Absorption of Ultrashort Laser Pulses by Plasmonic Nanoparticles: Not

Article Cite This: ACS Photonics 2018, 5, 3856−3863

pubs.acs.org/journal/apchd5

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

ACS Photonics 2018.5:3856-3863. Downloaded from pubs.acs.org by UNIV OF KANSAS on 09/25/18. For personal use only.

S Supporting Information *

ABSTRACT: Exciting plasmonic nanostructures by subpicosecond laser pulses can generate many interesting phenomena due to hot electrons, which can be further exploited in photonics or in chemical or biomedical applications. In order to quantitatively analyze and optimize these effects, proper evaluation of the light pulse power absorbed by the nanoparticles is highly required. However, in the literature only stationary properties are considered for that purpose. Here, we show that this may be invalid owing to the optical nonlinearity associated with the photogenerated hot electron distribution. We demonstrate through a simple optical transmission experiment the influence 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, the experimental results are interpreted through a model that accounts for the nonthermal nature of the electron distribution and for the multiphoton excitation. The variation of the effective optical absorption cross section, ⟨σabs⟩, with laser peak intensity reveals a strong and complex nonlinearity, which in addition depends on laser wavelength and nanoparticle shape, ⟨σabs⟩ 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

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therefore necessary to assess properly the absorption cross section of the latter. Following the absorption of an ultrashort light pulse, the conduction electron distribution in metal is strongly modified: a nonthermal distribution is first created, which evolves to internal equilibrium by eletron−electron scattering. The hot electron gas then cools by energy transfer to the metal lattice by electron−phonon scattering, and heat is released toward the surrounding medium through the interface. In addition, multiphoton absorption can lead within the first 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 nanoobject. The dynamics of the optical response of plasmonic NPs has been widely studied by using time-resolved pump−probe spectroscopy and appropriate modeling.21−23 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 affects directly the quantity of energy absorbed under ultrashort pulse excitation.

lasmonic nanoparticles (NPs) are widely studied and exploited because of their high optical absorption cross section, associated with the strong enhancement of the local electromagnetic field and their high photothermal conversion efficiency. 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 toward the nearinfrared transparency window of biological tissues (650 to 1350 nm),6 NPs with nonspherical shape, such as nanorods or core−shell-like particles, 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 confined temperature increase in the close vicinity of the NPs12 but also generate, by multiphotonic processes, a broadband photoluminescence,13,14 a local plasma,15 nanocavitation,15 and the production of reactive oxygen species16,17 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 © 2018 American Chemical Society

Received: July 24, 2018 Published: August 20, 2018 3856

DOI: 10.1021/acsphotonics.8b01012 ACS Photonics 2018, 5, 3856−3863

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However, in the literature the energy absorbed by the NP excited by ultrashort pulses is most often 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 influence 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 that accounts for the nonthermal nature of the electron distribution and the multiphotonic electron emission. We also investigate with this model the influence 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 that can be reached by the AuNRs.

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EXPERIMENTAL RESULTS We aim at determining the effective optical absorption of plasmonic NPs during a laser pulse. For this purpose, the optical transmittance of an aqueous solution of AuNRs, with a mean AR 4.0 and an effective longitudinal localized surface plasmon resonance (LgSPR) peak at 772 nm, has been measured in a double laser beam configuration (see Supporting Information for details). Briefly, the transmittance is determined with a 100 fs pulsed laser at λlaser = 800 nm wavelength (Tfs) and with a continuous wave (cw) laser at 808 nm wavelength in the absence (T0cw) and in the presence (Tfscw) of the femtosecond laser pulses. In the latter case, the cw laser power is kept constant at a low value. Hence, measuring Tfscw 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 Figure 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, - eq , as the equivalent fluence of one pulse at equal power for the two lasers (upper x-axis in Figure 1a). In other words, - eq denotes the actual pulse fluence for the fs-pulsed laser, and for the cw laser it is defined as -

eq

= 0cw /frep

Figure 1. Transmittance of the AuNR solution measured only with the cw laser, T0cw (blue triangles), measured with the fs-pulsed laser at f rep = 2.5 kHz, Tfs (red circles), and measured with the cw laser during illumination by the fs-pulsed laser, Tfscw (black stars). The upper x-axis (blue) is common for the two types of laser. The lower x-axis (black) is the fs-pulsed laser excitation peak intensity, suited for measurefs . The error bars account for the ments of both Tfs and Tcw measurement uncertainty of the power meters. (a) Peak intensity from 1 to 10 GW cm−2. (b) Peak intensity from 0.1 to 4 GW cm−2 (below the partial melting threshold).

(1)

where f rep is the fs-pulsed laser repetition rate and 0cw is the reference cw laser intensity. As can be seen in Figure 1a, when the AuNR solution is illuminated only by the cw laser, the response is linear; that is, T0cw (Figure 1a, blue triangles) is constant within our range of incident power. However, when the AuNRs are excited by the fs-pulsed laser, Tfs (Figure 1a, red circles) increases with increasing excitation peak intensity. The value of Tfs is sensitive only to the optical properties of the solution during the laser pulses. This ultrashort optical response can be ascribed to both (i) the transient ultrafast phenomena induced in the AuNRs during each pulse and (ii) 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 effects that may modify the NP optical properties but cannot contribute to the Tfs signal detected by our experiment. These effects arise within a time scale larger than the pulse width and relax along durations much smaller than the delay between two successive pulses (400 μs), as (i) formation and collapse of nanobubbles; the bubble formation

time (∼80 ns) is much larger than the pulse width, 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) noncumulative thermal effects, 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 between two successive pulses;27 and (iii) mechanical effects 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 that are 3857


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smaller,36 and the LgSPR absorption band is blue-shifted compared to the initial one (see Supporting Information, Figure S4 and discussion). As the transmittance is still measured at 800 nm, it increases due to this blue-shift. Higher peak intensity induces a stronger melting, then resulting in the increase in Tfscw. Let us note that this should also affect the value of Tfs; however, as the absorption cross section at 800 nm decreases due to the NP shape modification, the magnitude of the nonlinearity due to electronic effects decreases as well, which compensates for the shape-related increase of transparency. Consequently, no significant change in the slope of Tfs 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 Information, part 3). The curve for Tfs seems to tend to the stationary value, namely, T0cw, 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 in Figure 1b. Surprisingly, Tfs values lower than T0cw are found in the range 0.1−0.4 GW cm−2. This result will be interpreted in the following section.

much larger than the pulse width; 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 effects do then not affect 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 Tfs, can stem either from pure ultrafast electronic effects in the metal during the laser pulse or from slow or irreversible photothermal effects, 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 effect could only be ascribed to the cumulative local heating by successive pulses;12 and (ii) the permanent morphology changes, including the aggregation or the partial melting of the NRs.32−34 On 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 effect (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 wavelengths close to λLgSPR the absorbance decreases, while at wavelengths much higher than λLgSPR the absorbance increases. Compared with Tfs, Tfscw is sensitive only to slow varying or irreversible effects. For instance, the possible generation of nanobubbles by the fs pulses does not influence Tfscw, as the laser repetition period is much larger than the nanobubble lifetime, as stated above. Therefore, in order to know if the nonlinearity observed (through Tfs) is due to electronic or photothermal effects, we should compare T0cw and Tfscw (Figure 1a, red circles and black stars, respectively). As long as the excitation peak intensity is lower than 5 GW cm−2, Tfscw overlaps with T0cw. This means that for weak excitation intensity the morphology of AuNRs is not modified and there is no significant cumulative heating of the solvent around NPs. The rising difference between Tfs and Tfscw is then due to fast electronic effects generated during the laser pulses. Let us again note that, while the optical properties of the NPs are modified by the ultrashort laser pulses, the time range along which these changes are significant (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 modification to the signal measured with the continuous laser beam is then fully negligible, and Tfscw accounts for the stationary transmittance of the sample only. This explains that Tfscw overlaps with T0cw in the weak excitation intensity range. Nevertheless, if the peak intensity is increased over 5 GW cm−2, Tfscw increases. The existence of a threshold in the power dependence of Tfscw reveals that the permanent or long-lasting modification 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 that is detected is then due to the partial melting of the NRs. AuNRs begin to melt partially, their aspect ratio becomes

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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 developed in our group19 (see Supporting Information). The effective mean absorption cross section, ⟨σabs⟩, is then deduced. In addition, the theoretical and experimental values exp of the relative variation of the cross section, Δtheo abs and Δabs , are extracted from the simulation and experimental results, respectively (Supporting Information Sections 1.3 and 2.3). Influence of Peak Intensity. Let us focus on the variation of the effective absorption with varying laser peak intensity, I0. Figure 2a reports the simulated variation of Δabs with increasing peak intensity in a logarithmic scale. The effective absorption cross section first increases for intensity values up to I0 = 100 MW cm−2 and then decreases, becomes lower than the stationary value (Δabs < 0), and still decreases linearly with log I0. The corresponding experimental variation is displayed in Figure 2b. Within the experimental range for I0 the comparaison with Figure 2a shows that the calculated variations of Δabs agree well with the experimental ones as long as I0 remains below the AuNR reshaping threshold discussed above. As in the simulation, Δabs goes from positive to negative values with increasing peak intensity, the sign inversion occurring 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 Figure 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 3858


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Figure 3. Calculated absorption cross section spectrum of a 50-by12.5 nm2 AuNR, excited by a 100 fs pulse centered at t = 0, linearly polarized along the AuNR long axis, at three instants: before the pulse (blue), during the first pulse half (red), and just after the pulse (yellow). The vertical dashed line denotes the laser wavelength.

evaluation yields 16 fJ. However, as they used the stationary absorption cross section in the exploitation of their experimental results, obtained with 100 fs laser pulses tuned to the NR LgSPR, their value of , tot melt may be overestimated, 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. Influence 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 Δtheo abs reproduce well the ones of Δexp abs . However, it can be noticed in Figure 2 that the predicted Δabs values 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 field 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 only the longitudinal polarization is considered. Nevertheless, the other NRs in the solution absorb less energy, as they are not aligned with the field. In other words, the effective 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 effect of the random orientation distribution, we should average the Δabs value over this range of effective peak intensity. Finally, the influence on our results in Figure 2a would be to flatten the curve and slightly shift the zero crossing point to higher intensity values, which would further improve the agreement with the experimental results (Figure 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 Δtheo abs with peak

Figure 2. Relative variation of the effective absorption cross section, Δabs, as a function of peak intensity. (a) Simulation result calculated with a 50-by-12.5 nm2 AuNR excited at λlaser = 800 nm with a 100 fs pulse linearly polarized along the AuNR long axis. The gray zone corresponds to our experimental range. (b) Δabs value determined from experimental results at two laser repetition rates: 5.0 kHz (blue triangles) and 2.5 kHz (red dots).

wavelength, λlaser, and especially on the spectral interval between λlaser and the LgSPR wavelength, λLgSPR, ⟨σabs⟩ can be larger or smaller than σ0abs. Now, increasing the pulse energy induces stronger plasmon damping and broadening. Consequently, at a fixed λlaser, the instantaneous variations of σabs along the pulse passage may depend on I0, which will affect the effective average value ⟨σabs⟩. This explains the sign inversion of Δabs reported in Figure 2a and b. Let us notice that the partial melting threshold I0melt = 5 GW cm−2 found in the present experiments corresponds to an energy absorbed by one part = I0melt⟨σabs⟩τp = 12.3 fJ. As in ref 35, AuNR of , melt thermodynamic considerations based on bulk gold properties led us to an energy of , tot melt = 21.5 fJ needed to totally melt a 50-by-12.5 nm2 AuNR. This value is on the same order of magnitude as our experimental finding, though slightly higher. This is nothing but surprising, as our experiment allows evaluating 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 contrast, Link and El-Sayed 2 determined a value of , tot melt = 65 fJ for a 44-by-11 nm AuNR 35 with AR = 4.1 in water, while the classical thermodynamic 3859


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intensity are reported in Figure 4. Following the discussion developed in the preceding section, the spectral interval

Figure 4. Calculated relative variation of the effective absorption cross section, Δtheo abs , at 800 nm wavelength vs peak intensity for AR = 3.8 (blue squares), AR = 4.0 (orange dots), AR = 4.2 (black diamonds), and AR = 4.6 (green triangles).

Figure 5. Same as Figure 1a but with an f rep = 5.0 kHz repetition rate.

lead to cumulative thermal effects.12 In that case, a thermal background settles and its mean temperature is as high as the pulse energy is large. We believe that this induces the heating of the solvent surrounding the NRs, which modifies their optical properties as evoked above. This effect occurs with no threshold and may explain the discrepancy of Tfscw and T0cw in Figure 5. The same experiment performed at a lower NP concentration confirms this analysis (see Supporting Information, Figure S4 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, Figure S6). The thermal background due to the cumulative effect then has only little influence on this threshold; however, the further changes of morphology probed by the modification of Δexp abs (Figure 2b) are obviously favored by the fact that for f rep = 5.0 kHz the AuNRs passing through the cw laser beam experience twice as many fs-laser pulses as for f rep = 2.5 kHz. It can then be inferred from these observations that the surface diffusion 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).25,33,34,36−38 The cumulative thermal background slightly reinforces this effect at higher f rep and high I0. Influence of Pulse Duration. As discussed in the introduction, many recent developments based on the LSPR exploit the specific properties brought by the use of ultrashort laser pulses rather than continuous light, especially for biomedical9 or ultrafast photonics1,39 purposes. Hence, all effects 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 benefits ultrashort pulse excitation, as it provides a higher and more localized heating as compared with cw excitation: the shorter the pulse duration, the more confined the heating.12,44 This is particularly interesting for photothermal cancer therapy by local hyperthermia or targeted drug delivery.9,41,45,46 Thus, it leads us to study the effect of pulse duration on Δabs. For this, we fix the pulse fluence value; that is, I0τp is a constant. We

between λlaser and λLgSPR varies as λLgSPR shifts with varying the AuNR AR, λlaser being fixed in the present calculation. This results in a very different I0 dependence of Δabs for the different ARs under consideration, as can be seen in Figure 4. Hence, we can have two antagonist effects: for the AuNR with λLgSPR = λlaser (case AR = 4.3), Δabs decreases with increasing peak intensity, whereas for the AuNR with λLgSPR far from λlaser Δabs can be either positive or negative, depending on the peak intensity. In the solution, all the contributions from the different ARs have to be added, which results in a spatially averaged value of Δabs over the shape distribution different from the one expected for the single most probable AR. Let us finally underline that when the laser line matches exactly the NR LgSPR (i.e., λlaser = λLgSPR) and the NR is aligned with the pulse polarization (black diamonds in Figure 4), the actual energy absorbed by the NR from the pulse is only half the value that would be evaluated from the stationary optical properties (σ0abs) 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 Δabs mean value of a AuNR solution, it is then necessary to account for both the orientation and shape distributions of the AuNRs. Influence of Laser Repetition Rate. Measurements have been performed at doubled repetition rate f rep = 5.0 kHz. The results are reported in Figure 5, where the transmittance is displayed as a function of peak intensity. It can be seen that Tfscw departs from T0cw even from low I0 values, which contrasts with what was observed at 2.5 kHz (Figure 1a). This trend is further enhanced after 5 GW cm−2, now as for f rep = 2.5 kHz. The corresponding Δexp abs value is reported in Figure 2b (blue triangles) as a function of I0. The curves at the two repetition rates overlap quite well below the partial melting threshold, since the difference between Tfscw and T0cw is about 1%, which cannot be detected in Figure 2b as being smaller than the error bar. Decreasing the delay between successive laser pulses can 3860


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choose the pulse energy as equivalent to the 100 fs pulse with I0 = 2 GW cm−2. Δabs is then calculated for a 50-by-12.5 nm2 AuNR for different values of τp. The shortest pulse is 50 fs long, with which the model is still valid.19 Figure 6 shows that

Figure 7. Maximum temperature increase reached by a AuNR excited by a 100 fs laser pulse at λlaser = 800 nm as a function of peak intensity, calculated either by accounting for the hot electron effect (red line) or with stationary σabs (blue line), displayed in double-logarithmic scale.

2 Figure 6. Δtheo abs calculated for a 50-by-12.5 nm AuNR aligned with the field polarization with a constant fluence of 200 μJ/cm2 as a function of pulse duration.

temperature reached at high laser fluence is lower than the one evaluated with only stationary properties. In our example of Figure 7, the discrepancy is about −64% at I0 = 1 GW cm−2: The simple use of σ0abs predicts a temperature rise of 1002 K, while the rigorous account for the hot electron distribution through the use of ⟨σabs⟩ gives 365 K only. This could explain, for instance, that the calibration method used by Petrova and co-workers in ref 25, based on the evaluation of the TNP 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 fluence.

Δabs is always negative and |Δabs| increases as the pulse duration decreases. This trend is totally expected. If τp → ∞, then ⟨σabs⟩ → σ0abs; that is, Δabs → 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 modified.12,15,22,24 We show here that this is all but true: the shorter the laser pulse, the more necessary it is to account for the effect of the hot electron distribution in the optical properties, except of course in the case of very weak incident fluence. In addition, let us finally underline that for a pulse duration shorter than the characteristic time of electron thermalization (∼500 fs47), the two-temperature model is not suited to describe the transient response of the NP during the pulse itself.19 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 ⟨σabs⟩. For this, we assume that all the energy absorbed by the AuNRs relaxes instantaneously into heat. Then the maximum temperature increase, ΔTNP, can be calculated as I0τpσabs ΔTNP = VNPρAu cAu (2)

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CONCLUSION We have studied both experimentally and theoretically the influence 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 50by-12.5 nm2 AuNR (AR = 4.0) excited by a 100 fs pulse at 800 nm wavelength linearly polarized along the long axis of the AuNR. The relative variation of the effective 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 fixed orientation. Besides, the simulation helped us to explain the sign of Δabs, which depends intricately on the pulse peak intensity, wavelength, and duration, as well as on the NR AR. Indeed, due to the pulseinduced 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 ⟨σabs⟩. Investigating the influence of the pulse

where ρAu is the mass density of gold (ρAu = 19.3 × 103 kg m−3) and cAu is the specific heat of gold (cAu = 129 J kg−1 K−1). ΔTNP represents the upper limit of the actual NP temperature rise. In Figure 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 the longitudinal plasmon mode (λlaser = λLgSPR), calculated with either ⟨σabs⟩ or σ0abs. Due to strong plasmon damping during the pulse passage, it can be observed that the actual NP 3861


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duration at fixed pulse energy, we demonstrated that the shorter the pulse duration, the larger the relative variation of the absorption cross section. This means that, when using subpicosecond laser pulses to generate any phenomenon from a plasmonic nanostructure, assessing the actual energy input requires considering the ultrashort variation of its optical properties along the pulse passage. In addition, due to the essential nonthermal nature of the hot electron distribution in this time range, this cannot be addressed by the twotemperature model. Finally, we applied the effective 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 actual heating is lower than the one evaluated by using the stationary σabs. There has recently been 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 blackbody-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 influence of hot electrons on the value of ⟨σabs⟩ in order to precisely assess the multiphoton order of the photoluminescence process and then gain a deeper understanding of the mechanisms involved.

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.8b01012.

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Article

Model: theoretical optical absorption cross section, dynamics of the absorption cross section, and effective 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; reversibility of experiments below the threshold (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Xue Hou: 0000-0002-5218-9891 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank T. Labouret for helpful discussions. This work has benefited from the financial support of the Labex LaSIPS (ANR-10-LABX0040-LaSIPS) managed by the French National Research Agency under the “Investissements d’Avenir” program (no. ANR-11-IDEX-0003-02), the “Plan Cancer” managed by the French ITMO Cancer (no. 17CP07700, project HEPPROS), and the Institut d’Alembert in Ecole Normale Supérieure Paris-Saclay (FR CNRS 3242) (project GESPER). 3862


ACS Photonics

Article

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Absorption of Ultrashort Laser Pulses by Plasmonic Nanoparticles: Not

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