## Structural control of nonlinear optical absorption and refraction in dense metal nanoparticle arrays

Optics Express, Vol. 17, Issue 17, pp. 15032-15042 (2009)

http://dx.doi.org/10.1364/OE.17.015032

Acrobat PDF (344 KB)

### 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

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. 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]

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]

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]

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/SiO_{2} 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:SiO_{2} 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]

## 2. Theory

*ε*of an isotropic composite with a position dependent isotropic dielectric function

_{c}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]

*V*, and the notation

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]

*ε*embedded in a host material with an isotropic dielectric function

_{in}*ε*. 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.

_{h}*χ*

_{c}^{(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. 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. 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]

*χ*

_{c}^{(3)}(

*ω*) must be represented by a complex fourth rank tensor. In this study we derive the effective

*χ*

_{c}^{(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

*χ*

_{c,xxxx}^{(3)}, which in the following will be denoted

*χ*

_{c}^{(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

*χ*

_{c}^{(3)}for excitation with a specific electric field direction with respect to a highly symmetric structure.

*χ*

_{in}^{(3)}and

*χ*

_{h}^{(3)}respectively, it can easily be shown that Eq. (2) can be written in the following form:where

*f*is the volume fraction of the inclusion in the composite,

_{in}*f*is the volume fraction of the host material given by

_{h}*f*= 1 -

_{h}*f*, and the factors

_{in}*g*represent susceptibility enhancement factors that satisfy the following relation:The subscript

_{j}^{(3)}*j*represents either the inclusion (‘in’) or the host (‘h’). It is important to note that the numerator is averaged over a limited volume

*V*indicating the volume of the inclusion or the host respectively. From Eq. (3) the factors

_{j}*g*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

_{j}^{(3)}*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]

*χ*enhancement, even for components with a small fill-fraction.

^{(3)}*χ*

_{c}^{(3)}one can obtain the composite nonlinear refractive index

*η*=

_{2,c}*n*+

_{2,c}*iκ*where

_{2,c}*n*and

_{2,c}*κ*represent the real and imaginary parts of the nonlinear refractive index. In highly absorptive composites the conversion from

_{2,c}*χ*

_{c}^{(3)}to the nonlinear refractive index

*η*must take into account linear loss in the composite [26

_{2}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]

*ε*is the permittivity of vacuum,

_{0}*c*is the speed of light in vacuum,

*η*is the complex linear refractive index of the composite, and

_{c}*n*and

_{c}*κ*are the real and imaginary parts of

_{c}*η*. The thus obtained nonlinear refractive index can be used to determine the nonlinear absorption coefficient of the composite

_{c}*β*according to

_{c}*β*= (4π/

_{c}*λ*)

*κ*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

_{2,c}*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

_{2}(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]

*ε*/(

_{in}= ε_{∞}- ω_{p}^{2}*ω*(

^{2}+ iω*Γ*)) where

_{0}+ Γ_{s}*ε*= 5.451,

_{∞}*ω*= 1.474 × 10

_{p}^{16}rad/s, and the bulk electron scattering rate

*Γ*= 8.354 × 10

_{0}^{13}s

^{−1}. The surface scattering rate

*Γ*is given by

_{s}*Γ*/

_{s}= Aυ_{f}*r*= 2.8 × 10

^{14}s

^{−1}, where

*A*is set to 1,

*υ*= 1.39 × 10

_{f}^{6}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

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]

*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

*L*= 24 nm (square arrangement), indicating that interparticle interactions are minimal in this specific geometry.

_{x}*g*

_{h}^{(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]

*L*= 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 (

_{x}*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 E

^{2}, 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. 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]

*g*

_{in}^{(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]

*L*= 24 nm), the magnitude of the enhancement

_{x}*g*

_{in}^{(3)}is seen to be significantly larger than that of

*g*

_{h}^{(3)}observed in Fig. 3. This is due to fact that the internal field enhancement that contributes to

*g*

_{in}^{(3)}occurs throughout the entire volume of the particle, while the external field enhancement that contributes to

*g*

_{h}^{(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.

*g*

_{j}^{(3)}it is now possible to evaluate the influence of the geometry-dependent field enhancement on the figure of merit for nonlinear absorption. The figure of merit is given by

*β*/

_{c}*α*, where

_{c}*β*is the nonlinear absorption coefficient of the composite. The figure of merit indicates the inverse of the irradiance required to achieve a nonlinear absorption coefficient equal to the linear absorption coefficient. For the following analysis the silver nonlinear response is approximated by a Kerr-type response with

_{c}*χ*

_{in}^{(3)}=

*i**10

^{−10}esu (1.75

*i*× 10

^{−17}V

^{2}/m

^{2}), while the host is assumed to be nonlinearly refractive with

*χ*

_{h}^{(3)}= 10

^{−14}esu (1.75 × 10

^{−21}V

^{2}/m

^{2}). For clarity of presentation these values are assumed to be frequency independent near the nanoparticle resonance. Note that while metal nonlinear optical properties are often described in terms of an effective Kerr nonlinearity, the underlying physical mechanisms include non-Kerr type effects such as Fermi smearing and thermal nonlinearities. Consequently, the metal contribution to the composite nonlinearity in real-world experiments may not reproduce the exact functional form derived here, however the predicted trends are expected to be observable.

*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

*χ*

_{in}^{(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. 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]

*λ*in the conversion from

*χ*

^{(3)}to

*β*.

## 5. Summary and conclusions

## Acknowledgements

## References and links

1. | C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science |

2. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science |

3. | H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science |

4. | J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science |

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 |

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 |

7. | J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A |

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 |

9. | D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B |

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 |

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 |

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 |

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 |

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. |

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. |

16. | D. C. Kohlgraf-Owens and P. G. Kik, “Numerical study of surface plasmon enhanced nonlinear absorption and refraction,” Opt. Express |

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 |

18. | H. B. Liao, W. Wen, and G. K. L. Wong, “Preparation and characterization of Au/SiO |

19. | N. Pinçon, B. Palpant, D. Prot, E. Charron, and S. Debrus, “Third-order nonlinear optical response of Au:SiO |

20. | O. Maruyama, Y. Senda, and S. Omi, “Non-linear optical properties of titanium dioxide films containing dispersed gold particles,” J. Non-Cryst. Solids |

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. |

22. | J. Jayabalan, A. Singh, R. Chari, and S. M. Oak, “Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs,” Nanotechnology |

23. | O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers,” Phys. Rev. B |

24. | J. C. M. Garnett, ““Colours in Metal Glasses and in Metallic Films,” Philos. Trans. R. Soc. London Ser. A |

25. | H. R. Ma, R. F. Xiao, and P. Sheng, “Third-order optical nonlinearity enhancement through composite microstructures,” J. Opt. Soc. Am. B |

26. | R. del Coso and J. Solis, “Relation between nonlinear refractive index and third-order susceptibility in absorbing media,” J. Opt. Soc. Am. B |

27. | P. B. Johnson and R. W. Christy, “Optical-Constants Of Noble-Metals,” Phys. Rev. B |

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. |

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 |

**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

- C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]
- 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]
- H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007). [CrossRef] [PubMed]
- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- P. B. Johnson and R. W. Christy, “Optical-Constants Of Noble-Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
- Microwave Studio, Computer Simulation Technology, Darmstadt, Germany.
- 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]
- 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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