Wavelength-Dependent Nonlinear Optical Properties of Ag

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Wavelength Dependent Nonlinear Optical Properties of Ag Nanoparticles Dispersed in a Glass Host Piero Ferrari, Sneha Upadhyay, Mikhail V. Shestakov, Jan Vanbuel, Bert De Roo, Yinghuan Kuang, Marcel Di Vece, Victor V. Moshchalkov, Jean-Pierre Locquet, Peter Lievens, and Ewald Janssens J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09017 • Publication Date (Web): 17 Nov 2017 Downloaded from http://pubs.acs.org on November 19, 2017

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The Journal of Physical Chemistry

Wavelength Dependent Nonlinear Optical Properties of Ag Nanoparticles Dispersed in a Glass Host Piero Ferrari1,*, Sneha Upadhyay1, Mikhail V. Shestakov

2,3

, Jan Vanbuel1, Bert De Roo1,

Yinghuan Kuang4, Marcel Di Vece5, Victor V. Moshchalkov2, Jean-Pierre Locquet1, Peter Lievens1 and Ewald Janssens1,* 1

Laboratory of Solid State Physics and Magnetism, KU Leuven, Celestijnenlaan 200D, 3001,

Leuven, Belgium 2

INPAC - Institute for Nanoscale Physics and Chemistry, KU Leuven, Celestijnenlaan 200D,

3001, Leuven, Belgium 3

Department of Chemistry, KU Leuven, Celestijnenlaan 200F, 3001, Leuven, Belgium

4

Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB

Eindhoven, The Netherlands 5

CIMAINA and Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano,

Italy

ACS Paragon Plus Environment

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ABSTRACT

The linear and nonlinear optical properties of metal nanoparticles are highly tunable by variation of parameters such as particle size, shape, composition and environment. To fully exploit this tunability, however, quantitative information of nonlinear absorption cross sections is required, as well as a sufficient understanding of the physical mechanism underlying these nonlinearities. In this work, we present a detailed and systematic investigation of the wavelength-dependent nonlinear optical properties of Ag nanoparticles embedded in a glass host, in which the most important parameters determining the nonlinear behavior of the system are characterized. This allows a proper quantification of absorption cross sections and elucidation of the excitation mechanism. Based on small-angle X-ray scattering measurements average particle diameters of 3 nm and 17 nm are estimated for the studied samples. The nonlinear optical properties of the nanoparticle-glass composite are studied in an extended wavelength range with the open aperture z-scan technique. The experiments reveal a strong dependence of the nonlinear optical response on the excitation wavelength. Based on the wavelength-dependent response, excited state absorption is determined as the excitation mechanism of the nanoparticles. Electromagnetic simulations demonstrate that the contributions from electric field enhancement and plasmonic coupling between the particles in the diluted glasses is limited, which implies that the very high two-photon absorption cross section at 460 nm ((6.9 ± 1.6)·106 GM for the 3 nm particles and (19.5 ± 2.2)·109 GM for the 17 nm particles) is an intrinsic property. In addition, irradiance dependent measurements elucidate the role of saturation of the excited-state absorption process on the observed nonlinearities.


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INTRODUCTION The optical properties of noble metal nanoparticles (NPs), such as Au and Ag NPs, have intensively been studied the past decades.1-3 The smallest particles, i.e., nanoclusters, show strong quantum-confinement effects and discrete absorption features.4 In contrast, the electronic structure of larger particles is characterized by semi-continuous bands. Their extinction spectra show a localized surface plasmon resonance (LSPR), i.e. collective oscillation of electrons in the conduction band near the Fermi energy, hence the term plasmonic NPs.5,6 Beyond the interesting fundamental scientific questions related to the collective electronic excitations, diverse applications can make use of plasmonic NPs, such as surface plasmon-based photonics (plasmonics)7-9 and efficiency enhancement in solar cells by plasmonic energy conversion.10-12 Besides their size, also other parameters influence the optical properties of nanoparticles, such as shape,13 composition,2 and environment.14 Despite the extensive research of the optical properties of Au NPs,15-18 Ag may have some advantages over Au. The heavy Au atoms are known to be largely affected by relativistic effects, which results in a reduced valence s-d energy separation.19 The s-d interaction in Au reduces the strength of the optical absorption bands because the valence s electrons are partly screened. In Ag the s-d energy separation is larger and the valence s electrons are more free, which leads to larger oscillator strengths in Ag NPs than in Au NPs.20 When NPs are exposed to intense electric fields, for instance by the interaction with pulsed laser light, nonlinear excitation processes may take place. Nonlinear optical (NLO) properties can be used in a multitude of applications such as all-optical ultrafast switching,21 optical limiting,22 and the generation of ultra-short pulses.23 In general terms, the nonlinear


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optical response of noble metal NPs can be manifested either by a decrease or an increase in optical transmission. Transmission decrease can be caused by simultaneous absorption of multiple photons via virtual states, such as two-photon absorption (2PA) and three-photon absorption (3PA), or by excited-state absorption (ESA), in which one photon is absorbed by an already excited-state. ESA leads to transmission decrease when the ground-state absorption cross section is smaller than that of the excited-state. The opposite situation, transmission increase, takes place when the linear absorption from the ground-state saturates, thus the name saturable absorption (SA), which is the case when the ground-state absorption cross section is greater than that of the excited-state.24 A term sometimes used to denote the process of transmission decrease is reverse saturable absorption (RSA), which strictly speaking corresponds to the ESA process leading to transmission decrease. When transmission decrease can be attributed either to multiphoton absorption or to ESA, the term RSA-like behavior can be employed. NLO properties of NPs can, among others, be studied with wave mixing and z-scan approaches.25 In a typical single beam z-scan experiment the sample is moved along the propagation direction of a focused laser beam and the transmitted signal is measured as a function of sample position with respect to the beam’s focal point.26 Using this technique, the NLO properties of a large variety of NPs, of different sizes and compositions, have been investigated.27-33 An important problem, however, is that because the NLO response of NPs is strongly dependent on the excitation conditions (incident laser fluence and wavelength) and by conditions of the sample (particle size distribution, concentration, environment,…), different, and sometimes even contradictory, behavior has been reported. In particular for Ag NPs, despite the large amount of studies that have been performed,34-41 there is not much quantitative


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information about the cross sections of multiple photon excitation processes and saturation intensities. Recent theoretical work on small ligand-protected Ag clusters has shown, by means of time-dependent density functional theory (TD-DFT) calculations, that 2PA coefficients are enhanced when the excitation wavelength is in resonance with the one-photon absorption.42,43 Despite the obvious relevance of λ-dependent studies of NPs, especially if one intends to use their nonlinear properties in applications with a wide spectral range,44 wavelength dependent zscan experiments are scarce. One possibility is the use of the so-called “white light” z-scan technique, in which the laser is replaced by a continuous light source and the detector by a spectrometer. This approach has been used, for instance, to investigate the wavelengthdependent NLO properties of graphene oxide nanosheets and of polymers in solution.45,46 A more conventional alternative, as applied in the current work, is to use a tunable laser with a broad spectral range.47,48 In this work, we present a systematic study of the dependence of the NLO properties of embedded Ag nanoparticles in a glass host on the excitation conditions. Two samples, containing NPs with average diameters of 3 nm and 17 nm, are studied. While the small NPs in the first sample show a small increase of absorption as compared to the undoped glass, the NPs in the second sample have a fully developed plasmon band, affecting significantly their NLO response. Using z-scan experiments and a tunable laser source the extended wavelength range from 445 nm to 660 nm and irradiance range of 1·105 to 21·107 W·cm-2 is investigated. These measurements allow to elucidate the mechanisms underlying the observed nonlinearities.


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RESULTS Characterization of the embedded Ag particles The average particle diameters and the interparticle distances were determined by small-angle Xray scattering (SAXS). Those values were used to calculate the particle concentration. The optical response of the samples in the linear regime is characterized by UV/visible optical absorption measurements. In addition, by using finite-difference time-domain (FDTD) simulations, possible effects of plasmonic coupling and electric field enhancement were investigated. SAXS has proven to be successful in the characterization of embedded NPs of different sizes and compositions.49 Figure 1 presents the SAXS characterization of both samples. Measurements on the undoped glass were used for background subtraction. The experimental data is shown as squares, whereas a Guinier fit,49 used to extract the average particle diameter, is presented by a continuous red line.


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Figure 1. Small-angle X-ray scattering (SAXS) characterization of (a) sample 1 and (b) sample 2, showing the logarithm scattered light intensity as a function of the squared magnitude of the scattering vector. Experimental data is presented as squares, while the continuous red line is a Guinier fit.

From the SAXS characterization average particle diameters of 3.0 ± 0.1 nm and 17 ± 0.3 nm are obtained for the NPs in the two studied samples, with uncertainties corresponding to the error in the Guinier fit. This error margin, however, should be taken with care since in the applied fit a spherical shape for the particles is assumed. Deviations from this shape are not accounted for in the uncertainty. The average particle diameter of sample with 3 nm NPs corresponds well with the value of 2.4 nm that was obtained by previous transmission electron microscopy (TEM) characterization on a similar sample.39 Since it is known that the atomic percentage of Ag atoms in the glass before heat treatment is 0.15%, the particle concentrations, D, can be estimated (see Ref. [39] for details). Those concentrations are (1.1 ± 0.2)·1024 m-3 and (5.5 ± 0.4)·1021 m-3, for the 3 nm and 17 nm NPs samples, respectively. Finally, using the


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average particle diameters and the estimated concentrations, the average interparticle distances can be calculated.50 The obtained values are 5.4 ± 0.3 nm for the 3 nm NPs sample and 31 ± 1 nm for the 17 nm NPs sample. Figure 2 shows the optical densities ( = − ) of the undoped glass and of both studied samples, as measured with a Fourier transform spectrometer. The absorbance of the undoped glass (dotted black line) is almost independent of wavelength in the visible range, except for a slight increase of the absorption below 400 nm. In the 3 nm NPs sample, an onset of an absorption band can be observed between 430 and 550 nm. The inset in Figure 2 shows a zoom to emphasize this. The OD of the glasses with Ag NPs can be compared with experiments on Au NPs in an alumina matrix with diameters between 2 and 4 nm; whilst a small increase in absorption was seen for the particles of sizes around 2 nm, a fully developed plasmonic feature was present for particle sizes of 4 nm.51 Thus, intense plasmonic absorption is expected to occur at particle sizes larger than those of the 3 nm NPs sample. For the 17 nm NPs sample an intense SPR band is observed, in addition to an overall increase of the optical density, related to a morphological modification upon the long heat treatment.52,53 Upon heat treatment, the glass becomes darker. The plasmon absorption band is located within the visible range between 410 nm and 600 nm with a maximum at 475 nm. Such plasmonic absorption is expected for NPs with diameters of the order of 20 nm and larger, with a shift to the red for increasing particle size.54 Close inspection of the OD of the 17 nm NPs sample shows two local maxima at 430 and 475 nm, which could correspond either to a bimodal size distribution of the NPs within the glass, or to an electromagnetic coupling between NP dimers (this possibility is discussed later). However, a deconvolution of these two bands using Gaussian functions (not shown) indicates that the contribution of the low-wavelength band to the optical absorption of this sample is


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minor. A feature that is observed for the three curves in Figure 2 is an increase of absorption below 400 nm. This absorption is produced by interband transitions, which take place at higher photon energies.

Figure 2. Optical densities of the undoped glass (black dotted line), the 3 nm NPs sample (red dashed line), and the 17 nm NPs sample (blue continuous line). The inset in the figure shows a zoom of the optical densities of the 3 nm NPs sample and the undoped glass.

Absence of strong plasmonic interparticle coupling and field enhancement effects Depending on the excitation wavelength, particle size and interparticle distance, the linear optical properties of plasmonic NPs can be affected by coupling effects.55 Finite-difference timedomain (FDTD) simulations were performed to elucidate if the measured optical properties originate mainly from individual particles or that they are influenced by interparticle coupling. Figure 3 presents a comparison of simulated absorption cross sections of a single Ag NP (intensity multiplied by 2), with that of two neighboring Ag NPs. The polarization of the


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incident light is perpendicular (P⊥ , or parallel (P//) to the axis connecting the particles. The simulation of the situation of the 3 nm NPs sample (Figure 3a), predicts a weak intensity absorption feature, consistent with the experimental OD spectrum of Figure 2. Comparing the P// curve with that of the single NP, one can conclude that the two particles are only slightly coupled, resulting in a small second absorption feature which is red-shifted (around 35 nm). This small second absorption peak is due to the plasmon resonance within the gap with a slightly different LC time as compared to a single particle.56 This effect is absent for incident light with P⊥ polarization, for which the absorption band is simply twice of that of a single particle. Because of the larger interparticle distances in the 17 nm NPs sample, the effect of coupling between the particles is even weaker for this sample; as shown in Figure 3b, only a small red shift (by about 10 nm) of the optical absorption is seen for parallel polarization, with no additional feature due to coupling. Thus, we can conclude that for both samples the observed linear optical absorption is mostly the response of single particles. However, should NP dimers be formed during heat treatment, electromagnetic coupling will be stronger. With respect to the effect of field enhancement on the glass around and in between the Ag NPs, the simulated absorption cross sections shown in Figure 3c demonstrate that the optical absorption in glass is orders of magnitude lower as that in silver. This eliminates the possibility that the non-linear effects in the subsequent experiments can be caused by field enhancement in the glass.


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Figure 3. FDTD simulated absorption cross sections σ of a single Ag NP (red continuous line) and two NPs with incident light polarization perpendicular P⊥ (blue dashed line) and parallel P// (black dotted line) to the direction connecting the particles. (a) 3 nm NPs at an interparticle distance of 5.4 nm. (b) 17 nm NPs at an interparticle distance of 31 nm. (c) Optical absorption cross section of two 17 nm Ag particles.

Wavelength dependent nonlinear optical properties The NLO absorption properties of the embedded Ag NPs are investigated by the z-scan technique in the open-aperture configuration.22,26 Along the direction of propagation, denoted as with = 0 the focal point, the beam radius is expressed by Eq. (1), where represents the beam waist radius (16.0 ± 0.3 µm) and the Rayleigh length. = 1 1

When samples are exposed to laser light in the far field, i.e. || ≫ 0, the beam radius is large and thus, the photon flux small. In the far field the transmission is a constant, i.e. independent of , since only one-photon processes are responsible for light absorption. In contrast, close to focus the photon flux is high and non-linear processes are possible. Typically,


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nonlinearities are distinguished on a z-scan experiment by a transmission decrease close to the focal point, RSA-like behavior,34,57-59 or transmission increase near = 0, revealing SA behavior.60,61 Z-scan measurements were carried out for both samples in an extended spectral range from 445 nm up to 660 nm, in steps of 20 nm (except for the first point of the series, with a step of 15 nm). For these measurements, a fixed laser energy of 10.5 µJ and 3.8 µJ (irradiance at focus of 16·107 W/cm2 and 5.9·107 W/cm2) was applied for the 3 nm NPs and the 17 nm NPs samples, respectively. Two examples of z-scan curves obtained from measurements of both samples are shown in Figure 4. In these examples, the samples were excited at 480 nm (in resonance) and at 660 nm (off resonance). As can be seen, both SA and RSA-like behavior contribute to the non-linear optical response of the samples, especially for the 17 nm NPs. For the 3 nm NPs sample, a small transmission increase, when approaching the focal point from the far field, is followed by a deep valley near the focal point ( ≤ 4). Thus, by increasing the irradiance, which is defined as the energy per unit of area and per unit of time, some SA takes place until a critical irradiance at which RSA-like behavior becomes accessible, resulting in a pronounced transmission decrease. Such behavior is found both at 480 nm and 660 nm. For the 17 nm NPs sample a more significant transmission increase is found when approaching the focal point from the far field, which is also followed by a transmission decrease near the focal point. This again indicates the coexistence of SA and RSA-like processes. For this sample, a strong dependence on the excitation wavelength is found, with a more pronounced z-dependence at the center of the plasmonic band of the NPs (480 nm).


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Figure 4. Open aperture z-scan curves for: (a) 3 nm NPs sample at 660 nm, (b) 3 nm NPs sample at 480 nm, (c) 17 nm NPs sample at 660 nm, and (d) 17 nm NPs sample at 480 nm. Solid lines represent a fit of the experimental data using Eq. (3). For the 3 nm NPs sample a laser energy of 10.5 µJ (irradiance at focus of 16·107 W/cm2) was applied, whereas for the 17 nm NPs sample a laser energy of 3.8 µJ (irradiance at focus of 5.9·107 W/cm2) was used.

The observation that with increasing particle size SA becomes more pronounced is consistent with earlier measurements on Ag and Au nanoclusters and NPs.22,34,62 This effect is understood in terms of size dependence of the electronic structure of the particles. For very small particles the discrete nature of their electronic states hinders plasmonic excitations, reducing considerably their linear absorption and thus, corresponding to very high saturation irradiance for the particle’s first-excited state.34 The measured transmission curves can be used to quantify the contributions of SA and RSA-like behavior. Within the sample, the irradiance I changes, in addition to focusing, by the optical absorption of the sample, according to


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= − 2 ′ with ′ a coordinate within the sample and an irradiance dependent absorption coefficient. In case nonlinearities are absent, i.e. =

,

Eq. (2) simplifies to the Beer-Lambert law of

optical absorption.63 When both SA and transmission decrease (either by ESA or 2PA) are present, is usually modelled by Eq. (3):60,64

=

where

1

"

#$%% 3

represent the linear absorption coefficient, " the absorption saturation irradiance and

#$%% a parameter representing all possible processes responsible for transmission decrease, hence effective.22 Combining Eqs. (2) and (3) with the Gaussian intensity profile of the laser beam, one obtains an expression that can be fitted numerically to the z-scan curves. In this procedure " and #$%% represent fitting parameters, while

is obtained from the far-field transmission. Examples

of such fits are shown in Figure 4 as solid lines. The extracted " and #$%% coefficients for both samples, as a function of wavelength, are discussed in the following section.

DISCUSSION Absorption cross sections The obtained wavelength dependence of

,

#$%% and " is shown in Figure 5. The nonlinear

absorption coefficients (#$%% ) tend to follow, for both samples, the wavelength dependence of the linear absorption (

),

as comparison of Figure 5a and Figure 5b shows. Such


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correspondence is expected in case of sequential two-photon absorption. Compensating for the absorbance, it is found that the wavelength dependence of #$%% is more pronounced for the 17 nm NPs sample: for the 17 nm NPs sample the ratio #$%% /

() *+

/#$%% /

)) *+

is 2.58,

whereas it is 0.82 for the 3 nm NPs sample. For the 17 nm NPs sample, #$%% has a local maximum around 460-480 nm, in agreement with the plasmonic absorption seen in the OD (Figure 2). The observed correspondence in the spectral behavior of

and #$%% agrees with

recently performed TD-DFT calculations on ligand-protected Ag nanoclusters, where cross sections involving two photons were found to be larger at excitation energies in resonance with the single photon absorption.42,43

Figure 5. (a) Linear (

)

and (b) nonlinear (#$%% ) absorption coefficients, as a function of excitation wavelength.

The inset in (b) presents a zoom of the #$%% coefficients of the 3 nm NPs sample. (c) Absorption saturation irradiance of the 17 nm NPs sample as a function of excitation wavelength. The 3 nm NPs sample is represented by black squares and the 17 nm NPs sample by red circles.

Samples with a higher concentration of NPs will have larger linear and nonlinear absorption coefficients. Therefore, more meaningful parameters to quantify the optical absorption properties of the samples are the one- and two-photon absorption cross sections, ,


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and -, respectively. These quantities account for the dependence of the optical properties on the NP concentrations, D: , = / 4 - = ℎ/ ∙ #$%% / where ℎ/ is the excitation photon energy. For the 3 nm and 17 nm NPs samples, D equals (1.1 ± 0.2)·1024 m-3 and (5.5 ± 0.4)·1021 m-3, respectively. Table 1 summarizes the absorption coefficients

and #$%% together with the absorption cross sections , and - for both samples at

selected wavelengths.

Table 1. Linear and nonlinear optical parameters of both samples measured by open aperture z-scan as a function of λ.

3 nm NPs

17 nm NPs

λ / nm

α0 / cm-1

βeff / 10-7·cm·W-1

σ0 / 10-18·cm2

δ / 106·GM*

460

4.0

1.8 ± 0.1

3.7 ± 0.6

6.9 ± 1.6

560

2.7

1.4 ± 0.1

2.5 ± 0.4

4.6 ± 1.2

660

2.0

1.1 ± 0.2

1.9 ± 0.3

2.9 ± 0.9

445

22.0

17.7 ± 1.0

(40 ± 3)·102

(14.3 ± 1.8)·103

460

22.3

24.8 ± 1.0

(41 ± 3)·102

(19.4 ± 2.2)·103

560

14.0

6.8 ± 0.2

(25 ± 2) ·102

(4.4 ± 0.5)·103

660

10.6

4.6 ± 0.2

(19.3 ± 1.4) ·102 (2.5 ± 0.3) ·103

* 1 GM = 10-58 m4·s Below we compare the obtained nonlinear absorption cross sections with values that have been reported in literature. While there exist many studies on the nonlinear optical properties of Au and Ag NPs, most studies do not quote cross sections because particle concentrations are


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unknown. Quantitative information is available for monolayer-protected Au clusters, although it must be stressed that these particles are intrinsically different from the Ag NPs in the current work because of their discrete absorption spectrum and the ligand effects. Ramakrishana et al.65 reported 2PA cross sections of 0.427·106 GM for Au25, 1.476·106 GM for Au309 and 0.905·106 GM for Au976 (1 GM = 10-58 m4·s). Assuming a spherical shape and using the bulk density, it is estimated that a 3 nm Ag NP contains about 800 atoms. Hence, the δ of the 3 nm Ag NPs sample (Table 1) is of the same order of magnitude but larger, especially at the center of the plasmon band, that the reported value for Au976. It is also worth noting, however, that in the studies of Ref. [65] size-selected clusters were investigated, whereas in this study samples are composed of particles with a size distribution. For small ligand-protected Au25 clusters deposited on polymeric substrate with different interparticle distances, 2PA cross sections ranging from 1·106 GM to 10·106 GM were found.66 Also, these values are in line with those reported for the 3 nm Ag NPs in the current work. For the 17 nm NPs sample, very high two-photon cross sections are found, which is consistent with the high optical response of the NPs despite their low concentration within the glass. A quantitative comparison of the results of this sample with literature is not possible because of the absence of information about particle concentrations. We can therefore only compare the effective nonlinear absorption coefficient. In Ref. [16] a twophoton absorption coefficient of approximately 0.9·10-7 cm·W-1 was obtained for 40 nm Au nanoparticles. In Ref. [67] gold nanorods on average 15 nm in diameter and 45 nm in length were studied, finding βeff values of the order of 0.2·10-7·cm·W-1. In Ref. [68] Ag nanoparticles up to 10 nm in size were investigated, obtaining two-photon absorption coefficients as high as 90·10-7 cm·W-1. Ag-Ti NPs of sizes between 20 and 40 nm, deposited onto glass, were investigated in Ref. [69], obtaining only SA and thus no indication for RSA-like behavior. In


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Ref. [40] silver NPs of sizes between 5 and 10 nm embedded in a polymer film were studied with femtosecond laser pulses. Two-photon absorption coefficients of approximately 2·10-9 cm·W-1 were reported, thus two orders of magnitude lower than those reported here. Finally, in the work of Zheng et al.41, Ag nanoparticles in solution and embedded in glasses were investigated, with sizes of the order of around 50 nm, however, only the shape of the z-scan curves were discussed, without any quantitative information. Finally, Figure 5c presents the absorption saturation irradiances, " , of the 17 nm NPs sample, as a function of λ. For the 3 nm NPs sample " remains, within the uncertainty of the fitting procedure, constant (~2·106·W·cm2). For this reason, the 3 nm data is not shown in the figure. In contrast, " of the 17 nm NPs sample clearly increases with increasing excitation wavelength. Because " represents the fluence needed to saturate the first-excited state, this result suggests that less fluence is needed to saturate the one-photon absorption when the excitation energy corresponds to the system’s plasmon resonance, which is expected in view of the much higher

coefficient of the NPs at these wavelengths.

Multiple photon absorption mechanism At this point it is worth commenting on the mechanism behind the observed multiple photon process. The transmission decrease near the focal point in the z-scan curve may be caused by the simultaneous absorption of two or more photons (2PA, 3PA, and so on) via virtual states, or by excited-state absorption (ESA), in which an electron is excited by the absorption of a first photon, followed by an additional electronic excitation to a higher excited state. For ESA, this is the case under the condition that the absorption cross section of the excited-state is higher than


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that of the ground-state. In the literature about the NLO properties of Ag NPs there are conflicting statements, with some studies suggesting that the observed transmission decrease is a consequence of ESA,68 2PA,38 or even 3PA.70 Many z-scan experiments have been performed at a single excitation wavelength and the underlying mechanism of NLO absorption is addressed simply by the fitting of a single z-scan curve, i.e. different models are assumed and the one that gives the best fit of the experimental data is assumed as the one describing the system. A more reliable alternative to distinguish between ESA, 2PA or 3PA is to analyze the wavelength dependent data of Figure 5. For a fixed excitation fluence, the absorption in a purely 2PA process is enhanced at a photon energy, which corresponds to half the energy of a single photon resonance. In the same way, an absorption maximum will appear for a purely 3PA process at an excitation wavelength that is three times larger than that of a single photon resonance. This effect has been seen, for example, in the work of Perumbilavil et al.46 where graphene oxide nanosheets were studied by white light z-scan in the 400-700 nm range. # was found to have a local maximum at exactly twice the wavelength for which α0 peaked. Because the electronic gap of the graphene nanosheets is larger than the energy at which the peak in # was observed, the only possible mechanism for the nonlinear absorption was the simultaneous absorption of two photons via a virtual state. In both studied samples here, the spectral dependence of #$%% follows that of α0 (see Figure 5) with local maxima around 460 nm, strongly suggesting that ESA, and not 2PA nor 3PA, is the underlying NLO absorption mechanism.

Saturation of the two-photon absorption


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Further analysis of the mechanism responsible for the observed NLO absorption can be obtained by measurements of fluence dependent z-scan curves at a fixed λ. Neglecting the process of SA, multi-photon absorption is accounted for by expanding the absorption coefficient α as a power series of irradiance:

=

# ∙ 2 ∙ . .. 5

If only the first two terms of the expansion are used to fit the experimental z-scan curves (as is the case when using Eq. (3)), a fluence-dependent z-scan experiment should yield a constant # for a two-photon absorption process (ESA or 2PA), while # should be a linearly increasing function of I with zero intercept in the case of a purely 3PA process. If both 2PA and 3PA processes contribute, # should also increase linearly, but having a nonzero intercept. For the 3 nm NPs sample, we observed neither of these behaviors. Figure 6 summarizes the result of a fluence-dependent z-scan experiment of this sample at a fixed λ of 480 nm. The top panel of figure 6 presents z-scan curves for the lower and higher measured irradiances (energy per unit of area per unit of time) at focus, of 4·107 W·cm-2 and 21·107 W·cm2

, respectively. By increasing energy even further, a damage threshold of 31·107 W·cm-2 could

be estimated. In the bottom panel, the extracted #$%% coefficients are plotted as a function of the irradiance at focus. As clearly seen from the figure, the #$%% values are far from constant. In contrast, a decrease for increasing irradiance is observed.


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Figure 6. Top: Two examples of open aperture z-scan measurements performed on the 3 nm NPs sample at 480 nm and irradiances at focus of 4·107 W·cm-1 and 21·107 W·cm-1. A fitting of the experimental data is applied in order to extract nonlinear coefficients (solid lines). Bottom: Nonlinear absorption #$%% coefficients as a function of laser fluence for the 3 nm NP sample. The red solid line represents a fit using Eq. (6).

A decrease in #$%% for increasing input fluence has been reported previously for different systems, such as few-layer films of WS2 and MoS2,71 bulk and nanocrystal CdS,72,73 and Pd metal-organic complexes.57 In general, this effect is attributed to saturation of the two-photon absorption process, in a similar way as the single photon absorption saturates in a normal SA process. Different models have been proposed to account for the saturation of the two-photon absorption.74 Several of these models were compared with the data of Figure 6 and the best


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agreement was obtained using Eq. (6), which is a similar expression as the one used to account for the SA of a one-photon process: #$%% =

# 6 1 5 "

In this expression, # represent the two-photon absorption coefficient at low irradiance and " 5 is the saturation irradiance of the two-photon process. Fitting the data in the bottom panel of Figure 6 by Eq. (6) provides a two-photon absorption saturation irradiance of " 5 = (1.7 ± 0.6)·107 W·cm-2 and a low-fluence two-photon absorption coefficient of # = (2.0 ± 0.7)·10-6 cm·W-1. It should be mentioned that combining Eqs. (3) and (6), in order to fit the zscan curves, leads to large uncertainties for the extracted NLO coefficients, since the corresponding fit has too many free parameters. It is worth stressing that both fitted values are positive numbers. A Taylor expansion of Eq. (6) gives a similar expression as in Eq. (5), however, with a negative 2 that is not physical. Thus, Eq. (6) better describes the saturation behavior of #$%% . Comparing the SA intensities of the one- and two- photon process for the 3 nm NPs sample at λ = 480 nm, we found " = (5 ± 1)·106 W·cm-2, being half the value obtained for the " 5 coefficient. Thus, as expected, saturation of the two-photon absorption process takes place at larger irradiances than " . In addition, it is interesting that the low-field two-photon absorption coefficient # is an order of magnitude larger than the obtained value at higher fluences, as presented in Figure 5. A calculation of the low-field two-photon absorption cross section gives the value of 75·106 GM, being larger than previously reported values for ligandprotected Au clusters in solution or as deposited thin films.65,66 For the 17 nm NPs sample a similar behavior is observed, i.e. a decrease of #$%% with increasing irradiance. However, due to


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a much lower damage threshold found for this sample, only few fluences could be studied. The measurements presented in Figures 4 were already performed at a fluence maximizing #$%% . Finally, we propose an interpretation of the nonlinear optical properties of the embedded Ag NPs. At lower fluences only one-photon processes are accessible via dipolar plasmon excitation of electrons within the conduction band (intraband transition). In Ag NPs, the energy gap between the d-band and the conduction s-p band is around 4 eV,75 so d→s-p interband transitions cannot be excited by low fluences laser light with wavelengths longer than 460 nm (2.69 eV). At moderate irradiances, most NPs are pumped into an excited state causing a reduction of the ground-state population with the concomitant bleaching of the ground-state plasmon absorption band, which is translated in SA of the one-photon process. At higher irradiances, the already excited electrons can be pumped to a higher excited state through ESA in an intraband process within the s-p conduction band (free carrier absorption), causing RSA-like behavior. Another energetically possible process at the used excitation wavelengths is the direct absorption of two photons from occupied states of the d-band to empty states in the s-p band. However, the observation that the spectral dependence of #$%% follows that of

,

strongly

suggests such interband transitions are not responsible for the observed transmission decrease. Finally, at the higher irradiances used, many excited electrons are pumped into a second excited state, reducing the first excited state population and leading to SA of the ESA.

CONCLUSIONS In this work, the linear and nonlinear absorption properties of glass embedded Ag particles with average sizes of 3 nm and 17 nm have been studied. For the sample composed of nanoparticles


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of 3 nm in size a low amount of linear optical absorption was found, resulting in a nonlinear behavior composed mainly of transmission decrease. For the sample containing 17 nm Ag NPs a fully developed plasmonic absorption behavior was found. In this case, strong saturation absorption was seen in the nonlinear regime, in addition to transmission decrease at even higher irradiances. The wavelength dependent z-scan measurements, performed in the wide range from 445 nm to 660 nm, revealed in both samples that the spectral dependences of the nonlinear and linear absorption coefficients are similar, suggesting that the mechanism responsible for the nonlinearities is excited-state absorption. FDTD simulations confirm that these results are caused by individual silver particles. In addition, irradiance dependent measurements showed that at higher fluences the two-photon absorption process can saturate, just as the single photon absorption process does. Thus, it is seen that by using moderate fluences and excitation wavelengths close to the plasmon resonance, strong two-photon absorption cross sections can be obtained for the studied glasses containing silver nanoparticles. Applications that make use of a wide spectral range, such as optical limiting or ultra-short pulse generation, can be designed, making use of the very strong fluence and excitation wavelength dependence of the nonlinear optical properties of the embedded Ag nanoparticles.

METHODS Sample preparation. The silver doped oxyfluoride glasses were prepared by a conventional melt-quenching method,76 using the chemicals SiO2, Al2O3, CdF2, PbF2, ZnF2, and AgNO3, supplied by Alfa Aesar. The chemicals were batched and mixed in a Pt crucible. Then, the batch was melted in a tube furnace at 1000 °C for 1 hour. The obtained melt was cast into an Al mold


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at room temperature. The selected glass composition corresponds to the chemical formula 33(SiO2)9.5(AlO1.5)32.5(CdF2)19.5(PbF2)5.5(ZnF2) mol%. This composition is a well-known proper glass-former with large capability to Ag nanoclusters and rare-earths dissolution.77 An atomic concentration of Ag of 0.15% is used. The glasses were cut into 1.35 mm thick pieces and polished. The pieces were heat-treated at 350 °C, below the glass transition temperature (370 °C), for 6 hours (3 nm NPs sample) and 78 hours (17 nm NPs sample). Such heat-treatment is known to lead to agglomeration of Ag nanoclusters into amorphous Ag NPs. More details about the morphology of the samples and its changes upon heat treatment can be found in references [52,53]. Small-angle x-ray scattering measurements. SAXS measurements are carried out with a Nanostar system (Bruker AXS), equipped with a MetalJet X-ray source (Excillum). The system is described in detail in Ref. [78]. Ga Kα X-rays with a wavelength of 1.34 Å are directed perpendicularly to the samples and the transmitted signal is measured by a two-dimensional detector (Våntec2000).79 All scattering experiments took 2 h of measuring and were carried out under low vacuum conditions (4 mbar) to avoid parasitic scattering from air. The obtained 2D images were azimuthally integrated to obtain 1D data in function of the scattering vector. SAXS data were calibrated using a silver behenate standard. For each measurement, a background subtraction is performed, corresponding to the signal of the undoped glass. Optical density measurements. Absorbance spectra are recorded with a Bruker Vertex 80 V Fourier transform spectrometer in air atmosphere at room temperature. The measurements were carried out in transmittance mode using Silicon (Si) diode as a detector and Tungsten (W) lamp as a light source.


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Z-scan measurements. Non-linear optical measurements were performed using the z-scan technique in an open-aperture configuration.26 The light source is an optical parametric oscillator (OPO) pumped by a Quanta-Ray Nd:YAG laser (8 ns pulse duration operated at 10 Hz), which was tightly focused by a lens (10 cm focal length) to generate a Gaussian beam profile. Using the knife-edge method, the beam waist (8 ) of the laser beam was measured to be 16.0 ± 0.3 µm at a wavelength of 480 nm. The Rayleigh length ( ) is estimated to be 2.3 mm. Samples were translated parallel to the laser beam propagation by a stage movement system (Zollix, SC3001B) and the transmitted light was measured by a silicon PIN detector (Newport 818-BB-40). The samples were moved in steps of 0.5 mm in the -15 mm ≤ ≤ 15 mm range, with = 0 corresponding to the focal point. The wavelength of the laser light is varied between 445 to 660 nm, in steps of 20 nm. The z-scan system is controlled by a LabVIEW program that sets a sample position and averages the signal from the transmitted light 256 times. Transmission curves were normalized by the signal in the far field. To avoid the influence of possible nonlinear refractive effects on the measurements, the detector used for measuring transmission was positioned such that its sensitive area was, for all sample positions, larger than the laser beam size. Measurements were repeated to confirm reproducibility and to assure that the samples are not damaged by the focused laser beam nor that gradual heating of the samples takes place, which could affect the measurements. Finite-difference time-domain (FDTD) simulations: Simulations of electromagnetic field around the embedded Ag nanoparticles and their optical absorption were performed with a Maxwell solver (Lumerical Solutions Inc.). For this, two silver (Palik) particles of sizes 3 nm and 17 nm were simulated both as single particle and in a pair of particles with the same size, separated by a distance (centre to centre) of 5.4 nm for the 3 nm particle and 31 nm for the 17


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nm particle. After testing convergence, a mesh size of 0.2 and 0.8 nm was used for the 3 and 17 nm particles respectively. The real (9) and imaginary (:) part of the glass host refractive index as a function of wavelength was used after ellipsometry measurements were carried out on the glass without silver particles.

AUTHOR INFORMATION Corresponding Authors *Ewald Janssens. [email protected] *Piero Ferrari. [email protected] Author Contributions P.F., S.U., and J.V. performed the Z-scan experiments. P.F and S.U. analyzed the data. M.V.S. prepared the samples and measured the linear absorbance spectra, B.d.R. performed the SAXS measurements. Y.K. did the ellipsometry on glass and M.D.V. did the FDTD simulations. E.J. and P.L. initiated and directed the research project. P.F. and E.J. prepared the first version of the manuscript. All authors discussed the results and participated in writing the manuscript.

ACKNOWLEDGMENT This work was supported by the Research Foundation-Flanders (FWO) and the KU Leuven Research Council (GOA/14/007). P.F. acknowledges CONICYT for a Becas Chile scholarship and J.V. thanks the FWO for financial support. M.V.S. is grateful to Methusalem funding and


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KU Leuven internal funds (PDM project) for financial support. The authors also acknowledge Flemish Government and the EU Snow Control FP7 project for financial support.

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Insert Table of Contents Graphic


35


E x p e r im e n t F it

4 .2

L n (I)

(a )

4 .0 3 .8

3 n m

N P s

0 .0 1 2 6

0 .0 1 5

0 .0 1 8

5

L n (I)

0 .0 2 1 E x p e r im e n t F it

4

1 7 n m 0 .0 0 1 2

N P s 0 .0 0 1 8

q

0 .0 0 2 4 2

/

0 .0 0 3 0

-2

2

3

Å

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Page 36 of 42


(b )

Page 37 of 42 2 .0

0 .3 0

U n d o p e d g la s s 3 n m N P s s a m p le 1 7 n m N P s s a m p le

1 .6

0 .2 5 0 .2 0

O p tic a l d e n s ity

1 2 3 4 5 6 7 8 9 10 11 12 13 14


0 .1 5

1 .2 0 .1 0 4 0 0

4 2 0

4 4 0

4 6 0

4 8 0

0 .8

0 .4


0 .0 4 0 0

4 5 0

5 0 0

5 5 0

W

6 0 0

a v e le n g th / n m

6 5 0

7 0 0

5 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

The (b) Journal of Physical Chemistry

Page 38 of 42

(c) Absorption / J·m-3

x 10-2 3

1

z / μm

(a)

-1

-3 -3 ACS Paragon Plus Environment

-1

1

x / μm

3

x 10-2

Page 39 of 3 42n m

of Physical Chemistry N P The s s a Journal m p le 1 7 n m N P s s a m p le

1 .5

N o r m a liz e d T

1 .2 0 .9 0 .6 0 .3

λ= 6 6 0 n m

(a ) -1 5

-1 2

-9

-6

-3

0

3

Z / Z

6

9

1 2

1 .2 0 .9 0 .6

1 5

-3

1 .2

1 .2

0 .9 0 .6

0

1

2

3

R

0 .9 0 .6

ACS Plus λ = 4 Paragon 8 0 n m λ= 4 8 0 n m d ) 0 . 3 ( Environment

(b ) -8

-1

R

1 .5

-1 0

-2

Z / Z

1 .5

0 .3

λ= 6 6 0 n m

(c )

0 .3

0 .0

N o r m a liz e d T

N o r m a liz e d T

N o r m a liz e d T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1 .5

-6

-4

-2

0

Z / Z R

2

4

6

8

1 0

-5

-4

-3

-2

-1

0

Z / Z R

1

2

3

4

5

2 5

(a )

(b )

Page 40 of 42

0 .1 8

(c )

1 2

0 .1 6

2 0

0 .1 4

-1

1 0

0 .0 8 5 0 0

5 5 0

6 0 0

6 5 0

8

/ 1 0

6

4 5 0

I s / 1 0 ⋅W ⋅c m

c m ⋅W -6

-1

0 .1 0

2

0 .1 2

2 1 5

ff

1 0

1

βe

α0 / c m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


3

6 4

5 2 4 5 0

5 0 0

5 5 0

6 0 0

W a v e le n g th / n m

6 5 0


4 5 0

5 0 0

5 5 0

6 0 0


6 5 0

4 5 0

5 0 0

5 5 0

6 0 0


6 5 0

-1 .2

-0 .8

-0 .4

m 0 .0

0 .4

0 .8

1 .2

1 .2

0 .8 0 .6 -2 -2

m

c

W

m

c

0

1

7

⋅

⋅

7

4 1

4

m

it

0

p

x

E F

⋅

W

-2

⋅

-2

⋅

c

W

m

c

7

⋅

W

0

1 7

1

2

⋅

0

⋅

1

p 1

it

F

0 .2

2

x

0 .4 E

N o r m a liz e d T

1 .0

m

c

⋅

-2

W

m

c W

-1

⋅

-6

0

1

)

.6

0

±

.7

⋅

7

0

1

)

.7

0

±

(2

= S

(1

c m ⋅W

5

⋅



-1



I

0

=

6

.0

7

-7

4 3

 / 1 0 2 1

1 4

⋅

1 8

c

W

0

1

/

e

c

n

ia

1 6 -2

1 2

m

1 0

7

8

d

6

ra

4

Ir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

c

/


Z

Page 41 of 42


2 0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42


Page 42 of 42

Wavelength-Dependent Nonlinear Optical Properties of Ag

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