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Abstract
The nonlinear absorption of 40 nm Ag nanoparticles (Ag NPs) was investigated using open aperture (OA) Z-scan technique at 532 nm. Experiments show that the nonlinear absorption behavior of Ag NPs is intensity dependent. Specifically, under low laser energy the Ag NPs shows saturable absorption (SA). At medium laser energy, the transformation of nonlinear absorption from SA to reverse saturable absorption (RSA) happens. While under stronger laser energy, double transformation (SA→RSA→SA) of nonlinear absorption occurs. The experimental results were analyzed theoretically using a model based on single-photon absorption and two-photon absorption saturation.
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1. Introduction
Nonlinear absorption is an important nonlinear optical property of materials. It has many applications [1–3], such as mode locking technology on the ground of saturable absorption (SA) [4,5], optical limiting techniques predicated on reverse saturable absorption (RSA) etc. [6,7]. Therefore, it is important to study nonlinear absorption properties of material and obtain the relevant optical parameters. Among all kinds of nonlinear optical materials, noble metal nanoparticles can exhibit relatively stronger nonlinear optical properties and ultrafast response because of local field enhancement caused by surface plasmon resonance (SPR) [8–10].
The plasmon resonance of Ag NPs lies in the visible wavelength band, and the significant separation of the interband absorption and plasmon resonance of Ag NPs makes the resonance excitation in Ag NPs more efficient than that in gold, which is expected to obtain stronger local field enhancement and larger nonlinear absorption in Ag NPs. Therefore, the nonlinear absorption of Ag NPs has been widely studied [11–18]. For example, in 2012, Fan et al. studied the nonlinear optical properties of AgNPs using 800 nm femtosecond laser pulse [11]. They found that the AgNPs always shows SA even under high intensity laser, and explained the physical mechanism of SA in terms of the band structure. In the same year, we investigated the nonlinear absorption of Ag NPs at resonant wavelength of 400 nm [12]. It was found that at low intensities, Ag nanoparticles exhibited SA, while at high intensities the transformation of nonlinear absorption from SA to RSA occurs. In 2014, Zheng et al. investigated the nonlinear optical behavior of Ag nano-pentagons using a 532 nm nanosecond pulsed laser [13]. They found Ag nano-pentagons shows SA at low intensity and RSA at high intensity. In 2012, M. Hari studied the nonlinear optical properties of Ag NPs under a 532 nm nanosecond laser [14]. They observed the transition of nonlinear absorption from SA to RSA when the input intensity was increased from 28.1 MW/cm2 to 175.8 MW/cm2.
From reports above we know the nonlinear absorption of Ag NPs is different depending on experimental conditions. In this work, we studied the nonlinear absorption of 40 nm Ag NPs via Z-scan technology using 532 nm nanosecond laser. To our surprise, we found the sign of nonlinear absorption of Ag NPs changes twice with increasing laser intensity, and analyzed the experimental results using a phenomenal model.
2. Theory
Under excitation of strong light, material may exhibit SA or RSA absorption depending on light intensity [11–14]. In the case of SA, nonlinear absorption coefficient will decrease with the increase of light intensity. Correspondingly, the nonlinear absorption coefficient α(I) can be described using the following Equation [18,19]:
where α0 is the linear absorption coefficient of the material, IS is the single-photon saturable intensity, I is the excitation light intensity. The nonlinear absorption coefficient α(I) can be shown visually in Fig. 1(a). It is worth noting that in Eq. (1), when the excitation light intensity is very weak (I<<IS, I/IS→0), the absorption coefficient α(I) is equal to the linear absorption coefficient α0, namely the nonlinear absorption will not occur.RSA refers to the increase of absorption coefficient with light intensity, and nonlinear absorption coefficient α(I) can be expressed as [20]:
where β is the two-photon absorption (TPA) coefficient. α (I) can be described using Fig. 1 (b).
Fig. 1. Nonlinear absorption coefficient α(I) as function of the incident intensity I of (a) SA, (b) RSA, (c) coexistence of SA and RSA
However, sometimes, Ag NPs can show the coexistence of SA and RSA, and the nonlinear absorption coefficient α(I) can be obtained by the combination of Eqs. (1) and (2) as [12,21,22]:
Figure 1(c) shows the changing of α(I) with I.
In fact, more complex nonlinear absorption process (for example, SA→RSA→SA) can also occur, in the case, nonlinear absorption coefficient α(I) can describe as follows [23]:
OA Z-scan is the technology used most widely to measure the nonlinear optical absorption. It is based on the relationship between normalized transmittance and sample position z [24]. The light intensity loss during the propagation of the beam in a thin medium is determined by the following differential Equation [9,23]:
where ${z^{\prime}}$ and I are the propagation distance and light intensity inside the sample, respectively, and α(I) denotes the nonlinear absorption coefficient depending on the light intensity. The Eq. (5) is organized as follows:Fig. 2. Nonlinear absorption coefficient α(I) including saturable intensity of single photon absorption and two-photon absorption as function of the incident intensity I.
After transmitting a short distance $d{z^{\prime}}$, the output intensity is expressed as:
Substituting Eq. (6) into Eq. (7) yields:
The transmittance T is obtained as:
When the thickness of materials L and the confocal parameter z0 of the Gaussian beam satisfy the condition $L \ll {{\rm{z}}_0}$, material can be regarded as a thin sample. Therefore, $d{z^{\prime}}$ in the Eq. (9) is approximated as the sample cell thickness L, and the transmittance can be expressed as:
As mentioned earlier, there are various expressions for the nonlinear absorption coefficient α(I) for different nonlinear absorption processes. For the liquid phase and inhomogeneous spreading of the sample under certain conditions, the nonlinear absorption coefficient is described by Eq. (4).
Substitute Eq. (4) into Eq. (10) yields:
The intensity I of a Gaussian beam can be expressed as:
where I0 is the peak laser intensity at the focus, z is the displacement of the sample from the focus, z0 is the Rayleigh rang. Therefore, in Z-scan the transmittance of sample can be expressed as:From Eq. (13), it can be found that the transmittance of samples in Z-scan experiment is related to α0, β, IS1, IS2 and I0. For a certain sample, α0 is linear absorption coefficient which is independent of the optical nonlinearity of the sample, and β, IS1 and IS2 are the nonlinear optical parameters which can be obtained by Z-scan data. Therefore, it is obvious that the transmittance of sample will change with I0. When parameters concerning are set to be: α0 = 0.2 mm-1, IS1 = 0.3 × 1012 W/m2, IS2 = 1.7 × 1012 W/m2, β=1.2 × 10−9 m/W. The laser intensity range I0 increases from 0.1 to 20 × 1012 W/m2, the normalized transmission VS sample position z is shown in Fig. 3. It can be found that as the laser intensity increases gradually, the transmittance curve transforms from a single peak to a peak-valley-peak, which demonstrates completely the all changing of nonlinear absorption (SA, SA→RSA, SA→RSA→SA).
In order to clearly express the effect of laser intensity on transmittance, representative transmittance curves when I0 is 0.1 × 1012 W/m2, 0.2 × 1012 W/m2, 0.4 × 1012 W/m2, 0.5 × 1012 W/m2, 5 × 1012 W/m2, 6 × 1012 W/m2, 10 × 1012 W/m2 and 17 × 1012 W/m2, respectively, were extracted from the Fig. 3 and shown in Figs. 4(a-h). It can be seen that when I0 is 0.1 × 1012 W/m2 and 0.2 × 1012 W/m2 (Fig. 4(a-b)), there is only a peak on curves, which implies the sample shows SA. When I0 is 0.4 × 1012 W/m2 and 0.5 × 1012 W/m2 (Fig. 4(c-d)), the transmittance curve starts to show a hump, which indicates that the conversion from SA to RSA occurs, and the valley of transmittance becomes lower as the intensity becomes larger. When I0 is 5 × 1012 W/m2 (Fig. 4(e)), the transmittance curve is characterized by a broadened valley, which is a harbinger of the conversion to SA. When I0 is 6 × 1012 W/m2, 10 × 1012 W/m2 and 17 × 1012 W/m2 (Fig. 4(f-h)), the transmittance curves show new peaks at the location of the valleys, and the new peaks become progressively higher with increasing intensity, which implies that the SA→RSA→SA transformation of nonlinear absorption happens.
Fig. 4. The transmittance curves under different light intensities extracted from the surface diagram. The peak intensities at the focus corresponding to Fig. 4 (a) ∼ (h) are 0.1 × 1012 W/m2, 0.2 × 1012 W/m2, 0.4 × 1012 W/m2, 0.5 × 1012 W/m2, 5 × 1012 W/m2, 6 × 1012 W/m2, 10 × 1012 W/m2 and 17 × 1012 W/m2 respectively
3. Experiment
The sample was provided by Nanjing Xianfeng nano material technology Co., Ltd. (Nanjing, China). The concentration of Ag NPs is 0.04 mg/ml. The morphology of Ag NPs was characterized by transmission electron microscopy (TEM). The linear absorption spectra of the sample were obtained by UV-2250 UV-Vis spectrophotometer.
The nonlinear absorption response of the sample was measured using the OA Z-scan technique. the Z-scan device is similar to that described in the available reports [24,25]. The pulsed laser (with pulse width of 5 ns, wavelength of 532 nm) provided by Nd: YAG laser system is used as the excitation source. In order to reduce the effect of thermal accumulation produced by using ns laser pulses, the experiment was conducted with a repetition frequency of 10 Hz. A lens with a focal length of 10 cm focuses the pulsed beam on the sample, which is mounted on a translation stage that can move near the focus of the beam. When the sample moves closer to the focal point, with the increase of laser irradiance, the nonlinear absorption effect of the sample gradually appears, and the variation of the transmitted light with the sample position can be recorded through the power meter.
4. Results and discussion
Figure 5(a) and (b) show the TEM image and size distribution of Ag NPs, respectively. From this, it can be determined that the average diameter of Ag NPs is about 40 nm and the sample has good dispersion, without agglomeration. Figure 5(c) shows the linear absorption spectrum of Ag NPs, where a strong absorption peak can be found at about 407 nm, which is generally attributed to the SPR [26], and there is a shoulder peak at 350 nm, which may be due to the presence of a small number of non spherical particles in the sample [27].
By using attenuator, the laser energy acting on the sample was varied to be 20 µJ, 80 µJ, 205 µJ and 370 µJ (The peak light intensities I0 are 9.7 × 1011 W/m2, 38.3 × 1011 W/m2, 98.1 × 1011 W/m2 and 177.1 × 1011 W/m2 at z = 0, respectively). Correspondingly, the OA Z-scan results are shown in Figs. 6(a-d).
Fig. 6. OA Z-scan results of Ag NPs at different energies, the dots are experimental data, while the solid curves are theoretical analysis, (a) 20 µJ, (b) 80 µJ, (c) 205 µJ, (d) 370 µJ, and the peak intensities I0 at the focus corresponding to (a) ∼ (d) are 9.7 × 1011 W/m2, 38.3 × 1011 W/m2, 98.1 × 1011 W/m2 and 177.1 × 1011 W/m2, respectively
From Fig. 6(a), it can be found that, at an excitation energy of 20 µJ, the transmittance curve of the OA Z-scan has a peak at z = 0, which indicates the sample shows SA behavior. The phenomenon is usually considered to be the result of ground state plasma bleaching [12–15]. When the excitation energy is increased to be 80 µJ, the experimental results are shown in Fig. 6(b). A hump can be found on both sides of the curve, which indicates that the transmittance first increases gradually with the increase of laser intensity during the movement of the sample, and then starts to decrease at a certain position near z = 0. This implies the conversion from SA to RSA occurs, and similar effect has been widely reported [11–13,17,28]. It is generally accepted that the decrease in transmittance at z = 0 is due to ESA or TPA. When the excitation energy is increased further to 205 µJ and 370 µJ (Figs. 6(c-d)) new peak appears at z = 0, which indicates the secondary transformation of nonlinear absorption occurs obviously, namely the complex behavior of SA→RSA→SA happens.
As mentioned earlier, the initial increase of laser intensity leads to the bleaching of ground state plasma, which directly results in SA, while the further increase of intensity, ESA and/or TPA leads to the conversion from SA to RSA. However, when the excitation intensity increases to the extent that most electronics in the first excited state jump to higher excited states, there will be a bleaching of the first excited electronics similar to the ground state plasma bleaching, which leads to the occurring the saturation of two-photon absorption [29]. Thus, as shown in Figs. 6(c-d), a small new peak appears at z = 0.
Furthermore, the Z-scan experimental data above were fitted with formula (13), and the theoretical results are shown by the red solid curves in Figs. 6(a-d). We can see the theoretical results agree well with the experimental data. Through the theoretical fitting, the saturable intensities and two-photon absorption coefficients are obtained and listed in Table 1.
Table 1. IS1, IS2 and β of Ag NPs obtained by theoretical fitting
It can be found from Table 1 that, in terms of order of magnitude, the saturable intensity of single-photon absorption is 1011 W/m2, the saturable intensity of two-photon absorption is 1012 W/m2, and the two-photon absorption coefficient is 10−10 m/W. The saturable intensity of single-photon absorption and two-photon absorption coefficient are close to the reported results [12,14].
As far as we know, the double transformation of nonlinear absorption has also been observed in Ag-29 nanoclusters by Reyna et al. [29]. The excitation intensities of laser they used is in the range of 1.5 to 15 × 1013 W/m2 to enable the transformation from SA→RSA→SA, and saturable intensity of single-photon absorption is ∼0.3 × 1013 W/m2, saturable intensity of two-photon absorption is ∼0.9 × 1013 W/m2, and two-photon absorption coefficient is ∼1 × 10−10 m/W. However, in our experimentwe, the excitation intensities in the range of 0.97 to 17.7 × 1012 W/m2 already resulted in double transformation of the nonlinear absorption of Ag NPs. This difference may result from SPR effect. Only when metal unit has sufficiently large diameter, can SPR occur. While nanocluster is composed of a small number of atoms, it exhibits macromolecular behavior, and SPR cannot be excited [23]. Thus, we observed double transformation of the nonlinear absorption of Ag NPs under less light intensities than Reyna et al. did. And saturable intensity and two-photon absorption coefficients obtained in our experiments are lower.
In fact, the nonlinear absorption of materials is related not only to the laser energy but also to the pulse width [30–35]. At present, most investigations on the nonlinear absorption of Ag NPs were conducted using femtosecond laser as the excitation source [2,11,35]. Our working group has also carried out corresponding research [35]. In the future, we will continue the research work on the double transformation of nonlinear absorption of Ag NPs with different pulse widths.
5. Conclusion
In summary, the evolution of the nonlinear absorption behavior of Ag NPs was investigated at different energies using the OA Z-scan technique. The results show that the nonlinear absorption of Ag NPs can exhibit double transformation from SA to RSA to SA during the increase of excitation intensity. The first SA and RSA are attributed to ground state plasma bleaching and two-photon absorption respectively, while the second SA can be explained as two-photon absorption saturation. The magnitude of the saturation intensity of single-photon absorption, the saturation intensity of two-photon absorption and the absorption coefficient of two-photon absorption is 1011 W/m2, 1012 W/m2 and 10−10 m/W, respectively, by analyzing the experimental data. Compared with Ag-29 nanoclusters studied by Reyna et al., the lower saturation intensity of Ag NPs is attributed to the enhancement of the local electric field caused by surface plasmon resonance.
Funding
Department of Education, Heilongjiang Province (145109320); Natural Science Foundation of Heilongjiang Province (LH2021D022).
Acknowledgments
We are thankful to Dr. Shuang Chen for providing support in the experiment.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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