clusters,” J. Phys. Chem. B 106(27), 6853–6863 (2002). [CrossRef]

13.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008). [CrossRef]

14.

R. Katouf, T. Komikado, M. Itoh, T. Yatagai, and S. Umegaki, “Ultra-fast optical switches using 1D polymeric photonic crystals,” Photonics Nanostruct. Fundam. Appl. 3(2-3), 116–119 (2005). [CrossRef]

15.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73(10), 1368–1371 (1994). [CrossRef] [PubMed]

16.

D. C. Kohlgraf-Owens and P. G. Kik, “Numerical study of surface plasmon enhanced nonlinear absorption and refraction,” Opt. Express 16(14), 10823–10834 (2008). [CrossRef] [PubMed]

17.

G. Piredda, D. D. Smith, B. Wendling, and R. W. Boyd, “Nonlinear optical properties of a gold-silica composite with high gold fill fraction and the sign change of its nonlinear absorption coefficient,” J. Opt. Soc. Am. B 25(6), 945–950 (2008). [CrossRef]

18.

H. B. Liao, W. Wen, and G. K. L. Wong, “Preparation and characterization of Au/SiO2 multilayer composite films with nonspherical Au particles,” Appl. Phys., A Mater. Sci. Process. 80(4), 861–864 (2005). [CrossRef]

19.

N. Pinçon, B. Palpant, D. Prot, E. Charron, and S. Debrus, “Third-order nonlinear optical response of Au:SiO2 thin films: Influence of gold nanoparticle concentration and morphologic parameters,” Eur. Phys. J. D 19, 395–402 (2002). [CrossRef]

20.

O. Maruyama, Y. Senda, and S. Omi, “Non-linear optical properties of titanium dioxide films containing dispersed gold particles,” J. Non-Cryst. Solids 259(1-3), 100–106 (1999). [CrossRef]

21.

G. Ma, W. Sun, S.-H. Tang, H. Zhang, Z. Shen, and S. Qian, “Size and dielectric dependence of the third-order nonlinear optical response of Au nanocrystals embedded in matrices,” Opt. Lett. 27(12), 1043–1045 (2002). [CrossRef]

22.

J. Jayabalan, A. Singh, R. Chari, and S. M. Oak, “Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs,” Nanotechnology 18(31), 315704 (2007). [CrossRef]

23.

O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers,” Phys. Rev. B 56(13), 8035–8046 (1997). [CrossRef]

24.

J. C. M. Garnett, ““Colours in Metal Glasses and in Metallic Films,” Philos. Trans. R. Soc. London Ser. A 203(1), 385–420 (1904). [CrossRef]

25.

H. R. Ma, R. F. Xiao, and P. Sheng, “Third-order optical nonlinearity enhancement through composite microstructures,” J. Opt. Soc. Am. B 15(3), 1022–1029 (1998). [CrossRef]

26.

R. del Coso and J. Solis, “Relation between nonlinear refractive index and third-order susceptibility in absorbing media,” J. Opt. Soc. Am. B 21(3), 640–644 (2004). [CrossRef]

27.

P. B. Johnson and R. W. Christy, “Optical-Constants Of Noble-Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

28.

Microwave Studio, Computer Simulation Technology, Darmstadt, Germany.

29.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss,” Appl. Phys. Lett. 81(9), 1714–1716 (2002). [CrossRef]

30.

D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects,” J. Opt. Soc. Am. B 14(7), 1625–1631 (1997). [CrossRef]

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(160.1245) Materials : Artificially engineered materials
(260.2065) Physical optics : Effective medium theory
(160.4236) Materials : Nanomaterials

ToC Category:
Materials

History
Original Manuscript: June 3, 2009
Revised Manuscript: August 5, 2009
Manuscript Accepted: August 6, 2009
Published: August 10, 2009

Citation
Dana C. Kohlgraf-Owens and Pieter G. Kik, "Structural control of nonlinear optical absorption and refraction in dense metal nanoparticle arrays," Opt. Express 17, 15032-15042 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-15032


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References

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  17. G. Piredda, D. D. Smith, B. Wendling, and R. W. Boyd, “Nonlinear optical properties of a gold-silica composite with high gold fill fraction and the sign change of its nonlinear absorption coefficient,” J. Opt. Soc. Am. B 25(6), 945–950 (2008). [CrossRef]
  18. H. B. Liao, W. Wen, and G. K. L. Wong, “Preparation and characterization of Au/SiO2 multilayer composite films with nonspherical Au particles,” Appl. Phys., A Mater. Sci. Process. 80(4), 861–864 (2005). [CrossRef]
  19. N. Pinçon, B. Palpant, D. Prot, E. Charron, and S. Debrus, “Third-order nonlinear optical response of Au:SiO2 thin films: Influence of gold nanoparticle concentration and morphologic parameters,” Eur. Phys. J. D 19, 395–402 (2002). [CrossRef]
  20. O. Maruyama, Y. Senda, and S. Omi, “Non-linear optical properties of titanium dioxide films containing dispersed gold particles,” J. Non-Cryst. Solids 259(1-3), 100–106 (1999). [CrossRef]
  21. G. Ma, W. Sun, S.-H. Tang, H. Zhang, Z. Shen, and S. Qian, “Size and dielectric dependence of the third-order nonlinear optical response of Au nanocrystals embedded in matrices,” Opt. Lett. 27(12), 1043–1045 (2002). [CrossRef]
  22. J. Jayabalan, A. Singh, R. Chari, and S. M. Oak, “Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs,” Nanotechnology 18(31), 315704 (2007). [CrossRef]
  23. O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers,” Phys. Rev. B 56(13), 8035–8046 (1997). [CrossRef]
  24. J. C. M. Garnett, ““Colours in Metal Glasses and in Metallic Films,” Philos. Trans. R. Soc. London Ser. A 203(1), 385–420 (1904). [CrossRef]
  25. H. R. Ma, R. F. Xiao, and P. Sheng, “Third-order optical nonlinearity enhancement through composite microstructures,” J. Opt. Soc. Am. B 15(3), 1022–1029 (1998). [CrossRef]
  26. R. del Coso and J. Solis, “Relation between nonlinear refractive index and third-order susceptibility in absorbing media,” J. Opt. Soc. Am. B 21(3), 640–644 (2004). [CrossRef]
  27. P. B. Johnson and R. W. Christy, “Optical-Constants Of Noble-Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
  28. Microwave Studio, Computer Simulation Technology, Darmstadt, Germany.
  29. S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss,” Appl. Phys. Lett. 81(9), 1714–1716 (2002). [CrossRef]
  30. D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects,” J. Opt. Soc. Am. B 14(7), 1625–1631 (1997). [CrossRef]

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