## Abstract

We present an integrated plasmonic nanocomposite showing a nonlinear optical response changing its sign with wavelength, depending on its position with respect to the surface plasmon resonance of the nanocomposite. This nanocomposite is a SiO_{2} matrix containing both, embedded quasi-spherical Ag nanoparticles and silicon quantum dots. The wavelengths used for the picosecond Z-scan study were 355 and 532 nm, which are localized at both sides of the surface plasmon resonance of the Ag nanoparticles (395 nm), and 1064 nm, which is localized well far away of it. The integrated plasmonic system shows a positive nonlinear refraction below the plasmon resonance, changing to a negative value for wavelengths above resonance. On the other hand, below resonance the nonlinear absorption is cancelled due to opposite responses from the individual nanosystems, while above resonance only saturable absorption is observed.

©2011 Optical Society of America

## 1. Introduction

Metallic nanoparticles (NPs) in a glassy matrix have been used in optics since medieval age due to its selective absorption. Gold, silver and copper NPs are responsible for the bright colors observed in ancient stained glasses [1]. However, it was only a few decades ago than these materials have attracted a great interest of researchers from different areas. Metallic nanostructures inside a dielectric matrix have the capability of quantum confinement of electromagnetic field, where the free electrons of the metal oscillate under the strength of the field. Quantum confinement of the field at the small NP and the collective oscillation of the gas of electrons have got many applications in different areas of optics, like nonlinear optics [2,3], spectroscopy [4–6], metamaterials [7], plasmonics [8] and bioluminescence [9], just to mention a few of them.

Optical properties of metallic NPs smaller than the wavelength of the incident light depend strongly on the size and shape of the nanostructure; this dependence provides parameters that can be manipulated to tune the optical properties of the resultant nanostructured material. Thus, the optical absorption is mainly dominated by the surface plasmon resonance, a unique feature presented by metallic nanosystems; while scattering becomes negligible for sizes below 10 nm, for example [10,11].

In the realm of nonlinear optics, there have been several works trying to understand the response of nanocomposites containing metallic NPs under different conditions, as wavelength and incident polarization [2,12–15]. Nevertheless, the nonlinear optical response resulting from the interaction between two different types of particles embedded in a single matrix, has not been yet fully explored. It would be easy to suppose that the optical response of the combined nanocomposite is a linear superposition of the individual response of each different nanostructure in the sample. However, it has been previously demonstrated that the collective response of the material may imply also a contribution from the interaction between all the involved structures. This interaction may lead to a stronger optical response, in comparison to the independent optical responses from the separated systems [16,17]. Besides, recent nonlinear optical results show that different combination of systems could be handled in order to improve their optical characteristics and responses [18,19].

In this work we have studied the third order nonlinear response of an integrated plasmonic nanocomposite formed by two different nanostructures: silver NPs and silicon quantum dots (QDs) embedded by ion implantation at different depths in a high quality glassy matrix. First, we had previously observed both, enhancement and quenching of the photoluminescence emitted by the system containing silver NPs and silicon QDs, with respect to the one containing only silicon QDs [20]. Now, exploring the effect that the combined system shows on the nonlinear optical properties of the nanocomposite, we used the standard Z-scan technique [21] to measure the nonlinear optical response of three samples, one containing only silver NPs, a second one containing only silicon QDs, and the last one containing both types of nanosystems at a given distance between them, this distance being the optimal for photoluminescence enhancement, according to the results shown in [20].

## 2. Sample preparation and characterization

The nanostructured samples under study were prepared by the ion implantation technique [22] using the Tandem accelerator NEC 9SDH-2 Pelletron at the Instituto de Física, UNAM. This method of fabrication allows a complete control on the parameters of implantation, which determine the physical characteristics of the final material. A piece of high quality SiO_{2} was implanted with 1.5 MeV silicon ions at a fluence of 2.5 × 10^{17} ions/cm^{2}. After implantation, the sample was cut in two pieces and both were thermally annealed in a reducing atmosphere for 1 hr at 1100°C in order to produce silicon nanoclusters (NcSi) in the SiO_{2}. Later, one of these two pieces was implanted with 1.0 MeV silver ions at a fluence of 9.47 × 10^{16} ions/cm^{2} and then annealed one more time in a reducing atmosphere at 600°C for 1 hr. The result after the second thermal treatment is a combined plasmonic nanocomposite containing one layer of silicon QDs and another one of silver NPs (AgSi), embedded at different depths into the matrix. A third sample (NpAg) was prepared by implantation of only silver ions (9.47 × 10^{16} ions/cm^{2} at 1 MeV energy) in a piece of high quality SiO_{2}, followed by a thermal treatment (1hr at 600 °C in reducing atmosphere).

The distribution of silver NPs in the samples was determined experimentally by Rutherford Backscattering Spectrometry (RBS) measurements, at the Instituto de Física, UNAM. The RBS is a reliable non destructive technique for determination of elemental profile in a matrix [
23
], however, in this case, it is not able to determine the Si QDs distribution because the amount of Si implanted ions do not exceed, at least 8%, the Si content in the SiO_{2} matrix in a wide region, due to the implantation energy and fluence used. For this reason the Si QDs profile distribution was only estimated using a SRIM-2008 program (www.srim.org), which simulates profiles applying Montecarlo method calculations. The simulated distribution of the silicon QDs in the sample, Fig. 1(a)
, shows a Gaussian-like distribution centered at 1.65 μm depth, with a full thickness of 0.9 μm. Figure 1(b) shows the silver distribution after thermal annealing measured by RBS (solid line), with its corresponding SRIM implantation simulation (dashed line). The silver NPs into the matrix are distributed in a 0.75 μm thickness layer beginning from the surface, which shows its maximum concentration at 0.48 μm depth. The difference between experimental distribution and the simulation is due to thermal effects. In this case, silver diffuses through damaged regions and accumulates in the zone where more damage is generated in the sample. The distribution of both nanosystems in the AgSi sample is shown in Fig. 1(c), where both layers of nanosystems are separated by a distance of 1.2 μm. Due to the low filling fraction of the NPs in each sample, less than 6 vol. %, and that the thickness of the layers is less than 1 μm, we used the linear refraction index of the SiO_{2} matrix (*n*
_{0} = 1.55) as the refraction index of the nanocomposite.

#### 2.2 Optical characterization of the samples

Linear characterization of the samples was done through the measure of the linear absorption of the samples. Figure (2) shows the optical linear absorption coefficient (α), which was obtained from the measured absorbance of the three samples. The absorption spectra seem different for the three samples, according to the implanted NPs. We can identify two different absorption bands: a strong band centered at λ = 395 nm due the plasmon resonance of the silver NPs (main resonance), and a weaker and more energetic band at λ = 230 nm, which is attributed to the absorption of silicon QDs.

## 3. Nonlinear experimental setup

The standard Z-scan technique has been widely used for many authors to study third-order optical non-linearities [24], the high popularity of this technique is due to its simplicity and easy analysis of the results. This technique consists in a focused beam that propagates on the z direction, as shown in Fig. 3 . The position z = 0 corresponds to the focal plane of the lens L1. The laser beam with a preferably Gaussian intensity profile is collimated by a second lens L2, split, and sent to photodiodes D1 and D2 to be detected. A nonlinear sample moving on z direction suffers a higher irradiance closer to z = 0, i.e. its optical response changes from linear to nonlinear as it moves across the focus of the beam.

An aperture placed in front of the photodiode D2 detects any change on the intensity profile of the beam. The change on the transmittance through aperture is sensible to nonlinear absorption and nonlinear refraction; however, removing the aperture, as for photodiode D1, the effect due to refraction is completely eliminated, and the nonlinear absorption is measured. Z-scans with and without aperture can be used to determine both nonlinear absorption and nonlinear refraction [21].

The change of phase induced by the sample ($\Delta \varphi $) is given in terms of the nonlinear refractive index (*n _{2}*), as:

*L*

_{eff}= (1-e^{-}

*is the effective length of the sample, which is dependent on the linear absorption coefficient (*

^{αL})/α*α*) and the thickness (

*L*) of the sample. For these materials, the thickness is that of the corresponding layer of NPs.

*I*is the irradiance on-axis for z = 0 and

*λ*is the laser wavelength in free-space. We can obtain |$\Delta \varphi $| from the experimental data, using an empirical equation proposed by Sheik-Bahae [21].where Δ

*T*is the difference between the maximal value (peak) and the minimal value (valley), on the normalized transmittance from closed aperture without nonlinear absorption, and

_{p-v}*S*is the linear transmittance through the aperture. We can subtract the nonlinear absorption contribution on the closed aperture transmittance by a simple division of curves (closed/open) [24].

Nonlinear absorption coefficient (*β*) can be obtained from open aperture transmittance by conducting the following equations:

We used a Nd:YAG picosecond pulse laser system, with second and third harmonic converters, as illumination source for the Z-scan experiments. The experimental setup was calibrated using 1 mm thickness of high purity CS_{2} solution. The valley followed by a peak for the closed aperture measurement, as we can see in Fig. 4
, shows evidence of a positive *n _{2}* for a wavelength of 532 nm. The

*n*value for CS

_{2}_{2}obtained from the conducted Z-scan experiments were in total agreement with values reported in literature [25]. The experimental data from the open aperture showed no evidence of nonlinear absorption, as we expected.

## 4. Results and discussion

The nonlinear optical response for the three samples was measured using the Z-scan experimental setup described above. The experiments were done using three different wavelengths: 1064 nm, 532 nm and 355 nm, corresponding to the fundamental, second and third harmonics of a Nd:YAG pulsed laser system, these wavelengths being situated at both sides of the optical resonance of the silver NPs (λ = 395nm). The laser gives a train of pulses with 26 ps duration (FWHM) and a Gaussian intensity profile, at a repetition rate of 1 Hz. The use of such short pulses helps minimizing possible thermal contribution to the nonlinearity, while the low repetition rate of the train ensures no pulse-to-pulse build-up effects being present.

Figure 5
shows experimental results for the AgSi sample, for two wavelengths on the right side of the main resonance. The results show evidence of negative nonlinear index (*n _{2}*) and negative nonlinear absorption (

*β*). However, for an irradiance quite similar (

*I*= 2.32

**×**10

^{14}W/m

^{2}for λ = 1064 nm, and

*I*= 2.0

**×**10

^{14}W/m

^{2}for λ = 532 nm), we can see that Δ

*T*is bigger for λ = 532 nm, with respect to that of λ = 1064 nm. This value gives the real part of the third order susceptibility,

_{p-v}*Re χ*, as it is shown in Table 1 .

^{(3)}As said before, due to the low filling fraction of the NPs in the nanocomposites, the values shown in Table 1 were calculated using the SiO_{2} refraction index, *n*
_{0} = 1.55. Due to the dispersion of our experimental data, the uncertainty of the calculated value of *Re χ ^{(3)}* was less than 15%. In that sense, for our case, a small variation of

*n*

_{0}, as due to the inclusions, would produce a change in

*Re χ*smaller than this uncertainty.

^{(3)}The nonlinearity of the silica glass is well known [26], but we also measured it in our laboratory, being clearly negligible compared to that of the implanted materials. It is worth mentioning that a comparison of the nonlinearities obtained here with those reported by other groups is rather difficult, since they depend on the temporal regime and the energy of the pulses used to perform the measurements. For example, it is widely known that the nonlinearities may be several orders of magnitude larger for nanosecond pulses than for picosecond or femtosecond pulses, mainly due to thermal effects [2]. The concentration of the NPs may also be a significant factor.

On the other hand, the AgSi sample shows a different nonlinear optical response when is illuminated with λ = 355 nm, as we can see in Fig. 6
for an irradiance of 6.7 **×** 10^{13} W/m^{2}. This irradiance was lower than the one used in the experiments at 1064 nm and 532 nm, however, the ΔT_{p-v} measured from the normalized transmittance is quite similar to the first ones. Peak and valley positions show evidence of a positive nonlinear index, and null nonlinear absorption is observed. That means that the sample shows a negative nonlinear refraction index for wavelengths longer than the corresponding to the plasmon resonance, and a positive nonlinear index for wavelengths shorter than it.

To better understand this difference in the nonlinear optical response of the plasmonic integrated nanocomposite, we also measured it for the NpAg and NcSi samples, using the same wavelength (355 nm) and a similar irradiance. Z-scan measurements for NpAg and NcSi samples are shown in Fig. 7 . By comparing the nonlinear optical response of the three samples (Figs. 6 and 7); we can observe that the nonlinear response of the combined system comes from the nonlinear contribution of both kinds of NPs. That is, the nonlinear refractive response of the combined system is dominated by the contribution of the silver NPs, although there is a negative contribution from the silicon QDs to this response. Regarding the nonlinear absorption, the individual contributions are similar in magnitude but opposite in sign, cancelling each other for the combined system. It is worth mentioning that, for 532 nm, the NpAg sample showed negative nonlinear refraction but positive nonlinear absorption, while the NcSi sample showed null nonlinear refraction and negative nonlinear absorption. By looking again at Fig. 5(b), we can see that the silver NPs gives the all nonlinear refractive behavior of the plasmonic integrated nanocomposite, but the silicon QDs dominates, this time, the nonlinear absorption of the all system. For 1064 nm, the NcSi sample gave no nonlinear response, leaving the all contribution to the silver nanoparticles for the plasmonic integrated nanocomposite, as shown in Fig. 5(a).

The discussion about these differences in sign can be understood as follows. Regarding the nonlinear refraction, since the Si QDs show no discernable nonlinear response for longer wavelengths, the total response is due only to the Ag NPs. We have already shown that, at wavelengths above resonance, at low irradiances, the metallic nanosystem shows a negative nonlinear refraction, and that this response is mainly due to intra-band transitions; on the contrary, for wavelengths below resonance the nonlinear refraction is positive, due to inter-band transitions [12–15]. On the other hand, regarding the nonlinear absorption, given the low irradiances used in the measurements, the intra-band transitions dominate at 532 nm for the metallic system [12–15], resulting in a positive nonlinear absorption; however, the Si QDs have a larger, opposite nonlinear response, resulting in a total negative nonlinear absorption of the integrated nanocomposite. For 1064 nm, a positive nonlinear absorption was also expected for the metallic system, but we had previously observed a large linear absorption due to the SiO_{2} matrix for this wavelength, which gives, in consequence, a total negative nonlinear absorption again for the integrated nanocomposite, but this time due to the matrix, since there is involved this linear absorption.

To be sure about the third-order origin of the nonlinear optical response of our nanocomposites, Fig. 8 shows the peak-valley difference from the normalized transmittance of the AgSi sample, measured as a function of the incident energy. The first point on the plot represents the dispersion of the data observed in the linear regime. Then, considering this dispersion, the behavior of the plot is quite linear, which is characteristic for a third order nonlinearity.

## 5. Summary

We conducted third-order nonlinear optical measurements for three different nanocomposites, using three different wavelengths. We observed that the sign of the nonlinear refraction changes with the wavelength of illumination: the integrated plasmonic nanocomposite, the one with both types of nanostructures, shows a negative nonlinear refraction for wavelengths above resonance, and positive nonlinear refraction for wavelengths below it. Actually, the total magnitude of the χ^{(3)} is also dependent on the used wavelength, since we measured a larger nonlinear coefficient for shorter wavelengths. On the other hand, from the results at λ = 355 nm, we observed that the nonlinear optical response for the integrated system comes from the optical contribution of the two types of nanoparticles. Despite the two contributions show opposite sign, the nonlinear refraction for the combined system is almost not affected; nevertheless, nonlinear absorption is totally cancelled for this last wavelength.

## Acknowledgments

The authors wish to acknowledge the technical assistance of K. López and F. J. Jaimes. We also acknowledge the financial support from PAPIIT-UNAM through grants IN108510, IN103609; from CONACyT through grants 80019, 102937; from CICESE; and from ICyT-DF through grant PICCT08-80.

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