Absorption of Ultrashort Laser Pulses by Plasmonic Nanoparticles: Not

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Absorption of ultrashort laser pulses by plasmonic nanoparticles: not necessarily what you might think Xue HOU, Nadia Djellali, and Bruno Palpant ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01012 • Publication Date (Web): 20 Aug 2018 Downloaded from http://pubs.acs.org on August 20, 2018

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ACS Photonics

Absorption of ultrashort laser pulses by plasmonic nanoparticles: not necessarily what you might think

Xue Hou, Nadia Djellali, and Bruno Palpant

∗

Laboratoire de Photonique Quantique et Moléculaire, CentraleSupélec, Ecole Normale Supérieure Paris-Saclay, Université Paris-Saclay, CNRS UMR 8537, 3 rue Joliot Curie, F-91190 Gif-sur-Yvette, France

E-mail: [email protected]

Abstract

Exciting plasmonic nanostructures by subpicosecond laser pulses can generate many interesting phenomena due to hot electrons, which can be further exploited in photonics, chemical or biomedical applications. In order to quantitatively analyze and optimize these eects, proper evaluation of the light pulse power absorbed by the nanoparticles is highly required. However, in the literature the only stationary properties are considered for that purpose. In this communication, we show that this may be invalid owing to the optical nonlinearity associated with the photo-generated hot electron distribution. We demonstrate through a simple optical transmission experiment the inuence of hot electrons on the absorption cross section of gold nanorods, excited by subpicosecond laser pulses tuned to the longitudinal plasmon resonance spectral domain. The partial melting threshold of the nanorods is reached for a peak intensity of 5 GW cm−2 , corresponding to a volume density of energy of 2.2 aJ nm−3 . Below this threshold,

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the experimental results are interpreted through a model which accounts for the nonthermal nature of the electron distribution and for the multiphoton excitation. The variation of the eective optical absorption cross section, hσabs i, with laser peak intensity reveals a strong and complex nonlinearity, which in addition depends on laser wavelength and nanoparticle shape, hσabs i being either larger or smaller than the stationary cross section value. Besides, we show that for a given pulse energy, the shorter the pulse duration, the greater this deviation. Finally, we illustrate the consequences of this discrepancy through the evaluation of the nanoparticle temperature reached after photothermal conversion. Keywords: plasmon; nanoparticles; hot electrons; ultrashort pulses; femtosecond laser; absorption; nonthermal

Plasmonic nanoparticles (NP) are widely studied and exploited because of their high optical absorption cross section, associated with the strong enhancement of the local electromagnetic eld and their high photothermal conversion eciency. This opens a path for many applications in diverse domains, such as photonics, 1 energy harvesting, 2 spectroscopic detection, 3,4 or photocatalysis. 5 In addition, thanks to the possibility to tune the plasmon resonance towards the near-infrared transparency window of biological tissues (650 to 1350 nm), 6 NPs with non-spherical shape like nanorods, or core-shell-like, can be exploited for applications in biomedical sensing, 7 biological imaging, 8 drug delivery 9,10 or cancer therapy. 9,11 Beyond, by combining a subpicosecond pulsed illumination with plasmonic NPs one can not only achieve a much higher and more conned temperature increase in the close vicinity of the NPs, 12 but also generate, by multiphotonic processes, a broadband photoluminescence, 13,14 a local plasma, 15 nanocavitation, 15 and further the production of reactive oxygen species 16,17 in an aqueous environment, all being attractive for biomedical imaging or therapeutic applications. The quantitative description of all these processes relies on the energy absorbed by the NPs; it is therefore necessary to assess properly the absorption cross section of the latter. Following the absorption of an ultrashort light pulse, the conduction electron distribution 2


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in metal is strongly modied: a nonthermal distribution is rst created, which evolves to internal equilibrium by eletron-electron scattering. The hot electron gaz then cools down by energy transfer to the metal lattice by electron-phonon scattering, and heat is released towards the surrounding medium through the interface. In addition, multiphoton absorption can lead within the rst instants to electron energy loss by radiation (photoluminescence), 14,17,18 as well as electron ejection. 19,20 These transient processes result in the modulation of the optical properties of the nano-object. The dynamics of the optical response of plasmonic NPs has been widely studied by using time-resolved pump-probe spectroscopy and appropriate modelling. 2123 Recently, a simulation work of our group showed a strong plasmon damping during the ultrashort pulse itself due to the hot electron distribution created. 19 This aects directly the quantity of energy absorbed under ultrashort pulse excitation. However, in the litterature the energy absorbed by the NP excited by ultrashort pulses is most of the time evaluated based on the metal stationary optical properties. 12,15,22,24,25 In this work, we demonstrate through a simple optical transmission experiment the inuence of the hot electron distribution on the absorption cross section of gold nanorods (AuNRs) in water, excited by a subpicosecond pulsed laser tuned in the longitudinal plasmon resonance domain. The results are interpreted through a model which accounts for the nonthermal nature of the electron distribution and the multiphotonic electron emission. We also investigate with this model the inuence of both the AuNR aspect ratio (AR) and the pulse duration on the NR absorption cross section. We apply these results to evaluate the maximum temperature increase which can be reached by the AuNRs.

Experimental Results We aim at determining the eective optical absorption of plasmonic NPs during a laser pulse. For this purpose, the optical transmittance of an aqueous solution of AuNRs, with mean AR 4.0 and eective Longitudinal localized Surface Plasmon Resonance (LgSPR) peak at 772

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nm, has been measured in a double laser beam conguration (see Supporting Information for details). Briey, the transmittance is determined with a 100-fs pulsed laser at λlaser = 800 nm wavelength (Tf s ), and with a continuous wave (cw) laser at 808 nm wavelength in the 0 fs ) and in the presence (Tcw ) of the femtosecond laser pulses. In the latter case, absence (Tcw fs the cw laser power is kept constant at a low value. Hence, measuring Tcw enables us to detect

any slow or permanent alteration of the AuNR optical properties induced by the ultrashort laser pulses (see Supporting Information). The experimental data are reported in FIG. 1a. To enable the comparison of the experimental results obtained with both the reference cw laser and the fs-pulsed laser, we build a common x-axis coordinate, F eq , as the equivalent uence of one pulse at equal power for the two lasers (upper x-axis in FIG. 1a). In other words, F eq denotes the actual pulse uence for the fs-pulsed laser, and for the cw laser it is dened as

F eq = Icw /frep ,

(1)

where frep is the fs-pulsed laser repetition rate and Icw is the reference cw laser intensity. As can be seen in FIG. 1a, when the AuNR solution is illuminated only by the cw laser the 0 response is linear, i.e., Tcw (FIG. 1a, blue triangles) is constant within our range of incident

power. However, when the AuNRs are excited by the fs-pulsed laser, Tf s (FIG. 1a, red circles) raises with increasing excitation peak intensity. The value of Tf s is sensitive only to the optical properties of the solution during the laser pulses. This ultrashort optical response can be ascribed to both the transient ultrafast phenomena induced in the AuNRs during each pulse, and the phenomena, induced by a laser pulse, which last longer than the delay between two successive pulses, so that they can be felt by the next pulse. For this reason, we can eliminate certain transient eects which may modify the NP optical properties but can not contribute to the Tf s signal detected by our experiment. These eects arise within a timescale larger than the pulsewidth and relax along durations much smaller than the delay

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between two successive pulses (400 µs), as: (i) formation and collapse of nanobubbles. The bubble formation time (∼ 80 ns) is much larger than the pulsewidth while the sum of this formation time and the bubble collapse time (∼ 300 ns) is much smaller than the repetition period of our pulsed laser; 26 (ii) non

cumulative

thermal eects, as the duration of one laser

pulse is much too small to be sensitive to any heating of the metal NPs and their environment in the case where the system would completely cool down between two successive pulses; 27 (iii) mechanical eects induced by a laser pulse, as for instance the generation of acoustic vibrations of the NPs, or their rotation in the solvent. 28,29 The sample used in our experiments is a colloidal solution where the NRs are oriented randomly. The possible vibrational or rotational motions of the NRs occur with characteristic times which are much larger than the pulsewidth; during the interaction of each laser pulse with the NRs, the latter can then be considered as "frozen". Due to the huge number of NRs probed by the beam, the mechanical eects do then not aect the transmittance. Finally, we can infer that the nonlinearity in the optical response of the AuNR solution optical response during the laser pulses, revealed by the variation of Tf s , can stem, either from pure ultrafast electronic eects in the metal during the laser pulse, or from slow or irreversible photothermal eects, or even both. The possible photothermal phenomena are: (i) the local heating of the solvent surrounding the NPs, leading to a local index decrease and then to a spectral blue-shift of the LgSPR; 30,31 let us note that, as explained before, this eect could only be ascribed to the

cumulative

local heating by successive pulses; 12 (ii) the permanent morphology changes, including the aggregation or the partial melting of the NRs. 3234 On the one hand, the partial melting of the NRs leads to a decrease in their AR and then to a blue-shift of the LgSPR mode. 25 Contrarily to the previous eect (surrounding solvent heating), this partial melting of AuNRs should occur only when a certain laser power threshold is reached. 25,33,35 On the other hand, the aggregation induces a decrease and an asymmetric widening of the LgSPR peak to the red, 32 so that at wavelength close to λLgSP R the absorbance decreases, while at wavelengths fs much higher than λLgSP R the absorbance increases. Compared with Tf s , Tcw is sensitive only

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to slow varying or irreversible eects. For instance, the possible generation of nanobubbles fs as the laser repetition period is much larger than by the fs pulses does not inuence Tcw

the nanobubble lifetime, as stated above. Therefore, in order to know if the nonlinearity 0 observed (through Tf s ) is due to electronic or photothermal eects, we should compare Tcw fs and Tcw (FIG. 1a, red circles and black stars, respectively). As long as the excitation peak fs 0 intensity is lower than 5 GW cm−2 , Tcw overlaps with Tcw . It means that for weak excitation

intensity, the morphology of AuNRs is not modied and there is no signicant cumulative fs is then due heating of the solvent around NPs. The raising dierence between Tf s and Tcw

to fast electronic eects generated during the laser pulses. Let us again note that, while the optical properties of the NPs is modied by the ultrashort laser pulses, the time range along which these changes are signicant (a few picoseconds to a few nanoseconds at maximum) remains much smaller than the delay between two sucessive pulses (400 µs). The contribution of this fast modication to the signal measured with the continuous laser beam is then fs fully negligible, and Tcw accounts for the stationary transmittance of the sample only. This fs 0 explains that Tcw overlaps with Tcw in the weak excitation intensity range. Nevertheless, if fs increases. The existence of a threshthe peak intensity is increased over 5 GW cm−2 , Tcw fs reveals that the permanent or long-lasting modication old in the power dependence of Tcw

of the optical properties can be ascribed to the AuNR morphology change rather than to the solvent heating. NR melting and/or aggregation could correspond to this morphology change. Aggregation of NRs may be induced by thermal gradients, or destabilization of the solution by removing the surfactant molecules at the NR surface. However, we exclude this aggregation hypothesis by performing complementary experiments, the details and discussion about which can be found in the Supporting Information. In our experiment, the AuNR morphology change which is detected is then due to the partial melting of the NRs. AuNRs begin to melt partially, their aspect ratio becomes smaller, 36 and the LgSPR absorption band is blue-shifted compared to the initial one (see Supporting Information, FIG. S4 and discussion). As the transmittance is still measured at 800 nm, it increases due to this blue-shift. 6


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fs Higher peak intensity induces a stronger melting, then resulting in the increase in Tcw . Let

us note that this should also aect the value of Tf s ; however, as the absorption cross section at 800 nm decreases due to the NP shape modication, the magnitude of the nonlinearity due to electronic eects decreases as well, which compensates for the shape-related increase of transparency. Consequently, no signicant change in the slope of Tf s can be observed above the partial melting threshold at ∼ 5 GW cm−2 . Let us now focus on the weak excitation regime. First, it is worth underlining that in this regime the measurements are fully reversible (see the discussion in the Supporting In0 , formation, part 3). The curve for Tf s seems to tend to the stationary value, namely, Tcw

as the peak intensity tends to zero. In order to asses this, we have carried out additional measurements for I0 in the range 0.1 − 4.0 GW cm−2 . For this, we keep the same laser power as before and widen the beam diameter to reach low intensities. The results are reported on 0 FIG. 1b. Surprisingly, Tf s values lower than Tcw are found in the range 0.1 − 0.4 GW cm−2 .

This result will be interpreted in the following section.

Analysis To have a deeper understanding of the experimental results, we simulate the optical response of a single 50-by-12.5 nm2 AuNR in water excited by a 100-fs laser pulse linearly polarized along the long axis of the AuNR at 800 nm wavelength. The simulation is based on the nonthermal approach previously developped in our group 19 (see Supporting Information). The eective mean absorption cross section, hσabs i, is then deduced. In addition, the theoretical exp and experimental values of the relative variation of the cross section, ∆theo abs and ∆abs , are ex-

tracted from the simulation and experimental results, respectively (Supporting Information 1.3 and 2.3).

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Inuence of peak intensity Let us focus onto the variation of the eective absorption with varying laser peak intensity,

I0 . FIG. 2a reports the simulated variation of ∆abs with increasing peak intensity in a logarithmic scale. The eective absorption cross section rst increases for intensity values up to I0 = 100 MW cm−2 , and then decreases, becomes lower than the stationary value (∆abs < 0) and still decreases linearly with logI0 . The corresponding experimental variation is displayed on FIG. 2b. Within the experimental range for I0 the comparaison with FIG. 2a shows that the calculated variations of ∆abs agree well with the experimental ones as long as I0 remains below the AuNR reshaping threshold discussed above. As in the simulation,

∆abs goes from positive to negative values with increasing peak intensity, the sign inversion occuring at about 0.5 − 0.7 GW cm−2 in both cases. This complex nonlinearity can be explained by the ultrafast plasmon damping during the pulse absorption as illustrated in FIG. 3, where the absorption cross section spectrum at three instants during the passage of the laser pulse is presented. It can be observed that while the plasmon damping results in a permanent decrease of σabs during the pulse in a narrow range around the LgSPR peak (772 nm here), it can on the contrary increase in the low and high wavelength wings. The situation at 800 nm is intermediate: σabs increases at the beginning of the pulse, and then decreases. Thus, depending on the laser wavelength, λlaser , and especially on the spectral interval between λlaser and the LgSPR wavelength, λLgSP R , hσabs i can be larger or smaller than 0 σabs . Now, increasing the pulse energy induces stronger plasmon damping and broadening.

Consequently, at a xed λlaser , the instantaneous variations of σabs along the pulse passage may depend on I0 , which will aect the eective average value hσabs i. This explains the sign inversion of ∆abs reported on FIG. 2a and 2b. Let us notice that the partial melting threshold I0melt = 5 GW cm−2 found in the present experiments corresponds to an energy part absorbed by one AuNR of Emelt = I0melt hσabs iτp = 12.3 fJ. As in Ref. [35], thermodynamic tot considerations based on bulk gold properties lead us to an energy of Emelt = 21.5 fJ needed

to totally melt a 50-by-12.5 nm2 AuNR. This value is of the same order of magnitude as 8


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our experimental nding, though slightly higher. This is nothing but surprising as our experiment allows to evaluate the partial, and not total, melting threshold. In addition, the melting point is known to decrease from its bulk value with decreasing NP size. 27 In tot contrast, Link and El-Sayed determined a value of Emelt = 65 fJ for a 44-by-11 nm2 AuNR

with AR=4.1 in water, 35 while the classical thermodynamic evaluation yields 16 fJ. However, as they used the stationary absorption cross section in the exploitation of their experimental tot results, obtained with 100-fs laser pulses tuned to the NR LgSPR, their value of Emelt may be

over-estimated, as demonstrated in the present work. Finally, the volume density of energy needed to reach the partial melting (reshaping) threshold is found to be 2.2 aJ nm−3 in our experiment.

Inuence of the real sample morphology As the nanorod considered for the simulation corresponds to the most representative of the NR distribution in the experimental sample, the simulated variations of ∆theo abs reproduce well the ones of ∆exp abs . However, it can be noticed in FIG. 2 that the predicted ∆abs value are larger than the ones measured for the same peak intensity. This discrepancy can be ascribed to two elements linked with the morphology of the NR distribution in the colloidal solution. First, the NRs are randomly oriented. As the light pulse is linearly polarized, the response of the NRs oriented parallel to the electric eld will contribute for the main part to the total response as they receive the highest energy input. This case corresponds exactly to the simulation where the only longitudinal polarization is considered. Nevertheless, the other NRs in the solution absorb less energy as they are not aligned with the eld. In other words, the eective peak intensity felt by the randomly-oriented AuNRs varies between 0 and I0 , so that their plasmon damping during the pulse is weaker depending on their orientation, which results in a weaker evolution of σabs (t). Consequently, to take into account the eect of the random orientation distribution we should average the ∆abs value over this range of eective peak intensity. Finally, the inuence on our results in FIG. 2a would be to atten the curve 9


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and slightly shift the zero crossing point to higher intensity values, which would further improve the agreement with the experimental results (FIG. 2b). Second, the actual sample contains NRs with varying shapes around the most probable one, while the calculation is performed for one AR only. In order to understand the role of the shape distribution, we have considered three additional AR values for the calculation, having the same volume as the 50-by-12.5 nm2 NR regarded up to now. The corresponding variations of ∆theo abs with peak intensity are reported in FIG. 4. Following the discussion developed in the preceding section, the spectral interval between λlaser and λLgSP R varies as λLgSP R shifts with varying the AuNR AR, λlaser being xed in the present calculation. This results in a very dierent I0 -dependence of ∆abs for the dierent ARs under consideration, as can be seen on FIG. 4. Hence, we can have two antagonist eects: for the AuNR with λLgSP R = λlaser (case AR=4.3), ∆abs decreases with increasing peak intensity, whereas for the AuNR with λLgSP R far from λlaser

∆abs can be either positive or negative, depending on the peak intensity. In the solution, all the contributions from the dierent ARs have to be added, which results in a spatiallyaveraged value of ∆abs over the shape distribution dierent from the one expected for the single most probable AR. Let us nally underline that when the laser line matches exactly the NR LgSPR (i.e., λlaser = λLgSP R ) and the NR is aligned with the pulse polarization (black diamonds on FIG. 4), the actual energy absorbed by the NR from the pulse is only 0 half the value which would be evaluated from the stationary optical properties (σabs ) for a

yet relatively weak peak intensity of 500 MW cm−2 . This factor even falls down to 20% at 10 GW cm−2 . This highlights the need to account for the ultrafast optical response in the determination of the initial energy input from ultrashort pulses in plasmonic nanostructures. To calculate the exact ∆abs mean value of a AuNR solution, it is then necessary to account for both the orientation and shape distributions of the AuNRs.

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Inuence of laser repetition rate Measurements have been performed at doubled repetition rate frep = 5.0 kHz. The results are reported in FIG. 5, where the transmittance is displayed as a function of peak intensity. 0 fs even from low I0 values, which contrasts with departs from Tcw It can be seen that Tcw

what was observed at 2.5 kHz (FIG. 1a). This trend is further enhanced after 5 GW cm−2 , now as for frep = 2.5 kHz. The corresponding ∆exp abs value is reported in FIG. 2b (blue triangles) as a function of I0 . The curves at the two repetition rates overlap quite well fs 0 below the partial melting threshold, since the dierence between Tcw and Tcw is about 1%,

which can not be detected on FIG. 2b as being smaller than the error bar. Decreasing the delay between successive laser pulses can lead to cumulative thermal eects. 12 In that case, a thermal background settles and its mean temperature is as high as pulse energy is large. We believe that this induces the heating of the solvent surrounding the NRs, which modies their optical properties as evoked above. This eect occurs with no threshold and fs 0 may explain the discrepancy of Tcw and Tcw in FIG. 5. The same experiment performed at

a lower NP concentration conrms this analysis (see Supporting Information, FIG. S5 and discussion). Besides, the NP partial melting is initiated at almost the same value of I0 as for the low repetition rate; in addition, it does not depend on NP concentration (see Supporting Information, FIG. S6). The thermal background due to cumulative eect then has only little inuence on this threshold; however, the further changes of morphology probed by the modication of ∆exp abs (FIG. 2b) are obviously favored by the fact that for frep = 5.0 kHz the AuNRs passing through the cw laser beam experience twice as many fs-laser pulses as for

frep = 2.5 kHz. It can then be inferred from these observations that the surface diusion of atoms at the nanoparticle surface, responsible for the NR reshaping, is produced by each pulse and stops between successive pulses (the AuNRs do not remain hot for long after each pulse). 25,33,34,3638 The cumulative thermal background slightly reinforces this eect at higher

frep and high I0 .

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Inuence of pulse duration As discussed in the introduction, many recent developments based on the LSPR exploit the specic properties brought by the use of ultrashort laser pulses rather than continuous light, especially for biomedical 9 or ultrafast photonics 1,39 purposes. Hence, all eects relying on multiphoton processes, such as broadband photoluminescence, 14,17,18,40 low-density plasma generation, 19,41 nanocavitation, 15,42 or production of reactive oxygen species in water 16,17,43 need short and intense light absorption. Photothermal conversion by plasmonic NPs also benets ultrashort pulse excitation, as it provides a higher and more localized heating as compared with cw excitation: the shorter the pulse duration is, the more conned the heating is. 12,44 This is particularly interesting for photothermal cancer therapy by local hyperthermia or targetted drug delivery. 9,41,45,46 Thus, it leads us to study the eect of pulse duration on

∆abs . For this, we x the pulse uence value, i.e., I0 τp is a constant. We choose the pulse energy as equivalent to the 100-fs pulse with I0 = 2 GW cm−2 . ∆abs is then calculated for a 50-by-12.5 nm2 AuNR for dierent values of τp . The shortest pulse is 50 fs long with which the model is still valid. 19 Figure 6 shows that ∆abs is always negative and |∆abs | increases as 0 the pulse duration decreases. This trend is totally expected as if τp → ∞, then hσabs i → σabs ,

that is, ∆abs → 0. In the literature, for ultrashort pulse excitation, the hypothesis usually put forward to justify the use of the stationary value of σabs for assessing the light energy input is that the pulse is so short that the system can be considered as not yet modied. 12,15,22,24 We show here that this is all but true: the shorter the laser pulse is, the more necessary it is to account for the eect of the hot electron distribution in the optical properties, except of course in the case of very weak incident uence. Beyond, let us nally underline that for a pulse duration shorter than the characteristic time of electron thermalization (∼ 500 fs 47 ), the two-temperature model is not suited to describe the transient response of the NP during the pulse itself. 19

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Application to photothermal conversion The key quantity we are interested in for applications of the nanoscale photothermal conversion is the temperature increase reached by the AuNRs (that is, the metal lattice temperature) and their environment. We can estimate the maximum temperature increase reached by the AuNRs with a single pulse using hσabs i. For this, we assume that all the energy absorbed by the AuNRs relaxes instantaneously into heat. Then the maximum temperature increase, ∆TN P , can be calculated as:

∆TN P =

I0 τp σabs VN P ρAu cAu

(2)

where ρAu is the mass density of gold (ρAu = 19.3 × 103 kg m−3 ), and cAu is the specic heat of gold (cAu = 129 J kg−1 K−1 ). ∆TN P represents the upper limit of the actual NP temperature rise. In FIG. 7 we compare on a logarithmic scale the temperature increase of a AuNR in water, the AR=4.3 of which allows for the matching of the laser line and 0 the longitudinal plasmon mode (λlaser = λLgSP R ), calculated with either hσabs i or σabs . Due

to strong plasmon damping during the pulse passage, it can be observed that the actual NP temperature reached at high laser uence is lower than the one evaluated with the only stationary properties. In our example of FIG. 7, the discrepancy is about −64% at I0 = 1 0 GW cm−2 : The simple use of σabs predicts a temperature rise of 1002 K, while the rigorous

account for the hot electron distribution through the use of hσabs i gives 365 K only. This could explain, for instance, that the calibration method used by Petrova and coworkers in Ref. [25], based on the evaluation of the TN P from the period of the laser-pulse induced mechanical vibration of the NP measured by pump-probe transient absorption experiments, fails above a certain laser uence.

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Conclusion We have studied both experimentally and theoretically the inuence of the nonthermal hot electron distribution generated by an ultrashort laser pulse on the absorption cross section of plasmonic nanoparticles. We demonstrated with a simple optical experiment that the absorption cross section of AuNRs evolves along the excitation pulse. The variation of the transmittance of the AuNR solution can be positive or negative depending on the peak intensity. The partial melting threshold measured experimentally is reached for a peak intensity of 5 GW cm−2 , which corresponds to a mean energy absorbed of 12.3 fJ per AuNR. We simulated the optical response of a 50-by-12.5 nm2 AuNR (AR=4.0) excited by a 100fs pulse at 800 nm wavelength linearly polarized along the long axis of the AuNR. The relative variation of the eective absorption cross section was calculated and compared with the experimental result, showing good agreement. We explained how both orientation and shape distributions of the NRs in the solution can modify the response of the real sample as compared with the case of a single NR with xed orientation. Besides, the simulation helped us to explain the sign of ∆abs , which depends intricately on the pulse peak intensity, wavelength and duration, as well as on the NR AR. Indeed, due to the pulse-induced plasmon damping, the instantaneous variation of σabs along the pulse passage at a given λlaser can be either positive or negative, or even both successively, which impacts on the value and sign of hσabs i. Investigating the inuence of the pulse duration at xed pulse energy, we demonstrated that the shorter the pulse duration, the larger the relative variation of the absorption cross section. It means that, when using subpicosecond laser pulses to generate any phenomenon from a plasmonic nanostructure, assessing the actual energy input requires to consider the ultrashort variation of its optical properties along the pulse passage. Beyond, due to the essential nonthermal nature of the hot electron distribution in this time range, this cannot be addressed by the two-temperature model. Finally, we applied the eective absorption cross section value to evaluate the maximum temperature increase that could be reached by the AuNRs. For a wavelength matching the longitudinal plasmon mode, the 14


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actual heating is lower than the one evaluated by using the stationary σabs . There has been recently a controversy in the interpretation of multiphoton photoluminescence from plasmonic nanostructures irradiated by subpicosecond laser pulses, 13,14,17,18,40,48,49 with the possible involvement of individual electron-hole excitation relaxing into a plasmon, or the black-body-like radiation from the hot electron gas modulated by the local electromagnetic density of states. After the present work it appears relevant to account for the inuence of hot electrons on the value of hσabs i in order to precisely assess the multiphoton order of the photoluminescence process and then gain deeper understanding of the mechanisms involved.

Acknowledgement The authors thank T. Labouret for helpful discussions. This work has beneted from the nancial support of the Labex LaSIPS (ANR-10-LABX0040LaSIPS) managed by the French National Research Agency under the "Investissements d'avenir" program (n°ANR-11-IDEX000302), the "Plan Cancer" managed by the French ITMO Cancer (n°17CP077-00, project HEPPROS) and the Institut d'Alembert in Ecole Normale Supérieure Paris-Saclay (FR CNRS 3242) (project GESPER).

Supporting Information Available The following les are available free of charge. Model: theoretical optical absorption cross section, dynamics of the absorption cross section, and eective cross section during the pulse passage Experiment: AuNR colloidal solution (Figure S1), transmittance measurements (Figure S2), experimental variation of the absorption cross section Discussion on the change of morphology above the threshold

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Reversibility of experiments below the threshold

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Graphical TOC Entry 20

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20 0 -20

100-fs pulse @ 800 nm

Gold nanorod aspect ratio = 4

Relative variation of the effective absorption cross section (%)

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Absorption of Ultrashort Laser Pulses by Plasmonic Nanoparticles: Not

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