Wavelength-dependent nonlinear absorption and ultrafast dynamics process of Au triangular nanoprisms

Shuang Chen; Ruipeng Niu; Wenzhi Wu; Degui Kong; Yachen Gao

doi:10.1364/OE.27.018146

1. Introduction

Over the past decades, noble metal nanoparticles have attracted much attention because their surface plasma resonance (SPR) is in the visible region. The SPR results from collective oscillations of the free electrons in metal when interacting with electromagnetic fields. The effect causes metal nanoparticles to have enhanced nonlinearity and fast response [1,2]. Thus metal nanoparticles may be used in many applications such as all-optical ultrafast switching [3], biological sensors [4,5], catalytic agents and medicine [6–8]. The most widely studied metal nanoparticles are nanospheres and nanorods [9–14]. With the rapid development of nanometer preparation technology, nanoparticles with different shapes, such as triangular nanoparticles [15], nanostars [11], and nanocages have also been prepared [16]. Among them, the triangular nanoparticles can greatly limit the electric field around its tips, which causes a large enhancement of electric field [17,18] and enhanced optical non-linearity [19]. The triangular nanoprisms are promising materials for surface enhanced Raman scattering structures and nanoantennas [20,21]. Until now, nonlinear optical absorption and photo-dynamics of Au triangular nanoprisms have been rarely reported [22,23]. Li et al. investigated nonlinear optical properties of Au triangular nanoprisms with femtosecond Z-scan experiments at wavelengths of 800 nm and 1240 nm. They found that the third order optical polarizability at 1240 nm is 19 times higher than that at 800 nm. They also studied optical response time of Au triangular nanoprisms with the optical Kerr effect technique at a wavelength of 800 nm. The results show that the ultrafast light response time is about 482 fs [22]. Chen et al. investigated nonlinear optical properties of Au triangular nanoprisms with femtosecond Z-scan experiments at wavelengths of 1100-1300 nm. They found that the nonlinear refractive index is sensitively dependent on the excitation wavelength and the value is the largest at resonant absorption peak, but the nonlinear absorption coefficient varies little with the wavelength [23]. In fact, nonlinear optical properties is strongly pulse width-dependent and wavelength-dependent. However, the research of Au triangular nanoprisms above was conducted only with femtosecond laser near the infrared band (800-1300nm). Therefore, it is necessary to study nonlinear absorption further under laser pulse with other wavelengths and pulse-widths. Moreover, we investigate the ultrafast dynamics process of Au triangular nanoprisms with femtosecond transient absorption measurements.

2. Sample and experiments

The Au triangular nanoprisms investigated in our experiments were obtained from Nanjing XFNANO Materials Tech Co. Ltd. The Au triangular nanoprisms were examined by scanning electron microscopy (SEM). Linear optical absorption measurements were taken with an ultraviolet−visible (UV−vis) spectrophotometer.

The nonlinear absorption was studied using the typical open-aperture Z-scan technique [24,25]. For Z-scan measurements, a nanosecond Nd:YAG laser (6 ns pulse duration operated at 10 Hz) and an optical parametric oscillator (OPO, Continuum, APE OPO) were used to produce laser pulse with tunable wavelength. The spatial distribution of the pulse is nearly a Gaussian profile. The laser pulses were focused on a 2mm quartz cuvette containing the Au triangular nanoprisms water dispersion. The linear transmittance of the sample is 55% at 550 nm. The sample was mounted on a translation stage so that it could move precisely as it passes through the focus area of the laser beam. The incident and transmitted laser pulses for each z point were recorded by a computer.

In order to evaluate the response time of nonlinearity, the ultrafast dynamics process was also studied using femtosecond time-resolved transient absorption spectra. Details of the spectrometer configuration and the data acquisition procedure can be found elsewhere [26–28]. Transient absorption measurement was performed using mode-locked Ti:Sapphire laser (Mira 900, Coherent) with a frequency of 1 kHz and output 130 fs laser pulse. The output of the laser was split into two beams. The main part of the output passed through a 1mm thick BBO crystal, and the generated 400 nm wavelength pulses were used as the pump beam. The other beam through the delay system passed through a 2 mm thick Ti: sapphire plate to produce supercontinuum white light (450 nm-755 nm) used as the probe beam. After transmitting the probe pulse through the sample, the signal was incident on a monochromator, and detected by a Si photodetector. The output signal of the photodetector was input into the Lock-in amplifier. After the Lock-in processing the signal was input to the computer for direct observation.

3. Result and discussion

The SEM image of Au triangular nanoprisms is shown in Fig. 1(a). It can be seen that the edge-length and thickness of Au triangular nanoprisms are about 120 nm and 10 nm, respectively. The linear absorption spectra of Au triangular nanoprisms is presented in Fig. 1(b). It is obvious that Au triangular nanoprisms exhibit two absorption peaks at 530 nm and 700 nm. The Peak at around 530 nm is assigned to the SPR of Au spherical nanoparticles and the out-of-plane resonance of Au triangular nanoprisms; the other at approximately 700 nm is caused by the plasmon mode of Au triangular nanoprisms [29].

Fig. 1 (a) SEM image of Au triangular nanoprisms, (b) linear absorption spectra of Au triangular nanoprisms.

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Open-aperture nanosecond Z-scan measurements were conducted to investigate the nonlinear absorption of Au triangular nanoprisms. In the experiment, a low repetition rate of 10Hz is chosen, thus the thermal effect can be ignored [30,31]. The input wavelengths were tuned to cover a broadband range from 550 nm to 700 nm. A fixed laser energy of 300 μJ and 600 μJ (irradiance at focus of 3.6 $\times$ 10¹³ W/m² and 7.2 $\times$ 10¹³ W/m²) was applied for Z-scan measurements. In Figs. 2(a) and 2(b) we present four representative results at wavelengths of 550 nm, 600 nm, 650 nm and 700 nm.

Fig. 2 Normalized transmission of Au triangular nanoprisms position for open aperture Z-scan at different wavelengths (550 nm, 600 nm, 650 nm and 700 nm). (a) laser energy of 300 μJ (irradiance at focus of 3.6 $\times$ 10¹³ W/m²), (b) laser energy of 600 μJ (irradiance at focus of 7.2 $\times$ 10¹³ W/m²). The dots are experimental data while the solid lines are theoretical fit.

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When excitation energies is low (300 μJ), as shown in Fig. 2(a), the normalized transmittance of Au triangular nanoprisms at four different wavelengths increases gradually when it comes towards focal point (z = 0), indicating that the sample shows SA. Specifically, at 600 nm, the transmittance of sample at focal point is the smallest, and at 700 nm the transmittance is the largest. While at 550 nm and 650 nm, the magnitude of normalized transmittance of Au triangular nanoprisms is smaller than that at 700 nm and larger than that at 600 nm.

As shown in Fig. 2(b), under relatively higher intensities (600 μJ), as the sample moves towards beam focal point, the transmission increases correspondingly, indicating SA, and the magnitude of SA is the same as that in Fig. 2(a). However, when the sample moves further to the focal point, the transmittance of sample begins to decrease, which implies that the transformation from SA to RSA occurs. It can be seen that the behavior of SA and RSA in the nonlinear absorption of Au triangular nanoprisms coexist [9]. Specifically, at 600 nm, magnitude of RSA is the largest, and at 700 nm is the smallest. While at 550 nm and 650 nm, the magnitude of RSA is smaller than that at 600 nm and larger than that at 700 nm.

The mechanism can be visualized as follows. The SA and RSA are related to the interplay of plasmon band bleaching and free-carrier absorption [32]. When irradiance is moderate, the bleaching of ground-state plasmon band resulting in SA occurs. As laser energy increases further, free-carrier absorption resulting in RSA dominates [33]. We think that the difference of SA and RSA at different wavelengths results from SPR of Au triangular nanoprisms. In Fig. 1(b), there are two SPR peaks at about 530 nm and 700 nm, and the latter is stronger than the former, which makes a stronger SA at 700 nm than that at 650 nm and 550 nm, and a weaker RSA at 700 nm than that at 650 nm and 550 nm. In the case of 600 nm far from two SPR wavelengths (530 nm and 700 nm), it is the non-resonance that makes the sample exhibit the weakest SA and strongest RSA.

When there is only two-photon absorption in open-aperture Z-scan experiment, the normalized transmittance is [24]:

T (z) = \sum_{m = 0}^{\infty} \frac{{[\frac{- β I_{0} L_{e f f}}{(1 + z^{2} / z_{0}^{2})}]}^{m}}{{(m + 1)}^{3 / 2}}

Where

L_{e f f} = (1 - e^{- α_{0} l}) / α_{0}

,

L_{e f f}

is the effective interaction length,

α_{0}

is the linear absorption coefficient,

β

is the nonlinear absorption coefficient,

I_{0}

is the peak intensity at the focus,

z

is the displacement of the sample from the focus (

z = 0

). L is the sample length,

z_{0}

is the Rayleigh rang. In general, numerical simulations require only the first few terms when

| β I_{0} L_{e f f} |

is compered to one. Therefore,

β

can be determined by fitting Eq. (1) with experimental results.

In order to explain the transformation from SA to RSA, we define a nonlinear absorption coefficient as follows [34]:

α (I) = \frac{α_{0}}{1 + (I / I_{s})} + β I

The first term describes SA, and the second describes RSA. $α_{0}$ is the linear absorption coefficient of the material, $I$ is the laser intensity, $I_{s}$ is the saturation intensity, $β$ is the positive nonlinear absorption coefficient. As we know that can be expressed as:

I = \frac{I_{0}}{1 + z^{2} / z_{0}^{2}}

So Eq. (2) can be denoted further as:

α (I_{0}) = \frac{α_{0}}{1 + \frac{I_{0}}{(1 + z^{2} / z_{0}^{2}) I_{s}}} + \frac{β I_{0}}{1 + z^{2} / z_{0}^{2}}

Thus, a theoretical fit to the experimental data could be conducted by replacing $β I / (1 + z^{2} / z_{0}^{2})$ in Eq. (1) by Eq. (4). The dots in Fig. 2 are experimental data while the solid lines are theoretical fit. We can find that the theoretical fit agrees well with the experimental results. As shown in Table 1, the saturation strength $I_{s}$ and nonlinear absorption coefficient $β$ can be obtained by theoretical fit.

Table 1. Nonlinear Optical Parameters of Au triangular nanoprisms

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In Fig. 3, in order to reflect intuitively the dependence of nonlinear absorption on wavelength and SPR (as seen in Table 1), we used dotted lines for the saturation strength $I_{s}$ , nonlinear absorption coefficient $β$ vs. wavelength. For comparison, linear absorption was also provided in Fig. 3 with solid lines. In Figs. 3(a) and 3(b), it can be seen that the saturation strength of the Au triangular nanoprisms increases obviously when the excitation wavelength is close to SPR peak. While in Fig. 3(c), we can find that the nonlinear absorption coefficient increases when the excitation wavelength is away from SPR peak. We think the increase of saturation strength near SPR wavelength arises from the resonant enhancement of nonlinear properties [1,2]. When irradiance is moderate, the bleaching of ground-state plasmon band results in SA. Moreover, when the excitation wavelength is different, the number of Au triangular nanoprisms pumped to the conduction band is different. When excitation wavelength is near SPR, more Au triangular nanoprisms will be pumped to the conduction band, and the ground state absorption of the sample decreases, resulting in the increase of saturation strength near SPR wavelength. The same phenomenon has also been found in the nonlinear measurement of gold nanorods [35]. The increase of nonlinear absorption coefficient away from SPR is due to the enhanced free carrier absorption.

Fig. 3 The dotted lines are theoretical fit Saturation strength $I_{s}$ and nonlinear absorption coefficient $β$ of Au triangular nanoprisms vs. wavelength. (a) 3.6 $\times$ 10¹³ W/m² ( $I_{0}$ ), (b) 7.2 $\times$ 10¹³ W/m² ( $I_{0}$ ) and (c) 7.2 $\times$ 10¹³ W/m² ( $I_{0}$ ). The solid lines are the linear absorption spectra.

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Femtosecond transient absorption spectra performed using 190 fs pump pulse at a wavelength of 400 nm with power of 9 mw were presented in Figs. 4(a) and 4(b) using contour plot and surface plot. Several representative transient absorption spectra at different delay times were given in Fig. 4(c). Among them, the signal at −0.2 ps is the reference signal when the sample has not been excited. In Fig. 4(c), we find that there are three peaks at about 485 nm, 590 nm and 745 nm which corresponding to photo-induced absorption signal. Besides, there are two valleys at about 530 nm and 700 nm which are referred to as the bleaching of plasma signal, and the related phenomenon is observed as SA in Z-scan [36,37]. Both signals decrease rapidly with the delay time, indicating that the dynamics process is ultrafast. The maximum of the bleach signal is at the wavelengths of 530 nm and 700 nm, corresponding to two surface plasmon absorption peaks [37].

Figures 4 (a) and (b) Time and wavelength resolved transient absorption data of Au triangular nanoprisms. (c) Transient absorption spectra for Au triangular nanoprisms at different delay times. (d) Dynamic traces of Au triangular nanoprisms at two wavelengths 530 nm and 700 nm, respectively (The dots are experimental data while the solid lines are theoretical fit generated).

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As shown in Fig. 4(d), normalized dynamics curves at two resonant peaks (530 nm, 700 nm) were extracted from the contour plot shown in Fig. 4(a), which is very similar for both signals. In Fig. 4(d), curves show rapid descent and decay processes. The rapid descent process is due to the ground state plasma bleaching of the system, which is also called electron-electron scattering (time-scale of a few hundred fs) [38,39]. Because of the limited time resolution of our laser system, the process cannot be accurately determined. The decay includes a fast process and a slow one. The former results from the balance of excited electrons with the nanoparticle lattice through electron–phonon interaction. The latter (subsequent slower decay) is ascribed to phonon–phonon interaction with the surrounding medium. In general, the two-temperature model (TTM) can be used to describe the process if only one decay occurs. However, in the current experiments, because there are two decay components we used double-exponential functions shown in Eq. (5) to fit the photodynamic curves.

\frac{Δ T}{T} = A_{1} \exp (- \frac{t}{τ_{1}}) + A_{2} \exp (- \frac{t}{τ_{2}})

Where $A_{1}$ , $A_{2}$ are the amplitudes of two decay components, and $τ_{1}$ and $τ_{2}$ represent time constants of the two decay components, respectively. The fitting to the experimental data is shown in Fig. 4d. From the fitting, we obtained an initial fast relaxation time of 4.3 ps and a slow relaxation time of 317 ps. In the case of Au triangular nanoprisms, the ultrafast response is different from corresponding Au nanospheres, which results from different SPR depending on shape. In fact, we have found that the relaxation times in Au triangular nanoprisms is longer than that reported in Au nanospheres ( $τ_{1}$ = 2.5 ps, $τ_{2}$ = 50 ps) because Au triangular nanoprisms have higher initial temperatures of hot electrons [40,41].

In order to study the influence of pump laser intensity on dynamics process of Au triangular nanoprisms, femtosecond transient absorption measures at 530 nm and 700 nm were also performed at different pump powers of 2 mw, 5 mw, 8 mw and 11 mw. Figures 5(a) and 5(b) show the experimental results of transient absorption. Under different pump powers, Au triangular nanoprisms have different dynamic traces. In Figs. 5(a) and 5(b) using solid lines, the experimental data were fit via Eq. (5). Correspondingly, the fast and slow decay times obtained are shown in Table. 2. The inset shows a plot of electron-phonon coupling time as a function of pump laser power. It can be seen that Au triangular nanoprisms have the same electron-phonon coupling time at two resonant peaks (530 nm, 700 nm). While the decay time is intensity-dependent, and increases obviously with the laser intensity. This is because the electron exchanges energy with phonon sub-systems in a way that is related to their temperature differences [42,43]. The higher the energy, the more electrons are in the higher electronic states, and the longer the time required for electrons to transfer energy to the phonons.

Fig. 5 (a) and (b). Normalized dynamics curves for Au triangular nanoprisms at different pump fluencies at two resonant peaks, respectively (The dots are experimental data while the solid lines are theoretical fit generated). The insert shows the decay constant versus ( $τ_{1}$ ) change plotted as a function of pump laser power.

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Table 2. Fitting results for the decay processes for Au triangular nanoprisms at different powers.

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We also extracted dynamics curves at a non-resonant wavelength of 547 nm from the contour plot shown in Fig. 4(a). As seen in Fig. 6, we found that the dynamics curves show the modulation response on the basis of exponential decay. The phenomenon can be analyzed as follows. After ultrafast excitation, energy flows out of the electrons and enters the lattice within a few picoseconds, causing a rise in the lattice temperature, resulting in a small amount of expansion. The heating time is faster than the vibration mode period associated with the expansion coordinate, so it can coherently excite the modes of the particles, which produces modulations in transient absorption traces [44,45].

Fig. 6 Dynamic traces of Au triangular nanoprisms at 547 nm (The dashed line is experimental data while the solid line is theoretical fit generated). The inset shows a plot of vibrational frequencies, which is obtained by Fourier transforming the modulated portion of the data.

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The transient absorption traces is fitted using a damped cosine function plus an exponential decaying background as [46]:

S (t) = A \cos (\frac{2 π t}{T} + φ) e^{- \frac{t}{τ_{v}}} + A_{1} e^{- \frac{t}{τ_{1}}} + A_{2} e^{- \frac{t}{τ_{2}}} + B

Where $T$ is the vibrational period, $φ$ is the phase for the vibration, and $τ_{v}$ is the vibrational damping time. Where $A_{1}$ , $A_{2}$ are the amplitudes of two decay components, $τ_{1}$ and $τ_{2}$ represent time constants of the two decay components, respectively. The fitting to the experimental data is shown in Fig. 6. The vibrational period obtained for this trace was 17.5 ps. As shown in the inset of Fig. 6, by Fourier transforming the modulated portion of the data in Fig. 6, vibrational frequencies can be determined to be approximately 57 GHz, which is almost the same as that measured in silver nanocubes nanoparticles [47,48]. The electron–phonon coupling and heat dissipation investigation are very important for the application of thermally or electrically conductive particles. At the same time, the Elastic moduli studies provide basic information about the properties of nanomaterials [41].

4. Conclusion

In summary, we have investigated the nonlinear absorption of Au triangular nanoprisms. The results show that the nonlinear absorption of Au triangular nanoprisms is sensitively wavelength-dependent and intensity-dependent. In addition, we have investigated the ultrafast dynamics process of Au triangular nanoprisms. We found that the relaxation process contains an initial fast decay with time constant of 4.3 ps and a slow decay with time constant of 317 ps, and the decay depends strongly on the laser intensity. When probe wavelength is away from the plasma resonance peak, the decay of relaxation also shows a modulation due to the vibration mode of the coherent excitation. The vibrational frequencies were approximately 57 GHz. These nonlinear optical properties of the Au triangular nanoprisms are indicative of the feasibility of their application in ultrafast optoelectronics.

Funding

Heilongjiang Province Natural Science Fund (F2018027)

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$P$ (mw)	$τ_{1}$ (ps)	$τ_{2}$ (ps)
2	1.853	298
5	2.857	262.5
8	4	309.3
11	4.805	307

$P$ (mw)	$τ_{1}$ (ps)	$τ_{2}$ (ps)
2	1.853	298
5	2.857	262.5
8	4	309.3
11	4.805	307

Wavelength-dependent nonlinear absorption and ultrafast dynamics process of Au triangular nanoprisms

Abstract

1. Introduction

2. Sample and experiments

3. Result and discussion

4. Conclusion

Funding

References

Cited By

Figures (6)

Tables (2)

Equations (6)

Optics Express

$λ$ (nm)	$I_{0}$ (W/m²)	$I_{s}$ (W/m²)	$β$ (m/W)
550	3.6 $\times$ 10¹³	1.5 $\times$ 10¹²	0
550	7.2 $\times$ 10¹³	6.2 $\times$ 10¹²	2.3 $\times$ 10⁻¹¹
600	3.6 $\times$ 10¹³	1.4 $\times$ 10¹²	0
600	7.2 $\times$ 10¹³	7.1 $\times$ 10¹²	2.6 $\times$ 10⁻¹¹
650	3.6 $\times$ 10¹³	1.9 $\times$ 10¹²	0
650	7.2 $\times$ 10¹³	6.5 $\times$ 10¹²	1.6 $\times$ 10⁻¹¹
700	3.6 $\times$ 10¹³	2.4 $\times$ 10¹²	0
700	7.2 $\times$ 10¹³	7.0 $\times$ 10¹²	1.5 $\times$ 10⁻¹¹