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Nonlinear Absorption and Ultrafast Dynamics of Ag Nanoparticle

Nonlinear Absorption and Ultrafast Dynamics of Ag Nanoparticle hv photonics Article Nonlinear Absorption and Ultrafast Dynamics of Ag Nanoparticle 1 , 2 1 , 3 1 1 , Jijuan Jiang , Jun Wang , Tong Wu and Yachen Gao * College of Electronic Engineering, Heilongjiang University, Harbin 150080, China; jijuanjiang@126.com (J.J.); wangjun1003@163.com (J.W.); 124wutong@163.com (T.W.) College of Communication and Electronic Engineering, Qiqihar University, Qiqihar 161000, China College of Light Industry, Harbin University of Commerce, Harbin 150028, China * Correspondence: gaoyachen@hlju.edu.cn Abstract: Resonant nonlinear optical absorption of silver nanoparticles was studied experimentally via open aperture Z-scan using 130 fs, 400 nm laser pulses. Experimental results show that, at low laser intensity, silver nanoparticles can exhibit saturated absorption. While at high laser intensity, it shows reverse saturated absorption. The saturable absorption is explained in terms of ground state plasmon bleaching, while the reverse saturable absorption is believed to be from two-photon absorption. Saturable optical intensity and two-photon absorption coefficient were obtained to be 10 2 10 1.3  10 W/m and 3.3  10 m/W, respectively. The energy relaxation process of Ag nanoparti- cles after laser excitation was studied via pump-probe technique at 400 nm. Experimental results demonstrated that energy relaxation included electron-phonon coupling process with time constant = (713  50) fs, and phonon-phonon coupling process with time constant  = (25.2  3) ps, 1 2 respectively. Keywords: nonlinear absorption; nanoparticle; surface plasmon resonances; Z-scan; pump-probe; energy relaxation Citation: Jiang, J.; Wang, J.; Wu, T.; Gao, Y. Nonlinear Absorption and Ultrafast Dynamics of Ag Nanoparticle. Photonics 2021, 8, 233. https://doi.org/10.3390/ 1. Introduction photonics8070233 Around specific wavelengths, noble metal nanoparticles can exhibit strong nonlinear optical properties and ultrafast response, which results in their having possible applica- Academic Editor: Yuri Kivshar tions for photonic devices and attracting special interest [1–16]. Specially, Au and Ag nanoparticles have been the subject of most studies since both show strong surface plas- Received: 11 May 2021 mon resonance (SPR) absorption [1–16]. Moreover, SPR can induce an enhanced local Accepted: 19 June 2021 field which can bring a variety of significant optical characteristics. Specially, non-linear Published: 23 June 2021 absorption is critical because it is able to change strong light propagation in the medium, and induce many novel applications. Publisher’s Note: MDPI stays neutral In Au nanoparticles, plasmon resonance absorption and interband absorption over- with regard to jurisdictional claims in lap partly, which substantially decreases the plasma excitation efficiency. However, for published maps and institutional affil- Ag, the wavelength of interband absorption is about 320 nm and the SPR wavelength is iations. about 400 nm, leading plasmon excitation of silver nanoparticles stronger than that of Au nanoparticles. Therefore, multiple studies focused on non-linear absorption and optical limiting of Ag nanoparticles [15]. Previous study demonstrated the optical nonlinearity of silver nanodots under 532 nm picosecond pulsed laser [8]. Zheng et al. evaluated nanosec- Copyright: © 2021 by the authors. ond nonlinear absorption of Ag nanowires/silica gel glass composite at 532 nm [9,10]. The Licensee MDPI, Basel, Switzerland. nonlinear absorption of silver nano sol was investigated at 456, 477, and 532 nm by open This article is an open access article aperture Z-scan technique [11]. These data demonstrated that saturable absorption (SA) distributed under the terms and flipped to reverse saturated absorption (RSA) behavior under higher input excitation. A conditions of the Creative Commons parallel switching behavior was observed in ZrO [12] and silver nanoparticles in poly- Attribution (CC BY) license (https:// 2 methyl methacrylate (PMMA) [13] under 532 nm nanosecond laser pulse. This observed creativecommons.org/licenses/by/ behavior was discussed based on different mechanisms in the literatures. Regarding to 4.0/). Photonics 2021, 8, 233. https://doi.org/10.3390/photonics8070233 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 233 2 of 8 silver nanowires/silica gel glass composite [9], the switching behavior could be explained from various environmental and electronic dynamics in both liquid and solid matrices. For silver nano sol [10], the data was interpreted by SPR bleach, photochemical alters and po- tential particle size selective excitation effects. While for Ag nanoparticles in ZrO [12], the mechanism of this switch was proposed from the viewpoint of electron Kerr nonlinearity and non-linear light scattering. Almost all studies above were not carried under the resonant wavelength of 400 nm. Only R.A. Ganeev et al. [14] evaluated the nonlinear optical absorption in Ag nanoparticles at 397.5 nm. Their data demonstrated that silver nanoparticles present either SA for 1.2 ps pulsed laser or RSA for 8 ns pulsed laser. As we know, non-linear optical characteristics of metal nanoparticles rely on both laser wavelength and laser pulse-width. Until now, at res- onant wavelength, the optical nonlinearities of Ag nanoparticle have not been investigated in the femtosecond time scale. Although we have previously investigated the non-linear absorption of Ag nanopar- ticles using 130 fs pulsed laser at 400 nm, we focused mainly on a cumulative effect on asymmetrical open-aperture Z-scan signal [15]. In fact, to further evaluate the exact processes occurring in Ag nanoparticle on laser irradiation, a time-resolved study is nec- essary [11]. In the current study, we study resonant non-linear absorption and dynamics process of silver nanoparticles, respectively. 2. Experiments A Coherent Mira 900 laser system and a Coherent Legend-F regenerative amplifier were used to prepare silver nanoparticles and used as the excitation source for Z-scan measurement and pump-probe spectroscopy. The combined system provides linearly polarized, 800 nm pulsed laser with a duration of 130 fs. The femtosecond laser was used to ablate silver metal plates to prepare silver nanopar- ticles [16]. In order to remove the oxide layer and prevent simultaneous oxidation, the pure silver target material is ultrasonically treated and then washed with ethanol. Silver nanoparticles are synthesized by laser ablation of a silver target placed on the bottom of a glass container which is containing 5 mL of ethanol containing 1 mg poly (N-vinyl- 2-pyrrolidone) (PVP). Thirty minutes later, Ag nanoparticles dispersed in ethanol were successfully prepared. The UV-vis linear absorption spectrum of the sample was measured by USB4000 spectrometer. The shape and size of the nanoparticles was observed with a transmission electron microscope (TEM). Non-linear absorption characteristics were researched by open-aperture Z-scan ex- periment [17]. The experiment performed with a 400 nm femtosecond laser obtained by doubling frequency of 800 nm laser. A lens with focal length of 15 cm is applied to focus femtosecond laser pulse to obtain ! = 30 m focal spot, and the Rayleigh length is z = ! / = 7.1 mm. The sample is filled with a quartz cuvette with 2 mm path length, z  L, it accords with the approximate condition of thin medium. In order to study the nonlinear absorption properties of Ag nanoparticles, experiments were performed under different energies. The energy change is achieved through the attenuator. To avoid the cumulative effect and thermal effect, the laser repetition rate was choose to be 1 Hz [5]. Considering that the non-linearity of the quartz cuvette and the solvent may affect the experimental results, before testing the sample, we performed a Z-scan test on a quartz cuvette filled with ethanol solvent. The results show that, under the energy used in our experiment, no nonlinearity was observed. Resonant dynamics process of Ag nanoparticles was studied using pump-probe experiment. Details of the experiment can be found in reference [18]. By frequency doubling 800 nm laser, 400 nm pulsed femtosecond laser was generated to act as pump pulse and probe pulse. A Glan–Taylor polarizer and a half wave plate were used to adjust the pulse energy. Two lenses with focal length of 40 cm and 20 cm were applied to focused pump and the probe beam, which makes the pump and the probe beam radius be 32 m and 16 m, respectively. A prism was mounted on a moving stage to produce the time Photonics 2021, 8, 233 3 of 8 Photonics 2021, 8, x FOR PEER REVIEW 3 of 9 delay t of pump beam and the probe beam. The probe signal was sent to a digital lock-in μm, respectively. A prism was mounted on a moving stage to produce the time delay t amplifier and recorded. The differential transmission DT(t)/T is obtained as a function of pump beam and the probe beam. The probe signal was sent to a digital lock-in amplifier of t. ( )⁄ and recorded. The differential transmission ∆T t T is obtained as a function of t. 3. Result and Discussion 3. Result and Discussion Figure 1 illustrated TEM image and absorption spectrum. From the TEM image of the Figure 1 illustrated TEM image and absorption spectrum. From the TEM image of Ag nanoparticles, the average radius was detected to be about 25 nm. From the spectrum the Ag nanoparticles, the average radius was detected to be about 25 nm. From the spec- of absorption, a strong SPR peak at 403 nm can be found. In addition, the results show trum of absorption, a strong SPR peak at 403 nm can be found. In addition, the results that there is an increase in linear absorption in the range of 350 nm to 300 nm, which is show that there is an increase in linear absorption in the range of 350 nm to 300 nm, which generally considered to be caused by interband absorption [19–21]. is generally considered to be caused by interband absorption [19–21]. Figure 1. Spectrum of absorption spectrum and image of TEM of Ag nanoparticles. Figure 1. Spectrum of absorption spectrum and image of TEM of Ag nanoparticles. Figures 2 and 3 displayed open aperture Z-scan experiment graphs which were ob- Figures 2 and 3 displayed open aperture Z-scan experiment graphs which were ob- tained with four different pulse energies. As shown in Figure 2, the curves are symmetrical tained with four different pulse energies. As shown in Figure 2, the curves are symmet- on the beam waist, when the energies were relatively low (45 nJ and 90 nJ). The normalized rical on the beam waist, when the energies were relatively low (45 nJ and 90 nJ). The nor- transmissions of sample increase with laser energies, which indicate SA occurs in the malized transmissions of sample increase with laser energies, which indicate SA occurs in sample. the samp As le.shown As shoin wn Figur in Fie gur 3, e when 3, wh the en th laser e laener ser egies nerg(110 ies (1nJ 10and nJ a150 nd 1nJ) 50 n wer J) w ee rr elatively e rela- high, the curves show two peaks and a valley. It is well known that an increase in pulse tively high, the curves show two peaks and a valley. It is well known that an increase in ener pulsgy e ecan nergcause y can local causethermo-optical local thermo-op ef ti fectors cal effein cto solvents rs in solv or en nonlinear ts or nonle in ff eects ar efin fec quartz. ts in The qualight rtz. Th ener e lig gy ht used energin y us this edexperiment in this experis im low ent , iand s low the , an pulse d the p repetition ulse repeti frti equency on freque isnonly cy 1is Hz, onlwhich y 1 Hz,is wnot hichenough is not en to oug cause h to obvious cause obv photot ious phermal hotothephenomenon. rmal phenomen As on.mentioned As men- earlier tioned, under earlier,our undexp er o erimental ur experim intensity ental inte , ther nsity e,is thno ereobvious is no obnonlinearity vious nonlinein arithe ty in quartz the cell quafilled rtz celwith l filled ethanol. with eth Ther anolefor . The e, re we fore believe , we belth iev at e the that configuration the configuratiwith on wtwo ith tw peaks o peak and s valleys and valshows leys shthe owsswitch the swfr itc om h fr SA omto SA RSA. to RIt SA is. also It is observed also obsera ve similar d a simswitching ilar switchin ing other in nanoparticles other nanopar[ti 1c –l13 es]. [1–13]. Ganeev et al. used a nanosecond laser at 397.5 nm to study the nonlinear absorption of silver nanoparticles, and they obtained the result of pure saturated absorption [14]. Fan et al. used a femtosecond laser at 800 nm to study the nonlinear absorption of silver nanoparticles, and they also obtained pure saturated absorption [19]. The results of these related studies are the same as the results of our experiments under low intensity. The SPR peak of the Ag nanoparticles was located at 403 nm, and the wavelength of excitation laser is 400 nm. Therefore, SA was related to the ground state plasmon bleaching [14,15]. The increasing excitation flux causes the ground state plasma to bleach when the silver nanoparticles move towards the beam focus. The difference is that, when the excitation intensity is increased, RSA appears in our experiment. For Ag nanoparticles, the interband transition absorption band is at about 320 nm, corresponding energy is about 4.1 eV, which is larger than that of 400 nm laser (about 3.1 eV) [20–23]. Therefore, the interband transitions induced by two-photon absorption (TPA) can occur, which causes RSA [10,12,24]. Photonics 2021, 8, 233 4 of 8 Photonics 2021, 8, x FOR PEER REVIEW 4 of 9 Photonics 2021, 8, x FOR PEER REVIEW 4 of 9 Figure 2. Single peak at relatively low energies (45 nJ and 90 nJ). Figure 2. Single peak at relatively low energies (45 nJ and 90 nJ). Figure 2. Single peak at relatively low energies (45 nJ and 90 nJ). Figure 3. Double peak and a valley at relatively high laser energies (110 nJ and 150 nJ). Figure 3. Double peak and a valley at relatively high laser energies (110 nJ and 150 nJ). Figure 3. Double peak and a valley at relatively high laser energies (110 nJ and 150 nJ). Ganeev et al. used a nanosecond laser at 397.5 nm to study the nonlinear absorption Ganeev et al. used a nanosecond laser at 397.5 nm to study the nonlinear absorption In open-aperture Z-scan experiments, normalized transmittance can be formulated of silver nanoparticles, and they obtained the result of pure saturated absorption [14]. Fan of silver nanoparticles, and they obtained the result of pure saturated absorption [14]. Fan as [17] et al. used a femtosecond laser at 800 nm to study the no2 nlin 2ear absorption of silver nano- et al. used a femtosecond laser at 800 nm to study the nonlinear absorption of silver nano- I L / 1 + z /z 0 eff T z = (1) ( ) particles, and they also obtained på ure saturated absorption [19]. The results of these re- particles, and they also obtained pure saturated absorption [19]. The results of these re- m=0 (m + 1) lated studies are the same as the results of our experiments under low intensity. The SPR lated studies are the same as the results of our experiments under low intensity. The SPR peak of the Ag nanoparticles was located at 403 nm, and the wavelength of excitation laser where is the TPA coefficient, I represents on-axis laser intensity at the focus, peak of the Ag nanoparticles was located at 403 nm, and the wavelength of excitation laser is 400 nm. Therefore, SA was related to the ground state plasmon bleaching [14,15]. The L = [1 exp( L)]/ is length of effective interaction, L represents thickness of is 400 nm. Therefore, SA was related to the ground state plasmon bleaching [14,15]. The eff 0 0 increasing excitation flux causes the ground state plasma to bleach when the silver nano- samples, represents the linear absorption coefficient, z represents distance of samples to increasing excitation flux causes the ground state plasma to bleach when the silver nano- particles move towards the beam focus. The difference is that, when the excitation inten- focus (z = 0), z represents Rayleigh diffraction size. particles move towards the beam focus. The difference is that, when the excitation inten- sity is increased, RSA appears in our experiment. For Ag nanoparticles, the interband sity iT so in analyze creased,the RSswitching A appears of in nonlinear our experi absorption ment. For A above, g nano we pardefine ticles, a thnon-linear e interbandab- transition absorption band is at about 320 nm, corresponding energy is about 4.1 eV, sorption transition coef abs ficient orption as b below and is[ 24 at ]about 320 nm, corresponding energy is about 4.1 eV, which is larger than that of 400 nm laser (about 3.1 eV) [20–23]. Therefore, the interband which is larger than that of 400 nm laser (about 3.1 eV) [20–23]. Therefore, the interband transitions induced by two-photon absorption (TPA) can occur, which causes RSA transitions induced by two-photon absorption (TPA) can occur, which causes RSA (I) = + I (2) 1 + I/I [10,12,24]. [10,12,24]. In open-aperture Z-scan experiments, normalized transmittance can be formulated In open-aperture Z-scan experiments, normalized transmittance can be formulated where represents linear absorption parameter, I intensity of saturation, I the laser 0 s as [17] as [17] intensity, and is TPA coefficient. Thus, I can be expressed as I = (3) 2 2 1 + z /z Photonics 2021, 8, x FOR PEER REVIEW 5 of 9 [−βI L ⁄(1 + z ⁄z )] T(z) = (1) (m + 1) where β is the TPA coefficient, I represents on-axis laser intensity at the focus, L = [1 − exp (−α L)]⁄α is length of effective interaction, L represents thickness of samples, α represents the linear absorption coefficient, z represents distance of samples to focus (z = 0), z represents Rayleigh diffraction size. To analyze the switching of nonlinear absorption above, we define a non-linear ab- sorption coefficient as below [24] Photonics 2021, 8, 233 α(I) = + βI 5 of 8 (2) 1 + I⁄I where α represents linear absorption parameter, I intensity of saturation, I the laser intensity, and β is TPA coefficient. Thus, I can be expressed as It can be simplified as I = (3) 1 + z ⁄z I 0 0 (I ) = + (4) I 2 1 + z /z 1 + It can be simplified as 2 0 1+z /z I ( ) s α βI 2 2 α(I ) = + In Equation (1), I / 1 + z /z is replaced by Equation (4). Then the modified 0 I 0 ⁄ (4) 1 + z z 1 + Equation (1) can be used to fit the experimental data. The coefficient of positive non- (1 + z ⁄z )I linear absorption and saturable intensity I were obtained to be 3.3  10 m/W and In Equation (1), βI ⁄(1 + z ⁄z ) is replaced by Equation (4). Then the modified Equa- 10 2 1.3  10 W/m , respectively. The theoretical curves are presented using solid line in tion (1) can be used to fit the experimental data. The coefficient of positive non-linear ab- Figure 3. sorption β and saturable intensity I were obtained to be 3.3 × 10 m/W and 1.3 × To evaluate the ultrafast response time and recovery time of the observed nonlinear 10 W/m , respectively. The theoretical curves are presented using solid line in Figure 3. absorption above, pump-probe experiment was carried out. The time ration DT/T is To evaluate the ultrafast response time and recovery time of the observed nonlinear determined at various absorption energies of 30, 50, 80, and 100 nJ are displayed in absorption above, pump-probe experiment was carried out. The time ration ΔT/T is de- Figure 4. termined at various absorption energies of 30, 50, 80, and 100 nJ are displayed in Figure 4. Figure 4. Transient differential transmissions ΔT/T determined at the pump energies of 100, 80, 50, Figure 4. Transient differential transmissions DT/T determined at the pump energies of 100, 80, 50, and 30 nJ. and 30 nJ. In Figure 4, it is observed that, following ultrafast laser excitation, there are a rapid In Figure 4, it is observed that, following ultrafast laser excitation, there are a rapid ascent process and two decay ones, which is reported previously [25]. Specifically, the ascent process and two decay ones, which is reported previously [25]. Specifically, the fast-rise signal origins from the ground status plasma of the system. We can find that the fast-rise signal origins from the ground status plasma of the system. We can find that start-up time of the signal is larger than the FWHM of instrument response function the start-up time of the signal is larger than the FWHM of instrument response function (180 fs). Then ΔT/T value falls back in two different time scales, namely a fast one and a (180 fs). Then DT/T value falls back in two different time scales, namely a fast one and a slow one. The process is ‘two-exponential decay’. The fast decay is due to the electron– phonon (e–ph) coupling which causes energy leave the excited electron for the phonon. The following slow decay is a phonon–phonon (ph–ph) coupling process in which energy transfers to medium [26,27]. Then the equilibrium between the electrons and lattice is built. In Figure 4, it is found that, with the increase of pump energy from 30 nJ to 100 nJ, the transient bleach increases. In Figure 5, the change of DT/T with pump energy is shown. Obviously, DT/T increase almost linearly with pump energy. As shown in Figure 6, The normalized transient differential transmission is given. It can be found that all signals are almost same, which implies pump fluence has no effect on decay rate. This is because the pump energies are low, which causes a low perturbation in measurements. In this regime, electron–phonon coupling can be determined precisely. Photonics 2021, 8, x FOR PEER REVIEW 6 of 9 Photonics 2021, 8, x FOR PEER REVIEW 6 of 9 Photonics 2021, 8, 233 6 of 8 slow one. The process is ‘two-exponential decay’. The fast decay is due to the electron– slow one. The process is ‘two-exponential decay’. The fast decay is due to the electron– phonon (e–ph) coupling which causes energy leave the excited electron for the phonon. phonon (e–ph) coupling which causes energy leave the excited electron for the phonon. The The follotransmittivity wing slow decchange ay is a p(hD o T n/ oT n) –p ishan ono ultrafast n (ph–ph ener ) cogy uplrielaxation ng procespr s iocess n whic which h enercan gy The following slow decay is a phonon–phonon (ph–ph) coupling process in which energy transfers to medium [26,27]. Then the equilibrium between the electrons and lattice is be evaluated using a bi-exponential decay function based on the two-temperature model transfers to medium [26,27]. Then the equilibrium between the electrons and lattice is built. In Figure 4, it is found that, with the increase of pump energy from 30 nJ to 100 nJ, built. In Figure 4, it is found that, with the increase of pump energy from 30 nJ to 100 nJ, DT t t the transient bleach increases. = A exp( ) + A exp( ) (5) the transient bleach increases. 1 2 In Figure 5, the change of ΔT/T with pump energy is shown. Obviously, ΔT/T in- In Figure 5, the change of ΔT/T with pump energy is shown. Obviously, ΔT/T in- crease almost linearly with pump energy. As shown in Figure 6, The normalized transient where  ,  and A , A are the time constant and amplitude of two decays, respectively. 1 2 1 2 crease almost linearly with pump energy. As shown in Figure 6, The normalized transient differential transmission is given. It can be found that all signals are almost same, which The solid line in Figure 6 is theoretical fit of the experimental data by using Equation (5). differential transmission is given. It can be found that all signals are almost same, which implies pump fluence has no effect on decay rate. This is because the pump energies are As a result, the initial fast relaxation time  = (713  50) fs and a slow relaxation time implies pump fluence has no effect on decay rate. This is because the pump energies are low, which causes a low perturbation in measurements. In this regime, electron–phonon = (25.2  3) ps were obtained. low, which causes a low perturbation in measurements. In this regime, electron–phonon coupling can be determined precisely. coupling can be determined precisely. Figure 5. Pump pulse energy increases with peak value ΔT/T. Figure 5. Pump pulse energy increases with peak value DT/T. Figure 5. Pump pulse energy increases with peak value ΔT/T. Figure 6. Normalized transient differential transmission at the different pump energies of 30, 50, 80, Figure 6. Normalized transient differential transmission at the different pump energies of 30, 50, 80, Figure and 106. 0 n Normalized J. transient differential transmission at the different pump energies of 30, 50, 80, and 100 nJ. and 100 nJ. The transmittivity change (ΔT/T) is an ultrafast energy relaxation process which can The transmittivity change (ΔT/T) is an ultrafast energy relaxation process which can A series of energy relaxation process occur under the excitation of light [26,27]. The be evaluated using a bi-exponential decay function based on the two-temperature model be evaluated using a bi-exponential decay function based on the two-temperature model first is the interaction between photons and electrons, and the electrons absorb the energy of the photons and become hot electron. Then, the energy exchange between electrons occurs. The third process is the lattice vibration caused by the temperature rise of hot electrons under the action of pulsed light, which is regarded as the interaction between electrons and phonons. The last process is the interaction of phonons and phonons, lattice Photonics 2021, 8, 233 7 of 8 vibration transfers energy to the surrounding ethanol solvent. As the photon–electron and electron–electron relaxation is so quick that cannot be got using 130 fs laser. We believe = (713  50) fs is e–ph relaxation time,  = (25.2  3) ps is ph–ph relaxation time. 1 2 Relatively, the fast component contributes to the recovery of differential transmission signal more. The fast process time constant of 713 fs agrees with the value of 700 fs determined for 3 nm ‘Ag clusters in a glass matrix’ [26]. Arbouet et al. obtained a smaller time constant of approximately 530 fs for silver cluster of the same size in different medium [28]. It should be noted that although the 25 nm in our experiment and the 3 nm ‘Ag clusters in a glass matrix’ are different in size, the approximate e–ph relaxation time is obtained. Maurya et al. studied the size dependence of ultrafast dynamics of silver nanoparticles and found that the e–ph relaxation time ranges from 1.5 ps to 2.3 ps for nanoparticles with sizes ranging from 25 nm to 37 nm [29]. The size of the nanoparticles studied by Maurya et al. is not different from ours completely, but the e–ph relaxation time is different. We consider that the differences may be caused by the different preparation processes of Ag nanoparticles. After all, the crystal structure of the nanoparticles prepared by the laser ablation method and the chemical reduction method is different. In addition, compared with bulk materials, the electron-phonon relaxation process in Ag nanoparticles is slow. This can be explained from two aspects: the quantization of the energy level of the silver nanoparticles and the vibrational dynamics density of the solvent around the silver nanoparticles. First, compared with bulk materials with band structures, the quantized energy level structure of nanoparticles may reduce the overall e–ph interaction, thereby slowing down the relaxation process. Secondly, silver nanoparticles are dispersed in ethanol solvent. Because the liquid vibration density is low and the contact between silver nanoparticles and the surrounding solvent is weak, this may cause the interaction between electrons and solvent to be weaker than that between electrons and bulk materials, thereby slowing down the relaxation process [30]. 4. Conclusions We investigated non-linear absorption and ultrafast relaxation dynamics of silver nanoparticles in ethanol solvent by 130 fs laser pulse at 400 nm. Our data showed that silver nanoparticles exhibit either SA or RSA under different laser intensities. The SA might be related to ground state plasma bleaching, while RSA results from TPA absorption. 10 2 Saturable optical intensity I and TPA coefficient determined to be 1.3  10 W/m and 3.2  10 m/W, respectively. Two component energy relaxations with the fast time constant  = (713  50) fs and the slower one  = (25.2  3) ps were demonstrated 1 2 using pump-probe technique. The present results show Ag nanoparticle can be used as passive mode lockers and optical limiters in ultrafast lasers. Author Contributions: Conceptualization, J.J. and Y.G.; Methodology, J.J. and Y.G.; Formal analysis, J.J. and J.W.; Investigation, J.J. and T.W.; Resources, Y.G.; Data curation, J.W. and T.W.; Writing— original draft preparation, J.J.; Writing—review and editing, Y.G.; Visualization, J.J.; Supervision, Y.G.; Project administration, Y.G. 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Nonlinear Absorption and Ultrafast Dynamics of Ag Nanoparticle

Photonics , Volume 8 (7) – Jun 23, 2021

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hv photonics Article Nonlinear Absorption and Ultrafast Dynamics of Ag Nanoparticle 1 , 2 1 , 3 1 1 , Jijuan Jiang , Jun Wang , Tong Wu and Yachen Gao * College of Electronic Engineering, Heilongjiang University, Harbin 150080, China; jijuanjiang@126.com (J.J.); wangjun1003@163.com (J.W.); 124wutong@163.com (T.W.) College of Communication and Electronic Engineering, Qiqihar University, Qiqihar 161000, China College of Light Industry, Harbin University of Commerce, Harbin 150028, China * Correspondence: gaoyachen@hlju.edu.cn Abstract: Resonant nonlinear optical absorption of silver nanoparticles was studied experimentally via open aperture Z-scan using 130 fs, 400 nm laser pulses. Experimental results show that, at low laser intensity, silver nanoparticles can exhibit saturated absorption. While at high laser intensity, it shows reverse saturated absorption. The saturable absorption is explained in terms of ground state plasmon bleaching, while the reverse saturable absorption is believed to be from two-photon absorption. Saturable optical intensity and two-photon absorption coefficient were obtained to be 10 2 10 1.3  10 W/m and 3.3  10 m/W, respectively. The energy relaxation process of Ag nanoparti- cles after laser excitation was studied via pump-probe technique at 400 nm. Experimental results demonstrated that energy relaxation included electron-phonon coupling process with time constant = (713  50) fs, and phonon-phonon coupling process with time constant  = (25.2  3) ps, 1 2 respectively. Keywords: nonlinear absorption; nanoparticle; surface plasmon resonances; Z-scan; pump-probe; energy relaxation Citation: Jiang, J.; Wang, J.; Wu, T.; Gao, Y. Nonlinear Absorption and Ultrafast Dynamics of Ag Nanoparticle. Photonics 2021, 8, 233. https://doi.org/10.3390/ 1. Introduction photonics8070233 Around specific wavelengths, noble metal nanoparticles can exhibit strong nonlinear optical properties and ultrafast response, which results in their having possible applica- Academic Editor: Yuri Kivshar tions for photonic devices and attracting special interest [1–16]. Specially, Au and Ag nanoparticles have been the subject of most studies since both show strong surface plas- Received: 11 May 2021 mon resonance (SPR) absorption [1–16]. Moreover, SPR can induce an enhanced local Accepted: 19 June 2021 field which can bring a variety of significant optical characteristics. Specially, non-linear Published: 23 June 2021 absorption is critical because it is able to change strong light propagation in the medium, and induce many novel applications. Publisher’s Note: MDPI stays neutral In Au nanoparticles, plasmon resonance absorption and interband absorption over- with regard to jurisdictional claims in lap partly, which substantially decreases the plasma excitation efficiency. However, for published maps and institutional affil- Ag, the wavelength of interband absorption is about 320 nm and the SPR wavelength is iations. about 400 nm, leading plasmon excitation of silver nanoparticles stronger than that of Au nanoparticles. Therefore, multiple studies focused on non-linear absorption and optical limiting of Ag nanoparticles [15]. Previous study demonstrated the optical nonlinearity of silver nanodots under 532 nm picosecond pulsed laser [8]. Zheng et al. evaluated nanosec- Copyright: © 2021 by the authors. ond nonlinear absorption of Ag nanowires/silica gel glass composite at 532 nm [9,10]. The Licensee MDPI, Basel, Switzerland. nonlinear absorption of silver nano sol was investigated at 456, 477, and 532 nm by open This article is an open access article aperture Z-scan technique [11]. These data demonstrated that saturable absorption (SA) distributed under the terms and flipped to reverse saturated absorption (RSA) behavior under higher input excitation. A conditions of the Creative Commons parallel switching behavior was observed in ZrO [12] and silver nanoparticles in poly- Attribution (CC BY) license (https:// 2 methyl methacrylate (PMMA) [13] under 532 nm nanosecond laser pulse. This observed creativecommons.org/licenses/by/ behavior was discussed based on different mechanisms in the literatures. Regarding to 4.0/). Photonics 2021, 8, 233. https://doi.org/10.3390/photonics8070233 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 233 2 of 8 silver nanowires/silica gel glass composite [9], the switching behavior could be explained from various environmental and electronic dynamics in both liquid and solid matrices. For silver nano sol [10], the data was interpreted by SPR bleach, photochemical alters and po- tential particle size selective excitation effects. While for Ag nanoparticles in ZrO [12], the mechanism of this switch was proposed from the viewpoint of electron Kerr nonlinearity and non-linear light scattering. Almost all studies above were not carried under the resonant wavelength of 400 nm. Only R.A. Ganeev et al. [14] evaluated the nonlinear optical absorption in Ag nanoparticles at 397.5 nm. Their data demonstrated that silver nanoparticles present either SA for 1.2 ps pulsed laser or RSA for 8 ns pulsed laser. As we know, non-linear optical characteristics of metal nanoparticles rely on both laser wavelength and laser pulse-width. Until now, at res- onant wavelength, the optical nonlinearities of Ag nanoparticle have not been investigated in the femtosecond time scale. Although we have previously investigated the non-linear absorption of Ag nanopar- ticles using 130 fs pulsed laser at 400 nm, we focused mainly on a cumulative effect on asymmetrical open-aperture Z-scan signal [15]. In fact, to further evaluate the exact processes occurring in Ag nanoparticle on laser irradiation, a time-resolved study is nec- essary [11]. In the current study, we study resonant non-linear absorption and dynamics process of silver nanoparticles, respectively. 2. Experiments A Coherent Mira 900 laser system and a Coherent Legend-F regenerative amplifier were used to prepare silver nanoparticles and used as the excitation source for Z-scan measurement and pump-probe spectroscopy. The combined system provides linearly polarized, 800 nm pulsed laser with a duration of 130 fs. The femtosecond laser was used to ablate silver metal plates to prepare silver nanopar- ticles [16]. In order to remove the oxide layer and prevent simultaneous oxidation, the pure silver target material is ultrasonically treated and then washed with ethanol. Silver nanoparticles are synthesized by laser ablation of a silver target placed on the bottom of a glass container which is containing 5 mL of ethanol containing 1 mg poly (N-vinyl- 2-pyrrolidone) (PVP). Thirty minutes later, Ag nanoparticles dispersed in ethanol were successfully prepared. The UV-vis linear absorption spectrum of the sample was measured by USB4000 spectrometer. The shape and size of the nanoparticles was observed with a transmission electron microscope (TEM). Non-linear absorption characteristics were researched by open-aperture Z-scan ex- periment [17]. The experiment performed with a 400 nm femtosecond laser obtained by doubling frequency of 800 nm laser. A lens with focal length of 15 cm is applied to focus femtosecond laser pulse to obtain ! = 30 m focal spot, and the Rayleigh length is z = ! / = 7.1 mm. The sample is filled with a quartz cuvette with 2 mm path length, z  L, it accords with the approximate condition of thin medium. In order to study the nonlinear absorption properties of Ag nanoparticles, experiments were performed under different energies. The energy change is achieved through the attenuator. To avoid the cumulative effect and thermal effect, the laser repetition rate was choose to be 1 Hz [5]. Considering that the non-linearity of the quartz cuvette and the solvent may affect the experimental results, before testing the sample, we performed a Z-scan test on a quartz cuvette filled with ethanol solvent. The results show that, under the energy used in our experiment, no nonlinearity was observed. Resonant dynamics process of Ag nanoparticles was studied using pump-probe experiment. Details of the experiment can be found in reference [18]. By frequency doubling 800 nm laser, 400 nm pulsed femtosecond laser was generated to act as pump pulse and probe pulse. A Glan–Taylor polarizer and a half wave plate were used to adjust the pulse energy. Two lenses with focal length of 40 cm and 20 cm were applied to focused pump and the probe beam, which makes the pump and the probe beam radius be 32 m and 16 m, respectively. A prism was mounted on a moving stage to produce the time Photonics 2021, 8, 233 3 of 8 Photonics 2021, 8, x FOR PEER REVIEW 3 of 9 delay t of pump beam and the probe beam. The probe signal was sent to a digital lock-in μm, respectively. A prism was mounted on a moving stage to produce the time delay t amplifier and recorded. The differential transmission DT(t)/T is obtained as a function of pump beam and the probe beam. The probe signal was sent to a digital lock-in amplifier of t. ( )⁄ and recorded. The differential transmission ∆T t T is obtained as a function of t. 3. Result and Discussion 3. Result and Discussion Figure 1 illustrated TEM image and absorption spectrum. From the TEM image of the Figure 1 illustrated TEM image and absorption spectrum. From the TEM image of Ag nanoparticles, the average radius was detected to be about 25 nm. From the spectrum the Ag nanoparticles, the average radius was detected to be about 25 nm. From the spec- of absorption, a strong SPR peak at 403 nm can be found. In addition, the results show trum of absorption, a strong SPR peak at 403 nm can be found. In addition, the results that there is an increase in linear absorption in the range of 350 nm to 300 nm, which is show that there is an increase in linear absorption in the range of 350 nm to 300 nm, which generally considered to be caused by interband absorption [19–21]. is generally considered to be caused by interband absorption [19–21]. Figure 1. Spectrum of absorption spectrum and image of TEM of Ag nanoparticles. Figure 1. Spectrum of absorption spectrum and image of TEM of Ag nanoparticles. Figures 2 and 3 displayed open aperture Z-scan experiment graphs which were ob- Figures 2 and 3 displayed open aperture Z-scan experiment graphs which were ob- tained with four different pulse energies. As shown in Figure 2, the curves are symmetrical tained with four different pulse energies. As shown in Figure 2, the curves are symmet- on the beam waist, when the energies were relatively low (45 nJ and 90 nJ). The normalized rical on the beam waist, when the energies were relatively low (45 nJ and 90 nJ). The nor- transmissions of sample increase with laser energies, which indicate SA occurs in the malized transmissions of sample increase with laser energies, which indicate SA occurs in sample. the samp As le.shown As shoin wn Figur in Fie gur 3, e when 3, wh the en th laser e laener ser egies nerg(110 ies (1nJ 10and nJ a150 nd 1nJ) 50 n wer J) w ee rr elatively e rela- high, the curves show two peaks and a valley. It is well known that an increase in pulse tively high, the curves show two peaks and a valley. It is well known that an increase in ener pulsgy e ecan nergcause y can local causethermo-optical local thermo-op ef ti fectors cal effein cto solvents rs in solv or en nonlinear ts or nonle in ff eects ar efin fec quartz. ts in The qualight rtz. Th ener e lig gy ht used energin y us this edexperiment in this experis im low ent , iand s low the , an pulse d the p repetition ulse repeti frti equency on freque isnonly cy 1is Hz, onlwhich y 1 Hz,is wnot hichenough is not en to oug cause h to obvious cause obv photot ious phermal hotothephenomenon. rmal phenomen As on.mentioned As men- earlier tioned, under earlier,our undexp er o erimental ur experim intensity ental inte , ther nsity e,is thno ereobvious is no obnonlinearity vious nonlinein arithe ty in quartz the cell quafilled rtz celwith l filled ethanol. with eth Ther anolefor . The e, re we fore believe , we belth iev at e the that configuration the configuratiwith on wtwo ith tw peaks o peak and s valleys and valshows leys shthe owsswitch the swfr itc om h fr SA omto SA RSA. to RIt SA is. also It is observed also obsera ve similar d a simswitching ilar switchin ing other in nanoparticles other nanopar[ti 1c –l13 es]. [1–13]. Ganeev et al. used a nanosecond laser at 397.5 nm to study the nonlinear absorption of silver nanoparticles, and they obtained the result of pure saturated absorption [14]. Fan et al. used a femtosecond laser at 800 nm to study the nonlinear absorption of silver nanoparticles, and they also obtained pure saturated absorption [19]. The results of these related studies are the same as the results of our experiments under low intensity. The SPR peak of the Ag nanoparticles was located at 403 nm, and the wavelength of excitation laser is 400 nm. Therefore, SA was related to the ground state plasmon bleaching [14,15]. The increasing excitation flux causes the ground state plasma to bleach when the silver nanoparticles move towards the beam focus. The difference is that, when the excitation intensity is increased, RSA appears in our experiment. For Ag nanoparticles, the interband transition absorption band is at about 320 nm, corresponding energy is about 4.1 eV, which is larger than that of 400 nm laser (about 3.1 eV) [20–23]. Therefore, the interband transitions induced by two-photon absorption (TPA) can occur, which causes RSA [10,12,24]. Photonics 2021, 8, 233 4 of 8 Photonics 2021, 8, x FOR PEER REVIEW 4 of 9 Photonics 2021, 8, x FOR PEER REVIEW 4 of 9 Figure 2. Single peak at relatively low energies (45 nJ and 90 nJ). Figure 2. Single peak at relatively low energies (45 nJ and 90 nJ). Figure 2. Single peak at relatively low energies (45 nJ and 90 nJ). Figure 3. Double peak and a valley at relatively high laser energies (110 nJ and 150 nJ). Figure 3. Double peak and a valley at relatively high laser energies (110 nJ and 150 nJ). Figure 3. Double peak and a valley at relatively high laser energies (110 nJ and 150 nJ). Ganeev et al. used a nanosecond laser at 397.5 nm to study the nonlinear absorption Ganeev et al. used a nanosecond laser at 397.5 nm to study the nonlinear absorption In open-aperture Z-scan experiments, normalized transmittance can be formulated of silver nanoparticles, and they obtained the result of pure saturated absorption [14]. Fan of silver nanoparticles, and they obtained the result of pure saturated absorption [14]. Fan as [17] et al. used a femtosecond laser at 800 nm to study the no2 nlin 2ear absorption of silver nano- et al. used a femtosecond laser at 800 nm to study the nonlinear absorption of silver nano- I L / 1 + z /z 0 eff T z = (1) ( ) particles, and they also obtained på ure saturated absorption [19]. The results of these re- particles, and they also obtained pure saturated absorption [19]. The results of these re- m=0 (m + 1) lated studies are the same as the results of our experiments under low intensity. The SPR lated studies are the same as the results of our experiments under low intensity. The SPR peak of the Ag nanoparticles was located at 403 nm, and the wavelength of excitation laser where is the TPA coefficient, I represents on-axis laser intensity at the focus, peak of the Ag nanoparticles was located at 403 nm, and the wavelength of excitation laser is 400 nm. Therefore, SA was related to the ground state plasmon bleaching [14,15]. The L = [1 exp( L)]/ is length of effective interaction, L represents thickness of is 400 nm. Therefore, SA was related to the ground state plasmon bleaching [14,15]. The eff 0 0 increasing excitation flux causes the ground state plasma to bleach when the silver nano- samples, represents the linear absorption coefficient, z represents distance of samples to increasing excitation flux causes the ground state plasma to bleach when the silver nano- particles move towards the beam focus. The difference is that, when the excitation inten- focus (z = 0), z represents Rayleigh diffraction size. particles move towards the beam focus. The difference is that, when the excitation inten- sity is increased, RSA appears in our experiment. For Ag nanoparticles, the interband sity iT so in analyze creased,the RSswitching A appears of in nonlinear our experi absorption ment. For A above, g nano we pardefine ticles, a thnon-linear e interbandab- transition absorption band is at about 320 nm, corresponding energy is about 4.1 eV, sorption transition coef abs ficient orption as b below and is[ 24 at ]about 320 nm, corresponding energy is about 4.1 eV, which is larger than that of 400 nm laser (about 3.1 eV) [20–23]. Therefore, the interband which is larger than that of 400 nm laser (about 3.1 eV) [20–23]. Therefore, the interband transitions induced by two-photon absorption (TPA) can occur, which causes RSA transitions induced by two-photon absorption (TPA) can occur, which causes RSA (I) = + I (2) 1 + I/I [10,12,24]. [10,12,24]. In open-aperture Z-scan experiments, normalized transmittance can be formulated In open-aperture Z-scan experiments, normalized transmittance can be formulated where represents linear absorption parameter, I intensity of saturation, I the laser 0 s as [17] as [17] intensity, and is TPA coefficient. Thus, I can be expressed as I = (3) 2 2 1 + z /z Photonics 2021, 8, x FOR PEER REVIEW 5 of 9 [−βI L ⁄(1 + z ⁄z )] T(z) = (1) (m + 1) where β is the TPA coefficient, I represents on-axis laser intensity at the focus, L = [1 − exp (−α L)]⁄α is length of effective interaction, L represents thickness of samples, α represents the linear absorption coefficient, z represents distance of samples to focus (z = 0), z represents Rayleigh diffraction size. To analyze the switching of nonlinear absorption above, we define a non-linear ab- sorption coefficient as below [24] Photonics 2021, 8, 233 α(I) = + βI 5 of 8 (2) 1 + I⁄I where α represents linear absorption parameter, I intensity of saturation, I the laser intensity, and β is TPA coefficient. Thus, I can be expressed as It can be simplified as I = (3) 1 + z ⁄z I 0 0 (I ) = + (4) I 2 1 + z /z 1 + It can be simplified as 2 0 1+z /z I ( ) s α βI 2 2 α(I ) = + In Equation (1), I / 1 + z /z is replaced by Equation (4). Then the modified 0 I 0 ⁄ (4) 1 + z z 1 + Equation (1) can be used to fit the experimental data. The coefficient of positive non- (1 + z ⁄z )I linear absorption and saturable intensity I were obtained to be 3.3  10 m/W and In Equation (1), βI ⁄(1 + z ⁄z ) is replaced by Equation (4). Then the modified Equa- 10 2 1.3  10 W/m , respectively. The theoretical curves are presented using solid line in tion (1) can be used to fit the experimental data. The coefficient of positive non-linear ab- Figure 3. sorption β and saturable intensity I were obtained to be 3.3 × 10 m/W and 1.3 × To evaluate the ultrafast response time and recovery time of the observed nonlinear 10 W/m , respectively. The theoretical curves are presented using solid line in Figure 3. absorption above, pump-probe experiment was carried out. The time ration DT/T is To evaluate the ultrafast response time and recovery time of the observed nonlinear determined at various absorption energies of 30, 50, 80, and 100 nJ are displayed in absorption above, pump-probe experiment was carried out. The time ration ΔT/T is de- Figure 4. termined at various absorption energies of 30, 50, 80, and 100 nJ are displayed in Figure 4. Figure 4. Transient differential transmissions ΔT/T determined at the pump energies of 100, 80, 50, Figure 4. Transient differential transmissions DT/T determined at the pump energies of 100, 80, 50, and 30 nJ. and 30 nJ. In Figure 4, it is observed that, following ultrafast laser excitation, there are a rapid In Figure 4, it is observed that, following ultrafast laser excitation, there are a rapid ascent process and two decay ones, which is reported previously [25]. Specifically, the ascent process and two decay ones, which is reported previously [25]. Specifically, the fast-rise signal origins from the ground status plasma of the system. We can find that the fast-rise signal origins from the ground status plasma of the system. We can find that start-up time of the signal is larger than the FWHM of instrument response function the start-up time of the signal is larger than the FWHM of instrument response function (180 fs). Then ΔT/T value falls back in two different time scales, namely a fast one and a (180 fs). Then DT/T value falls back in two different time scales, namely a fast one and a slow one. The process is ‘two-exponential decay’. The fast decay is due to the electron– phonon (e–ph) coupling which causes energy leave the excited electron for the phonon. The following slow decay is a phonon–phonon (ph–ph) coupling process in which energy transfers to medium [26,27]. Then the equilibrium between the electrons and lattice is built. In Figure 4, it is found that, with the increase of pump energy from 30 nJ to 100 nJ, the transient bleach increases. In Figure 5, the change of DT/T with pump energy is shown. Obviously, DT/T increase almost linearly with pump energy. As shown in Figure 6, The normalized transient differential transmission is given. It can be found that all signals are almost same, which implies pump fluence has no effect on decay rate. This is because the pump energies are low, which causes a low perturbation in measurements. In this regime, electron–phonon coupling can be determined precisely. Photonics 2021, 8, x FOR PEER REVIEW 6 of 9 Photonics 2021, 8, x FOR PEER REVIEW 6 of 9 Photonics 2021, 8, 233 6 of 8 slow one. The process is ‘two-exponential decay’. The fast decay is due to the electron– slow one. The process is ‘two-exponential decay’. The fast decay is due to the electron– phonon (e–ph) coupling which causes energy leave the excited electron for the phonon. phonon (e–ph) coupling which causes energy leave the excited electron for the phonon. The The follotransmittivity wing slow decchange ay is a p(hD o T n/ oT n) –p ishan ono ultrafast n (ph–ph ener ) cogy uplrielaxation ng procespr s iocess n whic which h enercan gy The following slow decay is a phonon–phonon (ph–ph) coupling process in which energy transfers to medium [26,27]. Then the equilibrium between the electrons and lattice is be evaluated using a bi-exponential decay function based on the two-temperature model transfers to medium [26,27]. Then the equilibrium between the electrons and lattice is built. In Figure 4, it is found that, with the increase of pump energy from 30 nJ to 100 nJ, built. In Figure 4, it is found that, with the increase of pump energy from 30 nJ to 100 nJ, DT t t the transient bleach increases. = A exp( ) + A exp( ) (5) the transient bleach increases. 1 2 In Figure 5, the change of ΔT/T with pump energy is shown. Obviously, ΔT/T in- In Figure 5, the change of ΔT/T with pump energy is shown. Obviously, ΔT/T in- crease almost linearly with pump energy. As shown in Figure 6, The normalized transient where  ,  and A , A are the time constant and amplitude of two decays, respectively. 1 2 1 2 crease almost linearly with pump energy. As shown in Figure 6, The normalized transient differential transmission is given. It can be found that all signals are almost same, which The solid line in Figure 6 is theoretical fit of the experimental data by using Equation (5). differential transmission is given. It can be found that all signals are almost same, which implies pump fluence has no effect on decay rate. This is because the pump energies are As a result, the initial fast relaxation time  = (713  50) fs and a slow relaxation time implies pump fluence has no effect on decay rate. This is because the pump energies are low, which causes a low perturbation in measurements. In this regime, electron–phonon = (25.2  3) ps were obtained. low, which causes a low perturbation in measurements. In this regime, electron–phonon coupling can be determined precisely. coupling can be determined precisely. Figure 5. Pump pulse energy increases with peak value ΔT/T. Figure 5. Pump pulse energy increases with peak value DT/T. Figure 5. Pump pulse energy increases with peak value ΔT/T. Figure 6. Normalized transient differential transmission at the different pump energies of 30, 50, 80, Figure 6. Normalized transient differential transmission at the different pump energies of 30, 50, 80, Figure and 106. 0 n Normalized J. transient differential transmission at the different pump energies of 30, 50, 80, and 100 nJ. and 100 nJ. The transmittivity change (ΔT/T) is an ultrafast energy relaxation process which can The transmittivity change (ΔT/T) is an ultrafast energy relaxation process which can A series of energy relaxation process occur under the excitation of light [26,27]. The be evaluated using a bi-exponential decay function based on the two-temperature model be evaluated using a bi-exponential decay function based on the two-temperature model first is the interaction between photons and electrons, and the electrons absorb the energy of the photons and become hot electron. Then, the energy exchange between electrons occurs. The third process is the lattice vibration caused by the temperature rise of hot electrons under the action of pulsed light, which is regarded as the interaction between electrons and phonons. The last process is the interaction of phonons and phonons, lattice Photonics 2021, 8, 233 7 of 8 vibration transfers energy to the surrounding ethanol solvent. As the photon–electron and electron–electron relaxation is so quick that cannot be got using 130 fs laser. We believe = (713  50) fs is e–ph relaxation time,  = (25.2  3) ps is ph–ph relaxation time. 1 2 Relatively, the fast component contributes to the recovery of differential transmission signal more. The fast process time constant of 713 fs agrees with the value of 700 fs determined for 3 nm ‘Ag clusters in a glass matrix’ [26]. Arbouet et al. obtained a smaller time constant of approximately 530 fs for silver cluster of the same size in different medium [28]. It should be noted that although the 25 nm in our experiment and the 3 nm ‘Ag clusters in a glass matrix’ are different in size, the approximate e–ph relaxation time is obtained. Maurya et al. studied the size dependence of ultrafast dynamics of silver nanoparticles and found that the e–ph relaxation time ranges from 1.5 ps to 2.3 ps for nanoparticles with sizes ranging from 25 nm to 37 nm [29]. The size of the nanoparticles studied by Maurya et al. is not different from ours completely, but the e–ph relaxation time is different. We consider that the differences may be caused by the different preparation processes of Ag nanoparticles. After all, the crystal structure of the nanoparticles prepared by the laser ablation method and the chemical reduction method is different. In addition, compared with bulk materials, the electron-phonon relaxation process in Ag nanoparticles is slow. This can be explained from two aspects: the quantization of the energy level of the silver nanoparticles and the vibrational dynamics density of the solvent around the silver nanoparticles. First, compared with bulk materials with band structures, the quantized energy level structure of nanoparticles may reduce the overall e–ph interaction, thereby slowing down the relaxation process. Secondly, silver nanoparticles are dispersed in ethanol solvent. Because the liquid vibration density is low and the contact between silver nanoparticles and the surrounding solvent is weak, this may cause the interaction between electrons and solvent to be weaker than that between electrons and bulk materials, thereby slowing down the relaxation process [30]. 4. Conclusions We investigated non-linear absorption and ultrafast relaxation dynamics of silver nanoparticles in ethanol solvent by 130 fs laser pulse at 400 nm. Our data showed that silver nanoparticles exhibit either SA or RSA under different laser intensities. The SA might be related to ground state plasma bleaching, while RSA results from TPA absorption. 10 2 Saturable optical intensity I and TPA coefficient determined to be 1.3  10 W/m and 3.2  10 m/W, respectively. Two component energy relaxations with the fast time constant  = (713  50) fs and the slower one  = (25.2  3) ps were demonstrated 1 2 using pump-probe technique. The present results show Ag nanoparticle can be used as passive mode lockers and optical limiters in ultrafast lasers. Author Contributions: Conceptualization, J.J. and Y.G.; Methodology, J.J. and Y.G.; Formal analysis, J.J. and J.W.; Investigation, J.J. and T.W.; Resources, Y.G.; Data curation, J.W. and T.W.; Writing— original draft preparation, J.J.; Writing—review and editing, Y.G.; Visualization, J.J.; Supervision, Y.G.; Project administration, Y.G. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Jun 23, 2021

Keywords: nonlinear absorption; nanoparticle; surface plasmon resonances; Z-scan; pump-probe; energy relaxation

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