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Abstract
The process and condition of saturable absorption (SA) and reverse saturable absorption (RSA) of ultrafast nonlinear optics in metal nanoparticles are essential for applications including light generation, amplification, modulation, and switching. Here, we first discover and explore the multiple transformations (SA-RSA-SA) of ultrafast nonlinear absorption behavior of metal nanoparticles in femtosecond pulses. Correspondingly, the energy level model and fitting formula of multiple transformations are established to illustrate the process of optical response. The femtosecond transient absorption spectra provide information about their ultrafast dynamics process and vibrational mode, which further reveals the multiple transformation mechanisms of nonlinear absorption in gold nanobipyramids (Au-NBPs). Furthermore, Au-NBPs exhibit a significantly higher SA modulation depth up to 42% in the femtosecond, which is much higher than the reported values of other nanomaterials. Our results indicate that Au-NBPs can be used as broadband ultrafast Q-switching and mode-locking, and the conversion offers new opportunities for metal nanostructures in applications of optical switching.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Noble metal nanoparticles have attracted tremendous interest and been extensive studies owing to the outstanding surface plasmon resonance (SPR) characteristics and large optical nonlinearities. These have promising applications in surface-enhanced Raman spectroscopy [1,2], ultrasensitive plasmonic biological sensing [3–5], all-optical switching [6,7], and ultrafast information processing [8,9]. Gold nanobipyramids (Au-NBPs) are a distinctive structure that possess better tunability of the SPR peak over a wide range from the visible to near-infrared region [10,11], and the structure contains multiple tips that generate greater enhancement of the electric field [12,13].
Noble metal nanoparticles exhibit large nonlinear optical susceptibility and ultrafast nonlinear response [14–18]. The optical response of metal nanoparticles excited with single-shot ultrashort pulsed lasers is due to intraband transitions (within the sp conduction band) and the interband transitions (between the d valence band and sp conduction band) [19,20]. The energy of photons is absorbed, leading to a nonthermal distribution of electrons in metal nanoparticles. Excited electrons equilibrate through electron–electron (e–e) interactions in the first few hundred femtoseconds. Subsequently, the energy is transferred to the lattice through electron−phonon (e–p) scattering within a few picoseconds [21]. In the latter phase, phonon–phonon (p–p) scattering occurs, and energy is dissipated into the environment. At present, the nonlinear properties of silver and gold nanoparticles have been investigated under different excitation conditions. Gold nanoparticles exhibit a transition from saturable absorption (SA) to reverse saturable absorption (RSA) that depends on the incident laser intensity and wavelength [22–27]. Although the existing mechanism describes the SA to RSA nonlinear behavior of metal nanoparticles at moderate intensities, the phenomenon of RSA to SA has recently been reported [28,29]. Oliveira et al. believe that only the phenomenon of RSA to SA conversion was observed, and RSA was also converted from SA at moderate intensities, but it was not observed [29]. The relationship between the two transformations (SA-RSA and RSA-SA) is still unclear, and the clarification of the processes and mechanisms of these phenomena is essential for understanding the light–matter interaction and the further precise design of ultrafast optoelectronic devices based on metal nanomaterials. The study of multiple transformations will provide new opportunities for the control of the nonlinear optical response in metal nanoparticles.
Here we study the multiple transformations of the ultrafast nonlinear absorption behavior of Au-NBPs in the femtosecond regime. The energy level model and fitting formula of multiple transformations are established to illustrate the effect of wavelength and incident intensity on the nonlinear absorption. The femtosecond transient absorption spectra provide information about their dynamics process, which reveals the multiple transformation mechanisms of nonlinear absorption in Au-NBPs. Furthermore, Au-NBPs exhibit a significantly higher modulation depth in ultrafast pulses, which is much higher than the reported values of other nanomaterials.
2. Experimental section
2.1 Chacterization of Au-NBPs
The Au-NBPs studied in the experiments were obtained from a commercial company (NanoSeedz). Transmission electron microscopy (TEM) image of the sample was recorded using an electron microscope (Tecnai G2 F30). The absorbance spectrum was measured with an ultraviolet-visible-near infrared spectrophotometer (Specord 200).
2.2 Z-scan measurements and characterization of ultrafast broadband saturable absorber
The nonlinear absorption was measured by using a standard Z-scan setup, as shown in Fig. S1 (Supplement 1). The output laser pulses were obtained from an optical parameter amplifier (OPA, Light Conversion ORPHEUS), which was pumped by a mode-locked Yb:KGW fiber laser (190 fs, 20 Hz). The output wavelength of the OPA was tuned to cover a broadband range 650 nm to 850 nm in the Z-scan measurements. The Au-NBPs water dispersion at a concentration of 1.0 × 10 −3 mol/L was transferred to a 2 mm quartz cuvette. The beam splitter divided the laser beam into two paths. One beam was measured by detector 1 as a reference, and the other beam was measured by detector 2 after passing through Au NBPs. In addition, all nonlinearities excluded the solvent effect.
The same equipment was used for the saturable absorption characterization of Au-NBPs and Z-scan measurements, and the material was placed at the focus position (z = 0) of the system.
2.3 Femtosecond time-resolved transient absorption
The time-resolved transient absorption measurements were performed using 190 fs (FWHM) pulses generated by a mode-locked Yb:KGW femtosecond laser system (Light Conversion, PHAROS-SP) with a repetition rate of 6 kHz. The experimental setup is shown in Fig. S2 (Supplement 1). The main part of the fundamental output was used to pump an optical parameter amplifier (OPA, Light Conversion ORPHEUS). The OPA output was used as the pump beam and set as a wavelength of 825 nm in this study, which was modulated by a chopper at 140 Hz. The probe light was supercontinuum white light, which carried the excited-state signal through a grating spectrometer.
3. Results and discussion
3.1 Characterization
Figure 1(a) shows the TEM image of Au-NBPs. It can be seen that the length and width of the Au-NBPs are approximately 115 nm and 35 nm, respectively. Figure 1(b) shows the absorption spectrum of Au-NBPs. Two absorption bands can be easily observed, and the band located at approximately 516 nm is due to the transverse dipole resonance [30]. The stronger absorption peak located at approximately 825 nm is the longitudinal surface plasmon resonance (LSPR) of Au-NBPs.
3.2 Ultrafast nonlinear absorption properties
Femtosecond open-aperture Z-scan experiments were conducted at 650 nm, 700 nm, 750 nm, 800 nm, 825 nm and 850 nm to characterize the ultrafast nonlinear absorption properties of Au-NBPs.
When the input wavelength is far from the LSPR (650 nm and 700 nm), as shown in Fig. 2, the Au-NBPs exhibit multiple transformations of ultrafast nonlinear absorption. The normalized transmittance is obtained by dividing the linear transmittance. For 700 nm, the Au-NBPs present a conversion from SA to RSA at relatively weak incident intensities (see Fig. 2(a)). At relatively higher intensities, the transformation from RSA to SA occurs. With the further increase of energy, RSA is completely converted into SA. Figure 2 (b), (c), (d) also presents the dependence of nonlinear absorption properties versus light intensity for Au-NBPs at 650 nm. When the incident wavelength is near LSPR (750 nm, 800 nm, 825 nm and 850 nm), as shown in Fig. 3, Au-NBPs exhibit SA when the incident light is relatively weak. Under higher intensities, the Au-NBPs still show SA, and the transmittance at the focus is further increased. As the input wavelength increases from 750 nm to 850 nm, the transmittance at the focal point is the largest at the LSPR peak.
Fig. 2. Nonlinear absorption properties of Au-NBPs (a) at wavelength of 700 nm, (b), (c), (d) at wavelength of 650 nm with different intensities. The circles denote the experimental data, and the solid lines denote the theoretical fit using Eqs. (1)–(4).
Fig. 3. Nonlinear absorption properties of Au-NBPs. The input wavelengths are (a) 750 nm, (b) 800 nm, (c) 825 nm, and (d) 850 nm. The circles denote the experimental data, and the solid lines denote the theoretical fit.
The nonlinear absorption properties of Au-NBPs can be analyzed according to the simplified band scheme in Fig. 4. The optical bandgap d-band to Fermi level EF of Au is 2.4 eV [31]. The incident light may result in: (a) intraband transitions between filled and empty within the sp band, (b) interband transitions between the d-band and the sp-band, and (c) two-photon absorption (TPA) under the high photon flux illumination.
Fig. 4. Simplified band scheme of Au-NBPs. EF is the Fermi level, and E1 is the transition energy of d-band to the Depletion.
As the input wavelengths are 650 nm and 700 nm, low energy photons can only excite intraband electrons of sp-band, which corresponds to (1) of the simplified band scheme (see Fig. 4). Excited by the light pulse, external field induces the collective oscillation of electrons within the conduction band. The outermost electrons in the sp-band near the Fermi level transition above the Fermi level, leading to ground-state free electron reduction and plasma bleaching. The bleaching of the sp′-band (Depletion) results in SA, and first photon creates a hole in the sp′-band below EF. The hole is filled with d-band electron excited by the second photon, which can be described by (2) of the simplified band scheme. Imura et al. were the first to propose sequential two-photon absorption (STPA) in Au nanorods [32]. The STPA leads to the conversion of Au-NBPs from SA to RSA. In addition, in high-intensity regime, the interband transitions can excite a great quantity of electrons to high energy states, leading to depletion of the d-band that satisfies the transition requirement and consequently saturation of the nonlinear absorption. When the input wavelength is near LSPR (750 nm, 800 nm, 825 nm and 850 nm), the (1) process of the simplified band scheme occurs, and the first photon creates a hole in the sp′-band below EF. At high incident light intensity, the hole cannot be filled with the d-band electron because the incident photon is lower than the transition energy of d-sp′ band. Only process (1) occurs and the Au-NBPs still exhibit SA.
Hence, following the approach of Gao [33] and Cesca et al [28], we assumed the intensity-dependent nonlinear absorption coefficient given by the following expression with three components:
The light intensity distribution expressed as:
The variation of laser intensity inside the material can be expressed by using:
z′ is the propagation distance of the beam in the material.Therefore, the normalized transmission is calculated by using the equation:
T0 is the linear transmittance of Au-NBPs, Iinand Ioutare the light intensity on the input and output surfaces of material, respectively. The circles in Figs. 2 and 3 denote the experimental data, and the solid lines are the theoretical fitting. The nonlinear optical parameters of Au-NBPs Is, β+, Ι β-and β- obtained by theoretical fitting are summarized in Table 1.
Table 1. Nonlinear optical parameters of Au-NBPs
It can be seen in Table 1 that Is decreases when the incident wavelength is near SPR. This decrease is caused by the resonant enhancement of nonlinear properties [34]. In particular, the value of Is is 2.9 GW/cm2 at the LSPR absorption peak, which is much lower than that reported for other plasmonic nanostructures [35–37]. Au-NBPs present excellent SA properties in the near-infrared region and the comparison of SA characteristics is shown in Table 2.
Table 2. SA characteristics of plasmonic nanostructures
3.3 Ultrafast broadband saturable absorber
Currently, materials with SPR were found to exhibit SA and the modulation depth up to 20%, which is useful for mode locking in fiber-based femtosecond lasers [38–40]. The maximum change in transmittance of the SA material at a specific wavelength is defined as the modulation depth, ΔT$=$Tmax$-$T0. Tmax is the maximum transmittance. Nonetheless, some challenges in SA materials still exist including the large modulation depth and high optical damage thresholds. Femtosecond Z-scan results indicate that the Au-NBPs have multipulse SA around the LSPR absorption band. To evaluate the ultrafast SA characteristics of Au-NBPs, the relationship between the transmittance and incident fluence of Au-NBPs was measured at 750 nm, 800 nm and 825 nm. Au-NBPs exhibit a single SA at 750 nm to 825 nm, so only the first term exists on the right-hand side of Eq. (1). The Is obtained from the Z-scan experiment is brought into Eq. (1) and correlated with Eqs. (1)–(4). The dependence of the transmission ratio and incident fluence of the Au-NBPs can be calculated theoretically. The circles in Fig. 5 represent the experimental data, and the solid lines denote the theoretical fit.
Fig. 5. The dependence of the transmission ratio and incident fluence of the Au-NBPs at wavelengths of (a) 750 nm, (b) 800 nm, and (c) 825 nm. The circles denote the experimental data, and the solid lines denote the theoretical fit.
The ΔT of Au-NBPs at wavelengths of 750 nm, 800 nm, and 825 nm was determined to be 21%, 36%, and 42%, respectively. Table 3 compares the ΔT for metallic nanostructures reported in the literature with those from our studied. It should be noted that the ΔT at 825 nm of Au-NBPs is nearly several times higher than those of other metallic nanostructures. This large modulation depth of Au-NBPs is highly useful for the application of induced Q-switching [45].
Table 3. Summary of the ΔT (SA) for metallic nanostructures
3.4 Ultrafast transient absorption measurements: energy relaxation and vibrational mode
Femtosecond transient absorption spectra with a pump power of 10 mW are presented in Fig. 6 (a). We find that the spectra at approximately 650 nm and 700 nm correspond to the light-induced absorption signals. In addition, the spectra at about 800 nm correspond to the bleaching of the plasma signal. For Au-NBPs, the pump laser pulses of 825 nm can only excite electrons through intraband transitions. These signals further reveal that the d-band electron excited can achieve the d-sp′ transition at 650 nm and 700 nm. The Au-NBPs maintain SA around 800 nm because the hole (sp′) cannot be filled by the d-band electron.
Fig. 6. (a) Transient absorption spectra for Au-NBPs with 190 fs laser pulses. (b) Dynamic traces of Au-NBPs at 700 nm and 800 nm (the circles denote the experimental data, and the solid lines denote the theoretical fit). The inset shows the vibrational frequencies of 800 nm.
Figure 6(b) describes the electron dynamics at 700 nm and 800 nm. The energy of the excited electrons is rapidly throughout the whole electron distribution by e–e scattering in the first few hundred femtoseconds, exceeds the temporal sensitivity of the pulses and is therefore not revealed in the transient signal [46]. The second process is predominant for a time period on the order of a picosecond, which is due to the balance between the excited electrons and the lattice of nanoparticles through e–p interaction [47]. The latter is p–p scattering typically for another 100 ps. At the same time, the dynamic curves show the modulation based on exponential relaxation. After ultrafast excitation, energy flows into the phonon of the metal nanoparticles within a few picoseconds. The change in lattice temperature is about two orders of magnitude smaller than that of electronic temperature, because the heat capacity of electrons and lattice is different. The increase of the lattice temperature leads to expansion, and the heating time is faster than the period of the phonon mode related to the expansion coordinate. The transient absorption traces show a modulation, which can be attributed to the vibrational mode of the coherent excitation [20].
Through global analysis, the dynamic curves for Au-NBPs can be described by a damped cosine function and an exponential decaying background and the curve using the fitting equation [48]:
Table 4. Dynamic parameters of Au-NBPs at different powers
No modulation signal was detected in the transverse plasmon band. Thus, the modulations of the transient absorption trace probably arise from the change in the length of the Au-NBPs caused by the extensional mode (LSPR). Continuum mechanics calculations for the sample, the periods of the extensional modes as [49]:
where L is the length of the Au-NBPs, ρ is the density of bulk gold, and E is the Young’s modulus. The period of the modulations is consistent with the expected period of fundamental extensional mode. Taking Young’s modulus of 79 GPa, the density is 19.32 g/cm3. The experimental (14 GHz) and calculated frequencies (14.7 GHz) are in excellent agreement. This indicates that the elastic constant of gold nanoparticles is identical with that of bulk gold in this size range. Theoretical calculations also show that the modulation frequency measured in the transient experiments is the phonon signal. In the process of e−p coupling, the energy of the hot electrons rapidly flows into the phonons and the increase in the lattice temperature leads to expansion, bring about the vibrational modes of the coherent excitation. The study of e–p scattering and heat dissipation measurements is extremely important for applications of nanoparticles involving heat conduction and electrical conduction. Moreover, the elastic modulus provides fundamental information about the properties of nanoparticles. For samples with known elastic constants, the size distribution can be determined according to the transient absorption measurements.To further investigate the effect of pump laser intensity on the dynamics of Au-NBPs, femtosecond transient absorption measurements were carried out at different pump powers of 5 mW, 10 mW, 12.5 mW and 15 mW. As shown in Fig. 7, Au-NBPs have different dynamic traces under different pump powers. The circles denote the experimental data, and the solid lines denote the theoretical date fitted by Eq. (5). Accordingly, the fitted decay parameters for the Au-NBPs at different powers are summarized in the Table. 1. It can be seen that the e−p decay time is related to the pump laser intensity and increases significantly with the pump power. This is because the energy exchange of e-p subsystems is related to their temperature difference [50]. As the energy increases, the more electrons are in high electronic states, and the longer it takes for the electrons to transfer energy to phonons.
Fig. 7. Dynamics curves for Au-NBPs at different pump powers. (The circles denote the experimental data, and the solid lines denote the theoretical fit.)
4. Conclusion
In conclusion, we explored the ultrafast nonlinear absorption with multiple transformations of Au-NBPs. The SA is attributed to the intraband transition of sp′-band, whereas STPA leads to the conversion of Au-NBPs from SA to RSA. In the high-intensity regime, the d-band that satisfies the transition requirement is depleted, resulting in the saturation of STPA and the conversion from RSA to SA. Au-NBPs exhibit a significantly higher SA modulation depth up to 42% in ultrafast pulses, which is much higher than the reported values of other nanomaterials.
We report the ultrafast dynamics response in Au-NBPs, which exhibit two characteristic lifetimes for e-p and p-p energy relaxation and depend strongly on the laser intensity. The exponential decay also shows a modulation, which can be attributed to the vibrational mode of coherent excitation. The tunable nonlinear response of the Au-NBPs will deepen the understanding of light–matter interactions and provide new opportunities for the control of the nonlinear optical response in metal nanoparticles.
Funding
National Natural Science Foundation of China (12174169).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. S. J. Lee, H. Lee, T. Begildayeva, Y. Yu, J. Theerthagiri, Y. Kim, Y. W. Lee, S. W. Han, and M. Y. Choi, “Nanogap-tailored Au nanoparticles fabricated by pulsed laser ablation for surface-enhanced Raman scattering,” Biosens. Bioelectron. 197, 113766 (2022). [CrossRef]
2. C. C. Andrei, A. Moraillon, S. Lau, N. Felidj, N. Yamakawa, J. Bouckaert, E. Larquet, R. Boukherroub, F. Ozanam, S. Szunerits, and A. C. Gouget-Laemmel, “Rapid and sensitive identification of uropathogenic Escherichia coli using a surface-enhanced-Raman-scattering-based biochip,” Talanta 219, 121174 (2020). [CrossRef]
3. A. Loiseau, V. Asila, G. Boitel-Aullen, M. Lam, M. Salmain, and S. Boujday, “Silver-Based Plasmonic Nanoparticles for and Their Use in Biosensing,” Biosensors 9(2), 78 (2019). [CrossRef]
4. S. K. Kailasa, J. R. Koduru, M. L. Desai, T. J. Park, R. K. Singhal, and H. Basu, “Recent progress on surface chemistry of plasmonic metal nanoparticles for colorimetric assay of drugs in pharmaceutical and biological samples,” Trac-Trend Anal Chem 105, 106–120 (2018). [CrossRef]
5. H. Gao, P. Wu, P. Song, B. Kang, J.-J. Xu, and H.-Y. Chen, “The video-rate imaging of sub-10 nm plasmonic nanoparticles in a cellular medium free of background scattering,” Chem. Sci. 12(8), 3017–3024 (2021). [CrossRef]
6. X. J. Wang, J. Jian, H. H. Wang, J. C. Liu, Y. Pachaury, P. Lu, B. X. Rutherford, X. Y. Gao, X. S. Xu, A. El-Azab, X. H. Zhang, and H. Y. Wang, “Nitride-Oxide-Metal Heterostructure with Self-Assembled Core-Shell Nanopillar Arrays: Effect of Ordering on Magneto-Optical Properties,” Small 17(5), 2007222 (2021). [CrossRef]
7. F. Chalikkara and S. N. Varanakkottu, “Optofluidic modulator based on thermoplasmonically controlled liquid-liquid interface,” Opt. Lett. 46(16), 3993–3996 (2021). [CrossRef]
8. E. M. Roller, L. V. Besteiro, C. Pupp, L. K. Khorashad, A. O. Govorov, and T. Liedl, “Hotspot-mediated non-dissipative and ultrafast plasmon passage,” Nat. Phys. 13(8), 761–765 (2017). [CrossRef]
9. X. Luo, R. Pan, M. Y. Cai, W. J. Liu, C. H. Chen, G. C. Jiang, X. Y. Hu, H. J. Zhang, and M. L. Zhong, “Atto-Molar Raman detection on patterned superhydrophilic-superhydrophobic platform via localizable evaporation enrichment,” Sensors and Actuators B: Chemical 326, 128826 (2021). [CrossRef]
10. J. Burgin, I. Florea, J. Majimel, A. Dobri, O. Ersen, and M. Treguer-Delapierre, “3D morphology of Au and Au@Ag nanobipyramids,” Nanoscale 4(4), 1299–1303 (2012). [CrossRef]
11. M. Liu, P. Guyot-Sionnest, T.-W. Lee, and S. K. Gray, “Optical properties of rodlike and bipyramidal gold nanoparticles from three-dimensional computations,” Phys. Rev. B 76(23), 235428 (2007). [CrossRef]
12. X. Zhu, H. K. Yip, X. Zhuo, R. Jiang, J. Chen, X.-M. Zhu, Z. Yang, and J. Wang, “Realization of Red Plasmon Shifts up to similar to 900 nm by AgPd-Tipping Elongated Au Nanocrystals,” J. Am. Chem. Soc. 139(39), 13837–13846 (2017). [CrossRef]
13. W. Rao, Q. Li, Y. Wang, T. Li, and L. Wu, “Comparison of Photoluminescence Quantum Yield of Single Gold Nanobipyramids and Gold Nanorods,” ACS Nano 9(3), 2783–2791 (2015). [CrossRef]
14. Y. X. Zhang and Y. H. Wang, “Nonlinear optical properties of metal nanoparticles: a review,” RSC Adv. 7(71), 45129–45144 (2017). [CrossRef]
15. X. Wang, L. H. Yao, S. Li, and M. H. Cai, “Extraordinarily Large Third-Order Optical Nonlinearity in Au Nanorods under Nanowatt Laser Excitation,” J. Phys. Chem. C 124(12), 6838–6844 (2020). [CrossRef]
16. 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), 18146–18156 (2019). [CrossRef]
17. H. Baida, D. Mongin, D. Christofilos, G. Bachelier, A. Crut, P. Maioli, N. Del Fatti, and F. Vallee, “Ultrafast Nonlinear Optical Response of a Single Gold Nanorod near Its Surface Plasmon Resonance,” Phys. Rev. Lett. 107(5), 057402 (2011). [CrossRef]
18. Z. Y. Chen, H. W. Dai, J. M. Liu, H. Xu, Z. X. Li, Z. K. Zhou, and J. B. Han, “Dipole plasmon resonance induced large third-order optical nonlinearity of Au triangular nanoprism in infrared region,” Opt. Express 21(15), 17568–17575 (2013). [CrossRef]
19. C. Sonnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002). [CrossRef]
20. G. V. Hartland, “Optical Studies of Dynamics in Noble Metal Nanostructures,” Chem. Rev. 111(6), 3858–3887 (2011). [CrossRef]
21. T. Heilpern, M. Manjare, A. O. Govorov, G. P. Wiederrecht, S. K. Gray, and H. Harutyunyan, “Determination of hot carrier energy distributions from inversion of ultrafast pump-probe reflectivity measurements,” Nat. Commun. 9(1), 1853 (2018). [CrossRef]
22. E. V. Garcia-Ramirez, S. Almaguer-Valenzuela, O. Sanchez-Dena, O. Baldovino-Pantaleon, and J. A. Reyes-Esqueda, “Third-order nonlinear optical properties of colloidal Au nanorods systems: saturable and reverse-saturable absorption,” Opt. Express 24(2), A154–167 (2016). [CrossRef]
23. S. Chen, S. Y. Yang, Y. Huang, W. Y. Jiao, G. H. Fan, and Y. C. Gao, “Wavelength-dependent nonlinear absorption of gold nanocages,” Chin. Opt. Lett. 18(1), 011901 (2020). [CrossRef]
24. P. Ferrari, S. Upadhyay, M. V. Shestakov, J. Vanbuel, B. De Roo, Y. H. Kuang, M. Di Vece, V. V. Moshchalkov, J. P. Locquet, P. Lievens, and E. Janssens, “Wavelength-Dependent Nonlinear Optical Properties of Ag Nanoparticles Dispersed in a Glass Host,” J. Phys. Chem. C 121(49), 27580–27589 (2017). [CrossRef]
25. Y. Hua, K. Chandra, D. H. M. Dam, G. P. Wiederrecht, and T. W. Odom, “Shape-Dependent Nonlinear Optical Properties of Anisotropic Gold Nanoparticles,” J. Phys. Chem. Lett. 6(24), 4904–4908 (2015). [CrossRef]
26. S. Chen, Y. C. Gao, R. P. Niu, W. F. Zhou, Y. X. Wang, Y. L. Song, and X. R. Zhang, “Wavelength-dependent nonlinear absorption of gold nanobipyramids with large saturable modulation depth,” Opt. Laser Technol. 147, 107686 (2022). [CrossRef]
27. J. Olesiak-Banska, M. Gordel, R. Kolkowski, K. Matczyszyn, and M. Samoc, “Third-Order Nonlinear Optical Properties of Colloidal Gold Nanorods,” J. Phys. Chem. C 116(25), 13731–13737 (2012). [CrossRef]
28. T. Cesca, P. Calvelli, G. Battaglin, P. Mazzoldi, and G. Mattei, “Local-field enhancement effect on the nonlinear optical response of gold-silver nanoplanets,” Opt. Express 20(4), 4537–4547 (2012). [CrossRef]
29. N. T. C. Oliveira, A. S. Reyna, E. H. L. Falcao, and C. B. de Araujo, “Light Scattering, Absorption, and Refraction due to High-Order Optical Nonlinearities in Colloidal Gold Nanorods,” J. Phys. Chem. C 123(20), 12997–13008 (2019). [CrossRef]
30. A. Lombardi, M. Loumaigne, A. Crut, P. Maioli, N. Del Fatti, F. Vallee, M. Spuch-Calvar, J. Burgin, J. Majimel, and M. Treguer-Delapierre, “Surface Plasmon Resonance Properties of Single Elongated Nanoobjects: Gold Nanobipyramids and Nanorods,” Langmuir 28(24), 9027–9033 (2012). [CrossRef]
31. N. E. Christensen and B. O. Seraphin, “Relativistic Band Calculation and the Optical Properties of Gold,” Phys. Rev. B 4(10), 3321–3344 (1971). [CrossRef]
32. K. Imura, T. Nagahara, and H. Okamoto, “Near-Field Two-Photon-Induced Photoluminescence from Single Gold Nanorods and Imaging of Plasmon Modes,” J. Phys. Chem. B 109(27), 13214–13220 (2005). [CrossRef]
33. 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]
34. Y. Tsutsui, T. Hayakawa, G. Kawamura, and M. Nogami, “Tuned longitudinal surface plasmon resonance and third-order nonlinear optical properties of gold nanorods,” Nanotechnology 22(27), 275203 (2011). [CrossRef]
35. Y. Fu, R. A. Ganeev, P. S. Krishnendu, C. Y. Zhou, K. S. Rao, and C. L. Guo, “Size-dependent off-resonant nonlinear optical properties of gold nanoparticles and demonstration of efficient optical limiting,” Opt. Mater. Express 9(3), 976–991 (2019). [CrossRef]
36. Y. H. Lee, Y. L. Yan, L. Polavarapu, and Q. H. Xu, “Nonlinear optical switching behavior of Au nanocubes and nano-octahedra investigated by femtosecond Z-scan measurements,” Appl. Phys. Lett. 95(2), 023105 (2009). [CrossRef]
37. S. D. G. Mariano, N. A. M. Saraiva, J. C. S. Costa, C. A. Sousa, N. J. B. Silva, H. A. Garcia, and F. E. P. Santos, “Nonressonant nonlinear optical switching behavior of Ag monometallic and Ag@Au bimetallic investigated by femtosecond Z-Scan measurements,” Opt. Laser Technol. 142, 107247 (2021). [CrossRef]
38. J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. R. Mu, Y. S. Wang, J. Yuan, P. F. Li, S. Thakur, M. Ashrafi, K. McCoubrey, Y. P. Zhang, S. J. Li, H. Zhang, and Q. L. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016). [CrossRef]
39. S. Q. Li, Z. Kang, N. Li, H. Jia, M. Y. Liu, J. X. Liu, N. N. Zhou, W. P. Qin, and G. S. Qin, “Gold nanowires with surface plasmon resonance as saturable absorbers for passively Q-switched fiber lasers at 2 mu m,” Opt. Mater. Express 9(5), 2406–2414 (2019). [CrossRef]
40. Z. Wang, H. Mu, J. Yuan, C. Zhao, Q. Bao, and H. Zhang, “Graphene-Bi2Te3 Heterostructure as Broadband Saturable Absorber for Ultra-Short Pulse Generation in Er-Doped and Yb-Doped Fiber Lasers,” IEEE J. Select. Topics Quantum Electron. 23(1), 195–199 (2017). [CrossRef]
41. Z. Kang, X. Guo, Z. Jia, Y. Xu, L. Liu, D. Zhao, G. Qin, and W. Qin, “Gold nanorods as saturable absorbers for all-fiber passively Q-switched erbium-doped fiber laser,” Opt. Mater. Express 3(11), 1986–1991 (2013). [CrossRef]
42. Z. Kang, M. Y. Liu, Z. W. Li, S. Q. Li, Z. X. Jia, C. Z. Liu, W. P. Qin, and G. S. Qin, “Passively Q-switched erbium doped fiber laser using a gold nanostars based saturable absorber,” Photonics Res. 6(6), 549–553 (2018). [CrossRef]
43. C. Zhang, D. Wang, S. Huang, J. Yang, J. Liu, and J. Fang, “Nonlinear Optical Response of Gold Nanobipyramids for a Doubly Q-Switched Ho-Doped Laser at a Wavelength of 2.1 mu m,” Nanomaterials 11(2), 535 (2021). [CrossRef]
44. Z. Kang, X. Gao, L. Zhang, Y. Feng, G. Qin, and W. Qin, “Passively mode-locked fiber lasers at 1039 and 1560 nm based on a common gold nanorod saturable absorber,” Opt. Mater. Express 5(4), 794–801 (2015). [CrossRef]
45. Q. Li, C. Wei, H. Chi, L. Zhou, H. Zhang, H. Huang, and Y. Liu, “Au nanocages saturable absorber for 3-mu m mid-infrared pulsed fiber laser with a wide wavelength tuning range,” Opt. Express 27(21), 30350–30359 (2019). [CrossRef]
46. G. V. Hartland, “Measurements of the material properties of metal nanoparticles by time-resolved spectroscopy,” Phys. Chem. Chem. Phys. 6(23), 5263–5274 (2004). [CrossRef]
47. P. K. Jain, W. Qian, and M. A. El-Sayed, “Ultrafast electron relaxation dynamics in coupled metal nanoparticles in aggregates,” J. Phys. Chem. B 110(1), 136–142 (2006). [CrossRef]
48. M. Hu, H. Petrova, J. Y. Chen, J. M. McLellan, A. R. Siekkinen, M. Marquez, X. D. Li, Y. N. Xia, and G. V. Hartland, “Ultrafast laser studies of the photothermal properties of gold nanocages,” J. Phys. Chem. B 110(4), 1520–1524 (2006). [CrossRef]
49. M. Hu, X. Wang, G. V. Hartland, P. Mulvaney, J. P. Juste, and J. E. Sader, “Vibrational response of nanorods to ultrafast laser induced heating: Theoretical and experimental analysis,” J. Am. Chem. Soc. 125(48), 14925–14933 (2003). [CrossRef]
50. G. V. Hartland, “Coherent vibrational motion in metal particles: Determination of the vibrational amplitude and excitation mechanism,” J. Chem. Phys. 116(18), 8048–8055 (2002). [CrossRef]
