# Quantification of ultrafast nonlinear photothermal and photoacoustic effects in molecular thin films via time-domain Brillouin scattering

Valentin Cherruault, Franck Camerel, Julien Morin, Amédée Triadon, Nicolas

Godin, Ronan Lefort, Thomas Pezeril, Olivier Mongin, Jean-François

Bergamini, Antoine Vacher, et al.

► To cite this version:

Valentin Cherruault, Franck Camerel, Julien Morin, Amédée Triadon, Nicolas Godin, et al. Quantification of ultrafast nonlinear photothermal and photoacoustic effects in molecular thin films via time-domain Brillouin scattering. The Journal of Chemical Physics, 2025, 163 (2), pp.024201. 10.1063/5.0271460. hal-05343818

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Distributed under a Creative Commons Attribution 4.0 International License
Quantification of Ultrafast Nonlinear Photothermal and Photoacoustic Effects in Molecular Thin Films via Time-Domain Brillouin Scattering

Valentin Cherruault,¹ Franck Camerel,² Julien Morin,¹ Amédée Triadon,²,³ Nicolas

Godin,¹ Ronan Lefort,¹ Olivier Mongin,² Jean-François Bergamini,² Antoine Vacher,²

Mark G. Humphrey,³ Maciej Lorenc,¹, * Frederic Paul,², † and Thomas Pezeril¹, ‡

¹Institut de Physique de Rennes, UMR CNRS 6251, Université de Rennes, 35042 Rennes, France

²Institut des Sciences Chimiques de Rennes, UMR CNRS 62226, Université de Rennes, 35042 Rennes, France

³Research School of Chemistry, Australian National University, Canberra, ACT 2601, Australia

(Dated: Tuesday 3rd June, 2025)

Improving the efficiency of photothermal (PT) therapies and photoacoustic (PA) imaging at the microscopic scale hinges on developing multiphoton-absorbing photothermal molecules or contrast agents that operate in the near-infrared (NIR) range. These advanced agents or molecules will enable excitation with NIR lasers, in an improved transparency range for biological tissues, while enabling minute, highly localized spatial control of the excitation area. However, progress in this field requires innovative experimental techniques to characterize photothermal and photoacoustic effects under multiphoton excitation. In this article, we showcase a study of a model organometallic molecular compound excited via two-photon absorption (2PA) using femtosecond laser pulses. Based on a time-domain Brillouin scattering technique, well adapted for investigating ultrafast nonlinear optical absorption processes in ultrathin films on substrates, we determine the effective nonlinear absorption coefficients of the compound directly linked to PT/PA. Our findings provide a practical approach for exploring and optimizing nonlinear PT/PA absorbers and contrast agents.

INTRODUCTION

Photoacoustic imaging has emerged as one of the fastest-growing fields in molecular bioimaging over the last decade [1]. This imaging technique relies on the unique capabilities of “contrast agents,” which are photothermal substances that absorb light, convert the captured photon energy into heat [2, 3], and release acoustic waves through rapid thermal expansion. Upon photoexcitation, these acoustic waves propagate through the medium and can be detected at various locations. By applying sonar-inspired principles to analyze and process the detected signals, it becomes possible to reconstruct detailed 3D images of biological tissues surrounding the emitting sources [1, 4].

Despite significant technical advances in image processing, photoacoustic microscopy still faces substantial challenges, particularly rapid resolution losses when imaging deeper tissues. Anticipating that the evolution of contrast agents might follow a similar trajectory to photosensitizers used in photodynamic therapy [5], researchers have recently proposed transitioning from one-photon absorbing (1PA) contrast agents to two-photon absorbing (2PA) ones [6]. The net result of such a shift is not only to shift the photoexcitation energy to longer wavelengths –typically within a spectral range where biological tissues are more transparent–thereby allowing the laser beam to penetrate deeper into samples, but also to minimize collateral photodamage. This is because mul-

tiphoton absorption is confined to the focal point of the excitation laser beam, unlike the broader absorption profile seen in 1PA processes [5]. Furthermore, the exquisite 3D spatial control and nonlinear intensity dependence of the 2PA process are expected to significantly enhance imaging contrast compared to the more conventional one-photon approach [6–8]. However, despite a few promising experiments in this domain [6, 7, 9], further work is needed to translate these expectations into practical outcomes. It is worth noting that many techniques currently employed to study linear PT [10–13] or PA effects [14] are often ill-suited for investigating their nonlinear counterparts due to the highly localized nature of multiphotonic excitation.

In this context, the development of experimental methods capable of characterizing and optimizing nonlinear PT and PA phenomena is highly desirable to accelerate the design of advanced multiphotonic contrast agents. There remains an urgent need to identify high-performance 2PA chromophores for nonlinear photoacoustic imaging, as most clinically used contrast agents are still based on 1PA mechanisms. Unfortunately, techniques that enable accurate screening of 2PA-absorbing chromophores through direct monitoring of their nonlinear photothermal or photoacoustic effects are still scarce [15, 16].

In this article, we present a modified femtosecond pump-probe technique tailored for investigating 2PA properties of molecules organized in ultrathin film layers on substrates. The ultrafast 2PA process is characterized through time-domain Brillouin scattering, providing insights into the laser absorption dynamics of the compound. The technique draws inspiration from our previous work [17], where multi-photon absorption was de-

<footnote>* maciej.lorenc@cnrs.fr</footnote>

<footnote>† frederic.paul@cnrs.fr</footnote>

<footnote>‡ thomas.pezeril@cnrs.fr</footnote>
<figure><img src="image_2.png" /><figcaption>FIG. 1. (a) Organoruthenium compound 1 used in the study. (b) Classical deactivation pathways for a singlet excited state populated by one- (1PA) or two-photon (2PA) absorption and non-radiative relaxation that gives rise to heat release and phonons emission. (c) Sketch of the spinning femtosecond pump-probe setup depicting the circular laser trajectory on the sample surface.</figcaption></figure>

tected in nanocrystals. However, unlike our study[17] of a quasi-3PA (sequence of 2PA and 1PA from the excited state), our results focus now on a model organometallic molecule 1 presenting a textbook 2PA absorption band at the NIR pump wavelength and with a fairly large 2PA cross-section[18]. Additionally, we outline a streamlined method to accurately extract at once the nonlinear op- tical parameters of interest for this compound by com- bining 1PA and 2PA measurements, eliminating the need for additional assessments like heat capacity or thermal expansion measurements, but providing instead key data on its PT and PA effects at very short timescales.

METHODS

The investigated complex 1, spin-coated as an ho- mogenous thin-film on a fused silica substrate, is the known organoruthenium molecular compound depicted in Fig. 1(a). The film thickness at the vicinity of the laser-excited area is of 100 nm, with a thickness distri- bution or roughness below 5 nm and no apparent poly- crystallinity (see Supplementary for more details). Its relatively large 2PA cross-section expressed in Goppert- Mayer (GM) units σ$_{2}$ = 1075 ± 190 GM [18] at a 800 nm laser wavelength (with 1 GM equal to 10 − $^{50}$cm$^{4}$s), makes it an ideal molecular “model” for testing the propensity of time-domain Brillouin scattering to study nonlinear PT and PA effects. In the following, we demonstrate how to extract the effective nonlinear absorption coefficient α (2) from time-domain Brillouin scattering. The coefficient is linked to the 2PA cross section σ$_{2}$ (expressed in units of Goppert-Mayer (GM)) through the relationship [19],

$$
\alpha^{(2)} = \sigma_2 N_0 / E \quad (1)
$$

where N$_{0}$ is the molecular density of the compound (num- ber of molecules per unit volume) and E the photon en- ergy.

For diamagnetic, non-emissive molecules such as the one investigated in this study, heat release into the sur- rounding medium is driven by various non-radiative re- laxation processes and the simultaneous generation of

acoustic phonons. While the latter phenomenon has re- ceived limited attention since its initial exploration in the late 1960s, it is evident that not all non-radiative relaxation pathways contribute equally to the formation of acoustic waves, as their kinetics and temporal order- ing differ[2, 3]. The overall thermal relaxation process is traditionally conceptualized as depicted in Fig. 1(b) [3]. Briefly, after photoexcitation of the molecule into its first absorption band, the resulting Franck-Condon state un- dergoes a fast vibrational cooling into the singlet state S$_{1}$ (S$_{n}$), followed by internal conversion into the ground state S$_{0}$. A competing pathway involves stepwise decay to S$_{0}$ via the first triplet state T$_{1}$, initiated by intersys- tem crossing from S$_{n}$ to the triplet manifold, followed by vibrational cooling to T$_{1}$. Subsequently, reverse intersys- tem crossing returns the molecule to vibrationally excited (”hot”) S$_{0}$, followed by vibrational cooling. For many organic molecules, this instersystem crossing-mediated pathway is kinetically much slower and often irrelevant to the buildup of acoustic waves [15], as it leads to tem- porally delayed heat release. In short, the mechanism of heat release from a photoexcited molecule depends on the relative kinetics of competing internal conversion and in- stersystem crossing processes. Additionally, vibrational cooling efficiency is determined by the availability and nature of vibrational modes that facilitate energy trans- fer to the surrounding medium, typically a solvent acting as the heat acceptor.

In this study, time-domain Brillouin scattering (TDBS) is employed to investigate these non-radiative processes on femtosecond to picosecond timescales, pro- viding insights into the energy dissipation mechanisms that contribute to PT and PA effects. Our TDBS exper- iment has been thoroughly detailed in earlier work [17]. In essence, the setup uses a femtosecond Ti-sapphire Co- herent RegA 9000 regenerative amplifier, emitting 250 fs pulses at a 250 kHz repetition rate, centered at 780 nm with a maximum pulse energy of 4 µ J. The beam is split into pump and probe beams, with the pump beam pass- ing through a motorized delay stage for temporal control between the pump-probe beams on the sample. A key feature of the setup is the spinning wedge mirror, rotat- ing at 50 Hz, which enables pump-probe measurements
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<figure><img src="image_6.png" /><figcaption>FIG. 2. TDBS data at varying pump fluences at a pump wavelength of 780 nm. (a) Time-domain transient reflectivity data. (b) FFT of the time domain transient reflectivity data after slow background removal. (c) FFT amplitude of the Brillouin peak at 44 GHz versus pump fluence. (d) FFT phase of the Brillouin peak at 44 GHz versus pump fluence.</figcaption></figure>

at alternating locations on the sample, mimicking single-shot pump-probe experiments. This method is crucial for preventing cumulative heating or laser damage during measurements obtained at high laser fluences as in this paper. Both the pump (14 µm at $1/e^2$ for the 780 nm and 10 µm at $1/e^2$ for the 390 nm) and probe (8 µm at $1/e^2$) beams are spatially overlapped on the sample surface and scanned thanks to the spinning mirror in a circular trajectory of ~200 µm in diameter, as sketched in Fig. 1(c).

The organoruthenium molecular compound is totally transparent at the laser pump wavelength of 780 nm but exhibits a very strongly absorbing near-UV band corresponding to 2PA at half the pump wavelength of 390 nm, see Supplementary information. In fact, regardless of whether laser energy absorption in the thin film occurs via single-photon or multiphoton processes, it results in an ultrafast local temperature rise throughout the entire film thickness. This rapid thermal expansion generates an acoustic wavepacket, whose spatial profile closely matches the full film thickness, that travels through the

film and is simultaneously partially transmitted into the glass substrate at each propagation cycle. As the acoustic wave propagates, it is detected by the time-delayed probe pulse using TDBS. The overall probe beam, reflected from the sample interface and scattered from the acoustic wave packet, is directed to a photodiode in order to measure transient differential reflectivity $\Delta R/R$ as a function of time delay between pump and probe pulses.

## RESULTS AND DISCUSSIONS

In order to monitor the nonlinear excitation of propagating strains caused by nonlinear optical absorption in the film, a series of TDBS measurements across a wide range of pump fluences were conducted. Fig. 2(a) presents the TDBS data recorded at varying pump fluences at a pump wavelength of 780 nm for which the available laser energy is the highest. The TDBS data exhibit several characteristic features. First, there is a pronounced spike near zero time delay, which corresponds
to the absorption of the pump photons by the electrons in the material, leading to rapid changes in the compound optical properties and a strong reflectivity change of the probe light. This is followed by a long-lasting background signal, spanning hundreds of picoseconds, which represents the relaxation of the excited electrons back to the ground state (S₀) as illustrated in Fig. 1(b). The sharp rise in the background close to time zero indicates a fast relaxation from the excited state to the singlet state (S₁), while the flatter, prolonged background likely corresponds to the slower relaxation from the first triplet (T₁) to the ground state, which in the case of 1 might kinetically dominate internal conversion from the S₁ state given the existence of triplet ligand field states at low energy [18]. Both of these relaxation processes result in the release of heat and the generation of acoustic phonons within the compound. Superimposed on this electronic transitions background are oscillations that arise from the propagation of the acoustic wavepacket into the transparent glass substrate, see Fig. 2(a). These oscillations, known as Brillouin frequency oscillations, are characterized by a frequency v, which is linked to the velocity of the acoustic waves v and the refractive index n of the glass substrate, following the well-known relation [20],

$$v_B = \frac{2nv}{\lambda},$$

where λ is the probe wavelength. The refractive index of the glass substrate at 390 nm probe wavelength is well known, as is its sound velocity, so the ~44 GHz frequency peak highlighted in the fast Fourier transform (FFT) of Fig. 2(b), can be unambiguously identified as the Brillouin frequency of fused silica.

Since the thin film is transparent at the pump wavelength, the Brillouin signals observed in the experiment must originate from nonlinear optical absorption processes, which exhibit a nonlinear dependence on the pump fluence. As shown in Fig. 2(c), the Brillouin FFT amplitude increases in a highly nonlinear manner with increasing laser pump fluence. Specifically, the amplitude demonstrates a quadratic dependence on the pump fluence, indicating a second-order response. This quadratic relationship becomes evident above a threshold fluence of approximately 300 mJ/cm². Below this threshold, as seen in Fig. 2(b) at 240 mJ/cm², no distinct Brillouin frequency can be detected. We also performed control experiments using the glass substrate alone, which is transparent at both the one-photon 780 nm and two-photon 390 nm absorption wavelengths. These tests confirmed that the substrate itself does not contribute to the Brillouin signal. Thus, we attribute the observed nonlinear optical absorption solely to the thin film, reinforcing the conclusion that the Brillouin signals are a result of the nonlinear 2PA properties of the organoruthenium compound, in line with our expectations [18].

It is not only the amplitude of the Brillouin oscillations that carries information about the laser excitation

<figure><img src="image_7.png" /><figcaption>FIG. 3. Brillouin and electronic transitions background amplitudes of Fig. (2), plotted on a logarithmic scale.</figcaption></figure>

process, but also the phase [21, 22]. This marks a significant departure from conventional Brillouin spectroscopy, where the phase is typically random and lacks informative value. In the time-domain Brillouin scattering experiments presented here, the Brillouin phase is directly linked to the characteristic timescale of the onset of laser-induced acoustic excitation. As a result, Brillouin oscillations provide two complementary insights: the amplitude reflects changes in the efficiency of the excitation process, while the phase reveals shifts in the temporal dynamics of energy deposition. The observed rather constant Brillouin phase in Fig. 2(d), indicates that the excitation mechanism remains fundamentally stable across the explored fluence range, up to the threshold where optical damage becomes apparent.

These results conclusively demonstrate that the investigated organoruthenium compound is effectively photothermally and photoacoustically activated through 2PA within the NIR-I transparency window, validating its potential use for nonlinear PA or PT applications.

An essential aspect of TDBS is its sensitivity to acoustic phonon wavepackets on the picosecond timescale. TDBS is not suitable to detect phonons with durations longer than a portion of the Brillouin period [21]. Therefore, the detection of Brillouin oscillations in the glass substrate indicates that the relaxation from the excited state (S₁) to the triplet state (T₁) is faster than a few picoseconds. If the relaxation would be slower, no Brillouin signal would be observed. This selective sensitivity of TDBS allows it to probe fast relaxation channels while excluding slower ones, which may still manifest in the reflectivity data as a slow electronic transitions background signal, as seen in Fig. 2(a).

To scrutinize the relationship between the Brillouin signal and the slow electronic transitions background, we plotted Fig. 2(c) on a logarithmic scale and included the electronic transitions background amplitude, arbitrarily estimated as the average transient reflectivity between 10 and 100 ps. This range avoids the time-zero spike
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>FIG. 4. TDBS data at varying pump fluences at a pump wavelength of 390 nm. (a) Time-domain transient reflectivity data. (b) FFT of the transient reflectivity data after slow background removal. (c) FFT amplitude of the Brillouin peak at 44 GHz versus pump fluence. (d) FFT phase of the Brillouin peak at 44 GHz versus pump fluence.</figcaption></figure>

and averages out the Brillouin oscillations, giving a more accurate measure of the thermal baseline. In Fig. 3, the quadratic dependence observed in both the electronic transitions background and the Brillouin amplitude with respect to pump fluence indicates that both channels are connected to 2PA process. This confirms that while Brillouin scattering represents the fast response, the slower background attributed to electronic transitions is also driven by the same 2PA mechanism.

From the theoretical point of view, the laser-excited strain linked to 2PA, derived from Zeuschner et al. [23], can be expressed in the form,

$$ \eta_{33}^{2PA} = \frac{\gamma}{\rho C_p} \sqrt{\frac{\ln 4}{\pi}} \left( \alpha^{(2)} \frac{\mathcal{F}_{2PA}^2}{\tau} \right) \quad (2) $$

where $\eta_{33}^{2PA}$ is the unidirectional longitudinal strain propagating along the sample normal, $\mathcal{F}_{2PA}$ the effective laser fluence for 2PA processes, $\rho$ the film density, $C_p$ the specific heat, $\gamma$ the linear thermal expansion coefficient, $\tau$ the FWHM laser pulse duration, and $\alpha^{(2)}$ the 2PA coefficient. Note that in Eq. (2), the effective fluence

$\mathcal{F}_{2PA}$ is linked to the laser fluence in air $\mathcal{F}_0$ through $\mathcal{F}_{2PA} \equiv \mathcal{F}_0(1 - \mathcal{R})$ with $\mathcal{R}$ being the air/film optical reflectivity at the pump wavelength. The strain given by Eq. (2) is directly proportional to the amplitude of the Brillouin signal recorded in the glass substrate. To go beyond a qualitative analysis and extract the coefficient $\alpha^{(2)}$ quantitatively from Eq. (2), several key parameters, such as density, heat capacity and thermal expansion, are required. Typically, these quantities are difficult to measure for thin films and can require separate, time-consuming experiments. However, we demonstrate that by performing measurements at two different pump wavelengths, one can bypass the need for these additional measurements.

With this goal, additional experiments have been conducted by changing the pump wavelength from 780 nm (2PA) to 390 nm (1PA), keeping the probe wavelength unchanged at 390 nm. The 390 nm pump is obtained by second harmonic generation in a $\beta$-BBO crystal from the 780 nm beam, for which the efficiency is in the percents range; the pump fluence in this case is a few percents
of the fluence reached for 2PA. Although the 1PA pump could not reach the same fluence as the 2PA, Fig. 4(a) evidences that Brillouin scattering can be detected from a 1PA process. In contrast to Fig. 2(a), Fig. 4(a) does not show any pronounced thermal or electronic transitions baseline, and the different TDBS acquisitions are superimposed. The Brillouin frequency in glass is very apparent in the FFT of the time-resolved data, see Fig. 4(b). As expected, the evolution of the Brillouin amplitude against pump fluence is linear, see Fig. 4(c). Moreover, the Brillouin phase in Fig. 4(d), is constant within the small fluctuations, indicating no modification of the 1PA excitation at this fluence range.

Notably, the Brillouin amplitude from 1PA in Fig. 4(c) reaches approximately $1 \times 10^{21}$ at a fluence of 6 mJ·cm$^{-2}$, while for 2PA in Fig. 2(c), the amplitude reaches around $1 \times 10^{21}$ at a fluence as high as 450 mJ·cm$^{-2}$. This indicates that 2PA is about 75 times less efficient than 1PA in this context. While this statement might appear as a limitation for using 2PA excitation for performing PA imaging, we must stress here that an even worse efficiency between 1PA and 2PA was stated for fluorescence imaging for which 2PA excitation is clearly recognized as being more advantageous [5]. The same will hold for PA imaging. This is because the lower excitation efficiency of 2PA is largely compensated by specific advantages of this kind of excitation which are: (i) deeper penetration of light into tissues when excitation takes place in proper NIR windows [5], (ii) better resolution achievable in 2PA due to the nonlinear dependance of the response used for imaging [7–9] and (iii) lower photodamages to tissues due to the more localized nature of the excitation during sampling [5]. These findings therefore highlight the potential for our technique to be used in screening a wide range of compounds, optimizing those that might show better performance under 2PA conditions.

The analytical expression of the laser-excited strain linked to 1PA, derived from Zeuschner et. al [23], can be expressed in the form,

$$ \eta_{33}^{1PA} = \frac{\gamma}{\rho C_p d} (1 - e^{-\alpha^{(1)} d}) \mathcal{F}_{1PA} \quad (3) $$

where d is the film thickness, $\alpha^{(1)}$ the 1PA optical absorption coefficient, and $\mathcal{F}_{1PA}$ the effective fluence of the 1PA pump. Note that Eq. (3) expresses the strain amplitude averaged over the film, while Eq. (2) expresses the homogeneous–constant–strain amplitude in the film. Since the probe wavelength is kept the same for both 1PA and 2PA experiments, the Brillouin amplitudes and the strains in Eq. (2) and Eq. (3) scale linearly for both situations. This linear relationship can be expressed as,

$$ \begin{aligned} A_B^{1PA} &= K_{1PA} \eta_{33}^{1PA}, \\ A_B^{2PA} &= K_{2PA} \eta_{33}^{2PA}. \end{aligned} \quad (4) $$

The Brillouin amplitude $A_B$ in Eq. (4) is related to various physical parameters, encapsulated in the scaling factors $K_{1/2PA}$, which includes the photoelastic coefficient

of the glass substrate, the refractive index, the acoustic properties of the film and on the shape of the strain profile excited [24]. If we make the reasonable assumption that laser excitation in the 1PA case is rather homogeneous through the film thickness, as it is in the 2PA case, then the strain profile generated in both cases should be identical, such that,

$$ K_{1PA} = K_{2PA} = K, \quad (5) $$

This assumption becomes more accurate as the film thickness decreases, simplifying the problem. Under this assumption, there is no need even to run TDBS simulations based on Finite Element Modeling (FEM) used in our previous studies [17] to extract $K_{1PA}$ and $K_{2PA}$. This allows for the direct extraction of the nonlinear absorption coefficient $\alpha^{(2)}$ without resorting to complex side-calculations for determining the strain profiles.

Numerically, the quadratic fit of Fig. 2(c) and of the linear fit of Fig. 4(c), lead to

$$ \begin{aligned} A_B^{2PA} &= a \mathcal{F}_{2PA}^2, \\ A_B^{1PA} &= b \mathcal{F}_{1PA}, \end{aligned} \quad (6) $$

with $a = 7.9 \times 10^{-9} \text{ mJ}^{-2} \cdot \text{cm}^4$ and $b = 7.4 \times 10^{-5} \text{ mJ}^{-1} \cdot \text{cm}^2$. By dividing these coefficients $a$ and $b$ by each other, we obtain from Eq. (3) and Eq. (2), an analytical expression that takes the form,

$$ \frac{a}{b} = \sqrt{\frac{\ln 4}{\pi}} \left(\frac{\alpha^{(2)}}{\tau}\right) \frac{d}{(1 - e^{-\alpha^{(1)} d})}, \quad (7) $$

that no longer contains unknown constants except for the 1PA absorption coefficient $\alpha^{(1)}$, which can be easily measured through widely available techniques. We used the ellipsometry method to extract a value of $\alpha^{(1)} = 3.72 \times 10^4 \text{ cm}^{-1}$, see Supplementary information. Numerically, we can then calculate the nonlinear optical constant. We obtain:

$$ \alpha^{(2)} = 1.7 \text{ cm/GW}. \quad (8) $$

The values obtained for $\alpha^{(2)}$ in our experiments are consistent with results previously reported [17, 23], supporting the reliability of our approach. From this experimental value, we calculate using Eq. (1) the 2PA cross section expressed in GM at 800 nm wavelength. Considering that the molecular density $N_0$ is of $5.04 \times 10^{20} \text{ cm}^{-3}$ (X-ray value for 1 in [18]) and that 1 GM is equal to $10^{-50} \text{ cm}^4 \cdot \text{s}$, we obtain,

$$ \sigma_2 = 81 \text{ GM}. \quad (9) $$

Interestingly, this value is approximately one order of magnitude lower than that derived from the conventional z-scan technique. While both femtosecond methods are subject to measurement uncertainties, these uncertainties are well within acceptable limits and below one order of magnitude. This discrepancy highlights the specificity
of the time-domain Brillouin approach, which is sensi-
tive to thermoelastic excitation of acoustic waves on a
picosecond timescale. Consequently, the coefficient ex-
tracted from Brillouin measurements reflects only a por-
tion of the total 2PA coefficient obtained through z-scan,
as the latter is not tied to relaxation pathways but rather
to the onset of 2PA. Accordingly, we tentatively propose
that only approximately one-tenth (81 GM/1075 GM)
of the energy needed to excite complex 1 in its S₁ state
does actually contribute to heat and acoustic wave gen-
eration within the picosecond timescale. This distinction
between z-scan and Brillouin emphasizes the unique ca-
pabilities of time-domain Brillouin scattering in isolating
the fastest dynamics underlying PT/PA processes. Ex-
tending this method to a broader range of materials will
provide deeper insights into the nonlinear optical prop-
erties of potential contrast agents, thereby aiding the de-
velopment of advanced tools for biomedical imaging.

SUMMARY

We highlight the potential of a slightly modified con-
ventional time-domain Brillouin scattering technique for
the all-optical determination of the effective two-photon
absorption (2PA) coefficient associated with photother-
mal and photoacoustic mechanisms. In this article, we
present a streamlined approach based on multi-spectral
pump-probe measurements, enabling rapid screening and
optimization of the nonlinear absorption properties of
nanoscale samples. Using this method, we successfully
demonstrated 2PA in a potential contrast agent, an

organometallic molecular compound, operating within
the biological transparency window NIR-I. These find-
ings pave the way for future research into the nonlin-
ear optical response of organic materials at picosecond
timescales, using optical radiation spanning from NIR-I
to the NUV.

SUPPLEMENTARY MATERIAL

The supplementary material includes details on the ex-
perimental setup and on sample characterization (AFM,
VIS absorption, ellipsometry).

ACKNOWLEDGMENTS

The authors would like to thank Ievgeniia Chaban
for her valuable scientific advice throughout the study.
We also extend our deepest gratitude to Keith Nelson
from the Massachusetts Institute of Technology for his
generous donation of a complete Coherent Rega sys-
tem, without which this research would not have been
possible. This research was funded by the Agence Na-
tionale de la Recherche under grant ANR-22-CE42-0001
GigaSpin, ANR-22-CE50-0018 PulseCoMeth, as well by
Région Bretagne under the SAD grant CHOCONDE and
the ARED grant BIFOCROM. We are also grateful for
the Australian Research Council (half co-tutelle stipend
to A.T.), alongside the financial support provided by the
CNRS IRP MAITAI and Rennes Métropole.

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