Effect of Size on the Saturable Absorption and Reverse Saturable Absorption in Silver Nanoparticle and Ultrafast Dynamics at 400nm

Saturable absorption and reverse saturable absorption play an important role in the studies of the nonlinear optical properties of nanoparticles at resonant excitation. With this viewpoint, nonlinear absorption processes of chemically prepared silver nanoparticles in deionized water were studied using femtosecond laser pulses at 400 nm. Our nonlinear absorption study shows that there is competition between saturable absorption and two-photon absorption in prepared Ag NPs which depends on the size of the nanoparticles. We have also studied the ultrafast dynamics associated with nanoparticles which also results in the direct correlation between the ultrafast timescale and the size of the nanoparticle. The excitation of Ag NPs at 400 nm has shown the manifestation of damped oscillation which is attributed to the radial breathing mode oscillation due to acoustic vibration.


Introduction
Metal nanoparticles (NPs) have shown unique nonlinear optical (NLO) properties toward their potential application in various fields such as biomedicine [1][2][3], electronics [4,5], information storage [6,7], and sensing [8][9][10]. This is because of the appearance of the surface plasmon resonance (SPR) due to the reduced dimensionality responsible for the enhanced third-order optical nonlinearities. Several noble metal NPs have been studied under various conditions imposed by the intense light source [11][12][13].
Several groups have shown the behavior of metal NPs upon interaction with intense laser pulses [14][15][16][17][18][19][20][21][22]. Their studies show that different mechanisms are responsible for their NLO properties, which include saturable absorption (SA), two-photon absorption (2PA), optical limiting (OL), and optical Kerr nonlinearities. SA has a profound influence on the overall nonlinear optical response at suf-ficiently high power of the employed laser pulse [23]. Another phenomenon called reverse saturable absorption (RSA) [17,24,25] may counteract the absorption saturation processes. The RSA process occurs as a result of large absorption by the nonlinear absorber at high laser energy via excited state absorption because of the depletion of the ground state with the increase of the incident laser energies. The performance of such nonlinear materials is limited by the accompanying linear absorption at low input energy. In this case, the incident photons may be further absorbed by excited states when their population gets large enough in an excited state. These processes depend not only on the intensity of the incident photon but also on the frequency of the incident photon which plays an important role in their NLO properties depending on the resonant or nonresonant transitions. There are few reports on the competitive behavior of SA and RSA together due to the associated energy level of metal NPs, which provide the possibility to be investigated with the variation of the size of NPs [8,26].
Apart from NLO properties of materials, many-body interactions in a condensed matter and molecular system have been of great concern because the properties like electrical and thermal conduction, superconductivity through Raman scattering, and polaron formation are highly affected by an ultrafast process such as electron-phonon interactions [27][28][29]. It is found that the ultrafast process affects the electrical, thermal, and optical properties of bulk materials. Numerous efforts have been made and are still ongoing to understand the mechanism governing these ultrafast processes. There has been a great advancement to understand the role of electron-phonon interaction on the properties of reduced dimensional systems [30]. A vast literature is presented on electron-phonon interaction in NPs [31]. The interaction of NPs with short laser pulses undergoes various ultrafast processes such as electron-electron coupling, electron-phonon coupling, and phonon-phonon coupling. Apart from these ultrafast processes, various studies have focused on the dissipation of the acoustic vibrations in noble NPs upon ultrafast laser pulse excitation which is based on the size, shape, and surrounding mediums [31,32].
Among various metal NPs, silver (Ag) NPs pose unique optoelectronic and thermal properties which lead to efficient use in a wide range of technological advancements such as molecular diagnostics and photonic devices based on its optical properties [33,34]. Ag NPs exemplify amazingly efficient optical properties, which depend on the size and the shape of the particle. There have been several reports on the presence of SA and TPA in Ag NPs depending on the excitation wavelength [35][36][37][38]. At the same time, Ag NPs have been studied in order to observe ultrafast dynamics depending on their size and shape [39][40][41]. However, there are few reports on a systematic study in ultrafast dynamics associated with coherent oscillations depending on the size and shape of Ag NPs [42,43]. Thus, our objective was to investigate the NLO properties and ultrafast dynamics associated with Ag NPs under SPR which can effectively provide the correlation of NLO properties and ultrafast dynamics with the size of NPs.
In this paper, we present the results of systematic studies of the chemically prepared Ag NPs which can efficiently provide the variation in the size of NPs. We demonstrate the impact of the size of Ag NP on the SA and RSA using femtosecond pulses at 400 nm and 800 nm. Ultrafast dynamics of chemically prepared Ag NPs is studied using femtosecond 400 nm. We observed the presence of acoustic vibration in Ag NPs upon excitation with the resonant wavelength. The effect of the size of NPs on acoustic oscillations and associated damping time constants was discussed in detail.

Experiments
2.1. Ag NP Preparation. In this study, Ag NPs were prepared by chemical reduction of sodium nitrate (AgNO 3 ) from sodium borohydride (SBH) in an aqueous medium. In order to prepare Ag NPs in deionized water, first, 0.043 g AgNO 3 was dissolved in 50 mL deionized water, and 0.012 g SBH was dissolved in 150 mL deionized water, respectively, with constant stirring for 30 min. 3 mL of aqueous AgNO 3 solution was dripped slowly into 10 mL of aqueous SBH solution at three different temperature conditions of 0°C, 25°C, and 60°C. This mixture was stirred for a few seconds, which allowed AgNO 3 and NaBH 4 to react completely. With the addition of AgNO 3 , the solution gradually turned yellow, light gray, and dark gray which indicates that Ag NPs were formed. From here onward, we represent Ag NP suspensions as S1, S5, and S9 prepared by addition of AgNO 3 solution to SBH solution through the dripping method at 0°C, 25°C, and 60°C, respectively, whereas NP suspensions represented as S3, S7, and S11 were prepared by fast mixing of AgNO 3 and SBH solution at 0°C, 25°C, and 60°C, respectively. Thus, the Ag NPs prepared by these methods yield different sizes of the NPs. Prepared Ag NPs were characterized by a UV-Visible spectrometer (Cary Series, Agilent Technologies) and a scanning electron microscope (SEM, Hitachi S-4800).
Under the assumption that the optimal packing efficiency of Ag atoms under spherical NPs was estimated to be 74%, the concentration of Ag NP suspension was calculated by using the mean sizes of Ag NPs measured from respective SEM images. The concentrations of NP suspensions were determined to be 1.7, 2.4, 1.6, 2.4, 1.7, and 2 nmol/L for S1, S3, S5, S7, S9, and S11, respectively. The synthesized Ag NP suspensions were found to be stable up to 30 days which were confirmed by their UV-Visible spectroscopy measurements and SEM images. NLO studies were performed at low and high concentrations of Ag NP suspension. The change of the Ag NP concentration in deionized water was achieved through the dilution of synthesized Ag NPs using deionized water as a solvent.

Z-Scan Setup.
A conventional technique [44,45] was employed to study the NLO properties of the prepared Ag NPs in deionized water. Schematic of the experimental setup is shown in Figure 1(a). The pulse width of laser pulses at 800 and 400 nm was kept at 35 fs. 400 mm focal length lens were used to focus the laser pulse into the quartz cuvette containing NPs. We employed an open aperture scheme for determination of nonlinear optical parameters, like absorption saturation intensity and 2PA coefficient. The transmittance from the sample was obtained by moving the sample cuvette across the focal plane of the plano-convex lens along the beam propagation direction. The motorized translational stage was used to change the sample position with respect to the focal position of the lens, which is interfaced with a computer through the EPS301 motion controller. The transmitted beam after the sample was collected by a large area detector (silicon photodiode, Thorlabs PDA100A-EC) to ensure the collection of the full beam after passing through the sample cell. We fitted the experimental data with the following equations for the determination of SA and TPA coefficients: where q = βI 0 L eff / 1 + z 2 /z 2 0 , I 0 is the peak intensity of the 2 Journal of Nanomaterials laser pulse, I sat is the saturation intensity of the optically active medium which depends on the concentration of the medium, z 0 is the Rayleigh length defined as z 0 = k w 2 0 /2, ω 0 is the radius of the focused beam, L eff = 1 − exp −α 0 L /α 0 is the effective length of the medium, and α 0 is the linear absorption coefficient of the medium.

TA Measurements.
A conventional noncollinear degenerate pump-probe technique was employed to observe the transient absorption (TA) in chemically prepared Ag NP in deionized water at different temperatures. Schematic of TA setup is shown in Figure 1(b). The commercially available regenerative amplifier (Spitfire ACE, Spectra-Physics, 800 nm, 1 kHz) was used as a source for the femtosecond pulses for the TA study. TA studies were performed at resonant 400 nm obtained by doubling of the fundamental laser pulse at 800 nm from the amplifier using a nonlinear crystal (BBO). The laser pulse from the amplifier was split into two pulses using a 70-30 beamsplitter. One pulse was used as a pump, and another pulse was used as a probe, which was passed through the motorized delay line to control the time separation between the pump and probe pulses. The relative intensity and a beam diameter of the pump and the probe pulse were adjusted to be~20 : 1 and~1 : 2, respectively, to fulfill the condition required for the pump-probe experiment. Pump pulse power of 20 nJ was used for the TA study for all measurements. The pulse width of the laser pulse from the amplifier was found to be 35 fs, which was measured at the sample position using 0.2 mm BBO crystal. The measured pulse width was further confirmed by measuring it using a commercially available autocorrelator. The arrival time of probe pulses with respect to pump pulses was controlled by moving the motorized translational stage connected to the motion controller. An ultrafast photodiode (model: DET025AL, Thorlabs, China) connected to a lock-in amplifier was used to measure the transmittance of the probe pulse with respect to the position of the motorized stage. The lock-in amplifier was externally triggered with an optical chopper running at 300 Hz.  3 Journal of Nanomaterials suspensions in deionized water were measured using a UV-Visible spectrophotometer (Agilent Technologies). From Figure 2, we can observe distinctive surface plasmon resonance at 389 nm for S1 and S3, 381 nm for S5 and S7, and 385 nm for S9 and S11. The emergence of these peaks was the direct consequence of the size of Ag NPs. The SPRs of Ag NPs prepared at 0°C exhibit an absorption band at 389 nm with a side absorption band at 433 nm. These absorption peaks around 390 nm in all Ag NPs are the result of direct transition from occupied sp to unoccupied sp [32]. Our observation shows the emergence of the absorption band at 430 nm in prepared Ag NPs at 0°C and 25°C whereas the emergence of the absorption peak at 350 nm was observed at 60°C. The emergence of these absorption bands can be attributed to the Ag NP distortion which results in the formation of prolate and oblate spheroid NPs. These distorted NPs are responsible for the emergence of the SPR band at 350 and 430 nm due to the high multipolar excitation [46]. SEM images and their respective histograms of prepared Ag NPs at different temperatures are shown in Figures 3(a)-3(f). It is evident from the SEM images that the shape of the prepared Ag NPs is distorted. Size and its distribution of Ag NPs associated with S3, S7, and S11 are observed to be similar and narrow as compared to S1, S5, and S9, respectively. As mentioned in the experimental setup, S1, S5, and S9 were prepared using slow addition of aqueous AgNO 3 in aqueous SBH solution. The mechanism of creation of NPs involves the reduction of metal ions by a reducing agent which is followed by the nucleation process of clustering for reduced metal that acts as a seed to grow the different sizes of NPs. At first, the smaller-sized aggregates are mostly formed under the dripping method of addition. These aggregates grow in bigger-size NPs upon further addition of metal ions in the suspension. This process leads to the bigger-sized NPs compared to NPs prepared by mixing metal ion and reducing agent instantaneously, where the nucleation is the limiting process for the formation of NPs.

Result and Discussion
NLO properties of chemically prepared Ag NPs in deionized water were investigated using the Z-scan technique with amplified femtosecond pulses at resonant 400 nm and nonresonant 800 nm. Prior to the Z-scan measurement, the open aperture was measured for deionized water, which exhibits negligible optical nonlinearity with a maximal applied peak intensity of 1 2 × 10 11 W cm −2 at 400 nm and 2 5 × 10 11 W cm −2 at 800 nm. Figure 4 shows the open aperture trace of all NPs (S1, S3, S5, S7, S9, and S11) at the peak pulse intensity of 9 × 10 10 W cm −2 at 400 nm. As shown in Figure 4, all prepared Ag NPs show the increase in the transmittance of 400 nm wavelength as the sample approaches the focal point, which indicates that all materials exhibit SA at 400 nm. We analyzed the OA Zscan data by fitting the standard transmittance equation (equation 1) of SA. The estimated values of I sat were tabulated in Table 1 for respective NP suspension. The saturable absorption behaviors for all NP suspension can be explained by the presence of SPR resonance at 400 nm which resulted in the increase of transmittance through Ag NP suspensions.
Ag NPs exhibit an intense absorption band at~400 nm due to sp → sp transition in Ag which highly depends on the size of the Ag NPs [25,47]. At the employed peak intensity of femtosecond pulses, the intraband sp → sp transitions are possible. As the pulse energy at resonant 400 nm further increases, the d → sp transition can also occur through excitation of electrons from the occupied d state to unoccupied sp state which can open the channel for two-photon absorption shown in scheme (2) of Figure 5. Similarly, in addition to the d-sp transition, interband two-photon absorption at 400 nm is also possible via occupied sp to unoccupied sp band (sp → sp transition) shown in scheme (3) of Figure 5. The excitation of Ag NPs with 400 nm is considered as high energy photon absorption at a resonant wavelength which can lead to the equalization of electron population in occupied and unoccupied energy levels. Thus, the absorption saturation is evident at 400 nm which is the case for samples S1 to S11, and the mechanism is depicted in scheme (1) of Figure 5. Figure 6 shows the open aperture Z-scan at 800 for each Ag NPs. Similar to the Z-scan profile at 400 nm, S1, S3, S5, and S7 exhibit absorption saturation with I sat of 330 × 10 10 W cm −2 , 21 × 10 10 W cm −2 , 1 9 × 10 10 W cm −2 , and 3 1 × 10 10 W cm −2 , respectively. On the other hand, S9 and S11 exhibit reverse saturable absorption in addition to absorption saturation at an employed peak intensity of 2 7 × 10 11 W c m −2 . In order to fit the Z-scan profile for S9 and S11, a combination of equation 1 and equation 2 was used. The estimated value of I sat and β are 83 × 10 10 W cm −2 and 1 7 × 10 −11 cm −1 W for S9 and 27 × 10 10 W cm −2 and 4 6 × 10 −11 cm −1 W for S11. These profiles can be explained with scheme (4) of Figure 5 for absorption saturation in S1 to S7 and schemes (4) and (5) of Figure 5 for the explanation of S9 and S11. Under the high-intensity regime at 800 nm, the electronic excitation takes place via intraband sp → sp transition as shown in scheme (4) of Figure 5. Thus, the increase in the transmittance at 800 nm was observed for S1 to S7, whereas a 4 S1 S5 S7 S9 S11  Journal of Nanomaterials completely different scenario was observed where simultaneous absorption of two-photon at 800 resulting in the intraband transition from sp → sp was observed as shown in scheme (5) of Figure 5. This results in the decrease in the transmittance as the sample further moves toward the focus indicating the combined ramification of SA and TPA processes. Recently, several groups have measured the NLO properties of the Ag NPs with various laser pulse widths [26,48,49]. Particularly, the comparison of the application of 200 ps and 60 fs pulses, which clearly depict the effect of long pulses on the NLO properties of NPs, has been reported in [48]. These studies were mostly carried out using the average particle size of 13 nm. Present studies were performed using the average particle sizes ranging from 25 to 38 nm. We have also measured the NLO response of prepared Ag NPs with 30 times lower concentration at 400 nm. At a resonant wavelength of 400 nm with a low concentration of Ag NPs, the RSA was observed with absorption saturation (see Figure 7). Thus, the obtained profile was fitted with a combination of SA and TPA as mentioned in equation 1 and equation 2. The estimated values of I sat were 1 4 × 10 11 W cm −2 , 1 1 × 10 11 W cm −2 , 1 4 × 10 11 W cm −2 ,   3 × 10 11 W cm −2 , 1 3 × 10 11 W cm −2 , and 1 1 × 10 11 W c m −2 for S1, S3, S5, S7, S9, and S11, respectively, whereas the corresponding β values were 1 1 × 10 −10 cm W −1 , 1 3 × 10 −10 cm W −1 , 1 2 × 10 −10 cm W −1 , 1 4 × 10 −10 cm W −1 , 1 1 × 10 −10 cm W −1 , and 1 3 × 10 −10 cm W −1 for S1, S3, S5, S7, S9, and S11, respectively. These nonlinear optical properties were considered to be affected by electronic excitation schemes (2) and (3) in addition to scheme (1) of Figure 5. Under this condition, in addition to the saturable absorption at high intensity, the TPA process can occur either via interband d → sp transition or via intraband sp → sp transition. This leads to a decrease in the transmittance as the sample moves toward the focus.
It was observed that the RSA value is higher for S7 compared to other NPs which can be attributed to the smaller size of Ag NPs. It is evident from the calculated value of I SA and β that I SA decreases and β increases as the sizes of the Ag NPs increase as shown in Figure 8. It was observed that under resonant excitation SA can dominate over RSA. Various reports have shown the role of concentration in SA over RSA processes [50]. The result mentioned in this work was compared with the earlier work reported by us [49] where the dependence of the pulse width of the laser pulses on the NLO properties of chemically prepared NPs was investigated. The nonlinear absorption characteristics for Ag NPs at 800 nm in this work were found to be consistent with the   Journal of Nanomaterials previous report. The estimated values of nonlinear absorption for all samples are represented in Table 1.

Pump-Probe Study of Chemically Prepared Ag NP Suspensions.
We have performed the degenerate pumpprobe measurement of the chemically prepared Ag NPs in deionized water at 400 nm with 35 fs pulses. The intensities of the pump and probe pulses were 17 GW cm -2 and 1 GW cm -2 , respectively. Here, all NP suspensions exhibit photobleaching effect evident of saturable absorption as shown in Z-scan profile of Ag NPs at 400 nm. Figure 9 shows the temporal evolution of change in transmittance of probe pulses. In pump-probe experiments, the electron distribution in the particle is perturbed by femtosecond pump pulses which were probed by a time-delayed weak pulse either at the resonant wavelength or close to the resonant wavelength [51][52][53]. The energy relaxation upon excitation from pump pulses is generally described as a series of relaxation processes which include electron-electron scattering, electron-phonon coupling, and heat dissipation through the surrounding. Apart from these relaxation processes, the particle can go under acoustic vibrations through two distinct excitation mechanisms. First is the creation of pressure on the surface of the particle due to a sudden surge in electron temperature [54], and second is the energy transfer from the electron to the lattice leading to the increase in the equilibrium interatomic distance by thermal expansion [55]. The acoustic vibration time scale is longer than the electron-lattice relaxation time. Thus, the particles are brought out of equilibrium leading to the mechanical oscillations which are responsible for the periodic change in size and shape of NPs. These peri-odic oscillations are easy to probe by a wavelength closer to plasmonic resonance. In particles, the fundamental mode of vibration involves the radial breathing mode (RBM) which depends on both bulk and searing elastic moduli of metal. In chemically prepared Ag NPs, distinct damped oscillation in probe pulse transmittance was observed for S1, S3, S5, and S7 due to acoustic vibration, which is superposed with the exponentially decaying back of the excited Ag NPs to its ground state through cooling of the hot lattice. However, this acoustic vibration was not observed for S9 and S11. As seen in Figures 9(e) and 9(f)), the signal to noise ratio is poor as compared to the other transmission profiles which can be directly correlated with the impact of the low concentration of the Ag NPs in S9 and S11. The damping in the acoustic vibration was witnessed which is associated with the damping time of the breathing mode due to the effect of the surrounding solvent. These oscillations were observed within 20 ps after the 0-time delay between pump and probe pulses. Thus, in order to obtain the relaxation time constant and damping time of the vibrations, we fitted the obtained decay profile with the exponential decay equation represented in equation 3, which contains the electron thermalization (τ th ) and electron-phonon (e-ph) coupling (τ 2 ) time constants, whereas the characteristic time constant associated with RBM (τ RBM ) and frequency (ν) associated with oscillations is expressed in equation 4: where A 1 , A 2 , A 0 , and ϕ b are proportionality constants associated with three decay times and phase. In order to determine the time constant associated with Ag NPs, the obtained TA profile was first fitted with equation 3, which yields the time constant associated with electron thermalization and electro-phonon interaction. The residual of the fitted data with equation 3 was fitted with equation 4 to obtain the RBM frequency and the damping time constant. Figure 10 shows the fitting of the residual ΔT/T with equation (4) for S1, S3, S5, and S7. The obtained lifetime (τ th ) associated with Ag NPs was found to be 220 fs for S1 and S3 and 200 fs for S5, S7, S9, and S11, respectively. These time constants can be attributed to the electron thermalization. The τ th reflects the energy redistribution inside the electron cloud after absorption of a femtosecond pulse, which is generally determined by the electron-electron scattering process with certain energy range taking place alongside slow processes. The time constants (τ e-ph ) associated with Ag NPs were 2.3 ps for S1, 1.8 ps for S3, 1.5 ps for S5, 1.8 ps for S7, 2.1 ps for S9, and 1.4 ps for S11. However, the damping time constant τ RBM associated with the radial breathing mode was found to be 7 ps for S1, 9 ps for S3, 10 ps for S5, and 12 ps for S7 with their respective RBM frequencies of 181 Hz for S1, 198 Hz for S3, 166 Hz for S5, and 200 Hz for S7. These results were presented in Table 1 for their better understanding. This damping       Figure 8: Comparison of I sat and RSA coefficient of all prepared Ag NPs at 400 nm femtosecond laser pulses.

Conclusions
In conclusion, we have reported the nonlinear optical response of chemically prepared Ag NPs in deionized water using femtosecond laser pulses at 400 nm and 800 nm. It was observed that the size of Ag NPs can have a large influence on NLO probability. The smaller-size Ag NPs have shown large RSA coefficient (β) and small SA intensity. These absorption saturations can be attributed to the intraband sp → sp transition in Ag NPs whereas interband d-sp or intraband sp-sp transition is responsible for the RSA process which clearly explains the observed intensity profile in our Z-scan measurements. This study shows that saturable absorption has a dominating factor for a higher concentration of Ag NPs over the RSA process at resonance excitation. It is evident from the nonlinear optical characterization of Ag NPs that there is a correlation between SA and RSA. It is observed that Ag NP processing low I sat have large RSA probabilities.
The time-resolved studies of Ag NPs at 400 nm show 200 fs and 1.5-2.3 ps dynamics, which is attributed to the electron thermalization and electron-phonon relaxation process. Ultrafast dynamics also reveals the damped oscillation in Ag NPs associated with acoustic vibration at the excitation wavelength of 400 nm. Under our experimental condition, we observed the RBM vibration in prepared Ag NPs which depends on the size of NPs. These RBM vibrations have the decay time in picosecond which also depends on the size of NPs and the surrounding environments.

Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that they have no conflicts of interest.