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Nonlinear optical response of Au metallic nanoparticles, synthesized and embedded in sapphire by using ion implantation, as a function of their size and shape is studied. The size of the Au NPs was varied by controlling the annealing time of the gold-irradiated sapphire in a reducing atmosphere. Their shape was changed from approximately spherical to prolate by swift heavy-ion irradiation using Si3+, obtaining an anisotropic composite consisting in deformed NPs, all oriented in the direction of the Si beam irradiation. At 532 nm and 26 ps pulses, the isotropic system shows negative nonlinear absorption increasing with size, and positive nonlinear refraction. On the other hand, prolate nanoparticles show negative (null) absorption and null (positive) refraction for the minor (major) axis. This kind of system also shows figures of merit and relaxing times in the order of the picoseconds, appropriate for all-optical switching applications.
© 2013 Optical Society of America
1. Introduction
Nowadays, a general interest regarding the increased effective nonlinear optical (NLO) response of materials due to presence of plasmonic effects has been adopted by the scientific community. Such effects arise from coherent oscillations of conduction electrons near the surface of noble-metal structures, giving place to what is better known as surface plasmon resonance (SPR) [1–3]. In particular, it has been found that metallic nanoparticles (NPs) inside a dielectric matrix have the capability of quantum confinement of electromagnetic field, where the electrons of the metal oscillate under the strength of the electric field [4]. Together, quantum confinement of light at the small NPs and collective oscillation of the electron gas, have brought, in the last few years, special interest in the preparation, characterization, and exploitation of the SPR of composite materials based on dielectric matrices containing dispersed metal NPs, such as Au, Ag and Cu. This interest has been driven mainly by existing and predicted technological applications in different areas of optics among which stand out nonlinear optics [5–7], spectroscopy [8–10], metamaterials [11], plasmonics [12], and bioluminescence [13].
Among all possible combinations in fabricating composite materials, those made out of gold NPs embedded in a dielectric matrix are of particular importance given its strong SPR absorption band in the visible region of the electromagnetic spectrum [14]. This translates in the existence of unique linear and nonlinear (specially third order) optical properties of the material, which might be well suited for the upcoming of potential applications spanning from optical limiting [15,16], quantum information [17,18], cancer treatment [19–21], on to all-optical switching [14, 22,23]. In this direction, Au NPs embedded in different dielectric media have been widely studied because of their optical behavior due to their SPR, which is strongly dependent on the NPs geometry and environment [5,24]. Nevertheless, the physical mechanisms involved in NLO response for this type of systems are not totally understood, yet.
In this work, we aim to contribute to a better understanding of third-order NLO response of Au NPs synthesized and embedded in sapphire by ion implantation as a function of their size and shape; the resultant nanostructured material is hereafter referred as Au:Al2O3. The size of the Au NPs was varied by controlling the annealing time of the gold-irradiated sapphire in a reducing atmosphere [26]. Their shape was changed from spherical-like to a prolate one by swift heavy-ion irradiation using Si3+ions, obtaining an anisotropic composite consisting in deformed NPs, all oriented in the direction of the Si beam irradiation [27].
Experimental data obtained by performing typical Z-scan open- (OA) and closed-aperture (CA) measurements, with laser pulses of 26 ps at a wavelength of 532 nm, show a negative nonlinear absorption (NLA) that increases with size, and a positive nonlinear refraction (NLR) independent of size for the spherical-like NPs. On the other hand, a dependence on the incident polarization has been found for prolate NPs: negative NLA for the minor axis of the deformed NPs, whereas the response is null for the major axis. Regarding the NLR, the response is null for the minor axis, whereas it is positive for the major one. Similarly, regarding the dimensionless figures of merit (FOM) required for all-optical switching, as well as ultra-fast relaxation times [28–30], we obtained values of W (one-photon FOM) and T (two-photon FOM) appropriate for such application when the anisotropic system is stimulated by light polarized parallel to major axis of the deformed NPs. The relaxation time of the induced NLA was characterized by performing pump-probe measurements at 532 nm on the spherical-like NPs, finding fast relaxation times for this application. These times were also corroborated by calculations with the two-temperature model. Previous works reveal interesting third order NLO properties for similar isotropic systems for light’s wavelength far from the SPR (1064 nm), however no size neither shape of NPs were taken into account in such studies [31,32].
2. Experimental methods
2.1 Synthesis of isotropic and anisotropic Au:Al2O3 systems
Composite materials were produced by means of ion implantation method. This method of fabrication allows a complete control on the parameters of implantation, which determine the physical characteristics of the final material [33,34]. C-Sapphire single crystals (α-Al2O3 from Guild Optical Associates Inc.) were implanted at room temperature 8° off the optical axis, to prevent channeling effects, with Au++ ion beam with energy of 1.5 MeV. For the spherical-like NPs, the ion fluence was 5 × 1016 ions/cm2, producing an implanted region with a FWHM (effective thickness) of 140 nm, at a depth of 220 nm. The sample was cut and the pieces were all annealed at 1000 °C in a reducing atmosphere (50% N2, 50% H2), varying the duration of the annealing in 15, 60 and 90 min [26]. For the prolate NPs, the ion fluence was of 6 × 1016 ions/cm2, and the samples were annealed for 60 min. After this process, an irradiation with 12 MeV Si3+, at a fluence of 4.5 × 1016 ions/cm2, and an angle of 73° off-normal, was applied to this last sample in order to produce the anisotropic system [27].
All the samples were characterized by means of Rutherford Backscattering Spectroscopy (RBS), Optical Extinction Spectroscopy (OES) as a function of the incident polarization, and Transmission Electron Microscopy (TEM). The optical extinction spectra were analyzed using the Mie Lab code.
2.2 Optical measurements
Linear optical absorption measurements were performed with an Ocean Optics Dual Channel SD2000 UV–visible spectrophotometer. Experiments were done at normal incidence on the surface sample for isotropic systems. Optical response isotropy was verified by controlling polarization of incident light with the aid of a half-wave plate and an absorptive linear polarizer. In the case of deformed NPs, the sample was rotated off-normal 30° counterclockwise in order to achieve normal incidence with respect to the major axis of the NPs. Under such experimental conditions NPs’ minor axis (major axis) was parallel to horizontal (vertical) linearly polarized light.
Z-scan technique at 532 nm with variable polarization has been used to study the third order NLO properties of these samples which were scanned along the optical axis (z direction) and focused by a lens with a focal length of 500 mm. A detailed description of the Z-scan technique can be found elsewhere [4, 35]. The reference and transmitted beams (OA and CA) were measured with Thorlabs DET 10A fast photodiodes. By means of knife-edge method, a radius of the beam waist was measured to be of 31.707 ± 0.914 μm [36]. The Rayleigh length was calculated to be around 0.5 cm, much larger than the effective thickness of the samples. As light source, we used a PL2143A laser system by EKSPLA featuring 26 ps pulses with a 1-10 Hz repetition rate. The short pulse length allowed us to achieve sufficiently large peak irradiances with rather modest pulse energies, thus minimizing intra-pulse heating; while the low repetition rate (10 Hz) avoids any pulse to pulse thermal accumulation [6].
Irradiance and polarization of incident light were controlled by using the half-wave plate and absorptive linear polarizer mentioned above. Several irradiances were employed in these experiments, where rotation of the anisotropic sample by 30°, as mentioned above, was also done. Reversibility of results has been checked to confirm that no damage has been induced onto samples. The damage thresholds were measured to be around 7 GW/cm2 for the isotropic systems with spherical-like NPs of 13.4 and 14.2 nm, and 12 GW/cm2 for 5.1 nm and deformed NPs. It was also verified that the NLO response from the Al2O3 matrix was negligible when compared to that from the composite material.
Z-scan setup was calibrated using 1 mm thickness of high purity CS2 solution. The valley followed by a peak for the CA measurement, being evidence of a positive n2 at 532 nm, could be seen; experimental data from the OA measurement showed no evidence of nonlinear absorption, as expected. The n2 value for CS2 obtained from the conducted Z-scan experiments were in total agreement with values reported in literature [37].
Pump-probe technique was used to study the dynamics of the induced NLA. Two pulses with the same wavelength and linear polarization were focused into the sample following equal-length paths. While the high-intensity beam (pump) induces the NLO response of the sample, the low-intensity one (probe) detects the NLA when it reaches the sample at the same time as the pump. By introducing a variable length on the optical path of the probe beam, the dynamics of the induced NLO response can be obtained since this variable length introduces a controlled time delay on the probe with respect to the pump. In this way, the NLO response of the material is obtained with a time resolution given by the pulse duration, that is, around 26 ps.
3. Results and discussion
The absorption spectra of metallic nanocomposites are shown in Fig. 1; part (a) depicts the absorbance for the spherical-like NPs, whereas part (b) corresponds to the prolate NPs for different polarizations of the incident light. As it can be seen, all samples show a characteristic optical absorption dominated by a SPR, centered at a wavelength around 564 nm for spherical-like NPs. Likewise, for prolate NPs SPRs are centered at 536 and 602 nm for linearly polarized light parallel to the minor-axis or major-axis, respectively. The absorption peak is going to vary as a function of particle size and shape, since position and width of SPR depend on such parameters, as well as on the physical environment that contains the NPs [24–26]. As is shown in Fig. 1(a), for the case of isotropic systems, there is a slight blue shift as the size increases. By using the equation, the coefficient of linear absorption α0 is calculated from the experimental data. The α0s as well as the NLA coefficients β and NLR indexes n2, obtained in the different samples at λ = 532nm for different peak irradiances at the focus I0, are shown below in Table 1 (isotropic systems) and Table 2 (anisotropic system).
Fig. 1 (a) Optical absorption spectra of spherical-like Au NPs for different times of annealing treatment. (b) Optical absorption spectra of deformed Au NPs for different incident polarizations. Vertical line centered at 532 nm is used as visual guide.
Table 1. NLO results for the spherical-like NPs, as well as the diameters of the NPs for the different annealing times.
Table 2. NLO results for the deformed NPs, which had a diameter of 7 nm prior deformation.
The characteristic OA and CA Z-scan curves presented in Fig. 2, as well as data presented in Table 1 and Table 2, were fitted and calculated from approximate relationships given by ref [35]. That is, OA Z-scan measurements (Fig. 2(a)) were fitted by using equation:
which can be used as far as the condition holds, where Leff is the effective length (FWHM) of the sample, z0 the Rayleigh length, and z the scanned axis. This equation was also used to calculate the β coefficients, keeping fixed the rest of measured parameters. After this calculation, it was checked that such condition held for all cases. At the same time, the n2 coefficients were extracted directly from CA Z-scan curves by using Eq. (2)where is the difference between the maximal value (peak) and the minimal value (valley) on the normalized transmittance from closed aperture without nonlinear absorption, and S is the linear transmittance through the aperture. The change of phase induced by the sample is given by the following equation:Fig. 2 Typical NLO responses for the spherical-like and the deformed NPs embedded in sapphire for a given irradiance. a) NLA and b) NLR as a function of size for the isotropic system. c) NLA and d) NLR as a function of incident polarization for the anisotropic system (null signal for the minor axis is not shown for the sake of a better visualization).
In the case of isotropic systems, since a strong NLA is present, the CA Z-scan curves obtained directly from experiment did not feature the common valley-peak (peak-valley) pattern in transmittance. Therefore, in determining the NLR responses with the presence of a NLA response, the usual protocol proposed by Sheik-Bahae et al. was used; we subtracted the NLA contribution on the CA transmittance by a simple division of curves CA/OA [35]. In the same reference it is stated that such a procedure can be done only if the following conditions hold: 1) and 2) . Again, it has been verified that these requirements were satisfied in all measurements done. On the other hand, it is important to notice that the NLR optical response obtained for the anisotropic system when excited by light linearly polarized parallel to major axis is “pure”. In other words, there is no need of dividing CA/OA in order to extract the n2 values. These “pure” CA Z-scan curves are well fitted by means of the equation (also given in [35]):
As it can be appreciated in Table 1, the NLA is always negative, and increases in magnitude as the size does for the spherical-like NPs (Fig. 2a), whereas the NLR is always positive and, for practical purposes, size-independent (Fig. 2b). On the other hand, Table 2 shows the polarization-dependence of the NLO response for the anisotropic system. It can be appreciated how one can pass from negative to null NLA by tuning the incident polarization from the minor to the major axis of the deformed NPs (Fig. 2c). The opposite occurs for the NLR: one passes from null to positive NLR when the incident polarization goes from the minor to the major axis (Fig. 2d, null signal is not shown for the sake of a better visualization).
Furthermore, it is evident from Tables 1 and 2 that third order NLO response is highly sensitive to changes in the linear optical response. That is, size and geometry of NPs that affect linear optical response, also affect the NLO one. Thus the effective coefficient of absorption, α = α0 + I0β, and index of refraction, n = n0 + I0n2, depend upon magnitude and sign of β and n2, which at the same time depend upon size and shape of NPs as well as I0. These changes in α and n may be estimated using n0 = 1.703 as the linear refractive index of the composite system [26] and Tables 1 and 2, by calculating the ratios α/α0 and n/n0, respectively. For the spherical-like NPs, the absorption decreases with size from 30% to 70%, while the change for the refraction index varies around 22%, independently on size and on incident energy. For a given size, the absorption decreases with energy around another 10%. For the anisotropic system, the absorption of the minor axis decreases around 30% with respect to the isotropic one, decreasing another 10% when increasing the incident energy. Regarding the refraction index, it changes around 16%, independently of the incident energy.
On the other hand, for the anisotropic system when excited with linearly polarized light parallel to NPs’ major axis, it can be noticed that it might be employed in order to accomplish all-optical switching technologies since it presents both large NLR and small NLA. The FOM W (one-photon FOM) and T (two-photon FOM) are defined as:
where Is = -α0/β is the saturation intensity. For a certain material to be used for all-optical switching, it must satisfy both W > 1 and T < 1. In this particular case β is null, while its value is of the order of ~10−6 cmW−1 for the minor axis; therefore, in order to carry out calculations without having divergent values for Is, we use a constant value of β equal to −1 × 10−7 cmW−1. The values obtained for these parameters when increasing the incident energy are shown in Table 3. It can be seen that in all the cases W > 1 and T < 1.Table 3. All-optical switching FOMs.
Finally, the experimental results from pump-probe measurements for isotropic composites show an ultra-fast response following the envelope of the pulse shape through the first part of the induced delay, as can be observed in Fig. 3(a).However, as is shown in Fig. 3(b), where a bi-exponential fitting was used, there is also a second time response for longer delays of the probe beam of around 30 ps which may also be considered a fast recovery, confirming the fast relaxation times of these composites. According to previous reports [38], this fast recovery would be related to electron-phonon scattering, indicating how the excitation of SPRs releases energy to lattice. Likewise, calculations with the two-temperature model, similar to that proposed in [38,39], but using the complete two coupled heat equations [40,41], show firstly that the increase in the electron gas temperature is much larger for the 13 nm NPs than for the 5 nm ones, and consequently the cooling time is also larger. This agrees very well with the measured intensity of the NLA as well as with the measured temporal decay (lifetime) in the samples with NPs of different size.
Fig. 3 (a) Pump-probe measurements for isotropic composites. (b) Bi-exponential fitting for temporal recovery of the probe beam transmittance.
4. Conclusion
The third-order NLO response of Au NPs embedded in sapphire by using ion implantation presented a negative nonlinear absorption increasing with size, and size independent positive nonlinear refraction, for the spherical-like particles at 532 nm and 26 ps pulses. The increment of the NLA with size could be related to an additional quadrupolar light-matter interaction as the size increases. On the other hand, when the shape of the nanoparticles was changed from spherical-like to a prolate one by swift heavy-ion irradiation using Si3+, obtaining an anisotropic composite consisting in deformed NPs, all oriented in the direction of the Si beam irradiation, the system presented a tuning of the NLO response of the anisotropic system by varying the incident polarization, which, added to appropriate figures of merit and fast relaxation times, offers potential applications in ultra-fast all-optical switching and signal modulation.
Acknowledgments
The authors wish to acknowledge the technical assistance of K. López, F. J. Jaimes and J. G. Morales. We also acknowledge financial support from PAPIIT-UNAM through grants IT102013, IN108412 and IN108113; from CONACyT through grant 102937; from AFOSR through grant FA9550-12-1-0235; and from DGAPA.
References and links
1. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012). [CrossRef]
2. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rev. 408, 131–314 (2005).
3. M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011). [CrossRef] [PubMed]
4. L. Tamayo-Rivera, R. C. Fernández-Hernández, L. Rodríguez-Fernández, R. Rangel-Rojo, A. Oliver, and J. A. Reyes-Esqueda, “Wavelength-varying third-order nonlinear optical response of Ag nanoparticles-Si quantum dots integrated plasmonic system,” Opt. Mater. Express 1(5), 980–989 (2011). [CrossRef]
5. C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104(1), 014306 (2008). [CrossRef]
6. R. C. Fernández-Hernández, R. Gleason-Villagran, C. Torres-Torres, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, A. López-Suárez, R. Rangel-Rojo, A. Oliver, and J. A. Reyes-Esqueda, “On the physical contributions to the third-order nonlinear optical response in plasmonic nanocomposites,” J. Opt. 14(12), 125203 (2012). [CrossRef]
7. K. Wang, H. Long, M. Fu, G. Yang, and P. Lu, “Size-related third-order optical nonlinearities of Au nanoparticle arrays,” Opt. Express 18(13), 13874–13879 (2010). [CrossRef] [PubMed]
8. J. Fischer, N. Bocchio, A. Unger, H.-J. Butt, K. Koynov, and M. Kreiter, “Near-field-mediated enhancement of two-photon-induced fluorescence on plasmonic nanostructures,” J. Phys. Chem. C 114(49), 20968–20973 (2010). [CrossRef]
9. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997). [CrossRef]
10. C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005). [CrossRef] [PubMed]
11. V. Yannopapas, “Enhancement of nonlinear susceptibilities near plasmonic metamaterials,” Opt. Commun. 283(8), 1647–1649 (2010). [CrossRef]
12. S. Palomba, M. Danckwerts, and L. Novotny, “Nolinear plasmonics with gold nanoparticle antenna,” J. Opt. A, Pure Appl. Opt. 11(11), 114030 (2009). [CrossRef]
13. Y. H. Su, S. L. Tu, S.-W. Tseng, Y. C. Chang, S. H. Chang, and W. M. Zhang, “Influence of surface plasmon resonance on the emission intermittency of photoluminescence from gold nano-sea-urchins,” Nanoscale 2(12), 2639–2646 (2010). [CrossRef] [PubMed]
14. K. Wang, H. Long, M. Fu, G. Yang, and P. X. Lu, “Intensity-dependent reversal of nonlinearity sign in a gold nanoparticle array,” Opt. Lett. 35(10), 1560–1562 (2010). [CrossRef] [PubMed]
15. R. Philip, G. R. Kumar, N. Sandhyarani, and T. Pradeep, “Picosecond optical limiting in monolayer protected cluster gold, silver and gold-silver alloy nanoclusters,” Phys. Rev. B 62, 13160–13166 (2000). [CrossRef]
16. J. T. Seo, Q. G. Yang, W. J. Kim, J. H. Heo, S. M. Ma, J. Austin, W. S. Yun, S. S. Jung, S. W. Han, B. Tabibi, and D. Temple, “Optical nonlinearities of Au nanoparticles and Au/Ag coreshells,” Opt. Lett. 34(3), 307–309 (2009). [CrossRef] [PubMed]
17. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007). [CrossRef]
18. Y. Li, S. Zhang, J. Liu, and K. Zhang, “Quantum correlation between fundamental and second-harmonic field via second-harmonic generation,” J. Opt. Soc. Am. B 24(3), 660–663 (2007). [CrossRef]
19. L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” Proc. Natl. Acad. Sci. U.S.A. 100(23), 13549–13554 (2003). [CrossRef] [PubMed]
20. S. Lal, S. E. Clare, and N. J. Halas, “Nanoshell-enabled photothermal cancer therapy: Impending clinical impact,” Acc. Chem. Res. 41(12), 1842–1851 (2008). [CrossRef] [PubMed]
21. X. Huang, S. Neretina, and M. A. El-Sayed, “Gold nanorods: From synthesis and properties to biological and biomedical applications,” Adv. Mater. 21(48), 4880–4910 (2009). [CrossRef]
22. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, 1985)
23. J. E. Midwinter, Photonics in Switching (Academic Press, 1993)
24. C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007). [CrossRef]
25. A. L. González, J. A. Reyes-Esqueda, and C. Noguez, “Optical properties of elongated noble metal nanoparticles,” J. Phys. Chem. C 112(19), 7356–7362 (2008). [CrossRef]
26. P. E. Mota-Santiago, A. Crespo-Sosa, J. L. Jiménez-Hernández, H. G. Silva-Pereyra, J. A. Reyes-Esqueda, and A. Oliver, “Size characterization of noble-metal nano-crystals formed in sapphire by ion irradiation and subsequent thermal annealing,” Appl. Surf. Sci. 259, 574–581 (2012). [CrossRef]
27. P. E. Mota-Santiago, A. Crespo-Sosa, J. L. Jiménez Hernández, H. G. Silva-Pereyra, J. A. Reyes-Esqueda, and A. Oliver are preparing a manuscript to be called “Ion beam induced deformation of gold nano-particles embedded in Sapphire.”
28. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6(6), 953–970 (1988). [CrossRef]
29. G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spälter, R. E. Slusher, S. W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25(4), 254–256 (2000). [CrossRef] [PubMed]
30. K. Wang, H. Long, M. Fu, G. Yang, and P. Lu, “Intensity-dependent reversal of nonlinearity sign in a gold nanoparticle array,” Opt. Lett. 35(10), 1560–1562 (2010). [CrossRef] [PubMed]
31. A. L. Stepanov, C. Marques, E. Alves, R. C. da Silva, M. R. Silva, R. Ganeev, A. I. Ryasnyanskiy, and T. Usmanov, “Nonlinear optical properties of gold nanoparticles synthesized by ion implantation in sapphire matrix,” Tech. Phys. Lett. 31(8), 702–705 (2005). [CrossRef]
32. R. A. Ganeev, A. I. Ryasnyansky, A. L. Stepanov, C. Marques, R. C. da Silva, and E. Alves, “Application of RZ-scan technique for investigation of nonlinear refraction of sapphire doped with Ag, Cu, and Au nanoparticles,” Opt. Commun. 253(1-3), 205–213 (2005). [CrossRef]
33. M. Nastasi and J. W. Mayer, “Ion Implantation and Synthesis of Materials,” Springer, NY, (2006).
34. E. Cattaruzza and F. Gonella, “Metal Nanoclusters by Ion Implantation,” H. S. Nalwa (Ed), Encyclopedia of Nanoscience and Nanotechnology, Vol.5, American Scientific Publishers, 369–385 (2004).
35. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]
36. J. M. Khosrofian and B. A. Garetz, “Measurement of a Gaussian laser beam diameter through the direct inversion of knife-edge data,” Appl. Opt. 22(21), 3406–3410 (1983). [CrossRef] [PubMed]
37. G. Boundebs and K. Fedus, “Absolute measurement of the nonlinear refractive indices of reference materials,” J. Appl. Phys. 105(10), 103106 (2009). [CrossRef]
38. O. Kahl, D. Fishman, S. Webster, D. J. Hagan, E. W. Van Stryland, F. Niessler, and M. Wegener, “Thermal nonlinearities in gold nanostructures,” (personal communication, 2013).
39. S. I. Anisimov, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).
40. M. Toulemonde, C. Dufour, and E. Paumier, “Transient thermal process after a high-energy heavy-ion irradiation of amorphous metals and semiconductors,” Phys. Rev. B Condens. Matter 46(22), 14362–14369 (1992). [CrossRef] [PubMed]
41. Ch. Dufour, V. Khomenkov, G. Rizza, and M. Toulemonde, “Ion-matter interaction: the three-dimensional version of the thermal spike model. Application to nanoparticle irradiation with swift heavy ions,” J. Phys. D Appl. Phys. 45(6), 065302 (2012). [CrossRef]
