## Surface plasmon assisted optical nonlinearities of uniformly oriented metal nano-ellipsoids in glass |

Optics Express, Vol. 20, Issue 27, pp. 28655-28663 (2012)

http://dx.doi.org/10.1364/OE.20.028655

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### Abstract

The nonlinear optical properties of nanocomposites consisting of non-spherical silver nanoparticles in glass matrix have been studied using the femtosecond Z-scan technique. The spheroidal nanoparticles were uniformly oriented along a common direction. By polarization sensitive studies, longitudinal and transverse plasmon resonances can be addressed separately. A sign reversal in optical nonlinearity from negative to positive is observed while switching the light interaction from near to non-resonant regime, which can be done by simply rotating the light polarization by 90°. Studying samples with different aspect ratio, we obtained the dispersion of third-order nonlinearity in the near-resonant regime, showing an enhancement of the nonlinear processes by more than two orders of magnitude due to the electric field enhancement at the surface plasmon resonance.

© 2012 OSA

## 1. Introduction

*f*has to be regarded for each electric field involved in the process; for instance,

*χ*

^{(3)}-effects experience an increase proportional to

*f*

^{4}at the SPR (in electric dipole approximation). As a consequence, dielectrics containing metal nanoparticles are a very interesting class of optical nonlinear materials, mainly for two reasons: (i) its third-order nonlinear susceptibility

*χ*

^{(3)}has a sub-picosecond response time [1

1. D. Ricard, Ph. Roussignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett. **10**(10), 511–513 (1985). [CrossRef] [PubMed]

2. Y. Hamanaka, A. Nakamura, S. Omi, N. Del Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. **75**(12), 1712–1714 (1999). [CrossRef]

^{(3)}enhancement due to the SPR can be potentially tailored within a wide spectral range by controlling the material parameters like size, shape and filling factor of the NPs [3,4

4. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape and dielectric environment,” J. Phys. Chem. B **107**(3), 668–677 (2003). [CrossRef]

6. H. I. Elim, J. Yang, J.-Y. Lee, J. Mi, and W. Ji, “Observation of saturable and reverse-saturable absorption at longitudinal surface plasmon resonance in gold nanorods,” Appl. Phys. Lett. **88**(8), 83107–83109 (2006). [CrossRef]

8. J. Li, S. Liu, Y. Liu, F. Zhou, and Z.-Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold rods,” Appl. Phys. Lett. **96**(26), 263103 (2010). [CrossRef]

9. M. Kyoung and M. Lee, “Nonlinear absorption and refractive index measurements of silver nanorods by the Z-scan technique,” Opt. Commun. **171**(1-3), 145–148 (1999). [CrossRef]

10. R. Rangel-Rojo, J. McCarthy, H. T. Bookey, A. K. Kar, L. Rodriguez-Fernandez, J. C. Cheang-Wong, A. Crespo-Sosa, A. Lopez-Suarez, A. Oliver, V. Rodriguez-Iglesias, and H. G. Silva-Pereyra, “Anisotropy in the nonlinear absorption of elongated silver nanoparticles in silica, probed by femtosecond pulses,” Opt. Commun. **282**(9), 1909–1912 (2009). [CrossRef]

## 2. Experimental

11. A. Stalmashonak, G. Seifert, A. A. Ünal, U. Skrzypczak, A. Podlipensky, A. Abdolvand, and H. Graener, “Toward the production of micropolarizers by irradiation of composite glass with silver nanoparticles,” Appl. Opt. **48**(25), F37–F42 (2009). [CrossRef]

*p*to be in the range of

*p*≈5∙10

^{−3}(which is compatible with SEM results). The NPs are prolate spheroids, being uniformly oriented along the direction of mechanical stress applied during the thermo-mechanical stretching method used for preparation [12

12. H. Hofmeister, W.-G. Drost, and A. Berger, “Oriented prolate silver nanoparticles in glass-characteristics of novel dichoric polarizers,” Nanostr. Mat. **12**(1-4), 207–210 (1999). [CrossRef]

_{2}atmosphere. Stretching of the sample was done at 650°C by pulling at constant stress. Depending on the processing parameters, samples with different NP aspect ratios c/a can be prepared. For the present study we have chosen three different samples with increasing anisotropy, indicated by the peak position of the longitudinal plasmon bands (LSPR) observed at ≈450 nm, 550 nm and 1200 nm. This would correspond to NP aspect ratios of c/a ≈1.4, 2.4 and 6.5, respectively, if all the nanoparticles would have the same size and shape [12

12. H. Hofmeister, W.-G. Drost, and A. Berger, “Oriented prolate silver nanoparticles in glass-characteristics of novel dichoric polarizers,” Nanostr. Mat. **12**(1-4), 207–210 (1999). [CrossRef]

13. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. **26**(4), 760–769 (1990). [CrossRef]

*χ*

^{(3)}can be determined. Two different laser sources operating at 1030 nm (pulse duration 250 fs, repetition rate 1 kHz) and 800 nm (100 fs, 1 kHz) were used as excitation wavelengths. The Rayleigh ranges z

_{0}of the laser beams were measured to be ~2 mm and ~3 mm, respectively for 800 nm and 1030 nm pump wavelength, which is in both cases one order of magnitude larger than the thickness of the sample. Hence a thin sample approximation is valid irrespective of the excitation parameters. The spatial intensity profile of the laser beams was circular Gaussian in good approximation. Both laser systems provide linearly polarized light, enabling to realize either a parallel (p

_{||}) or perpendicular (p

_{⊥}) orientation of long NP axis and laser polarization vector. In p

_{||}configuration the laser polarization direction is set parallel to the stretched direction of the sample which enables the selective excitation of the longitudinal plasmon band (LSPR), whereas in p

_{⊥}configuration the transverse plasmon band (TSPR) is addressed (see Fig. 1(a) ).

_{||}configuration. The dotted arrows indicate possible two-photon resonance, which is almost precisely matched in the case of λ = 800 nm laser and p

_{⊥}configuration. The various combinations of sample, laser wavelength and polarization thus represent several relative energy distances of excitation and resonance, which can be used to study, at least qualitatively, the dispersion behavior of χ

^{(3)}. For this purpose, we will below use the abbreviations Δ

_{||}= ħ∙(ω

_{LSPR}- ω

_{Laser}) and Δ

_{⊥}= ħ∙(ω

_{TSPR}- ω

_{Laser}) to characterize the relative spectral position of the excitation laser; here, ω

_{LSPR}and ω

_{TSPR}denote the longitudinal and transverse plasmon resonance frequency of the respective sample.

## 3. Results and discussion

_{0}values; the only exception is the p

_{||}configuration on sample LSPR_550, which clearly indicates a negative nonlinear refractive index. Furthermore, the signal in the latter situation was obtained at a considerably lower peak pump intensity of 8 GW∙cm

^{−2}, while the other signals were measured using peak intensities of 200 GW∙cm

^{−2}or 330 GW∙cm

^{−2}, respectively.

_{||}configuration on sample LSPR_550, a transmission increase (bleaching) is seen, all other cases lead to a dip in the measured signals around z = 0 due to nonlinear absorption. Again the near resonant case yields the strong bleaching signal at much lower peak intensity (~7 GW∙cm

^{−2}) than is required for comparably strong induced absorption in the other cases (250 – 350 GW∙cm

^{−2}). And, also like for the CA scans, the linear extinction spectra provide a reasonable qualitative explanation: apparently bleaching can only occur when the sample has a substantial initial extinction, while the observed transmission decrease most probably comes from two-photon absorption at the respective SPR (see Fig. 1).

^{(3)}can thus be switched by a simple rotation of laser polarization by 90°.

_{||}configuration. In particular at the pump wavelength λ = 1030 nm, the energy distance to the SPR is only Δ

_{||}= −0.17 eV. As is clearly seen in Fig. 3(a) , this situation yields a positive nonlinear refraction, here obtained with a peak intensity of 25 GW∙cm

^{−2}. Switching to non-resonant excitation by polarization change in this case does not change the sign, but only decreases the magnitude of the nonlinear refractive index considerably. OA scans at λ = 1030 nm on the sample LSPR_1200 (Fig. 3(b)) yielded a very strong bleaching in p

_{||}configuration, but no measurable transmission change with perpendicular polarization p

_{⊥}. Both effects are also apparent, because the laser frequency is very close to a strongly absorbing resonance in the first case, while in the latter neither single- nor two-photon resonances are at hand (cf. Figure 1).

*I*) in first-order approximation by Δα

_{||,⊥}(

*I*) = β

_{||,⊥}∙

*I*, with a nonlinear absorption parameter β

_{||,⊥}which can take positive (e.g., in case of two-photon absorption) or negative values (for saturable absorption). Numerical solutions of the propagation equation

*dI*/

*dz*’ =

*I*∙[α

_{0}+ Δα(

*I*)] were used to calculate best fit curves for the OA scans (shown also as curves in the Figs. above). The values of the nonlinear absorption parameters β

_{||,⊥}obtained from these best fits are given in Table 1 . No values could be determined at the excitation wavelength 1030 nm for β

_{||}in case of sample LSPR_450, and for β

_{⊥}for all samples; apparently due to the SPR being too far off two-photon resonance, no noticeable transmission changes could be obtained in OA scans up to the highest intensities (I

_{0}≈350 GW∙cm

^{−2}) applied in this study.

14. M. Yin, H. P. Lin, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B **70**(4), 587–591 (2000). [CrossRef]

*T*is given by [13

13. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. **26**(4), 760–769 (1990). [CrossRef]

_{2||}and n

_{2⊥}denote the nonlinear refractive index for p

_{||}and p

_{⊥}configuration,

*I*

_{0}is the peak intensity at z = 0, and

*L*the effective sample length, which has been set to the approximate NP layer thickness of

_{eff}*L*= 1 µm. It has been verified by Z-scans on pure glass sheets of thickness comparable to the samples that the substrate contribution is negligible compared to those of the NP layer in all cases. The n

_{eff}_{2}values of the best fit results (shown as solid curves in Figs. 2 and 3) have also been collected as a function of the relative distance to SPR (Δ

_{||,⊥}) in Table 1. However, as mentioned above,

*L*= 1 µm is only an estimation because of the depth gradient of NP concentration. This puts a principal uncertainty of ~30% on all n

_{eff}_{2}and β values reported in this work.

_{⊥}configuration is always positive and has a nearly constant value of n

_{2⊥}

**≈**10

^{−17}m

^{2}∙W

^{−1}, irrespective of sample and laser wavelength. This is clearly the non-resonant case, which nonetheless shows an n

_{2}almost 3 orders of magnitude larger than in pure glass (which is typically of the order of n

_{2}

**≈**10

^{−20}m

^{2}∙W

^{−1}). In p

_{||}configuration, nonlinear refraction is considerably increased (by a factor of 4.5 to 26) for the samples LSPR_550 and LSPR_1200; positive or negative values of n

_{2||}are found depending on whether the laser is exciting on the high (Δ

_{||}< 0) or low (Δ

_{||}> 0) frequency side of the SPR. For LSPR_450, n

_{2||}is even smaller than in the non-resonant case for both laser wavelengths, indicating that here already a small (negative) contribution from the SPR enhancement is involved. The positive nonlinear absorption parameters derived for 800 nm laser wavelength (β

_{||}and β

_{⊥}for LSPR_450; β

_{⊥}for the other two samples) are apparently due to two-photon absorption, while the much (up to three orders of magnitude) larger, negative values of β

_{||}for the samples LSPR_550 and LSPR_1200 are assigned to saturation (bleaching) of the surface plasmon oscillation.

_{||,⊥}, can be used to look at the dispersion features of the χ

^{(3)}of uniformly oriented, spheroidal Ag nanoparticles in glass matrix. To do this, we have converted the obtained nonlinear parameters into real and imaginary part of χ

^{(3)}by taking into account the linear absorption of the sample [15

15. 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]

_{||}case are plotted in Fig. 4 , as a function of Δ

_{||}, which is comparable to a dispersion curve of χ

^{(3)}; it has to be regarded, though, that the different samples can actually not be compared quantitatively to each other because of the inhomogeneity of the real SPR bands, as caused by the polydispersity of NP sizes and shapes. The effective NP concentration which the laser is interacting with may thus be considerably different from sample to sample. Nonetheless the data show very clearly dispersion behavior as it is expected for a susceptibility around a resonance: the (negative) imaginary part increases towards the resonance (Δ

_{||}= 0) and is fairly symmetric, while the real part has the typical change of sign at resonance.

^{(3)}of silver-glass nanocomposites is the so-called hot electron contribution, whereas intraband transitions are generally much weaker, and interband transitions are in the UV for silver and thus not relevant in the spectral range studied here [16

16. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. **47**(4), 347–357 (1988). [CrossRef]

17. Y. Guillet, M. Rashidi-Huyeh, and B. Palpant, “Influence of laser pulse characteristics on the hot electron contribution to the third-order nonlinear optical response of gold nanoparticles,” Phys. Rev. B **79**(4), 045410 (2009). [CrossRef]

_{S}. In such an approach, the intensity dependent change of total susceptibility is modeled by a Lorentzian-shaped χ

^{(1)}, which is modified by a saturation denominator: <χ(I)> = χ

^{(1)}·[1 + (I/I

_{S})]

^{−1}; the averaged change due to the applied field is then calculated as Δχ = <χ(I)> − χ

^{(1)}, which can finally be used to calculate χ

^{(3)}via the relation Δχ = 3π χ

^{(3)}|E

_{l}|

^{2}. Here E

_{l}is the local field, which is obtained by considering the local field correction (E

_{l}=

*f*∙E

_{0}). For moderate changes, this model yields for χ

^{(3)}mainly the Lorentz shape of the linear susceptibility, but with a negative sign; this is qualitatively well compatible with our results, as demonstrated by the dashed curves in Fig. 4, which represent real and imaginary part of appropriately scaled Lorentzians.

18. Y. Hamanaka, N. Hayashi, A. Nakamura, and S. Omi, “Dispersion of third-order nonlinear optical susceptibility of silver nanocrystal-glass composites,” J. Lumin. **87–89**, 859–861 (2000). [CrossRef]

18. Y. Hamanaka, N. Hayashi, A. Nakamura, and S. Omi, “Dispersion of third-order nonlinear optical susceptibility of silver nanocrystal-glass composites,” J. Lumin. **87–89**, 859–861 (2000). [CrossRef]

*Im χ*

^{(3)}also takes small positive values in a certain range on the low frequency side of the SPR. In fact, we do also have a small positive value of

*Im χ*

^{(3)}at Δ

_{||}= 1.21 eV. However, the physical situation is different: in our study, due to the used near IR pulses two-photon absorption at the SPR itself is addressed, whereas in the previous work of Hamanaka et al. [18

18. Y. Hamanaka, N. Hayashi, A. Nakamura, and S. Omi, “Dispersion of third-order nonlinear optical susceptibility of silver nanocrystal-glass composites,” J. Lumin. **87–89**, 859–861 (2000). [CrossRef]

*χ*

^{(3)}, in contrast, we may assume the same physical origin for off-resonant as well as for (near) resonant interaction, namely the hot electron contribution of the Ag conduction band electrons. The latter has repeatedly been described as fairly independent of excitation frequency for bulk metals, so that the third-order nonlinearity of an effective medium with metal volume fraction

*p*can be described as local field-corrected intrinsic nonlinearity of the metal (

*χ*

_{m}^{(3)}) as given by [16

16. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. **47**(4), 347–357 (1988). [CrossRef]

17. Y. Guillet, M. Rashidi-Huyeh, and B. Palpant, “Influence of laser pulse characteristics on the hot electron contribution to the third-order nonlinear optical response of gold nanoparticles,” Phys. Rev. B **79**(4), 045410 (2009). [CrossRef]

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

*χ*

^{(3)}of the nanocomposite is completely governed by the fourth power of the complex local field factor

*f*. Thus, if we take our experimental value of

*Re χ*

^{(3)}(Δ

_{||}= 1.55 eV) as an approximation for

*f*≈1 (i.e., volume fraction

*p*times intrinsic metal nonlinearity

*χ*

_{m}^{(3)}), we can get an estimate for the local field factor. For instance,

*Re χ*

^{(}^{3)}(Δ

_{||}= −0.17 eV) ≈150 ∙

*Re χ*

^{(}^{3)}(Δ

_{||}= 1.55 eV); therefore, a maximum local field enhancement of at least |

*f*| ≈3.5 can be inferred, in good accordance with values obtained in previous work for silver NPs in glass. Thus, an effective medium approach appears well suitable to describe the third-order optical nonlinearity also in the case of uniformly oriented, spheroidal silver nanoparticles in glass.

## 4. Conclusions

*χ*

^{(3)}of these nanocomposite materials for interaction with femtosecond pulses is apparently based on the hot-electron contribution of the NPs, and shows a strong nonlinearity enhancement of more than two orders of magnitude with dispersion behavior around the surface plasmon resonance. This enhancement and dispersion can be identified with the local field factor

*f*used in established effective medium theories to describe the local effective field interacting with the nanoscopic inclusions. As this complex factor (or its fourth power, respectively) can take also negative values, nonlinear refraction can switch sign going from low to high frequency side of the SPR, or from a near resonant to a non-resonant situation. The results of this work demonstrate clearly that the latter can be realized for near IR laser wavelengths simply by 90° polarization rotation. The same effect has been observed for nonlinear absorption where, however, the switch of sign can clearly be associated with a switch in the physical process from saturation of the one-photon transition at the LSPR to two-photon absorption at the TSPR.

## Acknowledgment

## References and links

1. | D. Ricard, Ph. Roussignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett. |

2. | Y. Hamanaka, A. Nakamura, S. Omi, N. Del Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. |

3. | U. Kreibig and M. Vollmer, |

4. | K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape and dielectric environment,” J. Phys. Chem. B |

5. | C. F. Bohren and D. R. Huffman, |

6. | H. I. Elim, J. Yang, J.-Y. Lee, J. Mi, and W. Ji, “Observation of saturable and reverse-saturable absorption at longitudinal surface plasmon resonance in gold nanorods,” Appl. Phys. Lett. |

7. | M. Pelton, M. Liu, S. Park, N. F. Scherer, and P. Guyot-Sionnest, “Ultrafast resonant optical scattering from single rods,” Phys. Rev. B |

8. | J. Li, S. Liu, Y. Liu, F. Zhou, and Z.-Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold rods,” Appl. Phys. Lett. |

9. | M. Kyoung and M. Lee, “Nonlinear absorption and refractive index measurements of silver nanorods by the Z-scan technique,” Opt. Commun. |

10. | R. Rangel-Rojo, J. McCarthy, H. T. Bookey, A. K. Kar, L. Rodriguez-Fernandez, J. C. Cheang-Wong, A. Crespo-Sosa, A. Lopez-Suarez, A. Oliver, V. Rodriguez-Iglesias, and H. G. Silva-Pereyra, “Anisotropy in the nonlinear absorption of elongated silver nanoparticles in silica, probed by femtosecond pulses,” Opt. Commun. |

11. | A. Stalmashonak, G. Seifert, A. A. Ünal, U. Skrzypczak, A. Podlipensky, A. Abdolvand, and H. Graener, “Toward the production of micropolarizers by irradiation of composite glass with silver nanoparticles,” Appl. Opt. |

12. | H. Hofmeister, W.-G. Drost, and A. Berger, “Oriented prolate silver nanoparticles in glass-characteristics of novel dichoric polarizers,” Nanostr. Mat. |

13. | M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. |

14. | M. Yin, H. P. Lin, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B |

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

16. | F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. |

17. | Y. Guillet, M. Rashidi-Huyeh, and B. Palpant, “Influence of laser pulse characteristics on the hot electron contribution to the third-order nonlinear optical response of gold nanoparticles,” Phys. Rev. B |

18. | Y. Hamanaka, N. Hayashi, A. Nakamura, and S. Omi, “Dispersion of third-order nonlinear optical susceptibility of silver nanocrystal-glass composites,” J. Lumin. |

19. | D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancelation of photoinduced absorption in metal nanoparticles composites through a counterintuitive consequence of local fields,” J. Opt. Soc. Am. B |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(190.4400) Nonlinear optics : Nonlinear optics, materials

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

(160.4236) Materials : Nanomaterials

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 12, 2012

Revised Manuscript: November 13, 2012

Manuscript Accepted: November 13, 2012

Published: December 10, 2012

**Citation**

Sabitha Mohan, Jens Lange, Heinrich Graener, and Gerhard Seifert, "Surface plasmon assisted optical nonlinearities of uniformly oriented metal nano-ellipsoids in glass," Opt. Express **20**, 28655-28663 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28655

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### References

- D. Ricard, Ph. Roussignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett.10(10), 511–513 (1985). [CrossRef] [PubMed]
- Y. Hamanaka, A. Nakamura, S. Omi, N. Del Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett.75(12), 1712–1714 (1999). [CrossRef]
- U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
- K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape and dielectric environment,” J. Phys. Chem. B107(3), 668–677 (2003). [CrossRef]
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
- H. I. Elim, J. Yang, J.-Y. Lee, J. Mi, and W. Ji, “Observation of saturable and reverse-saturable absorption at longitudinal surface plasmon resonance in gold nanorods,” Appl. Phys. Lett.88(8), 83107–83109 (2006). [CrossRef]
- M. Pelton, M. Liu, S. Park, N. F. Scherer, and P. Guyot-Sionnest, “Ultrafast resonant optical scattering from single rods,” Phys. Rev. B73, 155419 (2006). [CrossRef]
- J. Li, S. Liu, Y. Liu, F. Zhou, and Z.-Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold rods,” Appl. Phys. Lett.96(26), 263103 (2010). [CrossRef]
- M. Kyoung and M. Lee, “Nonlinear absorption and refractive index measurements of silver nanorods by the Z-scan technique,” Opt. Commun.171(1-3), 145–148 (1999). [CrossRef]
- R. Rangel-Rojo, J. McCarthy, H. T. Bookey, A. K. Kar, L. Rodriguez-Fernandez, J. C. Cheang-Wong, A. Crespo-Sosa, A. Lopez-Suarez, A. Oliver, V. Rodriguez-Iglesias, and H. G. Silva-Pereyra, “Anisotropy in the nonlinear absorption of elongated silver nanoparticles in silica, probed by femtosecond pulses,” Opt. Commun.282(9), 1909–1912 (2009). [CrossRef]
- A. Stalmashonak, G. Seifert, A. A. Ünal, U. Skrzypczak, A. Podlipensky, A. Abdolvand, and H. Graener, “Toward the production of micropolarizers by irradiation of composite glass with silver nanoparticles,” Appl. Opt.48(25), F37–F42 (2009). [CrossRef]
- H. Hofmeister, W.-G. Drost, and A. Berger, “Oriented prolate silver nanoparticles in glass-characteristics of novel dichoric polarizers,” Nanostr. Mat.12(1-4), 207–210 (1999). [CrossRef]
- M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990). [CrossRef]
- M. Yin, H. P. Lin, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B70(4), 587–591 (2000). [CrossRef]
- R. del Coso and J. Solis, “Relation between nonlinear refractive index and third-order susceptibility in absorbing media,” J. Opt. Soc. Am. B21(3), 640–644 (2004). [CrossRef]
- F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process.47(4), 347–357 (1988). [CrossRef]
- Y. Guillet, M. Rashidi-Huyeh, and B. Palpant, “Influence of laser pulse characteristics on the hot electron contribution to the third-order nonlinear optical response of gold nanoparticles,” Phys. Rev. B79(4), 045410 (2009). [CrossRef]
- Y. Hamanaka, N. Hayashi, A. Nakamura, and S. Omi, “Dispersion of third-order nonlinear optical susceptibility of silver nanocrystal-glass composites,” J. Lumin.87–89, 859–861 (2000). [CrossRef]
- D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancelation of photoinduced absorption in metal nanoparticles composites through a counterintuitive consequence of local fields,” J. Opt. Soc. Am. B14(7), 1625–1631 (1997). [CrossRef]

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