Materials presenting high optical nonlinearity, such as materials containing metal nanoparticles (NPs), can be used in various applications in photonics. This motivated the research presented in this paper, where morphological, linear and nonlinear optical characteristics of gold NPs on the surface of bulk soda-lime glass substrates were investigated as a function of nanoparticle height. The NPs were obtained by annealing gold (Au) thin films previously deposited on the substrates. Pixel intensity histogram fitting on Atomic Force Microscopy (AFM) images was performed to obtain the thickness of the deposited film. Image analysis was employed to obtain the statistical distribution of the average height of the NPs. In addition, absorbance spectra of the samples before and after annealing were measured. Finally, the nonlinear refractive index (n2) and the nonlinear absorption index (α2) at 800 nm were obtained before and after annealing by using the thermally managed eclipse Z-scan (TM-EZ) technique with a Ti:Sapphire laser (150 fs pulses). Results show that both n2 and α2 at this wavelength change signs after the annealing and that the samples presented a high nonlinear refractive index.
© 2012 OSA
Metal nanoparticles (NPs) exhibit linear and nonlinear optical properties determined by the type of metal, size and shape of the NP [1–3]. Localized Surface Plasmon Resonance (LSPR), a linear optical phenomenon, is of particular usefulness for applications in sensing and biosensing, since it is dependent on the local dielectric environment surrounding the NPs and fairly straightforward to monitor [4,5]. Furthermore, because materials containing metal NPs present high nonlinearity, introducing metal NPs onto or into a glass host increases its third-order response [6,7]. A high third-order response is desirable for several applications in photonics. Recently, it has been shown that nickel oxide thin films exhibit a high nonlinearity and an n2 that increases with the thickness of the film . These results, along with the information above, fueled the motivation for the research presented in this paper. We have investigated morphological, optical linear and optical nonlinear (third order nonlinearity) characteristics of Au NPs on soda-lime glass substrates as a function of NP height.
The NPs were formed by depositing and annealing gold thin films on soda-lime glass substrates. The film thickness before and after annealing was estimated by the pixel intensity histogram of Atomic Force Microscopy (AFM) images. The statistical distribution of the average height of the NPs formed was obtained by digital image analysis on images with the strongest NP growth. Absorbance spectra [A = −log(Iout/Iin)] of the samples before and after the annealing were measured. The nonlinear refractive (n2 α Re χ(3)) and absorption (α2 α Imχ(3)) indices were obtained at a wavelength of 800 nm by using thermally managed eclipse Z-scan (150 fs pulses). Results show that both n2 and α2 at 800 nm change signs after annealing and that the samples presented a high nonlinear refractive index.
2.1 Sample preparation
The substrates used were 1.5 cm x 1.5 cm soda-lime commercial microscope slides. Prior to the Au deposition, the slides were thoroughly washed in an ultrasonic bath of acetone followed by an ultrasonic bath of isopropanol alcohol. After the cleaning, thin films of gold (99.99% purity) of different nominal thickness were deposited by dc sputtering at a pressure of 6 x 102 mbar and a rate of 2.6 Å/s. The deposited gold films were subsequently annealed for 4 minutes at three different temperatures (400 °C, 600 °C and 800 °C). The films are formed by gold islands which reshape and coalesce upon heating, forming the Au nanoparticles [9,10].
2.2 Morphological characterization
Morphological characterization of the samples was performed to obtain the average thickness of the deposited films (before annealing) and the average height of the NPs (after annealing). For this purpose, images of different regions of the samples were obtained with an Atomic Force Microscope (AFM), and two procedures were followed.
Lower magnification images containing part of the edge between the substrate and deposited film were analyzed to estimate the film thickness. The height histogram of the images showed two peaks, corresponding to the heights of the substrate and the film. A Gaussian fit was applied to each peak and the refined maxima positions were subtracted to calculate the average thickness. For the lowest thickness samples, for which the estimate was less reliable due to small local variations, a sigma filter (edge preserving lowpass)  was applied before histogram calculation and fitting. This improved the thickness measurement.
For thicker films with larger and taller NPs, higher magnification images allowed visualization of individual particle features. In order to extract reliable statistical information from the AFM images by measuring a large number of NPs, image analysis (IA) techniques were applied.
An IA procedure typically involves the steps of pre-processing, segmentation, post-processing and measurement . In our case, intensity threshold and edge detection segmentation methods were combined, and extensive morphological post-processing was employed in order to discriminate the individual NPs, since they appeared to be in contact or even partially overlapping in the AFM images. Once individual NPs were reliably discriminated, their morphological attributes were automatically measured. Using this procedure, it was possible to measure the average height of the NPs, but not their diameter, since the images were convoluted with the AFM probe used . The optimized algorithm was implemented as a macro in a commercial IA program.
2.3 Characterization of linear and nonlinear optical properties
Linear absorption (αo) measurements were performed using a spectrophotometer (Diode Array Spectrophotometer 8452A) operating from 300 nm to 800 nm.
Nonlinear optical properties of the Au NPs were obtained by applying the thermally managed eclipsed Z-scan technique (TM-EZ Scan) , i.e. the Z-Scan technique  combined with thermal management and eclipsed beam detection (Fig. 1 ). All Z-scan measurements were performed at 800 nm using a 76 MHz pulsed Ti:Sapphire laser with 150fs pulse width and intensity of 15 GW/cm2.
The TM-EZ scan experimental setup (Fig. 1) consists of a Ti:Sapphire laser, a chopper, five converging lenses (L1-L5), a beam splitter (B.S.), a disk, two detectors (Det 1 and Det 2) and a digital oscilloscope . The chopper, placed between the telescope formed by lenses L1 and L2, is blocked 95% of the time and is responsible for managing thermal and other cumulative effects. The sample, the beam splitter and the disk are placed between lenses L3 and L5, as shown in Fig. 1. The eclipsed beam is collected by lens L5, directed towards detector Det 1 and processed by a digital oscilloscope. It is used to measure the nonlinear refractive index (n2). The signal reflected by the beam splitter is directed towards detector Det 2 with the aid of lens L4 for the measurement of the nonlinear absorption (α2).
For large disk and small nonlinear phase shift (ΔΦ < 0.2) the relationship between ΔTpv (peak-to-valley difference in the sample transmittance) and ΔΦ can be written as ΔTpv = 0.68 *(1−Sd)−0.44 |ΔΦ|, where Sd is the fraction of the beam blocked by the disk, given by Sd = [1−exp(−2rd 2/ wd 2)], with rd being the disk radius and wd the beam radius at the disk position. The nonlinear phase shift is given by ΔΦ = kn2I0Leff, where I0 is the excitation peak intensity within the sample, k = 2π/λ, Leff = [1−exp(-αo L)]/αo and L is the sample length.
The TM-EZ scan method consists in acquiring the time evolution of the EZ- scan signal for the sample placed in the pre and post focal positions of the focal plane of lens L3. By extrapolating the time evolution curves for t < τ, where τ is the chopper opening time, noncumulative signals at both the pre and post focal positions are obtained. From these measurements, using the formalism described by Sheik-Bahae , the EZ-scan curves can be constructed and the contribution of cumulative effects, such as thermal effects and electronic nonlinearities, can be inferred, provided no other mechanism besides the electronic nonlinearity are present in the relatively short time of the chopper opening rise time.
Before the samples were measured in the setup, the system was calibrated by using a cell (optical path equal to 1 mm) containing carbon disulfide (CS2) as reference material. The beam waist was approximately 2.5 μm and the film was uniform at this scale. When the samples were tested, several scans (and retro scans) were performed at different positions to ensure that the measurements were reproducible and that the Au film was not damaged.
3. Results and discussion
3.1 Morphological characterization
Figure 2 shows the height histograms and corresponding AFM images (inset), before and after annealing, for typical samples with Au film deposited with thickness equal to 6 nm (Fig. 2(a) and Fig. 2(b)) and 15 nm (Fig. 2(c) and Fig. 2(d)). As explained in section 2.2, the two peaks in the height histograms correspond to the heights of the substrate and the film, and were used to obtain the average thickness of the films. For example, in Fig. 2(a) the measured heights of the substrate and the film were equal to ~3.8 nm and ~9.8 nm, respectively. The average thickness of the Au film deposited before annealing is given by the difference between the peaks and is ~6.0 nm. The average height of the film after annealing (Fig. 2(b)) is ~15 nm. For the second sample, the average heights before (Fig. 2(c)) and after annealing (Fig. 2(d)) are ~15 nm and ~42 nm, respectively. Both samples were annealed for 4 minutes at 600 °C.
The height values reported above are rounded off to the nearest one; the original (before rounding) measured heights for the first sample before and after annealing and for the second sample before annealing are shown in Table 1 (the height of the second sample after annealing will be accessed using another technique). By analyzing several films deposited with various values of thickness we found, as reported in literature , that the height of the NPs formed by the annealing is dependent on the thickness of the Au thin film deposited.
High resolution tapping mode AFM images with 2 μm x 2 μm showing the morphology of the films before and after annealing are shown in Fig. 3 . The Au thin film grows with island-morphology at 6 nm thickness (Fig. 3(a)); however, during annealing, neighboring Au islands coalesce to produce larger, rounder NPs, as described in literature [9, 15] and shown in Fig. 3(b). In fact, comparison of statistical analysis results obtained from AFM and Field Emission Scanning Electron Microscope (FESEM) images (not shown) showed that the NPs obtained after the annealing had an oblate-like shape (height shorter than width). At thicknesses of ~15 nm, a continuous film is observed before annealing (Fig. 3(c)). After annealing, a similar trend is observed with the coalescence of the Au to produce large NPs.
As mentioned previously, for thicker films with larger and taller NPs, image analysis (IA) techniques were applied to extract reliable statistical information from the AFM images. Shown in Fig. 4 is the distribution of the average NP height formed by annealing the 15 nm Au film (Fig. 2(d) and Fig. 3(d)), as determined by the IA routine described in Section 2.2. One can see that NPs have average height varying between 30 nm and 70 nm, with an average value of 48.3 nm, which is 15% larger than the value determined by the histogram fitting method, discussed previously. The uncertainty of this measurement is much smaller than the uncertainty of the histogram fitting method, 8.18 nm and 45.15 nm respectively. Thus, this measurement was used for this sample after annealing, as shown in Table 1.
3.2 Characterization of linear and nonlinear optical properties
The optical linear characterization of our samples involved investigating the optimum annealing temperature for sensing applications (narrow LSPR band desired), as well as investigating the dependence of the absorbance spectra with the thickness of the deposited Au thin film.
In order to find the optimum annealing temperature, thin films of thickness equal to 6 nm were deposited on bulk glass samples. Absorbance spectra at wavelengths from 350 nm to 800 nm were obtained before and after the samples were annealed for 4 minutes at various temperatures. Figure 5 shows typical absorbance spectra before the annealing (as deposited) and after the annealing at 400 °C, 600 °C and 800 °C. Before the annealing, there is a small absorption at shorter wavelengths, an absorption dip at about 475 nm and a wide absorption band at wavelengths above 550 nm. After the annealing, the absorbance spectra presented the typical LSPR absorption peak expected for spherical-like Au NPs [see, for example, ref. 16]. As the annealing temperature was increased, the LSPR band became narrower and shifted towards shorter wavelengths. This can be explained by the reshaping of the Au islands, tending from a flatter shape to an oblate/spherical-like shape . It is worth mentioning that, for small NP size, as in the case of the NPs obtained in the experiments in this paper, scattering effects are small and the extinction spectrum is mainly due to absorption .
Visual inspection of the samples showed that their color was grayish-blue before the annealing and pink after the annealing. These results are in agreement with other results in literature and are to be expected from their corresponding absorbance spectra.
As can be seen in Fig. 5, even though the LSPR absorption band is observed after the annealing at 400 °C, it is still somewhat wide when considering sensing applications. On the other hand, increasing the annealing temperature above 600 °C does not narrow the peak significantly. For these reasons, the results reported from here on were obtained using samples annealed at 600 °C.
The dependence of the LSPR band with the thickness of the deposited Au thin film was also investigated. For this purpose, absorbance spectra of samples on which Au thin films were deposited with various values of thickness were obtained before and after annealing. Figure 6 shows typical absorbance spectra before annealing (as deposited, Fig. 6(a)) and after annealing (Fig. 6(b)) for 4 minutes at 600 °C of samples with films of thickness equal to 6nm, 10nm and 15nm. Before annealing, as the Au film thickness increases, the wide absorbance peak shifts to longer wavelengths . The film with thickness equal to 15 nm presents a form that resembles the extinction spectrum for bulk Au.
As shown in Fig. 6(b), after annealing the LSPR band widens and shifts to longer wavelengths as the thickness of the deposited film increases, as expected . For all samples, the linear absorption at 800 nm exhibited a significant decrease after annealing.
The characterization of nonlinear optical properties involved measuring the nonlinear refractive (n2 α Re χ(3)) and absorption (α2 α Im χ(3)) indices at 800 nm. For this purpose, several samples with Au thin films deposited with thickness equal to 6 nm and 15 nm were characterized by the thermally managed eclipse Z-scan (TM-EZ scan) technique. Before the samples were measured, the system was calibrated with a cell containing CS2, yielding a measured n2 equal to 3.0 x 10−15 cm2/W, which is consistent with literature . In addition, a soda-lime microscope slide of the same kind as the substrate for the deposited Au films was used as reference. The samples with Au and the reference soda-lime substrate were measured before and after annealing at 600 °C for 4 minutes.
Figure 7 shows the TM-EZ scan profiles (normalized transmittance in the far field) obtained before and after the annealing of a sample with an Au film deposited with thickness of 15 nm (Fig. 7(a)) and of the reference soda-lime substrate (Fig. 7(b)). The symbols (open circle and open square) are data points and the solid lines are fitting curves. For such graphs, a peak-valley form is indicative of a positive n2, while a valley-peak result is indicative of a negative n2 . These results show that the sample had a positive n2 before the annealing and a negative n2 after the annealing, while the reference soda-lime glass had a positive n2, unchanged with annealing. The measured n2 for the sample in Fig. 7(a) was (1.6 ± 0.3)x 10−11 cm2/W and (−5.5 ± 0.9)x 10−11 cm2/W before and after annealing, respectively. For the soda-lime substrate the measured value of n2 (3 x 10−16 cm2/W) was orders of magnitude smaller and in accordance with previous reports . Samples with 6 nm deposited films also exhibited a positive n2 before the annealing and a negative n2 after the annealing. The finding that the n2 of samples with Au changes sign with annealing, while the n2 for the substrate remains the same, demonstrates that the change in n2 is due to the annealing of the Au film. Table 1 shows typical values of n2 measured before and after the annealing for samples with a deposited film of 6 nm and 15 nm.
Also shown in Table 1 are α2 for the two samples. Our results show that α2 also changes sign with annealing.
There are two possible mechanisms induced by annealing that could explain the sign reversal of n2 and α2 at 800 nm. The first mechanism is associated to the change in linear absorption at 800 nm and the second mechanism is associated to a change in conductivity. These mechanisms are discussed below.
Wang et al , observed an intensity-dependent sign reversal in n2 at 800 nm in an Au NP array through Z-scan measurements with a femtosecond laser (800 nm, 50 fs). As the excitation intensity increased, α2 changed from reverse-saturable absorption (RSA) to saturable absorption (SA) (from positive values to 0), and n2 changed from self-defocusing to self-focusing (from negative to positive values). In our case, the sign reversal of n2 and α2 occurs along with a modification on the linear absorption spectra (Fig. 5), where before annealing the absorption is dominant at 800nm and after annealing it is dominant at 400nm. In this case the absorption regime changes from SA before annealing to RSA after annealing, which can be associated to a change in the mechanism from one photon absorption to two photon absorption.
On the other hand, Smith et al  observed that the sign of the third-order susceptibility of a 5 nm Au film on a quartz substrate is different from the sign of the third-order susceptibility of gold NP composites (for example, gold NPs in water, gold colloid dispersed in acetone, etc.). This sign difference was attributed to a drastic change in conductivity occurring at the percolation threshold. In our case, NPs were formed by annealing an Au thin film on glass substrates by coalescence of the Au islands. The diameter and height of the formed Au NPs increased, leading to a larger mean free path of the electrons at the surface . Since conductivity is proportional to the mean free path of the electrons, it is also proportional to the dimensions of the NPs and will also change with the annealing. Therefore, the sign change in n2 could be attributed to a change of the conductivity due to the increase of the dimensions of the NPs.
Results in Table 1 show that after the annealing the absolute value of n2 at 800nm decreases for the 6 nm deposited film, whereas it increases for the 15 nm deposited film. The authors believe that this difference in behavior can be explained by analyzing the absorbance curves of the samples and by considering that metal NPs surrounded by dielectric material exhibit an increase of the third order susceptibility around the LSPR band due to the enhancement of the local electric field . Before the annealing, the 6 nm deposited film presents a wide absorption band from 550 nm to over 800 nm (Fig. 6(a), black line). This broad surface plasmon signal before annealing occurs due to the island morphology of the deposited Au film, i.e., the film deposited with 6 nm thickness is not homogeneous even before annealing. The annealing of this film leads to a blue-shift and a narrowing of the LSPR band (Fig. 6(b), black line), resulting in bleaching the linear absorption at 800 nm. Since n2 reported in our manuscript was measured at 800nm, which is away from the LSPR peak for the annealed sample with the thin film deposited with 6 nm, n2 decreases with the annealing.
On the other hand, the 15 nm deposited film does not present a surface plasmon signal before annealing; rather, its absorbance spectrum resembles the extinction spectrum for bulk Au (Fig. 6(a), blue line). This can be explained by observing that this film is more homogeneous (compare Fig. 3(a) and Fig. 3(c)). With the annealing, large Au NPs are formed and the absorbance spectrum presents a wide LSPR band with absorption still present at 800 nm (Fig. 6(b), blue line), leading to an increase of n2.
Our results also show that n2 increases as the thickness of the deposited film increases (before annealing) and as the height of the NPs increases (after annealing). Before the annealing, the 6 nm deposited film presents a non homogeneous morphology, whereas the 15 nm deposited film presents a more homogeneous morphology (Fig. 3(a) and Fig. 3(c)). The authors believe that this change in morphology can explain the increase in n2 as the film thickness increases. For the annealed samples, the observed increase in n2 as the NP height increases agrees with the behavior observed for Au NPs suspended in a PVA solution .
The observed high third-order nonlinearity can be explored for the development of photonic devices, which usually require a small linear and nonlinear absorption for applications such as optical switching . In order to evaluate the potential as a photonic device of the system (gold thin film/NP deposited on the surface of bulk soda-lime) studied in this paper, the figure of merit (T = |2α2λ/n2|) associated to the two photon absorption was calculated and is shown in Table 1 . The S15 samples present a T < 4, which indicates they are good candidates for nonlinear distributed feedback grating (NDFG) according to DeLong et al . It is important to point out that, although low nonlinear absorption coefficients are desirable for optical switching devices, materials with high two photon absorption, such as the S6 samples, could potentially be used as optical limiters.
Au thin films were deposited on glass (soda-lime) substrates and annealed to form Au nanoparticles on the surface of the glass. Morphological, optical linear and optical nonlinear properties were obtained, before and after annealing, as a function of the thickness of the deposited film (before annealing) and of the height of the NPs (after annealing).
The morphological characterization involved the use of two different procedures to extract reliable statistical information from AFM images regarding the average thickness of the deposited film (before annealing) and of the height of the NPs (after annealing). The improvement on the thickness/height measurement improves the reliability of the nonlinear optical characterization.
The nonlinear characterization involved using the TM-EZ scan technique to obtain n2 and α2 at 800nm before and after annealing. Results showed that n2 and α2 at 800 nm undergo a sign change after the annealing process; that as the thickness of the deposited film (before annealing) increases, so does the modulus of the nonlinear refractive index at 800 nm (before and after annealing); and that the annealing causes a decrease of the absolute value of n2 at 800 nm for the 6 nm deposited film and an increase of the absolute value of n2 at 800nm for the 15 nm deposited film.
For the NP system studied, n2 was equal to −1.7 x 10−12 cm2/W for NPs with height ~15 nm and equal to −5.5 x 10−11 cm2/W for NPs of height ~48 nm. These values are several orders of magnitude higher when compared to, for example, n2 of a 15 nm Au NPs colloidal system consisting of castor oil and Au NPs, also measured by Z-Scan with excitation at 800 nm (−1.53 x 10−14 cm2/W) ; they are about the same order when compared to n2 of an Au NP array (−0.33x10−11 cm2/W for 15 GW/cm2) .
The authors thank the Brazilian Agency CNPq for financial support of this work under the MCT/CNPq Nanophotonics Network and PRONEX FACEPE/CNPq program. I. C. S. Carvalho thanks the Rio de Janeiro State Agency FAPERJ for financial support of this work. The authors also thank the reviewers for the very useful and insightful comments and suggestions.
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