Broadband Spectral Signature of the Ultrafast Transient Optical

Article pubs.acs.org/JPCC

Broadband Spectral Signature of the Ultrafast Transient Optical Response of Gold Nanorods Xiaoli Wang,†,‡ Yannick Guillet,§,∥ Periasamy R. Selvakannan,⊥,# Hynd Remita,⊥ and Bruno Palpant*,† †

Laboratoire de Photonique Quantique et Moléculaire, UMR 8537, CNRS, Ecole Normale Supérieure de Cachan, CentraleSupélec, Grande Voie des Vignes, F-92295 Châtenay-Malabry Cedex, France ‡ Laboratory of Nanomaterials, National Center for Nanoscience and Technology, Beiyitiao No. 11, Zhongguancun, Beijing, 100190, P. R. China § Université de Bordeaux, I2M, UMR 5295, F-33405 Talence, France ∥ CNRS, I2M, UMR 5295, F-33405 Talence, France ⊥ Laboratoire de Chimie Physique, UMR 8000, CNRS, Bât 349, Université Paris-Sud, 91405 Orsay Cedex, France ABSTRACT: The ultrafast transient optical response of gold nanorods presents a complex spectral signature that is very sensitive to the nanoparticle aspect ratio. This stems from the different electronic contributions to the photoinduced dynamics of the metal dielectric function, which modify the transverse and longitudinal localized plasmon modes. Here, we analyze the physical origins of the ultrafast optical response of ensembles of nanorods over the whole visible range. Using broadband time-resolved spectroscopy, we determine within the first picoseconds after pump excitation the transient response of colloidal solutions containing gold nanorods with different mean aspect ratios. Supported by model calculation, it is shown that the contribution of interband electron transitions dominates at ultrashort times, even for photon energies far below their threshold. At longer times, a slower intraband transition component linked with the nanoparticle heating appears. We then describe how the ensemble effect modifies the global spectral profile. The initial athermal regime for the conduction electron gas is demonstrated to affect the first instants of the dynamics. Finally, the influence of the shape distribution is experimentally evidenced and analyzed through a double selection process.

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surface-enhanced Raman scattering (SERS).11,12 While these developments rely on the optical properties of gold NRs in the stationary regime of irradiation, interesting outlooks can be envisaged from their ultrafast transient optical response under pulsed excitation. This is the case, for instance, in the nanoscale generation of plasma and cavitation13 or in high-rate photonic signal processing, where positive or negative ultrafast light modulation can be obtained depending on photon energy.14 Controlling the spectral characteristics of the transient optical response of gold NRs irradiated by ultrashort light pulses is then a relevant issue. This response is ruled by the dynamics of energy exchanges between the initial photoexcited conduction electron population, the metal lattice ions, and the surrounding medium. They modify the probability of interband and intraband transitions mainly through the modification of the electron distribution close to the Fermi level, the electron−electron and electron−phonon scattering rates.15 Several studies have been devoted to the optical relaxation dynamics of gold NRs using pump−probe techniques. They have particularly analyzed the evolution of the relaxation time with pump pulse energy16−19

INTRODUCTION Gold nanorods (NRs) have attracted much attention because of their exceptional optical properties.1 Indeed, they present two localized surface plasmon resonance (SPR) modes corresponding to the wave-driven excitation of electron oscillations parallel (longitudinal mode) and perpendicular (transverse mode) to the rod long axis. Although the transverse SPR (TrSPR) is weakly sensitive to the nanorod morphology, the longitudinal SPR (LgSPR) significantly shifts to the red as the aspect ratio R (ratio of the long and short axis lengths) increases. Its spectral location can thus be tuned from green to near-infrared. In addition, the oscillating strength associated with the LgSPR increases with R, which is mainly due to the progressive decoupling of this plasmon mode from the monoelectronic interband transitions. Energy input in a NR by irradiating at its LgSPR is then more efficient than for a sphere having the same volume. As a result of these properties, NRs are good candidates for different applications. Especially, their LgSPR can match the spectral range of maximum transparency of biological tissues (∼800 nm), allowing for their use as effective photothermal sources for therapy2,3 or as imaging agents.4,5 The anisotropic character of their optical response can also be exploited for designing dichroitic optical media 6−8 or metamaterials.9 Near-field coupling of molecules with gold NRs can be used for plasmon-enhanced fluorescence10 or © 2015 American Chemical Society

Received: January 6, 2015 Revised: March 14, 2015 Published: March 16, 2015 7416

DOI: 10.1021/acs.jpcc.5b00131 J. Phys. Chem. C 2015, 119, 7416−7427

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The Journal of Physical Chemistry C and the generation of acoustic vibrational modes.20−26 The spectral signature of the response has been addressed under different aspects. As for nanospheres, a plasmon bleaching feature (transient quenching and broadening of the plasmon absorption band) is observed at the TrSPR of NRs, which contrasts with the situation at the LgSPR. The physical analysis of the dynamics in the vicinity of the LgSPR has been reported in ref 27 for a single gold NR. It first reveals in the short time range, that is, within the first picoseconds after excitation, pump-induced absorption and transparency for photon energies lower and larger than the LgSPR one, respectively. This feature has been also found in close-packed parallel NRs experiencing nonlocal interactions.14 By varying, via the NR mean aspect ratio of different colloidal solutions, the LgSPR energy relative to the fixed probe photon one, the authors of ref 26 have also revealed the antisymmetric behavior of the response around the LgSPR. In contrast, the authors of ref 19 have reported a LgSPR bleaching in the transient response of a NR solution at very short time after excitation (1 ps). Induced transparency has also been found at photon energies higher than the LgSPR one in an ensemble of NRs with very large aspect ratio,22 but in this study lower photon energies could not be probed. At longer times, a plasmon bleaching behavior appears, linked with the rise of the metal lattice temperature.14,16,27 Let us note that in ref 26 a reversible switch from photoinduced transparency to photoinduced absorption is demonstrated when increasing probe beam intensity, which is ascribed to the rising involvement of a two-photon absorption process. Only a few papers report the variation of the NR aspect ratio as to modify the LgSPR location. In ref 16 it is shown that the relaxation characteristics close to the TrSPR does not vary with NR shape, but the LgSPR domain is not probed. In ref 26, the probe wavelength is fixed which prevents analysis of the transient spectrum modification with NR shape. Hence, there is a lack of results regarding the spectral signature of the NR optical relaxation dynamics over the whole visible range and its variation with NR aspect ratio. The link between the pump-induced change of the dielectric function, Δε, and the transient optical signal is not straightforward. Indeed, the spectral variations of Δε are amplified in a complex way by the plasmon resonance activated by the probe pulse.28 However, we can extract general trends, following the work of Baida et al.27 Measuring the transient absorption of a single nanorod with R = 3.6 over a spectral range of ±40 nm around the LgSPR, they have analyzed the signal by expanding the differential absorption as the sum of the contributions of the real (Δε1) and imaginary (Δε2) components of Δε. Briefly, they show that the dynamics of the absorption cross section is governed by the dynamics of Δε1 at short times, while after reaching electron−phonon equilibrium it is ruled by Δε2 which is dominated by the intraband contribution stemming from the variation of the electron−phonon collision rate, ΔΓe−ph. Our objective here is to interpret the spectral signature of the transient optical response of NR solutions at short times over the whole visible range and for different mean NR aspect ratios, to examine separately the role of the different physical phenomena involved, and to point out the influence of the ensemble effect (that is, of the distribution of the NR aspect ratios). For this, both numerical simulations and pump−probe experiments have been performed. The broadband spectroscopy technique that we use allows us to get valuable information regarding the spectral dependence of the transient signal over the whole

visible range. It is then complementary to monochromatic techniques which are more sensitive but impose work with only one probe photon energy at each run, which makes the data interpretation much more complex as soon as the response evolves in the spectrum with time.17,22

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MATERIALS AND METHODS Nanorod Synthesis and Characterization. Gold NRs have been synthesized in solution by radiolysis using a one-pot method. The detailed methodology was described in a previous paper.29 Shortly, AuIII complexes are reduced in a micellar template formed by a mixture of cationic surfactants (cetyltrimethylammonium bromide and tetraoctylammonium bromide) and in the presence of acetone and silver ions. Cyclohexane is used to swell the micelles. Water radiolysis induces the formation of solvated electrons and H• and OH• radicals. The solutions are irradiated under N2 atmosphere in glass vessels with a rubber plastic septum. The γ-irradiation source is a 60Co γ-facility of 7000 Ci with a dose rate of 2.7 kGy h−1. The gold ions are slowly reduced by H• and by the alcohol radicals (CH3)2C•OH formed by the reaction of solvated electron (generated by the water irradiation) and acetone. The irradiated solution contains 0.082 M CTAB, 7.5 × 10−4 M TOAB, 1.9 × 10−3 M HAuCl4, 0.139 M cyclohexane, 0.266 M acetone, and different amounts of AgNO3: 4 × 10−5, 6 × 10−5, 1.0 × 10−4 M. The total irradiation dose is 32.2 kGy. The nanorod aspect ratio is increased by increasing the initial silver amount. In the present work, three solutions NR1, NR2, and NR3 have been studied, consisting of assemblies of gold NRs with different mean aspect ratios. The NRs contained in the colloidal solutions have been observed by transmission electron microscopy (TEM; see ref 29). The mean aspect ratios deduced from TEM are 1.7 ± 0.6 (NR1), 2.0 ± 1.0 (NR2), and 2.5 ± 0.6 (NR3), while their transverse diameters are 15 ± 1, 13 ± 2, and 12 ± 1 nm, respectively, and their lengths are 25 ± 6, 26 ± 8, and 30 ± 4 nm, respectively. The optical absorption spectra of the samples have been recorded with a Varian CARY 5 spectrophotometer and are displayed on Figure 1. In order to facilitate the comparison of the respective plasmon bands and as the metal volume fraction is not the same in the three solutions, the spectra have been normalized by the absorbance value at 3.1 eV (400 nm) to account for the quantity of gold probed by the light beam (indeed, absorption in this spectral range stems from interband transitions only and is then proportional to the amount of metal). The longitudinal and transverse plasmon resonance bands can be clearly identified on the spectra at longer and shorter wavelengths, respectively. It can be seen that, as expected, the longitudinal plasmon (LgSPR) maximum shifts to the red and its magnitude increases as the aspect ratio increases, while the transverse plasmon (TrSPR) experiences a very slight opposite trend. For samples NR1, NR2, and NR3 the apparent LgSPR energies (respectively wavelengths) are ELgSPR of 2.13 eV (λLgSPR = 584 nm), 2.01 eV (λLgSPR = 618 nm), and 1.87 eV (λLgSPR = 663 nm), respectively. Note that the actual individual plasmon energies might be slightly shifted relative to these values owing to the overlap of TrSPR and LgSPR bands, especially for NR1. The optical response of the nanorods has been simulated by using the discrete dipole approximation (DDA). We have calculated the absorption spectra of the nanorods in the three samples. For this, the code DDSCAT developed by Draine and Flatau has been used in the case of gold NRs with a random 7417


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The Journal of Physical Chemistry C

Figure 1. Optical absorbance of samples NR1 (blue), NR2 (green), and NR3 (red), normalized at 3.10 eV (400 nm) in order to compare the curves for the same metal volume fraction.

Figure 2. Absorbance spectra of solution NR3 (black thick line, left scale) and absorption cross section of virtual samples C (thin black) and D (dashed red) with NR aspect ratios R of 2.50 and 3.75, respectively (right scale). Vertical lines denote the spectral location of the two pump photon energies used in the experiments. Open dots emphasize the optical absorption of the different virtual samples at these energies.

field polarization.30,31 The actual shape of the NRs has been shown to have a significant influence on their optical properties.31,32 After examination of high-resolution TEM images of our samples (see Figure 4 of ref 29), hemispherecapped gold cylinders have been chosen for the simulation. Their diameter has been set at 10 nm whatever the sample, as its influence on the optical properties has been shown to be negligible within our range.31 Interactions between nanorods, which may strongly affect their optical response,33 are disregarded here as the colloidal solutions are sufficiently diluted (about 1 mM gold concentration). As the environment of the rods is similar to the one reported by Mulvaney et al. in ref 34, that is, CTAB-coated gold nanorods in an aqueous solution, the dielectric constant of the surrounding medium has been set to the value they used, εm = 2.025. The number of dipoles per nanorod, about N = 50 000, has been chosen as to ensure the stability of the numerical solution, which has been checked: increasing N results in negligible modifications of the absorption spectrum compared with the ones induced by the pump pulses in our calculation of the transient optical response. The aspect ratio R has been evaluated so that the LgSPR maximum wavelength simulated by the DDA roughly matches the experimental one for each sample. The three virtual samples are then designated by A, B, and C, corresponding to NR1, NR2, and NR3, respectively. The result is shown in Figure 2 for sample NR3. It can be seen that the simulated LgSPR band (C) is much narrower than the measured one, with particularly an absorption tail at small photon energies in the former case. In addition, the ratio of the LgSPR and TrSPR band magnitudes is smaller in the experiment than predicted by the DDA. This stems from the nanorod length distribution in the colloidal solution:29 as the LgSPR band spectral location is very sensitive to the particle aspect ratio,31,35 whereas the TrSPR one is not, the former is inhomogeneously broadened. Furthermore, as the absorption cross section of a particle associated with the LgSPR increases with both its volume and its aspect ratio within our size range, the presence among the particle assembly of a small proportion of nanorods being longer than the average can nevertheless

contribute to the global absorption, which explains the tail of the absorption curve in its red part. This is exemplified in Figure 2 where the absorption cross section of a long nanorod D (R = 3.75) having a LgSPR maximum at 1.55 eV is plotted. One can then define an effective “optical mean aspect ratio”, ⟨Ropt⟩, as for the mean radius in a nanosphere assembly with size distribution.36 It corresponds to the nanorod R value for which the LgSPR maximum coincides with the one of the experimental global distribution. ⟨Ropt⟩ is then worth 1.70, 2.05, and 2.50 for samples NR1, NR2, and NR3, respectively. These values are in excellent agreement with the ones extrapolated from the results of Link et al.37,38 with our λLgSPR values. Moreover, they match very well the experimental ones derived from TEM images. This is not surprising; whereas the aspect ratio distribution significantly influences the width of the LgSPR band, it has only a slight effect on its spectral location within our R range (see Figure 4 of ref 31). Measurement and Simulation of the Nanorod Ultrafast Transient Optical Response. Broadband Pump−Probe Spectroscopy Experiments. Pump−probe spectroscopy was used to determine the experimental differential absorption spectra of the three samples. The laser beam is supplied by an amplified laser source (Hurricane, Spectra Physics) and consists of 130 fs pulses at 800 nm wavelength and 5 kHz repetition rate. It is then split into two parts by a beam sampler. The main part is used as the pump beam after passing in an optical parametric amplifier (Topas, Light Conversion) which enables tuning of the wavelength over a large spectrum. The remaining weak part is converted into a white-light supercontinuum (1.65−2.82 eV, i.e., 440−750 nm) after focusing in a sapphire crystal and constitutes the probe beam. The pump−probe delay control is ensured by a retroreflector mirror mounted on a high-precision mechanical translation stage (Aerotech) and set on the probe path. An imaging spectrometer (Triax 180, Horiba Jobin-Yvon) allows measuring simultaneously the fluxes of both the probe beam transmitted by the sample and a reference beam used to free from laser energy fluctuations. Detection is operated by a chilled charge-coupled device (CCD) camera (Andor). Pump and probe field polarizations 7418


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The Journal of Physical Chemistry C are linear and perpendicular to each other. This setup enables us to measure with only one acquisition the transient absorption over a broad spectral range with a sensitivity of ∼0.1%. The quantity that is measured is the differential transmittance of the sample, ΔT/T. Neglecting the changes in reflectance, we can write ΔT/T = −ΔA, where A is the sample absorbance, following Beer−Lambert’s law. As the sample thickness is fixed and the colloidal solutions are sufficiently diluted, ΔA is directly proportional to the change in nanorod extinction cross section, Δσ, which is dominated by the change in absorption as the contribution of light scattering is negligible because of small NR size. Experiments were carried out with a pump photon energy set to 2.25 eV (550 nm). This choice will be explained in another section below. The peak intensities were set to 2.1, 2.6, and 3.0 GW cm−2 for NR1, NR2 and NR3, respectively, in order to roughly compensate for the variation of the mean absorption cross section revealed in Figure 2 as to inject the same energy density in all NRs. Transient absorption for sample NR3 has additionally been measured by pumping at 1.55 eV (800 nm) with 46 GW cm−2 intensity. Figure 3 displays the dynamics of the transient absorption spectra of samples NR1 to NR3 pumped at 2.25 eV. In order to compare the spectral signature of the transient optical response of the different nanorod solutions, the data have been normalized to −1 at signal minimum. The noise around 2.25 eV remaining at long pump−probe delays is due to the pump diffusion by the sample which cannot be totally eliminated in our experiment. The vertical arrows denote the position of the TrSPR and LgSPR in the stationary regime. Our measurement technique enables us to reveal the spectral evolution of the transient response. With monochromatic probe techniques, the transient profile is sometimes difficult to interpret22 whereas it appears more clearly when adding the spectral information. Hence, photoinduced absorption and transparency are alternately observed along the spectral domain of measurement. This is due to the modification of the dielectric function of gold amplified by the local field enhancement at the SPR.27,28,39 The features observed then result from the superimposition of the profiles associated with the two NR plasmon modes. As the color level chart representation can induce some artifacts in the interpretation, we have also plotted the differential absorption spectra at different times in Figure 4. These spectral profiles are similar to the ones measured by other groups on a given colloidal solution with one NR mean aspect ratio.14,19,22,27 For our three samples a similar transient plasmon bleaching signal can be observed in the high-energy range of the spectrum, that is, close to the TrSPR. A second feature can be detected at lower energies (successively negative and positive induced absorption) which follows the spectral location of the LgSPR. Experiencing a blue shift from its initial location at the end of the pump pulse, the photon energy at which the transient absorption changes its sign (i.e., the zero-crossing point) even reaches exactly the LgSPR peak energy (denoted by an arrow on the figures) for the three samples. Additionally, the variation of the relaxation dynamics with photon energy can be observed in Figures 3 and 4. Consequently, some features (local maxima or minima of the differential absorption) shift in the spectrum along their relaxation. This is obvious for the induced transparency peak in the blue wing of the LgSPR (at ∼2.10 and 2.07 eV for NR2 and NR3, respectively) which shifts to the blue along the relaxation, this shift being as large as the aspect ratio is high (namely, as the LgSPR energy is low). These

Figure 3. Time and spectral evolution of the normalized absorbance variation measured by pump−probe spectroscopy for the three samples. The arrows indicate the spectral locations of the TrSPR and LgSPR.

phenomena will be explained later, when discussing the influence of the athermal regime. The characteristic relaxation time has been extracted from our experimental data by monoexponential fitting of the transient signal within the delay span from 1 to 10 ps. For the three samples it ranges from ∼1 to ∼4 ps, which is in agreement with the values already reported in the literature for gold nanorods.17,22,27,40 It depends on the probe photon energy at which it is monitored. The 7419


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nanorod optical properties. Let us underline that our aim is to interpret the spectral signature of the measured dynamics over the whole visible range, by identifying the respective roles of the different mechanisms involved, rather than to reproduce the experimental results by comparing the precise magnitude of the different features in the transient response. According to Park et al.,17 the values of the peak intensity used in our experiments correspond to the upper limit of validity of the weak perturbation regime in the models, that is, for which a monoexponential decay can be associated with each of the sequential energy exchange processes. The input quantity of our model is the instantaneous power absorbed by the particle, Pabs(t), the actual time profile of which is identical to the one of the incident light pulse. The amplitude of Pabs(t) is proportional to the total energy absorbed by the particle, uabs, the value of which is given by the product of the absorption cross section of the nanorod at the pump wavelength (calculated by the DDA) and the incident light surface energy density per pulse. Of course, for a given pulse energy, the value of uabs depends on the incident field polarization relative to the nanorod main axes. The output quantity that is evaluated by our model is the absorption cross section variation, Δσ(ℏω,t), induced by the initial pump pulse. ω and t are the wave angular frequency and the delay after pump pulse maximum, respectively. As explained above, we will compare the spectral dependences of the calculated Δσ and of the experimental data, ΔA. Pump and probe fields being cross-polarized, there are three basis situations for the NR orientation in the solution: (i) pump and probe fields parallel to the NR long and short axes, respectively; (ii) pump and probe fields parallel to the NR short and long axes, respectively; (iii) both pump and probe fields parallel to the NR short axes. The longitudinal and transverse pumping, taking into account these three cases, have then been considered in the calculation of the average differential absorption cross section, corresponding to the signal that is actually measured in our pump−probe experiments on colloidal NR solutions. Let us now summarize the overall modeling procedure. The transient dielectric function of hemisphere-capped gold nanorods after ultrashort laser pulse absorption has been calculated by using the method that we used previously for nanopeanutshaped particles.39 This method is suited to describe the very first instants of the dynamics, as it accounts for the athermal distribution of the conduction electrons and disregards any thermal energy exchange with the surrounding medium. First, the dynamics of the conduction electron distribution function f(E,t), where t and E denote time and electron energy, respectively, is calculated by solving the Boltzmann equation in the weak perturbation limit and using the relaxation time approximation.41 The model will then be referred to as the Boltzmann transport equation (BTE) method. The variation of f is governed by the power input from the laser pulse absorption (source term) and the electron−electron (e−e) and the electron−phonon (e−ph) scattering processes. The source term is proportional to Pabs(t). The time evolution of f(E,t) can also be calculated in the thermal regime, that is, as soon as the electron gas reaches internal equilibrium and an electron temperature can be defined. In that case, the energy exchanges between electron gas, metal lattice, and surrounding medium are ruled by a set of classical coupled differential equations of thermodynamics, known as the three temperature model (3TM). Our approach assumes a perfect thermal contact at the interface and a purely

Figure 4. Spectral dependence of the normalized pump-induced absorbance change for the three samples at different times measured by pump−probe spectroscopy. The arrow denotes the location of the stationary LgSPR maximum.

precise analysis of these spectral variations is out of the scope of the present paper and will be presented in a forthcoming paper. Modeling of the Transient Optical Response. The transient optical response of gold nanorods after ultrashort laser pulse absorption has been simulated by using a two-step model which first evaluates the time evolution of the metal dielectric function and then calculates the subsequent time evolution of the 7420


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nanoparticles reveals these variations of ε(ω) in the absorption spectrum; this explains that while for nanospheres the transient signal lies in the vicinity of the interband transition threshold, in the case of nanorods an additional signal can be observed more in the red, that is, close to the LgSPR. Let us also recall that the oscillator strength of the LgSPR can be much larger than the one of the TrSPR (see Figure 2 for a single nanorod), thus emphasizing the small variation of ε(ω) in its spectral domain. If the contribution of interband transitions to the transient response dominates over a wide spectral range, this however does not mean that the intraband contribution is negligible. In particular, the electron scattering rate involved in this contribution may present variations due to the evolution of the electron−electron and electron−phonon scatterings after initial perturbation. The former exhibits a fast dynamics, linked with the cooling down of the electron gas, while the latter is expected to vary on a longer time scale as mainly driven by the dynamics of the lattice temperature. As the BTE method does not account for the contribution of the heat release toward the host medium to the evolution of the electron distribution and lattice temperature, we assume that the thermal regime is reached and examine the transient optical response by using the 3TM approach. Calculations including the temperature dependence of the scattering rates have been performed for nanorod C (R = 2.5). The transient modification of the intraband susceptibility χD(ℏω,t) has been added to the interband one, determined as described above, by calculating the dynamics of the electron collision rate. Neglecting the limited mean free path effect owing to the sufficiently large size of our nanorods, the two contributions to Γ are (i) the electron−electron scattering rate,

diffusive thermal transport in the host medium.42 Let us notice that accounting for a finite value of the interface thermal conductance may have negligible impact on the temperature dynamics within the short time range under consideration in the present study. Because of the nonspherical shape of the nanoparticle, the equations have been solved through a finite element method (COMSOL), providing the time evolution of the electron (Te) and lattice (Tl) temperatures in the NR as well as the topography of the host medium temperature.43 f(E,t) is then deduced from Te through the Fermi−Dirac distribution law. Once f(E,t) has been computed, either with the BTE or with the 3TM, the time evolution of the particle optical properties is determined. Pump pulse absorption might affect both intraband and interband contributions to the dielectric function of gold, ε(ω). The dynamics of the interband contribution, εIB(ω,t), is calculated by using the Rosei model44 and Lindhard’s theory of the dielectric function, as was done in ref 41. By addition of the Drude contribution to the total dielectric function, the dynamics of the latter is obtained. It is then used in the DDA to compute the spectral variation of the differential absorption cross section of the nanorod at each time step. The error tolerance is set to 10−5. Spectral and time resolutions are fixed to 4 nm and 100 fs, respectively. Each time-dependent spectrum requires about 15 h of computing on a multiprocessor machine.

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DISCUSSION Intraband and Interband Transition Contributions. Let us now go deeper in the analysis of the spectral signature of the nanorod transient optical response. For noble metal nanospheres the SPR band has been shown to broaden and damp under initial pump pulse absorption (plasmon bleaching). There had been a kind of controversy regarding the origin of this transient ultrafast signal. Indeed, some authors stated it stems from interband transitions (pump-induced modification of the final state distribution in the conduction band around the Fermi energy, EF) while others claimed that the origin lies in intraband transitions (mainly due to the increase of the electron collision rate, Γ).45−47 Whereas in gold spheres the SPR and the interband transition threshold share the same part of the visible spectrum, this is no more the case for the LgSPR in nanorods. It could then be intuitively expected that below the interband threshold the weight of the interband transition contribution is negligible against the one of the Drude component contribution.14 This point has already been addressed in our previous article about nonspherical gold nanoparticles,39 supported by conclusions reported in the literature in the weak15 and strong48 perturbation regimes for silver nanoparticles in which the interband transition threshold and SPR are spectrally well decoupled. While pump pulse absorption might affect both intraband and interband contributions to the dielectric function of gold, the latter is shown to dominate over the former in the particle transient response at very short time scale (up to a few picoseconds). Moreover, contrary to what can be read in ref 14, this is even verified for photon energies lower than the interband transition threshold. Indeed, the pump-induced perturbation of the electron distribution extends on both sides of EF over a typical range of the order of the pump photon energy and then may provide a contribution of interband transitions to the ultrafast transient variation of the dielectric function well below the threshold. The plasmon resonance of

Γe−e(ω ,Te) =

⎡ ⎛ ℏω ⎞2 ⎤ (kBTe)2 ⎢ + 1 ⎜ ⎟⎥ ℏ2ωp ⎢⎣ ⎝ 2πkBTe ⎠ ⎥⎦

(1)

after the work of Gurzhi based on the Landau theory of Fermi liquids,49 and (ii) the electron−phonon scattering rate, in the case where the metal lattice temperature is larger than the Debye temperature,50,51 Γe−ph(ℏω ,Tl) ≈

Tl ℏω

∫0

∞

E E + ℏω f (E)

[1 − f (E+ℏω)] dE

(2)

The proportionality factor is evaluated from the experimental values of Γ at room temperature in the visible spectrum following the results of Smith and Ehrenreich.52 kB and ℏωp denote the Boltzmann constant and the metal volume plasmon energy, respectively (ℏωp = 9.03 eV for gold). Let us note that for Te values ranging from room temperature up to several thousand kelvins, the e−ph collision contribution to the total collision factor, Γ = Γe−e + Γe−ph, dominates over the one of e− e collisions, as can be deduced by using eqs 1 and 2 and the experimental values of Γ. Γ is calculated at each time step from eqs 1 and 2 and is then inserted in the Drude expression of the intraband contribution to the susceptibility: D

χ (ℏω ,t ) = −

ωp2 ω[ω + iΓ(t )]

(3)

The calculation results are presented in Figure 5a and Figure 5b, which show the spectral variations of the differential absorption cross section at a pump−probe delay of 0.8 ps 7421


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dominant interband contribution. It is worth mentioning that the contribution of the increase of the electron scattering rate to the plasmon bleaching at the TrSPR is negligible. This bleaching mainly stems from the effect of the Fermi smearing on the interband transitions close to their threshold. Contrary to what occurs in the TrSPR range, Figure 5 shows that in the vicinity of the LgSPR at 3 ps the situation is reversed as compared with the one at 0.8 ps: the intraband component now dominates the transient response, which reflects a classical plasmon bleaching due to the increase of the scattering rate.27 Let us focus on this intraband component. We have examined the computed time variations of Γe−e and Γe−ph. At short times the e−e scattering contribution to the modification of Γ is significant, as Te reaches high values [see eq 1] and Tl has almost not yet varied, whereas at longer times the variation of the e−ph scattering completely dominates: Te has strongly decreased while Tl has increased. Note that the accurate weights of the two contributions to the modification of Γ depend on photon energy [see eqs 1 and 2]. It can be observed in Figure 5a and Figure 5b that the Drude component of the transient absorption presents very different trends at the precise LgSPR location (1.89 eV) depending on the time probed. This is not due to the difference between the effects of e−e and e− ph scatterings (which both lead to the plasmon bleaching) but to the short-time influence of Te [and then f(E); see eq 2] on the value of Γe−ph when Tl can still be considered as constant at room temperature (at lattice room temperature the e−ph contribution to Γ is 1 order of magnitude larger than the e−e one). It should be mentioned that the time required for reaching the maximum of Tl as well as the value of Tl itself depend on the input power, as the specific heat of the quasi-free electron gas increases with Te. Then the precise result obtained above regarding the relative weights of intra- and interband transition contributions to the transient signal may be modulated by this power dependence. The spectrum of the total response, as calculated by the 3TM and including the pump-induced transient modifications of both the intraband and interband contributions, is shown in Figure 6b at different times for virtual sample C. It is worth noticing that this time evolution of the spectral signature of the NR response is very similar to the one measured by Wurtz et al. (see Figure 2b of ref 14) on a monodisperse distribution of parallel nanorods. The stationary absorption spectrum of

Figure 5. Spectral variations of the differential absorption cross section (black line) of a gold NR C with random orientation at t = 0.8 ps (a, top) and t = 3 ps (b, bottom) as calculated with the 3TM. The respective contributions of interband (red line) and intraband (blue line) transitions are added. Inset: zoom-in of the LgSPR range of the seven curves (black) for an artificial ensemble of seven NRs with different aspect ratios around the actual one of NR C and their mean values (red), displayed at the same scale.

(maximum signal) and 3 ps (∼maximum lattice temperature), respectively. The values of the input energy are different in the longitudinal and transverse polarizations to account for the respective NR absorption cross sections. These values are chosen sufficiently low to limit the increase of the electron gas specific heat (which is proportional to electron temperature), which would otherwise slow the e−ph relaxation dynamics and then would require a computation over a longer time range. The corresponding electron and metal lattice temperatures are thus Te(t = 0.8 ps) = 559 K, Tl(t = 0.8 ps) = 296 K, Te(t = 3 ps) = 318 K, Tl(t = 3 ps) = 297 K in the transverse polarization and Te(t = 0.8 ps) = 843 K, Tl(t = 0.8 ps) = 296 K, Te(t = 3 ps) = 390 K, Tl(t = 3 ps) = 301 K in the longitudinal polarization, the initial room temperature being set to 295 K. The contributions of the induced transient changes of the interband and intraband transitions are distinctly displayed. As can be seen, the quasifree electron contribution (i.e., the contribution of the transient modification of Γ in the Drude model) remains negligible above ∼1.7 eV (below ∼700 nm) in the ultrashort time range [Figure 5a]. This is confirmed by the investigation of Baida and co-workers.27 Within the time interval probed the ratio of the interband and intraband contributions remains roughly constant in the spectral domain of the TrSPR, that is, a

Figure 6. (Top, a) Absorption cross section spectrum of virtual sample C. (Bottom, b) Spectrum of its differential absorption cross section at different times considering all contributions to the transient response. 7422


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Influence of the Athermal Regime on the Spectral Signature. In this part, we will analyze the role played by the athermal regime in the spectral dependence of the transient absorption signal at very short times after pump excitation (first picosecond). For this, we will compare the results of the BTE and 3TM approaches described in a previous section. In order to avoid introducing additional effects in the thermal model (linked with the Te dependence of the electron heat capacity), the energy absorbed per pulse is chosen to be very low here. Within these conditions the mean number of photons absorbed per pump pulse and per nanorod is 4.4 and 11.7 in the transverse and longitudinal polarizations, respectively. The calculation results for virtual sample C are reported in Figure 7b and Figure 7c, respectively. The color levels are kept

sample C is also displayed in Figure 6a. The transition from the interband dominant contribution to the intraband one can be clearly seen in the LgSPR domain, as measured in ref 14. The slow dynamics of Γe−ph driven by Tl also explains the presence of a persistent signal in the red wing of the LgSPR. Additionally, the slight opposite spectral shift of the two positive maxima in the wings of the TrSPR is also observed along the relaxation process. This stems from the increase of the relaxation time as photon energy gets closer to the interband transition threshold (which lies at about 2.4 eV). Indeed, the electron distribution around EF drives the interband transition probability in the vicinity of this threshold. The Fermi−Dirac distribution evolves along the cooling with a relative instantaneous variation |df(E,t)/f| which uniformly decreases as E tends to EF. For comparing the calculation results with the experimental ones, we first have to keep in mind that the position of the LgSPR is very sensitive to the NR aspect ratio. In order to emphasize the effect of shape distribution, the transient spectrum corresponding to the average over an arbitrary ensemble of seven nanorods, having different LgSPR wavelengths with the same oscillator strength, has been calculated at 0.8 and 3 ps, as displayed in the insets of Figure 5. Two features can be observed. First, the antisymmetric profile mainly associated with the interband contribution at very short times is damped by the averaging effect, especially in the low energy wing (inset of Figure 5a). This means that the shape distribution attenuates the relative weight of the signal in the LgSPR range compared to the one in the TrSPR range and modifies the balance between the high- and low-energy wings of the resulting transient signal spectral profile around the LgSPR. This explains the spectral profiles measured in our colloidal solutions (Figure 3) as compared with those simulated for a single NR. Second, the bleaching effect associated with the intraband contribution close to the LgSPR at long time is strongly lowered and broadened by the averaging (inset of Figure 5b). This is even larger than for the short-time antisymmetric feature just described above. The shape distribution then reinforces the relative weight of the interband contribution in this spectral range and at longer times blurs the signal stemming from the LgSPR bleaching associated with the dynamics of Tl through Γe−ph. This certainly explains why here no long-time signal can be observed in the red part of the experimental spectra (Figure 3). In contrast, this signal has indeed been observed in other studies working with a single NR27 or a narrow distribution of NR aspect ratio.14 In addition, the simulations have been carried out with a low input energy, as explained earlier. In the experiments, the electrons are brought to a higher temperature, leading to a slower electron cooling due to the dependence of Ce on Te. Consequently, (i) the perturbation of the conduction electron distribution, and then the interband contribution to the transient response, lasts for a longer time and (ii) the nanoparticle heating (Tl) is slower. Because of the thermal exchange at the NR surface, the ratio of the maximum lattice temperature reached, Tl,max, and the absorbed power (and then the ratio of Tl,max and the maximum electron temperature reached) is lower than with a weaker input energy. This results in a lower relative contribution of the intraband component to the transient response in our experiments than in the calculations, which explains further the absence of long-time signal in the red part of the experimental data.

Figure 7. Absorption cross section spectrum of virtual sample C (a). Transient variation of the differential absorption cross section spectrum within the first picoseconds after pump pulse, calculated with the Boltzmann transport equation (b) and the three-temperature model (c) at very low pump power.

the same. The stationary absorption spectrum of this sample is added in Figure 7a. The alternation of positive and negative pump-induced absorption variations matches very well the experimental one (Figure 3, bottom). Especially, the locations of these features relative to both the TrSPR and LgSPR are precisely reproduced. In contrast, the simulations seem to overestimate the relaxation rate of the signal as compared with the experimental results. This is all but surprising, as the models used here are carried out with a lower input energy. Indeed, because of the electron temperature dependence of the electron gas specific heat, the relaxation is slowed when increasing the initial power absorbed.40,53,54 7423


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distribution of nonspherical particles in thin films.39 Here, it will be shown that this ensemble effect may have a strong influence on the analysis of the spectral signature of the nanorod transient optical response. Figure 8 presents the

Let us now compare the results of the BTE and thermal approaches. Different characteristics can be drawn from this comparison. First, the relative weight of the transient signal in the domain 1.7−2.0 eV, corresponding to the pump-induced changes of the metal dielectric function amplified by the LgSPR, is reinforced by the athermal conduction electron distribution. This is due to the influence of the latter on interband transitions. Indeed, in the initial off-equilibrium regime the perturbation of f(E) at high (but smaller than ℏωpump) values of EF − E has a larger relative weight than in the thermal regime, as the perturbation due to pump photon absorption extends to EF − ℏωpump. Interband transitions are then affected below their threshold deeper in the spectrum than for a thermalized conduction electron distribution with equivalent total internal energy input. Second, the athermal regime results at first times after pump excitation in enhanced fast variations of the transient optical response as compared with the pure thermal description. These changes are manifested by a spectral shift of maxima and minima of the transient induced absorption which has already been pointed out in the experimental results as described above. This can be ascribed mainly to two phenomena: (i) The recovery of the internal equilibrium within the conduction electron gas under electron−electron scattering in the athermal regime occurs with a characteristic time inversely proportional to (EF − E)2, following the Landau theory of Fermi liquids.55 Consequently, the further from the interband transition threshold, the faster is the dynamics in the very first instants after pump excitation. (ii) The blue-shift of the zero-crossing point at the LgSPR location (cf. Figure 4) is linked with the fast relaxation of the athermal electron distribution. Indeed, the antisymmetric shape of the transient signal at the LgSPR originates from the linear (at first order) relation linking Δσ with Δε1 and Δε2, as suggested in ref 27. In the LgSPR spectral domain, both Δε1 and Δε2 are weakly dispersed. At short time after excitation, Δσ is mainly governed by Δε1.27 The proportionality factor is given by the spectral dispersion of σ, dσ(ℏω)/dω, which exhibits an antisymmetric profile, the inflection point corresponding to the LgSPR. This results in the sudden initial red-shift of the LgSPR band under pump pulse absorption. At the very precise stationary LgSPR location, the contribution of Δε1 is zero as dσ(ℏω)/dω = 0. The point of inflection for Δσ is nevertheless vertically shifted to negative values because of the residual contribution of Δε2 which stems from the athermal electron distribution and relaxes on an ultrashort time scale. This explains the effective blue-shift of the zero-crossing point of Δσ observed along the relaxation within the athermal regime (see the experimental Figure 3 and the calculated Figure 7b). This fast shift is thus absent in the transient spectrum simulated by using the purely thermal approach (Figure 7c). Let us note that this blue-shift explains the apparent plasmon bleaching reported around the LgSPR in ref 19: as the transient response is shown at 1 ps only after pumping, the zero-crossing point of the induced signal is still red-shifted relative to the precise LgSPR location. Selective Excitation and Detection in an Ensemble of Nanorods. It is well-known that the individual response of isolated particles may differ from the one of a particle distribution (ensemble effect), as it has already been illustrated in the stationary regime.27,35,56 This difference is further enhanced in pump−probe experiments, as two light beams are used and are then affected by the distribution. We previously addressed this point in the case of a random

Figure 8. Time and spectral evolution of the absorbance variation in sample NR3 pumped at 1.55 eV photon energy. The arrows indicate the spectral locations of the TrSPR and LgSPR. Pump and probe beam polarizations are now parallel.

spectral variations of the experimental differential absorption dynamics for sample NR3 pumped at 1.55 eV (800 nm). The pump and probe waves have now parallel polarizations. The response looks rather different from the one obtained by pumping at 2.25 eV (see Figure 3, bottom). Indeed, while around 2.4 eV a feature similar to the one of Figure 3, bottom, can be discerned (feebly, because of the plot color scale), a strong signal begins to rise at the red edge of the spectrum. Unfortunately, the spectral width limitation of the supercontinuum probe does not allow recording at higher wavelengths. This signal is not due to the saturation of the detector stemming from the possible pump beam diffusion, since the wavelength of the latter is out of the chosen detection range of the spectrometer CCD detector. Such a signal is similar to the one we reported previously for nanocomposite thin films.39 When pumping far from the apparent LgSPR of the global nanorod assembly, light energy is preferentially injected in nanoparticles, the absorption cross section maximum of which matches the pump wavelength (as nanorod D, having an aspect ratio of 3.75, the maximum absorption of which is denoted by a red circle in Figure 2). At the same time, the nanorods having the optical mean aspect ratio (nanorod C of Figure 2) absorb almost no energy at this wavelength (thin black circle). This inhomogeneous energy injection is designed as selective excitation.17 Furthermore, the pump-induced modification of the optical properties of the selectively excited nanorods is amplified in the vicinity of their LgSPR by the local field enhancement when these nanorods interact with the probe pulse.39 This selective detection process results in the photoinduced transmission signal in the red part of the spectrum, the high intensity of which is due to selective processes in the distribution. When pumping at 2.25 eV, on the contrary, all nanorods of the whole assembly receive approximately the same amount of energy from the pump pulse, since their absorption cross section does not depend on their aspect ratio at this photon energy, as can be seen in Figure 2 (thick black 7424


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characteristics of the spectral signature of the transient signal as compared with what is expected for single nanorods and (ii) our experimental investigations have demonstrated that the ultrafast transient optical response of an ensemble of nanorods is affected by a double selection process. Depending on the pump photon energy, a certain subset of nanorods, characterized by their aspect ratio, can be targeted among the whole assembly by the pump pulse, which corresponds to the selective excitation process. Then by addition of the selective detection by the probe associated with the LgSPR, the measured transient signal of the ensemble is dominated by the response of this targeted small subset. This points out the care with which the results of time-resolved spectroscopy measurements have to be analyzed. Beyond, this work could improve selecting nanorods for exploiting their ultrafast optical response, as its sign and magnitude are highly dependent on photon energy. For instance, nanorods could be used rather than nanospheres in hybrid plasmonic−photonic cavities57 for the tunability of their transient optical properties.

circle). The excitation is then roughly homogeneous, and the transient absorption spectrum measured reflects the ultrafast response of the whole assembly, that is, the addition of the responses of all the species present in the distribution weighted by their population, as in the stationary case of Figure 1. In order to support the mechanisms proposed, the spectra have been simulated by the method described above. For this, the transient optical response of the two nanorods C and D of Figure 2 (having an aspect ratio of 2.50 and 3.75) illuminated with the same laser power has been computed by accounting for their respective absorption cross sections at the pump photon energy of 1.55 eV. In the resulting spectra (not shown here) a very weak (owing to the weak absorption) transient signal is observed close to the two plasmon modes in the case of C, while a much larger one is revealed in the transient spectrum of nanorod D. This stems from the facts that (i) in nanorod D an energy much larger than in C has been input by pump pulse absorption and (ii) the strong LgSPR of D excited by the probe pulse amplifies the modification of the metal optical properties, initially induced by the pump, in this spectral range (around 1.55 eV), even if the latter lies far below the interband transition threshold as it has been discussed above.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +33-141131626.

CONCLUSION By use of a one-pot radiolysis method, three colloidal solutions of Au NRs in water have been synthesized, having different mean aspect ratios. Their ultrafast transient optical response has been measured by broadband pump−probe spectroscopy, allowing for monitoring of the spectral dependence of the complex dynamics associated with the existence of the two NR plasmon modes. In parallel, calculations based on both the BTE and the 3TM approaches have been carried out. The former is well suited for describing the first instants of the dynamics following pump pulse absorption and especially the athermal regime for the conduction electron gas but is restricted to weak perturbations and disregards the heat exchange with the surrounding medium. The latter permanently assumes a thermal distribution for the electron gas, accounts for heat release to the environment, and is then better suited for describing the dynamics at longer times after excitation, once the athermal regime is completed. On the basis of these models, we have been able to explain the main spectral characteristics of the measured transient optical response of our NR solutions. The evolution of the transient absorption spectrum with NR aspect ratio reveals the usual “plasmon bleaching” feature at the TrSPR, while an antisymmetric signal is exhibited close to the LgSPR and decays with a blue shift. Within a short time after pump pulse excitation the interband transition contribution is dominant even in the LgSPR spectral domain. In contrast, the intraband transition contribution can no more be neglected at longer time and becomes dominant in this spectral domain. The relative weights of these contributions, and then the spectral signature of the transient response, are affected by the ensemble effect in colloidal distributions. The athermal regime for the conduction electron distribution is responsible for fast spectral variations of the transient signal at first times after pump excitation. The thermal regime exhibits the influence of the lattice temperature dynamics and amounts to a slow component in the red part of the relaxation, which is blurred by the NR shape distribution. Finally, we have highlighted effects related to the aspect ratio distribution in an ensemble of nanorods: (i) our model calculations have shown that the ensemble effect modifies some

Present Address #

P.R.S.: Center for Advanced Materials and Industrial Chemistry (CAMIC), School of Applied Sciences, RMIT University, GPO Box 2476V, Melbourne, Australia.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS X.W. thanks the China Scholarship Council for financial support. The authors acknowledge C’Nano Ile-de-France, the Région Ile-de-France, and the French Agence Nationale de la Recherche (Project ANR-13-BS10-0008-01) for their financial support.

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REFERENCES

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