Abstract

We report on the fabrication of sapphire samples containing platinum nanoparticles (Pt-NPs) and platinum ions (Pt-ions) and the investigation of their third-order nonlinear (NL) optical properties. The presence of Pt-NPs was confirmed by electronic microscopy and by the linear absorption spectrum that shows a localized surface plasmon band centered at 290 nm. A sample without NPs but containing Pt-ions was also studied. The absorptive and refractive contributions to the nonlinearity were studied using the z-scan technique with 100 fs pulses at 800nm. The experiments revealed a NL refractive index, +3.8×10−13 < n2 < +1.3×10−12 cm2/W and NL absorption coefficient (β < 9.3 cm/GW). The results show enhancement of about five orders of magnitude with respect to the NL refractive index of sapphire.

© 2016 Optical Society of America

1. Introduction

Metal-dielectric nanocomposites (MDNCs) containing metallic nanoparticles (NPs) embedded in a transparent dielectric matrix have been attracting considerable attention due to their large linear and nonlinear (NL) optical properties that makes them promising materials for all-optical signal processing devices [1–10]. The optical absorption of MDNCs in the visible region is much influenced by the localized surface plasmon resonance (LSPR) associated to the NPs. For spherical NPs with dielectric function εm = ε′m + iε″m, embedded in a dielectric matrix with a real εd, the absorption coefficient, α0, of the MDNC is given by [1, 2]:

α0=p18πnd3λεm(εm+2εd)2+εm2,
where nd is the refractive index of the host, p is the NPs filling fraction (the volume fraction of the sample occupied by the NPs). Hence, α0 has a maximum at the LSPR frequency, ωsp, corresponding to ε′m(ωsp) + 2εd(ωsp) = 0.

It is also well recognized that the NL optical properties of the MDNC’s depend on the LSPR and then the optical response is very sensitive to the light wavelength. In particular the third order NL susceptibility, χ(3), shows a significant enhancement for wavelengths around the LSPR [5–10]. According to the effective medium theory, the MDNC’s effective third-order susceptibility, χeff(3) can be written as [3, 4, 11–13]:

χeff(3)=χh(3)+p[3εdεm+iεm+2εd]4χm(3)χh(3)+pf12|f1|2χm(3),
where f1 = 3εd/(ε′m + iε″m + 2εd) is the local field factor, χm(3) and χh(3) are the third-order susceptibility of the NPs and host matrix, respectively. In this way it is possible to tailor the NL response of the MDNCs by changing the density, size and shape of the NPs and the dielectric contrast between the metallic NPs and the host [11, 12, 14–17]. In particular, there has been large amount of work on Ag, Cu, and Au NPs embedded in silica or sapphire because their LSPR frequencies are located in the UV-visible range that is accessible using a large variety of lasers [17]. Other systems that are receiving more attention are silica or sapphire containing either platinum (Pt) NPs or Pt ions. In the case of Pt-NPs the LSPR is located in the UV for wavelengths smaller than 300 nm and therefore, large transparency and low propagation losses in the visible and infrared range are expected for Pt-NPs containing MDNCs; making then useful for building all-optical signal processing devices.

On the other hand; expression 2 shows that the effective nonlinearity of MDNCs depend in a strong way on the dielectric contrast between the host and the metal NPs, through the fourth power dependence on the local field factor f1. Therefore, by choosing a host with a high refractive index such as sapphire will result in a larger effective nonlinearity than silica, for example. It is worth mentioning that there are few studies of MDNCs consisting of sapphire containing Pt-NPs or Pt-ions [17,18] and NPs suspensions in liquids [19–23]. Other advantages associated to sapphire based MDNCs are the large thermal conductivity and high resistance to mechanical and optical damage.

There are many techniques to fabricate MDNCs, such as: laser ablation, chemical synthesis, sol gel, ion-implantation; each technique presents relative advantages and disadvantages. Among them, ion-implantation has been used to successfully produce different MDNCs with suitable properties [18, 24–27]. Some advantages of the technique are the production of relatively narrow particle size distributions, a well-controlled penetration depth, the capability of achieving high NPs filling fractions by appropriate control of the host temperature and atmosphere environment. Furthermore, it has been recently shown that channel waveguides can be successfully produced by a masked ion-implantation technique [18, 24–30]. Indeed, ion implantation is one of the most promising enhanced fabrication methods to produce MDNCs for photonics.

In this work we report on the use of the ion-implantation technique for fabrication of MDNCs containing Pt – NPs (and Pt – ions) embedded in sapphire. Also a study of their linear and third-order NL optical properties of the Pt based MDNCs is presented.

2. Preparation and characterization of samples

Three samples (labeled as A, B, and C) were produced by ion-implantation of Pt ions in sapphire substrates. The fabrication process consists of implanting 2 MeV Pt+ ions at room temperature in sapphire plates as host matrices using a Pt-ion fluence of 2.5 × 1016 Pt+/cm2. The resulting implanted ion distribution was measured by Rutherford Backscattering Spectrometry (RBS). Figure 1 shows the results from which an approximately gaussian distribution can be obtained, with a 190 nm FWHM with at a 330 nm depth, obtained from the analysis of the RBS data [31]. All ion-implantation processes and RBS measurements were made using the 3 MV Tandem accelerator (NEC 9SDH-2) at UNAM.

 figure: Fig. 1

Fig. 1 Rutherford Backscattering Spectrum of the sample as implanted. The Pt depth profile is fitted to a Gaussian with a maximum at 330 nm and a FWHM of 190 nm. The ion fluence was 2.8 × 1016 ions/cm2.

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After the ion implantation process, the samples A and B were thermally annealed at 1100°C for 60min and 800°C for 20min, respectively. The annealing process was performed using a 50%N2 + 50%H2 reducing atmosphere in order to obtain the highest amount of near-spherical Pt – NPs by nucleation of the implanted ions, similarly to the case of spherical Ag and Au NPs reported in [32]. Sample C was prepared using the same Pt+ dose as A and B but it was not annealed, and was made to provide a reference sample with no nanoparticles but the same Pt-ion doses for comparison.

The optical absorption spectra of the samples were measured using a Fluorescence Spectrophotometer (Hitachi F-7000) and Fig. 2 shows the results for the three samples; A, B and C in blue, green and red in continuous line, respectively. The black dashed-point line in Fig. 2 shows the theoretical fit to the absorption spectrum of spherical NPs determined by using the Eq. (1) and the frequency dependence of the dielectric functions of platinum and sapphire reported in [33] and [34], respectively. The absorption spectra of sample A shows a resonance band centered at ≈ 290 nm. In order to match the optical density value at the LSPR peak a filling fraction value of p = 0.015 was employed. The theoretical fit shows that this band corresponds to the LSPR of spherical Pt – NPs. Given the shorter annealing time, and slightly lower temperature, it is expected that sample B should have fewer and smaller NPs formed, as indicated by the absence of a well-formed LSPR peak, in Fig 2, but no quantitative determination was made. On the other hand, sample C did not show a defined resonance band in the same spectral region, since the formation of Pt – NPs is not expected in this case. Experimentally, it is well-known that the position of the LSPR moves for different particle sizes, and therefore polydisperse mixtures of NPs will have wide LSPR. In our case, the fact that the width of the calculated LSPR is very similar to that of the experimental data, indicates that the NPs size distribution is narrow. The presence of an absorption pedestal observed for this sample seems to be related to the LSPR.

 figure: Fig. 2

Fig. 2 Absorbance spectra of samples A, B and C. The presence of the LSPR for samples A and B indicates the formation of NPs, while its absorbance in C shows that no NPs are present. The dashed black points are the theoretical absorbance spectra of spherical Platinum nanoparticles in Sapphire.

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Figure 3 shows the transverse SEM images of sample A. Figure 3(a) shows the thin Pt – NPs layer embedded in the sapphire substrate near the surface of the sample. This is in good agreement with the results shown in Fig. 1. Figure 3(b) show the transverse SEM images of a sample that presents near-spherical Pt-NPs with average diameter of 6 nm.

 figure: Fig. 3

Fig. 3 Shows transversal SEM images of a sample implanted with Pt ions and annealed for 60 min in a reducing atmosphere. The images were formed capturing the backscaterred electrons, in order to appreciate the difference in atomic number between the matrix and the Pt nanoparticles. Both images were taken in different resolution scale a) in 100 nm and b) in 50 nm, respectively.

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In order to obtain the crystalline structure of the nanoparticles, we performed X-Ray Diffraction analysis and compared with well-known FCC crystalline structures. Figure 4 shows the X-Ray Diffraction spectrum of the sample A containing Pt NPs in sapphire as the black line, while the blue line is the theoretical simulation of FCC, which give us a size of 6 nm of Pt nanoparticles using Scherer formula.

 figure: Fig. 4

Fig. 4 X-Ray diffraction spectrum of sample A containing Pt nanoparticles in sapphire and compared with the theoretical FCC simulation.

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3. Third-order nonlinear optical properties

3.1. Experimental setup

In order to measure the NL optical properties, we based our studies in the z-scan technique, since it allows the measurements of the refractive and absorptive contributions to the nonlinearity as well as the determination of their sign. This is accomplished by scanning the position of the NL sample across the focal plane at a focused gaussian beam, while the far field transmittance is measured through an aperture (Closed z-scan). Due to the fact that NL absorption can also be present, this apertured detector is sensitive to changes in both NL absorption and refraction as well. Therefore a no-apertured detector is required (Open z-scan) to characterize the NL absorption effect [35]. The usual procedure is then to divide the closed aperture data over the open one to get only the refractive component.

Therefore, the NL parameters of the samples were investigated applying the z-scan technique using a Ti:Sapphire laser with a regenerative amplifier (100 fs pulses; 800 nm; 1 kHz). The dual-arm setup used is sketched in Fig. 5 where L1 – L2 are lenses with focal length of 15 cm, BS are beams splitters and D1 – D4 are photodetectors fitted to a boxcar and computer. The incident laser power, monitored by the detector D1, was controlled by a half-wave plate followed by a polarizer prism. The sample was mounted in a stage that moves along the beam propagation direction (Z axis). The beam waist at Z = 0 was 27 μm. Pre-focal and post-focal positions correspond to Z < 0 and Z > 0, respectively. After crossing the sample, the laser beam passes through a circular aperture of radius ra, placed in the far-field region, being detected by the photodiode D2. To detect variations in the beam wavefront due to the NL refractive index, ra should be smaller than the beam width, wa, in the aperture position (closed-aperture scheme). The ratio between the intensity transmitted through the aperture and the incident intensity in the aperture is given by S=1exp(2ra2/wa2). When the transmitted light is unblocked (S = 1) the NL absorption coefficient, β, can be determined (open-aperture scheme) and in our setup this signal is detected by the photodiode D3.

 figure: Fig. 5

Fig. 5 Dual-arm z-scan setup used. The detector D1 monitors the input laser power, while the detectors D2 and D4 monitor the closed aperture z-scan signal and fluctuations due to changes in the incident laser spatial profile, respectively. The detectors D3 and D5 monitor the open-aperture z-scan signal from the sample and for energy fluctuations in the profile of the reference beam, respectively.

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To compensate for fluctuations in the laser intensity, the use of a reference channel was very important to improve the signal-noise ratio by compensation of the laser pointing instability, hot-points in the incident beam profile, etc [36, 37]. Another important aspect concerning the use of this dual-arm setup is that the pulse widths of both arms are identical as the dispersion in the optical elements is the same in each arm. The photodiodes D4 and D5 monitor the reference beam.

The NL optical response was determined by scanning the samples in the focal region of lens L1. The difference between the normalized transmittances in the peak and valley of the Z-scan profile, ΔTpv, is proportional to the NL coefficients. For S < 1 we have ΔTpv = 0.406kLeffn2I0 and for S = 1 we obtain ΔTpv=8β0I0Leff, where k = 2π/λ, Leff = [1 − exp(−α0L)]/α0, L is the sample length, α0 is the linear absorption coefficient and I0 is the laser intensity at the beam axis.

3.2. Results and discussion

We studied the NL optical response of the three samples, A and B containing PtNPs and C containing Ptions in Sapphire as host. According to the spectrum in Fig 2, the wavelength of the laser used (λ = 800 nm) lies in the nonresonant regime for samples B and C, and with respect to sample A, this presents a small absorption. To determine the NL optical properties, the setup was previously calibrated using carbon disulfide (CS2), as a reference NL medium with well-known values of n2 and β at 800 nm and peak irradiance I0 = 5.3 × 1010 W/cm2 employed [38].

Figure 6 shows the open-aperture z-scan profiles of all samples studied. Notice that no NL absorption was detected even though sample A showed a small linear absorption at 800 nm. This indicates that the β value is smaller than the minimum value that our apparatus can detect (β < 9.31 cm/GW).

 figure: Fig. 6

Fig. 6 Open-aperture z-scan results for the samples containing near spherical platinum nanoparticles (A and B) and ion-platinum nanoparticles (C). For this experiments, the irradiance used was I0 = 5.3 × 1010 W/cm2

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Figure 7 shows the closed aperture z-scan profiles where the circles represent the experimental results and the continuous lines are the theoretical fits to the data. Notice that all samples manifest the signature of a positive n2, where we can see a pre-focal minimum followed by a post-focal maximum.

 figure: Fig. 7

Fig. 7 Closed-aperture z-scan results for the samples A, B and C. For these experiments, the irradiance used was I0 = 5.3 × 1010 W/cm2

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The pulse duration and laser repetition rate were chosen to minimize the possible thermal contributions to the NL response. Accordingly, the 100 fs pulse duration was too short compared to the slow rise time of the thermal response, therefore avoiding intrapulse heating of the samples. On the other hand, the temporal spacing between subsequent pulses (1 ms) is too long in comparison to the thermal characteristic time (tc, related to thermal diffusion coefficient D of the material), avoiding in this case cumulative pulse to pulse effects [38, 39].

In principle, the sapphire matrix may contributes to the effective NL response of the samples and because of this reason, we conducted z-scan experiments in a pure sapphire sample. Two irradiances were used: 5.3 × 1010 W/cm2 and 47.3 × 1010 W/cm2. In the lower irradiance case, the NL optical response was not discernible for either the NL absorption and NL refraction effects. The results for the largest irradiance we shown in Fig. 8, where it is possible to observe a positive n2, and non-discernible NL absorption.

 figure: Fig. 8

Fig. 8 Open (a) and closed-aperture (b) z-scan results for the sapphire matrix using a irradiance I0 = 47.3 × 1010 W/cm2

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The values of n2, determined from theoretical fits of the data, are given in Table 1. From the table it can be seen that both samples A and B have a larger value of n2 than sample C. This correlates very well with the fact that the former have NPs while the latter does not. The presence of the LSPR therefore enhances the NL response observed.

Tables Icon

Table 1. Nonlinear optical properties n2 and β, and figures of merit W and T, evaluated under the irradiances showed for samples A, B and C and n2 for sapphire matrix for two irradiances.

The photon energy employed is far smaller than the LSPR, therefore placing our experiments in the off-resonant regime. It has been shown that in this case, the main contribution to the NL response arises from intraband transitions experimented by the essentially free electrons in the NPs [40]. Although a contribution from hot electrons could be present, this is usually not relevant for such far from resonance wavelengths employed here [40]. Regarding the difference in the magnitude of the NL response observed for the NPs containing samples (A and B) compared to that with no annealing treatment (sample C), it is worth pointing that although we are away from resonance, the presence of the LSPR can enhance the nonlinearity by mechanisms such as a Two Photon Absorption resonance which is accounted for in the nonlinear Kramers-Kröning relations [41].

In order to evaluate the potential of the material for application in all-optical switching devices, it is useful to calculate the figures of merit devised to assess the potential of different materials [42]. The first figure of merit W is given by:

W=Δnmaxλα0,
where Δnmax is the maximum achievable refractive index change (when saturable absorption is present, Δnmax = n2Is, with Is the saturation irradiance). This figure of merit indicates whether a given refractive index change can be achieved within an absorption length (Łabs = 1/α0). The second one, T given by:
T=βλn2,
indicates whether NL absorption can limit or not the applicability of the materials. The acceptable values of W and T are device dependent, but we can assume that W > 1, and T < 1.

In our case, we use the experimental data taken at the highest irradiance employed in order to estimate Δnmax, and hence a lower bound for W. Although we were not able to measure the actual β values for the samples, because of the lack of a measurable signal, nevertheless we could establish an upper bound for them. We can use these bound values to calculate in turn upper bounds for the values of T. The calculated W and T values are shown in Table 1.

The calculated W values are marginally lower than those required, but it should be taken into account that we do not observe signs of saturation and therefore larger values of Δnmax can be achieved, taking the W values above the required threshold. All the T values on the other hand, are below the maximum admissible value, and because we only have an upper bound for their value, they are actually even smaller. In this way, the NL response of our samples is free of deleterious NL absorption effects, and the refractive nonlinearity is probably large enough to achieve switching within an absorption length.

On the other hand, the sapphire matrix showed a value for n2, in agreement with reference [43], that is almost five orders of magnitude smaller in comparison with the Pt+ implanted samples. It is worth noticing that in the calculation of the n2 values for sapphire, the NL interaction length L was taken to be a 1 mm, the width of the sapphire plate, while for the nanocomposites the width employed is that of the nanoparticles layer, 400 nm. Hence, although we only needed an irradiance one order of magnitude larger to record a z-scan signal in pure sapphire, the NL refractive index is almost five orders of magnitude smaller than for the fabricated samples. Therefore the contribution of the sapphire matrix for the effective nonlinearity represented by Eq. 2 is not relevant.

4. Conclusions

In summary, this work reported the fabrication by ion-implantation of nanocomposites containing Pt – NPs and Pt – ions. A study of the third-order NL optical properties of the composites fabricated was performed to evaluate the contributions of the Pt-NPs and Pt-ions to the NL response of the samples. All platinum implanted samples presented large positive NL refractive index, that are five orders of magnitude larger than the sapphire substrate. Comparing the results obtained, we note that the formation of Pt – NPs produced large enhancement in the NL response than in the sample containing Pt – ions. In all cases the NL absorption coefficient was smaller than β < 9.3 cm/GW. Considering the large n2 values and negligible NL absorption we claim that composites with platinum nanoparticles embedded in sapphire have very large potential for application in all-optical signal processing devices.

Acknowledgments

We want to acknowledge the partial support of this work by CONACyT-Mexico through the Grant No. 222485 and DGAPA-UNAM IN108113, both in Mexico and, the work in Brazil supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação de Amparoà Ciência e Tecnologia de Pernambuco (FACEPE). We also acknowledge Karim Lopez, Francisco Jaimes, Mauricio Escobar and Juan Gabriel-Morales for fabrication of the samples. B. Can-uc acknowledges the Scholarship No. 221750 provided by CONACyT-Mexico and H. Baltar acknowledges a post-doctoral fellowship supported by CNPq.

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43. I. P. Nikolakakos, A. Major, J. S. Aitchison, and E. W. Smith, “Broadband characterization of the nonlinear optical properties of common reference materials,” IEEE J. Quantum Electron. 10(5), 1164–1170 (2004). [CrossRef]  

References

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  30. E. Flores-Romero, G. V. Vázquez, H. Márquez, R. Rangel-Rojo, J. Rickards, and R. Trejo-Luna, “Optical channel waveguides by proton and carbon implantation in Nd:YAG crystals,” Opt. Express 15(14), 8513–8520 (2007).
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  37. M. R. Ferdinandus, M. Reichert, T. R. Ensley, H. Hu, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Dual-arm Z-scan technique to extract dilute solute nonlinearities from solution measurements,” Opt. Mater. Express,  2(12), 1776–1790 (2012).
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  40. 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. 4(12), 125203 (2012)
    [Crossref]
  41. D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Krnig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992)
    [Crossref]
  42. G. I. Stegeman, “All-optical devices: materials tequirements,” Proc. SPIE 1852, 75–89 (1993).
    [Crossref]
  43. I. P. Nikolakakos, A. Major, J. S. Aitchison, and E. W. Smith, “Broadband characterization of the nonlinear optical properties of common reference materials,” IEEE J. Quantum Electron. 10(5), 1164–1170 (2004).
    [Crossref]

2016 (1)

C. B. de Araújo, L. R. P. Kassab, C. T. Dominguez, S. J. L. Ribeiro, A. S. L. Gomes, and A. S. Reyna, “Photoluminescence and nonlinear optical phenomena in plasmonic random media a review of recent works,” J. Lumin. 169, 492–496 (2016).
[Crossref]

2015 (3)

R. Sato, M. Ohnuma, K. Oyoshi, and Y. Takeda, “Spectral investigation of nonlinear local field effects in Ag nanoparticles,” J. Appl. Phys. 117, 113101 (2015).
[Crossref]

A. S. Reyna and C. B. de Araújo, “An optimization procedure for the design of all-optical switches based on metal-dielectric nanocomposites,” Opt. Express 25, 7659–7666 (2015).
[Crossref]

B. Can-Uc, R. Rangel-Rojo, H. Márquez, L. Rodríguez-Fernández, and A. Oliver, “Nanoparticle containing channel waveguides produced by a multi-energy masked ion-implantation process,” Opt. Express 23(3), 3176–3185 (2015).
[Crossref] [PubMed]

2014 (3)

A. Chehreghani and M. J. Torkamany, “Nonlinear optical properties of laser synthesized Pt nanoparticles: Saturable and reverse saturable absorption,” Laser Phys. 24, 015901 (2014).
[Crossref]

T. J. Antosiewicz and S. P. Apell, “Plasmonic glasses: Optical properties of amorphous metal-dielectric composites,” Opt. Express 22, 2013–2042 (2014).
[Crossref]

A. S. Reyna and C. B. de Araújo, “Nonlinearity management of photonic composites and observation of spatial modulation instability due to quintic nonlinearity,” Phys. Rev. A 89, 063803 (2014).
[Crossref]

2013 (3)

B. Can-Uc, R. Rangel-Rojo, H. Márquez, L. Rodríguez-Fernández, and A. Oliver, “Polarization selectable nonlinearities in elongated silver nanoparticles embedded in silica,” Opt. Mater. Express 3(12), 2012–2021 (2013).
[Crossref]

H. Márquez, D. Salazar, R. Rangel-Rojo, J. L. Angel-Valenzuela, G. V. Vázquez, and E. Romero, “Sythesis of optical waveguides in SiO2 by silver ion implantation,” Opt. Mater. 35, 927–934 (2013).
[Crossref]

G. Fan, S. Ren, S. Qu, Z. Guo, Q. Wang, Y. Wang, and R. Gao, “Mechanisms for fabrications and nonlinear optical properties of Pd and Pt nanoparticles by femtosecond laser,” Opt. Commun. 295, 219–225 (2013).
[Crossref]

2012 (4)

2011 (1)

A. L. Stepanov, “Nonlinear optical properties of implanted metal nanoparticles in various transparent matrixes: a review,” Rev. Adv. Mater. Sci. 27, 115–145 (2011).

2010 (1)

A. Meldrum, R. Lopez, R. Magruder, L. Boatner, and C. White, “Structure and properties of nanoparticles formed by ion implantation,” Topics Appl. Physics 116, 255–285 (2010).
[Crossref]

2009 (3)

R. A. Ganeev, R. I. Tugushev, and T. Usmanov, “Application of the nonlinear optical properties of platinum nanoparticles for mode locking of Nd:glass laser,” Appl. Phys. B 94, 647–651 (2009).
[Crossref]

J. A. Reyes-Esqueda, V. Rodríguez-Iglesias, H. G. Silva-Pereyra, C. Torres-Torres, A. L. Santiago-Ramírez, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodriguez-Fernandez, A. López-Suárez, and A. Oliver, “Anisotropic linear and nonlinear optical properties from anisotropy-controlled metallic nanocomposites,” Opt. Express,  17(15), 12849–12868 (2009).
[Crossref] [PubMed]

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

2007 (1)

2006 (3)

F. Chen, L. Wang, Y. Jiang, X. L. Wang, K. M. Wang, G. Fu, Q.M. Lu, C. E. Rter, and D. Kip, “Optical channel waveguides in Nd : YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett. 88, 071123 (2006).
[Crossref]

A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velasquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Nóguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74, 245425 (2006).
[Crossref]

J. P. Huang and K. W. Yu, “Enhanced nonlinear optical responses of materials: composite effects,” Phys. Rep. 431, 87–172 (2006).
[Crossref]

2005 (3)

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251, 429–433 (2005).
[Crossref]

A. L. Stepanov and I. B. Khaibullin, “Fabrication of metal nanoparticles in sapphire by low-energy ion implantation,” Rev. Adv. Mater. Sci. 9, 109–129 (2005).

A. Gnoli, L. Razzari, and M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express,  13(20), 7976–7981, (2005).
[Crossref] [PubMed]

2004 (1)

I. P. Nikolakakos, A. Major, J. S. Aitchison, and E. W. Smith, “Broadband characterization of the nonlinear optical properties of common reference materials,” IEEE J. Quantum Electron. 10(5), 1164–1170 (2004).
[Crossref]

2003 (1)

Y. Hamanaka, A. Nakamura, N. Hayashi, and S. Omi, “Dispersion curves of complex third-order optical susceptibilities around the surface plasmon resonance in Ag nanocrystal-glass composites,” J. Opt. Soc. Am. 20, 1227–1232 (2003).
[Crossref]

2002 (1)

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203, 283–288 (2002).
[Crossref]

2000 (1)

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. C. Wang, D. B. Poker, and D. K. Hensley, “Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3,” Nucl. Instr. Meth. Phys. Res. B 166, 750–757 (2000).

1999 (1)

M. Falconieri, “Thermo-optical effects in z-scan measurements using high-repetition-rate lasers,” J. Opt. A: Pure Appl. Opt. 1, 662–667 (1999).
[Crossref]

1998 (1)

1994 (1)

R. J. Haglund, L. Yang, R. I. Magruder, C. White, R. Zuhr, L. Yang, R. Dorsinville, and R. Alfano, “Nonlinear optical properties of metal-quantum-dot composites synthesized by ion implantation,” Nucl. Instr. Meth. Phys. Res. B 91, 493–504 (1994).
[Crossref]

1993 (1)

G. I. Stegeman, “All-optical devices: materials tequirements,” Proc. SPIE 1852, 75–89 (1993).
[Crossref]

1992 (2)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Krnig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992)
[Crossref]

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

1991 (1)

H. Ma, A. S. L. Gomes, and C. B. de Araújo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[Crossref]

1990 (1)

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

Aitchison, J. S.

I. P. Nikolakakos, A. Major, J. S. Aitchison, and E. W. Smith, “Broadband characterization of the nonlinear optical properties of common reference materials,” IEEE J. Quantum Electron. 10(5), 1164–1170 (2004).
[Crossref]

Aktsipetrov, O. A.

Alfano, R.

R. J. Haglund, L. Yang, R. I. Magruder, C. White, R. Zuhr, L. Yang, R. Dorsinville, and R. Alfano, “Nonlinear optical properties of metal-quantum-dot composites synthesized by ion implantation,” Nucl. Instr. Meth. Phys. Res. B 91, 493–504 (1994).
[Crossref]

Angel-Valenzuela, J. L.

H. Márquez, D. Salazar, R. Rangel-Rojo, J. L. Angel-Valenzuela, G. V. Vázquez, and E. Romero, “Sythesis of optical waveguides in SiO2 by silver ion implantation,” Opt. Mater. 35, 927–934 (2013).
[Crossref]

Antosiewicz, T. J.

Apell, S. P.

Banks, C.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. C. Wang, D. B. Poker, and D. K. Hensley, “Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3,” Nucl. Instr. Meth. Phys. Res. B 166, 750–757 (2000).

Boatner, L.

A. Meldrum, R. Lopez, R. Magruder, L. Boatner, and C. White, “Structure and properties of nanoparticles formed by ion implantation,” Topics Appl. Physics 116, 255–285 (2010).
[Crossref]

Bookey, H. T.

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

Boyd, R. W.

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

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
[Crossref]

Can-Uc, B.

Chang, Q.

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251, 429–433 (2005).
[Crossref]

Cheang-Wong, J. C.

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. 4(12), 125203 (2012)
[Crossref]

J. A. Reyes-Esqueda, V. Rodríguez-Iglesias, H. G. Silva-Pereyra, C. Torres-Torres, A. L. Santiago-Ramírez, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodriguez-Fernandez, A. López-Suárez, and A. Oliver, “Anisotropic linear and nonlinear optical properties from anisotropy-controlled metallic nanocomposites,” Opt. Express,  17(15), 12849–12868 (2009).
[Crossref] [PubMed]

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

A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velasquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Nóguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74, 245425 (2006).
[Crossref]

Chehreghani, A.

A. Chehreghani and M. J. Torkamany, “Nonlinear optical properties of laser synthesized Pt nanoparticles: Saturable and reverse saturable absorption,” Laser Phys. 24, 015901 (2014).
[Crossref]

Chen, F.

F. Chen, L. Wang, Y. Jiang, X. L. Wang, K. M. Wang, G. Fu, Q.M. Lu, C. E. Rter, and D. Kip, “Optical channel waveguides in Nd : YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett. 88, 071123 (2006).
[Crossref]

Crespo-Sosa, A.

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. 4(12), 125203 (2012)
[Crossref]

J. A. Reyes-Esqueda, V. Rodríguez-Iglesias, H. G. Silva-Pereyra, C. Torres-Torres, A. L. Santiago-Ramírez, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodriguez-Fernandez, A. López-Suárez, and A. Oliver, “Anisotropic linear and nonlinear optical properties from anisotropy-controlled metallic nanocomposites,” Opt. Express,  17(15), 12849–12868 (2009).
[Crossref] [PubMed]

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

A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velasquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Nóguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74, 245425 (2006).
[Crossref]

Curley, M. J.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. C. Wang, D. B. Poker, and D. K. Hensley, “Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3,” Nucl. Instr. Meth. Phys. Res. B 166, 750–757 (2000).

de Araújo, C. B.

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B. Can-Uc, R. Rangel-Rojo, H. Márquez, L. Rodríguez-Fernández, and A. Oliver, “Nanoparticle containing channel waveguides produced by a multi-energy masked ion-implantation process,” Opt. Express 23(3), 3176–3185 (2015).
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B. Can-Uc, R. Rangel-Rojo, H. Márquez, L. Rodríguez-Fernández, and A. Oliver, “Polarization selectable nonlinearities in elongated silver nanoparticles embedded in silica,” Opt. Mater. Express 3(12), 2012–2021 (2013).
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Wang, K. M.

F. Chen, L. Wang, Y. Jiang, X. L. Wang, K. M. Wang, G. Fu, Q.M. Lu, C. E. Rter, and D. Kip, “Optical channel waveguides in Nd : YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett. 88, 071123 (2006).
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G. Fan, S. Ren, S. Qu, Z. Guo, Q. Wang, Y. Wang, and R. Gao, “Mechanisms for fabrications and nonlinear optical properties of Pd and Pt nanoparticles by femtosecond laser,” Opt. Commun. 295, 219–225 (2013).
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Zhang, X.

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251, 429–433 (2005).
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S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203, 283–288 (2002).
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S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203, 283–288 (2002).
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Appl. Opt. (1)

Appl. Phys. B (1)

R. A. Ganeev, R. I. Tugushev, and T. Usmanov, “Application of the nonlinear optical properties of platinum nanoparticles for mode locking of Nd:glass laser,” Appl. Phys. B 94, 647–651 (2009).
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Appl. Phys. Lett. (2)

F. Chen, L. Wang, Y. Jiang, X. L. Wang, K. M. Wang, G. Fu, Q.M. Lu, C. E. Rter, and D. Kip, “Optical channel waveguides in Nd : YVO4 crystal produced by O+ ion implantation,” Appl. Phys. Lett. 88, 071123 (2006).
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I. P. Nikolakakos, A. Major, J. S. Aitchison, and E. W. Smith, “Broadband characterization of the nonlinear optical properties of common reference materials,” IEEE J. Quantum Electron. 10(5), 1164–1170 (2004).
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J. Appl. Phys. (1)

R. Sato, M. Ohnuma, K. Oyoshi, and Y. Takeda, “Spectral investigation of nonlinear local field effects in Ag nanoparticles,” J. Appl. Phys. 117, 113101 (2015).
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J. Lumin. (1)

C. B. de Araújo, L. R. P. Kassab, C. T. Dominguez, S. J. L. Ribeiro, A. S. L. Gomes, and A. S. Reyna, “Photoluminescence and nonlinear optical phenomena in plasmonic random media a review of recent works,” J. Lumin. 169, 492–496 (2016).
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J. Opt. (1)

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. 4(12), 125203 (2012)
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Laser Phys. (1)

A. Chehreghani and M. J. Torkamany, “Nonlinear optical properties of laser synthesized Pt nanoparticles: Saturable and reverse saturable absorption,” Laser Phys. 24, 015901 (2014).
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Nucl. Instr. Meth. Phys. Res. B (2)

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. C. Wang, D. B. Poker, and D. K. Hensley, “Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3,” Nucl. Instr. Meth. Phys. Res. B 166, 750–757 (2000).

R. J. Haglund, L. Yang, R. I. Magruder, C. White, R. Zuhr, L. Yang, R. Dorsinville, and R. Alfano, “Nonlinear optical properties of metal-quantum-dot composites synthesized by ion implantation,” Nucl. Instr. Meth. Phys. Res. B 91, 493–504 (1994).
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Opt. Commun. (4)

G. Fan, S. Ren, S. Qu, Z. Guo, Q. Wang, Y. Wang, and R. Gao, “Mechanisms for fabrications and nonlinear optical properties of Pd and Pt nanoparticles by femtosecond laser,” Opt. Commun. 295, 219–225 (2013).
[Crossref]

S. Qu, Y. Song, H. Liu, Y. Wang, Y. Gao, S. Liu, X. Zhang, Y. Li, and D. Zhu, “A theoretical and experimental study on optical limiting in platinum nanoparticles,” Opt. Commun. 203, 283–288 (2002).
[Crossref]

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251, 429–433 (2005).
[Crossref]

R. Rangel-Rojo, J. McCarthy, H. T. Bookey, A. K. Kar, L. Rodriguez-Fernández, J. C. Cheang-Wong, A. Crespo-Sosa, A. López-Suares, A. Oliver, V. Rodríguez-Iglesias, and H. G. Silva-Pereyra, “Anisotropy in the nonlinear absorption of elongated silver nanoparticles in silica, probed by femtosecond pulses,” Opt. Commun. 282, 1909– 1912 (2009).
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Opt. Express (7)

A. S. Reyna and C. B. de Araújo, “An optimization procedure for the design of all-optical switches based on metal-dielectric nanocomposites,” Opt. Express 25, 7659–7666 (2015).
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S. Mohan, J. Lange, H. Graener, and G. Seifert, “Surface plasmon assisted optical nonlinearities of uniformly oriented metal nano-ellipsoids in glass,” Opt. Express 20, 28655–28663 (2012).
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B. Can-Uc, R. Rangel-Rojo, H. Márquez, L. Rodríguez-Fernández, and A. Oliver, “Nanoparticle containing channel waveguides produced by a multi-energy masked ion-implantation process,” Opt. Express 23(3), 3176–3185 (2015).
[Crossref] [PubMed]

J. A. Reyes-Esqueda, V. Rodríguez-Iglesias, H. G. Silva-Pereyra, C. Torres-Torres, A. L. Santiago-Ramírez, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodriguez-Fernandez, A. López-Suárez, and A. Oliver, “Anisotropic linear and nonlinear optical properties from anisotropy-controlled metallic nanocomposites,” Opt. Express,  17(15), 12849–12868 (2009).
[Crossref] [PubMed]

E. Flores-Romero, G. V. Vázquez, H. Márquez, R. Rangel-Rojo, J. Rickards, and R. Trejo-Luna, “Optical channel waveguides by proton and carbon implantation in Nd:YAG crystals,” Opt. Express 15(14), 8513–8520 (2007).
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A. Gnoli, L. Razzari, and M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express,  13(20), 7976–7981, (2005).
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Opt. Mater. (1)

H. Márquez, D. Salazar, R. Rangel-Rojo, J. L. Angel-Valenzuela, G. V. Vázquez, and E. Romero, “Sythesis of optical waveguides in SiO2 by silver ion implantation,” Opt. Mater. 35, 927–934 (2013).
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Opt. Mater. Express (2)

Opt. Quantum Electron. (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Krnig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992)
[Crossref]

Phys. Rep. (1)

J. P. Huang and K. W. Yu, “Enhanced nonlinear optical responses of materials: composite effects,” Phys. Rep. 431, 87–172 (2006).
[Crossref]

Phys. Rev. A (2)

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite materials in the Maxwell Garnett model,” Phys. Rev. A 46(3), 1614–1629 (1992).
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A. S. Reyna and C. B. de Araújo, “Nonlinearity management of photonic composites and observation of spatial modulation instability due to quintic nonlinearity,” Phys. Rev. A 89, 063803 (2014).
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Phys. Rev. B (1)

A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velasquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Nóguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74, 245425 (2006).
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Proc. SPIE (1)

G. I. Stegeman, “All-optical devices: materials tequirements,” Proc. SPIE 1852, 75–89 (1993).
[Crossref]

Rev. Adv. Mater. Sci. (2)

A. L. Stepanov, “Nonlinear optical properties of implanted metal nanoparticles in various transparent matrixes: a review,” Rev. Adv. Mater. Sci. 27, 115–145 (2011).

A. L. Stepanov and I. B. Khaibullin, “Fabrication of metal nanoparticles in sapphire by low-energy ion implantation,” Rev. Adv. Mater. Sci. 9, 109–129 (2005).

Topics Appl. Physics (1)

A. Meldrum, R. Lopez, R. Magruder, L. Boatner, and C. White, “Structure and properties of nanoparticles formed by ion implantation,” Topics Appl. Physics 116, 255–285 (2010).
[Crossref]

Other (5)

J. R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Material Analysis, (Material Research Society, 1995).

D. E. Gray, American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, Inc., 1972).

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[Crossref]

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
[Crossref]

S. A. Meier, Plasmonics Fundamentals and Applications (Springer, 2007).

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Figures (8)

Fig. 1
Fig. 1 Rutherford Backscattering Spectrum of the sample as implanted. The Pt depth profile is fitted to a Gaussian with a maximum at 330 nm and a FWHM of 190 nm. The ion fluence was 2.8 × 1016 ions/cm2.
Fig. 2
Fig. 2 Absorbance spectra of samples A, B and C. The presence of the LSPR for samples A and B indicates the formation of NPs, while its absorbance in C shows that no NPs are present. The dashed black points are the theoretical absorbance spectra of spherical Platinum nanoparticles in Sapphire.
Fig. 3
Fig. 3 Shows transversal SEM images of a sample implanted with Pt ions and annealed for 60 min in a reducing atmosphere. The images were formed capturing the backscaterred electrons, in order to appreciate the difference in atomic number between the matrix and the Pt nanoparticles. Both images were taken in different resolution scale a) in 100 nm and b) in 50 nm, respectively.
Fig. 4
Fig. 4 X-Ray diffraction spectrum of sample A containing Pt nanoparticles in sapphire and compared with the theoretical FCC simulation.
Fig. 5
Fig. 5 Dual-arm z-scan setup used. The detector D1 monitors the input laser power, while the detectors D2 and D4 monitor the closed aperture z-scan signal and fluctuations due to changes in the incident laser spatial profile, respectively. The detectors D3 and D5 monitor the open-aperture z-scan signal from the sample and for energy fluctuations in the profile of the reference beam, respectively.
Fig. 6
Fig. 6 Open-aperture z-scan results for the samples containing near spherical platinum nanoparticles (A and B) and ion-platinum nanoparticles (C). For this experiments, the irradiance used was I0 = 5.3 × 1010 W/cm2
Fig. 7
Fig. 7 Closed-aperture z-scan results for the samples A, B and C. For these experiments, the irradiance used was I0 = 5.3 × 1010 W/cm2
Fig. 8
Fig. 8 Open (a) and closed-aperture (b) z-scan results for the sapphire matrix using a irradiance I0 = 47.3 × 1010 W/cm2

Tables (1)

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Table 1 Nonlinear optical properties n2 and β, and figures of merit W and T, evaluated under the irradiances showed for samples A, B and C and n2 for sapphire matrix for two irradiances.

Equations (4)

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α 0 = p 18 π n d 3 λ ε m ( ε m + 2 ε d ) 2 + ε m 2 ,
χ eff ( 3 ) = χ h ( 3 ) + p [ 3 ε d ε m + i ε m + 2 ε d ] 4 χ m ( 3 ) χ h ( 3 ) + p f 1 2 | f 1 | 2 χ m ( 3 ) ,
W = Δ n max λ α 0 ,
T = β λ n 2 ,

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