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Abstract
Z-scan technology was used to study the nonlinear absorption (NLA) and nonlinear refraction (NLR) of silver nanoparticles (Ag NPs) with various sizes under different laser intensities. The results demonstrate that the NLA and NLR of Ag NPs were size-dependent. Specifically, the 10 nm Ag NPs exhibit saturation absorption (SA) and insignificant NLR. The 20 and 40 nm Ag NPs show the coexistence of SA and reverse saturation absorption (RSA). SA is believed to result from ground-state plasma bleaching, whereas RSA originates from excited state absorption (ESA). The 20 nm and 40 nm Ag NPs shows increasing self-defocusing with the increase of laser intensity. It was observed that the energy relaxation of Ag NPs mainly includes two processes of electron-phonon and phonon-phonon couplings on the order of picoseconds.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nonlinear optical (NLO) materials, such as semiconductor quantum dots [1,2], composite nanomaterials [3,4], and metal nanoparticles (NPs) [5–11], have been widely studied because of their unique properties and potential applications. Under laser excitation, the collective vibration of free electrons in the conduction band of precious metal NPs, known as surface plasmon resonance (SPR) [12,13], can lead to local field enhancement and an increase in third-order magnetic susceptibility [14,15]. Therefore, metal NPs have been extensively employed in photoswitches [16], optical limiting [17], biosensors [18], and information storage [19]. Au and Ag NPs have been extensively studied because of their SPR in the visible region. In comparison with Au, the SPR and interband absorptions of Ag NPs are clearly separated, resulting in Ag NPs having a higher SPR efficiency.
The NLO properties of Ag NPs is affected by energy [20,21], wavelength [22–24] of the laser, and shape [24–25] of the NPs. Studies have been conducted on the nonlinear absorption (NLA) of Ag nanomaterials. In 2012, Hari et al. investigated the NLO properties of Ag NPs using a nanosecond laser with a wavelength of 532 nm. In their research, it was discovered that when the laser intensity increased from 28.1 to 175.8MW/cm2, the NLA behavior of the sample changed from saturation absorption (SA) to reverse saturation absorption (RSA). They believed that ground-state plasma bleaching is the reason for the formation of SA whereas RSA comes from excited state absorption (ESA) [20]. In 2016, Kong et al. investigated the optical nonlinear response property of Ag triangular nanoplates using a 130 fs laser. The wavelengths of the laser used were 750, 800, 850, and 900 nm. They observed that the NLA properties of Ag nanoplates are wavelength-dependent, and that the third-order polarizability of Ag nanoplates is significantly larger than that of other shapes of Ag nanomaterials [23].
In 2019, Ganeev et al. observed that the nonlinear refraction (NLR) behavior of Ag nanowires under different excitation wavelengths exhibited the conversion of self-focusing to self-defocusing [22]. In 2019, Allu et al. conducted a similar research and obtained similar conclusions [24]. In 2012, Fan et al. investigated the NLR of Ag NPs at various energies [26]. The results demonstrated that energy does not affect the properties and coefficients of the NLR index.
The NLO of the Ag NPs may also be related to their size. In 2012, Fan et al. investigated the NLA and NLR of Ag NPs with sizes of 6, 33, and 46nm using an 800nm femtosecond laser in the infrared band far from the SPR region of the material [26]. In their research, they observed that the NLO properties of 6nm Ag NPs were unclear whereas 33 and 46nm Ag NPs exhibited SA and self-focusing behavior. In 2019, Maurya et al. investigated the size dependence of the NLA of Ag NPs with sizes of 25, 30, 37, and 38nm at 400 and 800 nm [27]. They found that, at 400 nm, the NLA of all sample with different sizes maintained SA, whereas at 800 nm, 30, 37nm samples exhibit a transition from SA to RSA. Although they have studied the size effect of optical nonlinearity of Ag NPs, it should be noted that the size distribution of their samples is relatively wide, which may influence their study of size effect. Moreover, both researches were conducted using femtosecond laser as the excitation source, in the case, only fast mechanism contributes to NLA. However, it is well known that in addition to the fast response, the carrier relaxation process in nanoparticles also has a slow response process, which may lead to the effect of pulse width on the NLO properties of Ag NPs. In addition, the excitation wavelength should also be considered when studying the effect of size on the NLO of Ag NPs. Therefore, it is necessary to study the size effect of NLO properties of Ag NPs by using nanosecond laser near SPR region.
In addition, the ultrafast response characteristics of Ag NPs have garnered significant attention [27–29]. In particular, several groups have attempted to investigate whether size influences the ultrafast dynamics of NPs [27,28]. As early as 1995, Roberti et al. studied the ultrafast dynamics process of 4 and 10 nm Ag NPs [28]. They observed that the two types of NPs behave similarly, with a fast relaxation time constant of approximately 2 ps and a slow relaxation time of approximately 40 ps. Furthermore, they explained the size independence of ultrafast dynamics. They believed that electronic relaxation is affected by two factors, namely the state density of the phonons in solid particles and energy levels of the phonons. In their report, they highlighted that the density of states for the phonons will decrease with a decrease in particle size, which is expected to cause a slower decay of the electronic relaxation due to electron-phonon coupling. In contrast, the decreasing size may change the distribution and energy levels of the phonons that obtain energy from electronic relaxation, which could consequently result in an increase in the electronic relaxation rate. Finally, the competition between the aforementioned two factors may make the overall relaxation dynamics independent of size [28]. However, at the end of the report, they emphasized that a larger size range is needed to describe the size effect of the dynamics more fully. In 2019, Maurya et al. investigated the ultrafast dynamics of Ag NPs with 25, 30, 37, and 38 nm using a 35 fs laser at 400 nm [27]. They observed that there are differences in the fast decay time constants of the electron–phonon energy exchange of NPs with different diameters. In particular, the samples with average diameters of 25, 30, 37, and 38 nm had fast attenuation time constants of 1.8, 2.1, 2.3, and 1.5 ps, respectively. They considered that within the allowable error range, the dynamic process of Ag NPs is nearly independent of size, which may be because the size distributions of the studied NPs are relatively wide. In recent years, the rapid development of the technology for preparing nanoparticles has enabled the preparation of NPs with uniform particle sizes, which has created conditions for the study of the size effect on the ultrafast dynamics of Ag NPs.
In this work, the size effects of NLA and NLR of Ag NPs were investigated via Z-scan technology, and the energy relaxation process of the particles irradiated by a laser was studied using pump-probe technology. By analyzing the experimental data, the saturated intensity, two-photon absorption (TPA) coefficient, and NLR index coefficient were obtained, and the physical mechanisms of NLA and NLR were discussed theoretically. The energy relaxation processes are described based on the theoretical analysis of the pump-probe experimental results.
2. Experiment
Nanjing XFNANO Material Technology Co., Ltd. provided Ag NPs for this research. Their shape and size were characterized using transmission electron microscopy (TEM). Linear absorption was studied using a spectrophotometer (UV-2250).
The NLA and NLR of Ag NPs were studied via Z-scan technology, which was proposed and reported in [29] for the first time. An Nd: YAG laser system was used to provide a pulse laser with an approximate Gaussian distribution (pulse width, 4 ns; wavelength, 532 nm; size of waist radius of beam, 40µm; and repetition rate, 10 Hz). An attenuator was used to adjust the laser energy. A lens with a focal length of 100 mm was used to focus the laser. The Ag NPs in n-hexan is contained in a cuvette with 2 mm thickness, and the cuvette mounted on the translation table was moved in the transmission direction of the laser beam. Two detectors were used to measure the pulsed laser energy of the samples. The detector without an aperture in front was used to measure the NLA, known as the open aperture Z-scan (OA), whereas the detector with an aperture was used to measure the NLR, known as the closed aperture Z-scan (CA). A pure NLR curve was obtained by dividing the transmittance of the CA by that of the OA.
The ultrafast dynamics of Ag NPs were studied using pump-probe technology. The principle of pump-probe technology can be found in [30–32]. A titanium sapphire laser (Mira 900, Coherent) was used as the excitation source. The laser wavelength, frequency, and pulse width were 800 nm, 1 kHz, and 130 fs, respectively. The laser output pulse was divided into strong and weak beams using a beam splitter. The strong beam becomes a 400 nm pump beam under the action of a frequency-doubling crystal BBO. The weak beam is focused by the lens and excites the supercontinuum white light generated by sapphire as the probe beam. A prism was installed on the moving table to generate the time delay t of the pump and probe lights. The probe beam was divided into two parts using another beam splitter. One beam was focused by the lens and irradiated onto the sample, and the transmitted light was received by the spectrometer. The other beam directly entered the spectrometer as the reference beam. The relationship between differential transmission ΔT(t)/T and time t can be determined by comparing the spectra of the two beams.
3. Results and discussion
3.1 Characterization of samples
The TEM images of three batches of Ag NPs are shown in Fig. 1(a)-(c). It is observed that the three samples are spherical particles with average particle sizes (diameters) of about 10, 20, and 40 nm. They were labeled as S1, S2, and S3, respectively.
Fig. 1. TEM images of samples with different sizes (a) S1 (10 nm), (b) S2 (20 nm), and (c) S3 (40 nm).
Figures 2 shows the linear absorption spectra of the samples. The typical SPR peaks of S1, S2, and S3 were observed at 410, 397, and 407 nm, respectively. When the particle size was reduced from 40 to 20 nm, the SPR peak position was blue-shifted. This is because under an external light field, the high-order multipole vibration modes (quadrupole and octupole) of larger particles cannot be ignored, resulting in a blue shift of the plasma resonance peak. Comparing the 20 and 10 nm particles, a red shift of SPR was present in the absorption peak, which can be explained by the small particle size and dipole vibration being the main influencing factor of extinction. When the size of the NPs is small, the electron density of the NPs decreases; thus, the frequency of the free electron plasma decreases. This leads to a red-shift in the plasma resonance peak [33].
3.2 NLA of Ag NPs
An OA Z-scan was used to study the NLA of Ag NPs. The cuvettes were filled with Ag NPs. A nanosecond-pulsed laser was used as the excitation source. The energy E was controlled by a variable attenuator to be 6, 10, and 20 µJ, the corresponding peak intensities at focus were I0= 0.88 × 1012, 1.46 × 1012, and 2.92 × 1012 W/m2, respectively.
The OA Z-scan experimental results for S1 under different intensities are represented by scattered points, as shown in Fig. 3(a)-(c). It is observed that an increase in the laser intensity does not change the curves of S1. At the focal point (z = 0), the normalized transmittance is the largest, transmittance on both sides of z = 0 decreases, and the peak value of the normalized transmittance increases with the increase in energy. This indicates that SA dominated the NLA of S1. Similar results were obtained in other studies [20–22,24–25]. SA is almost uniformly considered as the result of ground-state plasma bleaching [5–7].
Fig. 3. OA Z scan experimental data (dots) and theoretical fitting results (solid curves) of sample S1 (10 nm) when laser energies E is (a) 6 µJ (I0= 0.88 × 1012 W/m2), (b) 10 µJ (I0 = 1.46 × 1012 W/m2), and (c) 20 µJ (I0= of 2.92 × 1012 W/m2).
The OA Z-scan data of S2 and S3 are shown in Figs. 4 and 5, where (a)-(c) correspond to peak intensities of 0.88 × 1012, 1.46 × 1012, and 2.92 × 1012 W/m2, respectively. From Figs. 4 and 5, it is observed that S2 and S3 exhibit similar NLAs. The transmittance at z = 0 was the smallest, and the transmittance on both sides of z = 0 was the largest at a symmetrical position. This clarifies that the NLAs of S2 and S3 are both characterized by the coexistence of SA and RSA. Similar normalized transmittance curves have been reported in several previous Refs. [7–10]. It is generally believed that TPA or/and ESA induces RSA [5,10,11,20–28].
Fig. 4. OA Z scan experimental data (dots) and theoretical fitting results (solid curves) of sample S2 (20 nm) when laser energies E is (a) 6 µJ (I0= 0.88 × 1012 W/m2), (b) 10 µJ (I0 = 1.46 × 1012 W/m2), and (c) 20 µJ (I0= of 2.92 × 1012 W/m2).
Fig. 5. OA Z scan experimental data (dots) and theoretical fitting results (solid curves) of sample S3 (40 nm) when laser energies E is (a) 6 µJ (I0= 0.88 × 1012 W/m2), (b) 10 µJ (I0 = 1.46 × 1012 W/m2), and (c) 20 µJ (I0= of 2.92 × 1012 W/m2).
Second, we attempted to explain the microcosmic mechanism of the NLA. As we are aware, the optical properties of metal NPs mainly depend on the outermost electrons in the d band and the free electrons in the s-p conduction band [34]. The optical absorption of NPs is ascribed to the two transition behaviors of electrons: the interband and intraband transitions. The interband transition must overcome the bandgap (approximately 4 eV for Ag NPs), which is independent of the NP size. A laser pulse of 532 nm (approximately 2.33 eV) may lead to interband TPA under strong excitation, resulting in a valley in the OA Z-scan curves. However, the different OA Z-scan results of the samples rule out the possibility that the interband transition dominates the NLA.
Under the excitation of a laser pulse, most free electrons in the ground state transition to the first excited state, leading to ground-state plasma bleaching [34]. When the samples are far from the focus point, the weak laser intensity relative to the focal point cannot cause an NLA, and the transmittance is uniform. As the samples gradually moved to the focal point, the medium laser intensity caused the plasma to bleach to the ground state. There were no excess electrons in the ground state to absorb photons, resulting in an increase in transmittance near z = 0. The peaks in the Z-scan curve originate from plasma bleaching of the ground state.
It is highlighted in [35] that the density of occupied states (DOS) near the Fermi level is related to the NP size [27]. The first excited state of the NPs larger than 10 nm had a higher DOS. Under the same laser intensity excitation, the first excited state of Ag NPs with a size of 10 nm (S1) has a weaker ability to accept transition electrons, making the ground-state electrons insufficiently excited and leading to SA. For S2 and S3, the first excited state could accommodate more transition electrons. Before the sample moves from z = 0, the ground-state electrons in the conduction band transition almost completely to the first excited state, resulting in ground-state plasma bleaching. Therefore, the peak appeared before the focus position in the curves. When the samples are close to z = 0, the first excited state electrons continue to absorb energy and jump to a higher excited state, resulting in a decrease in the normalized transmittance and a valley in the experimental curves. Clearly, we cannot rule out the occurrence of intraband TPAs. In brief, SA is caused by plasma bleaching, and RSA is mainly the result of ESA.
Compared with the research of Maurya et al., our experimental results are different. In addition to the difference of sample, different pulse width of the laser may also be one of the reasons for this difference. Maurya used 35fs laser in their experiments [27], so only fast mechanism can contribute to NLA. While we used 4ns laser, which may make both fast and slow mechanism play role in the NLA process.
To quantitatively describe the NLA characteristics of Ag NPs of different sizes, the total NLA coefficient, including linear absorption and NLA, is defined as follows [5]:
Correspondingly, normalized transmittance of the sample can be expressed as follows [11]:
Thus, the experimental data could be fitted using Eq. (2). The fitting curves are denoted using the solid lines in Figs. 3–5. Correspondingly, the saturated intensity IS and the two-photon absorption coefficient β were also obtained according to Eq. (2) and shown in Table 1.
Table 1. Is and β of S1–S3 obtained by theoretical fitting
3.3 NLR of Ag NPs
A CA Z-scan was used to study the NLR of Ag NPs. The pure CA Z-scan results for S1, excluding the influence of the OA Z-scan, are shown in Fig. 6(a)-(b). It is observed that S1 exhibits ambiguous NLR at the energy used in our experiment. The experimental results of the CA Z-scan for S2 are shown in Fig. 7(a)-(b). S2 exhibits a relatively clear NLR under the same excitation condition as S1. In particular, when the laser intensity is 1.46 × 1012 W/m2, S2 exhibits clear self-defocusing behavior. In Fig. 8(a)-(b), even under low laser intensity of 0.88 × 1012 W/m2, S3 behaves clear self-defocusing. And it shows larger self-defocusing when laser intensity increases to 1.46 × 1012 W/m2.
Fig. 6. CA Z scan experimental data (dots) and theoretical fitting results (solid curves) of sample S1 (10 nm) when laser energies E is (a) 6 µJ (I0= 0.88 × 1012 W/m2), (b) 10 µJ (I0 = 1.46 × 1012 W/m2).
Fig. 7. CA Z scan experimental data (dots) and theoretical fitting results (solid curves) of sample S2 (20 nm) when laser energies E is (a) 6 µJ (I0= 0.88 × 1012 W/m2), (b) 10 µJ (I0 = 1.46 × 1012 W/m2).
Fig. 8. CA Z scan experimental data (dots) and theoretical fitting results (solid curves) of sample S3 (40 nm) when laser energies E is (a) 6 µJ (I0= 0.88 × 1012 W/m2), (b) 10 µJ (I0 = 1.46 × 1012 W/m2).
Theoretical calculation of the nonlinear refractive index is of paramount importance for quantitatively describing the NLR of materials. The third-order axial phase shifts can be expressed as follows [30]:
The normalized transmittance T(z) can be expressed as follows [30]:
The theoretical results obtained by fitting the experimental data with Eq. (4) are shown in the solid curves in Figs. 7–8. Meanwhile, the third-order NLR index γ was also obtained according to Eq. (4) and listed in Table 2.
Table 2. NLR index coefficients of Ag NPs
The mechanisms of self-focusing and self-defocusing in materials can be explained from two perspectives: electronic mechanisms and thermal effects [21]. According to existing reports, it can be considered that the self-defocusing arises from the heat accumulation effect. 10nm Ag NPs show insignificant NLR, which is due to less absorption and heat accumulation effect. While for 20 and 40nm Ag NPs, absorption and heat accumulation increase with size. Consequently, self-defocusing behavior becomes clearer.
3.4 Ultrafast dynamic process of Ag NPs
To evaluate the optical dynamic process, the transient absorption spectra of S1, S2, and S3 were measured using pump probe technology. The pulse width was 130 fs, repetition frequency was 10 Hz, excitation wavelength was 400 nm, laser pulse of 13 mW was the pump pulse, and supercontinuum white light worked as the probe beam. The extracted transient absorption experimental results at 532 nm are shown as scattered points in Fig. 9, where the solid curves were obtained via the two-exponential decay theoretical model described using Eq. (5). From Fig. 9(a-c), we observe that the ultrafast dynamics of Ag NPs of different sizes are very similar. Generally, the energy relaxation process of excited electrons can be divided into three stages [6,27,28,30–32]. First, the ground-state electrons are excited and immediately transition to the excited state. Then, the excited electrons exchange energy via electron-electron collision to form a hot electron gas, which occurs in the femtosecond order. After the electron is heated, a second process, electron–phonon coupling, occurs. The electron gas transmits energy from the laser to the crystal lattice through electron-phonon coupling to cool the electron gas. This process had a time constant of several picoseconds. The last process is phonon cooling with tens of picoseconds, which is completed by phonon-solvent (phonon-phonon) interactions.
Fig. 9. Dynamic traces of Ag NPs at a wavelength 532 nm. The dots represent experimental data whereas the solid lines represent theoretical fit generated, (a) S1 (10 nm), (b) S2 (20 nm), and (c) S3 (40 nm).
In our experiment, the rapidly rising signal is the result of ground-state plasma bleaching, that is, after the sample is excited by the pump laser, the transient differential transmission ΔT/T increases owing to the energy distribution between the electrons, leading to rapid bleaching. Unfortunately, because of the limitations of our experimental conditions, the electron-electron coupling relaxation time cannot be obtained in our experiment using a 130fs laser. Subsequently, the transmittance begins to recover, including the rapid decay process of electron–phonon coupling and slow decay process of phonon-phonon coupling.
To obtain the decay times of the two decay processes, a two-exponential decay theoretical model was used to fit the experimental data as follows [6,28,30]:
Table 3. Relaxation time of Ag NPs with different sizes
In 1995, Roberti et al. reported the size-dependence of the ultrafast dynamics of Ag NPs [28]. They concluded that the electron-phonon coupling time constant was 2 ps and the phonon–solvent interaction decay time constant was 40 ps. The decay time constant obtained in our experiment was significantly similar to that observed by Roberti. Although there are errors in the time constants of Ag NPs of different sizes obtained in our experiments, we believe that this is not the size that causes such small errors. The optical dynamic process is independent of the size.
4. Conclusion
In conclusion, we studied the NLO properties and ultrafast dynamic processes of Ag NPs. Research shows that the NLA and NLR properties of Ag NPs are size-dependent. In particular, in terms of NLA, 10 nm Ag NPs exhibit SA, whereas 20 and 40 nm Ag NPs exhibit SA and RSA coexistence. It is concluded that SA is caused by ground-state plasma bleaching whereas RSA is the result of ESA, including TPA. The saturated intensity and TPA coefficient were obtained by analyzing the experimental data. In terms of NLR, 10 nm Ag NPs has no clear NLR, whereas 20 and 40 nm Ag NPs exhibited self-defocusing at higher laser energies. The self-defocusing is considered to result from thermal accumulation. Pump-probe technology was used to study the ultrafast dynamics of the Ag NPs. Studies have shown that carriers in Ag NPs of different sizes exhibit a similar dynamic process under femtosecond laser excitation, namely, a rapid ascent process and two independent decay processes. The rapid ascent corresponds to the photon-electron energy coupling, and the two independent decay processes are electron-electron and electron-phonon energy relaxation processes. The decay times of Ag NPs with different sizes were obtained by fitting the experimental data with the two-exponential decay theoretical model. Based on these results, we believe that the ultrafast kinetic properties of Ag NPs are almost independent of size.
Funding
Natural Science Foundation of Heilongjiang Province (ZD2019F004); Department of Education, Heilongjiang Province (145109320).
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.
References
1. P. Linkov, P. Samokhvalov, K. Vokhmintsev, M. Zvaigzne, V. A. Krivenkov, and I. Nabievb, “Optical Properties of Quantum Dots with a Core–Multishell Structure,” JETP Lett. 109(2), 112–115 (2019). [CrossRef]
2. L. Hayati, C. Lane, B. Barbiellini, A. Bansil, and H. Mosallaei, “Self-consistent scheme for optical response of large hybrid networks of semiconductor quantum dots and plasmonic metal nanoparticles,” Phys. Rev. B 93(24), 245411 (2016). [CrossRef]
3. K. S. Giesfeldt, R. M. Connatser, M. A. De Jesús, N. V. Lavrik, P. Dutta, and M. J. Sepaniak, “Studies of the optical properties of metal-pliable polymer composite materials,” Appl. Spectrosc. 57(11), 1346–1352 (2003). [CrossRef]
4. Y. Hamanaka, A. Nakamura, N. Hayashi, and S. Omi, “Dispersion curves of complex third-order optical susceptibilities around the surface plasmon resonance in Ag nanocrystal–glass composites,” J. Opt. Soc. Am. B 20(6), 1227–1232 (2003). [CrossRef]
5. Y. C. Gao, X. R. Zhang, Y. L. Li, H. F. Liu, Y. X. Wang, Q. Chang, W. Y. Jiao, and Y. L. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005). [CrossRef]
6. C. Y. Chen, J. Wang, S. Yang, W. Wu, D. Kong, and Y. C. Gao, “Ultrafast dynamics process of platinum nanoparticles under femtosecond laser,” J. Nanopart. Res. 20(9), 242 (2018). [CrossRef]
7. Y. C. Gao, W. Z. Wu, D. Kong, L. Ran, Q. Chang, and H. Ye, “Femtosecond nonlinear absorption of Ag nanoparticles at surface plasmon resonance,” Phys. E 45, 162–165 (2012). [CrossRef]
8. C. Zheng, W. Li, W. Chen, and X. Ye, “Nonlinear optical behavior of silver nanopentagons,” Mater. Lett. 116(feb.1), 1–4 (2014). [CrossRef]
9. B. H. Yu, D. L. Zhang, Y. B. Li, and Q. B. Tang, “Nonlinear optical behaviors in a silver nanoparticle array at different wavelengths,” Chin. Phys. B 22(1), 014212 (2013). [CrossRef]
10. H. H. Mai, V. E. Kaydashev, V. K. Tikhomirov, E. Janssens, M. V. Shestakov, M. Meledina, S. Turner, G. V. Tendeloo, V. V. Moshchalkov, and P. Lievens, “Nonlinear Optical Properties of Ag Nanoclusters and Nanoparticles Dispersed in a Glass Host,” J. Phys. Chem. C 118(29), 15995–16002 (2014). [CrossRef]
11. C. Y. Chen, J. Wang, and Y. C. Gao, “Wavelength-Dependent Nonlinear Absorption in Palladium Nanoparticles,” Appl. Sci. 11(4), 1640 (2021). [CrossRef]
12. N. Khinevich, S. Zavatski, V. Kholyavo, and H. Bandarenka, “Bimetallic nanostructures on porous silicon with controllable surface plasmon resonance,” Eur. Phys. J. Plus 134(2), 75 (2019). [CrossRef]
13. S. Kim, J. Suh, T. Kim, J. Hong, and S. Cho, “Plasmon-enhanced performance of CdS/CdTe solar cells using Au nanoparticles,” Opt. Express 27(15), 22017 (2019). [CrossRef]
14. G. S. Boltaev, R. A. Ganeev, P. S. Krishnendu, S. K. Maurya, P. V. Redkin, K. S. Rao, K. Zhang, and C. Guo, “Strong third-order optical nonlinearities of Ag nanoparticles synthesized by laser ablation of bulk silver in water and air,” Appl. Phys. A 124(11), 766 (2018). [CrossRef]
15. J. Jayabalan, A. Singh, R. Chari, and S. M. Oak, “Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs,” Nanotechnology 18(31), 315704 (2007). [CrossRef]
16. B. K. Dadhich, S. Bhattacharya, S. Ballav, B. Bhushan, P. K. Datta, and A. Priyam, “Femtosecond-Laser-Induced Saturable Absorption and Optical Limiting of Hollow Silver Nanocubes: Implications for Optical Switching and Bioimaging,” ACS Appl. Nano Mater. 3(11), 11620–11629 (2020). [CrossRef]
17. Y. Yu, L. Yan, M. M. Yue, and H. H. Xu, “Femtosecond laser-assisted synthesis of silver nanoparticles and reduced graphene oxide hybrid for optical limiting,” R. Soc. Open Sci. 5(7), 171436 (2018). [CrossRef]
18. G. Doria, J. Conde, B. Veigas, L. Giestas, C. Almeida, M. Assuncão, J. Rosa, and P. V. Baptista, “Noble Metal Nanoparticles for Biosensing Applications,” Sensors 12(2), 1657–1687 (2012). [CrossRef]
19. H. Ditlbacher, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Spectrally coded optical data storage by metal nanoparticles,” Opt. Lett. 25(8), 563–565 (2000). [CrossRef]
20. M. Hari, S. Mathew, B. Nithyaja, S. A. Joseph, V. Nampoori, and P. Radhakrishnan, “Saturable and reverse saturable absorption in aqueous silver nanoparticles at off-resonant wavelength,” Opt. Quantum Electron. 43(1-5), 49–58 (2012). [CrossRef]
21. A. Ajami, W. Husinsky, B. Svecova, S. Vytykacova, and P. Nekvindova, “Saturable absorption of silver nanoparticles in glass for femtosecond laser pulses at 400 nm,” J. Non-Cryst. Solids 426, 159–163 (2015). [CrossRef]
22. R. A. Ganeev, “Characterization of the Optical Nonlinearities of Silver and Gold Nanoparticles,” Opt. Spectrosc. 127(3), 487–507 (2019). [CrossRef]
23. D. Kong, J. Xu, R. Zhan, X. Duan, and Z. K. Zhou, “Surface plasmon-enhanced third-order optical non-linearity of silver triangular nanoplate,” J. Mod. Opt. 63(21), 2396–2401 (2016). [CrossRef]
24. R. Allu, D. Banerjee, R. Avasarala, S. Hamad, and G. K. Podagatlapalli, “Broadband femtosecond nonlinear optical properties of silver nanowire films,” Opt. Mater. 96, 109305 (2019). [CrossRef]
25. S. Chen, R. P. Niu, W. Z. Wu, D. G. Kong, and Y. C. Gao, “Wavelength-dependent nonlinear absorption and ultrafast dynamics process of Au triangular nanoprisms,” Opt. Express 27(13), 18146 (2019). [CrossRef]
26. G. H. Fan, S. L. Qu, Z. Y. Guo, Q. Wang, and Z. G. Li, “Size-dependent nonlinear absorption and refraction of Ag nanoparticles excited by femtosecond lasers,” Chin. Phys. B 21(4), 047804 (2012). [CrossRef]
27. S. K. Maurya, A. Rout, R. A. Ganeev, and C. Guo, “Effect of Size on the Saturable Absorption and Reverse Saturable Absorption in Silver Nanoparticle and Ultrafast Dynamics at 400 nm,” J. Nanomater. 2019, 1–12 (2019). [CrossRef]
28. T. W. Roberti, B. A. Smith, and J. Z. Zhang, “Ultrafast electron dynamics at the liquid–metal interface: Femtosecond studies using surface plasmons in aqueous silver colloid,” J. Chem. Phys. 102(9), 3860–3866 (1995). [CrossRef]
29. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]
30. T. S. Ahmadi, S. L. Logunov, and M. A. El-Sayed, “Picosecond Dynamics of Colloidal Gold Nanoparticles,” J. Phys. Chem. C 100(20), 8053–8056 (1996). [CrossRef]
31. J. H. Hodak, I. Martini, and G. V. Hartland, “Spectroscopy and Dynamics of Nanometer-Sized Noble Metal Particles,” J. Phys. Chem. B 102(36), 6958–6967 (1998). [CrossRef]
32. J. Z. Zhang, R. H. O’Neil, and T. W. Roberti, “Femtosecond Studies of Photoinduced Electron Dynamics at the Liquid-Solid Interface of Aqueous CdS Colloids,” J. Phys. Chem. 98(14), 3859–3864 (1994). [CrossRef]
33. X. C. Yang, H. X. Liu, L. L. Li, M. Huang, and J. F. Zhao, “Review on influence factors of surface plasmon resonance for nobel metal nanoparticles,” Journal of Functional Materials 41(2), 341–345 (2010).
34. L. Yang, D. H. Osborne, R. F. Haglund, R. H. Magruder, C. W. White, R. A. Zuhr, and H. Hosono, “Probing interface properties of nanocomposites by third-order nonlinear optics,” Appl. Phys. A 62(5), 403–415 (1996). [CrossRef]
35. E. L. Falcão-Filho, Cid B. de Araújo, and J. J. Rodrigues Jr, “High-order nonlinearities of aqueous colloids containing silver nanoparticles,” J. Opt. Soc. Am. B 24(12), 2948–2956 (2007). [CrossRef]
