Broadband Transient Response and Wavelength-Tunable Photoacoustics in Plasmonic Hetero-nanoparticles

The optically driven acoustic modes and nonlinear response of plasmonic nanoparticles are important in many applications, but are strongly resonant, which restricts their excitation to predefined wavelengths. Here, we demonstrate that multilayered spherical plasmonic hetero-nanoparticles, formed by alternating layers of gold and silica, provide a platform for a broadband nonlinear optical response from visible to near-infrared wavelengths. They also act as a tunable optomechanical system with mechanically decoupled layers in which different acoustic modes can be selectively switched on/off by tuning the excitation wavelength. These observations not only expand the knowledge about the internal structure of composite plasmonic nanoparticles but also allow for an additional degree of freedom for controlling their nonlinear optical and mechanical properties.

( b ) ( c ) ( a ) Figure S1: TEM images of (a) Au/SiO 2 nanoparticles and (b,c) Au/SiO 2 /Au heteronanoparticles under different magnifications (please note that the nanoparticles tend to aggregate when deposited on a TEM substrate). The presence of the outer gold shell greatly reduces the visibility of the multilayer structure in the TEM images. In (c), the dominant nanoparticles are Au/SiO 2 /Au while smaller dot-like features are single ∼27 nm Au nanoparticles present in the solution as byproduct of the synthesis. The scale bar is 100 nm in (a, b) and 2 µm in (c).
SiO 2 shell coating. Before being coated by SiO 2 , the Au nanoparticles (Au60) were functionalized by mixing with a SH-PEG solution for at least 5 hours. Then, 16 mL of an Au60 solution (1 OD) was added to 6.4 mL of a functionalized-Au60 ethanol solution. The growth of SiO 2 was achieved using the classic Stöber method. 1 Briefly, 1.6 mL of a TEOS solution (2 µL in 2 mL ethanol) and 48 µL of NH 3 · H 2 O were added to the functionalized-Au60 ethanol solution. Then, the mixture was further stirred overnight. After being washed with ethanol three times, the SiO 2 coated particles (SiO 2 /Au) were dispersed in 14.8 mL of ethanol and were stored at 4 • C.
Gold shell growing. The Au seeds (2 nm diameter) were prepared using the method demonstrated by Duff et al., 2 the plating solution was prepared by mixing 50 mL of water, 12.5 mg of K 2 CO 3 , and 0.75 mL of an 1 wt% aqueous HAuCl 4 solution, and was aged at 4 • C overnight. Then, excessive APTMS was used to modify 6 mL SiO 2 /Au nanoparticles to provide amine groups for the attachment of the Au seeds on their surfaces. The solution was centrifuged to remove unattached Au seeds and dispersed in 1 mL of DI water. The Au-seed-SiO 2 /Au solution was mixed with a 8 mL plating solution as a source of Au 3+ and 34 µL of CH 2 O as a reductant. The gold shell appeared after 15 min further stirring. The thickness of the Au shell can be controlled by changing the ratio of Au-seed-SiO 2 /Au and  Orpheus, 150 fs) as a probe beam. The path length difference between the pump and probe beams is adjusted using a mechanical delay line. The probe beam is divided into a signal and reference beams, both focused non-collinearly into a cuvette with the nanoparticles with a 25x reflective objective (Thorlabs LMM-25x-UVV). The signal and pump beams were made collinear by a mirror arrangement so that only the propagation of the signal beam, but not the reference, is influenced by the pump beam. The signal and the reference were then aligned on the two photodiodes of a balanced detector. The detector was monitored with a lock-in amplifier (Stanford Research SR865A), which uses as its reference the frequency of an optical chopper positioned in the pump path. The probe wavelength can be tuned in the range 600-900 nm, which corresponds to the spectrum of interest for the plasmonic nanoparticles studied here. Simultaneous propagation of the signal and reference beams through the cuvette leads to automatic self-referencing when tuning the wavelength, allowing to record transient absorption spectra.

Numerical simulations.
Scattering on spherical Au/SiO 2 /Au multishells in water was simulated using the finite element method (COMSOL Multiphysics software) in a scattered field formulation. A single nanoparticle with the experimental geometric parameters (60 nm gold core, 10 nm silica shell, 20 nm gold shell) was simulated. The simulation domain was surrounded by a perfectly matched layer to assure the absence of back-reflection. The extinction efficiency was calculated dividing an extinction cross-section σ ext by its geometrical counterpart σ geom . The extinction cross-section σ ext is a sum of scattering (σ scat ) and absorption (σ abs ) cross-sections, which were obtained by integrating the scattered field power flow over a surface surrounding the nanoparticles and the total field power flow entering them, respectively, followed by the normalisation by the incident power flow. The energy absorption maps present the power dissipation density.
The optical properties of gold at various electron temperatures T e were calculated using the following approach. The gold permittivity can be decomposed into the contribution defined by interband transitions between occupied d-band states and unoccupied states in a hybridised sp-band ( inter (ω, T e )), and the intraband contribution of the conduction electrons in the sp-band ( intra (ω, T e )): (S1) In the visible spectral range, the interband permittivity of gold is defined by three optical transitions, one near the X point, and two near the L point (L + 4 and L + 5+6 ). 3 The imaginary part of the permittivity related to these transitions can be calculated using a theoretical approach developed by Rosei et al.: 4,5 Im where is the joint density of states (JDOS) for the corresponding transitions with j = X, L + 4 , L + 5+6 .
It is obtained by integration of the JDOS energy distribution D j (ω , E) over the excited states with an energy E in the conduction band taking into account Fermi-Dirac distributions f u (E, T e ) and f l (E −hω , T e ) of the carriers in the lower (l) and upper (u) bands, respectively, and energy-and temperature-dependent broadening of the upper (sp-band) due to electron scattering: which is similar to Lorenzian, but with exponential tails presenting a beter approximation of the transition lineshape in the considered wavelength range. 3,6 The total electron scattering rate γ(E, T e ) = γ el−ph + γ el−el (E, T e ) (S5) has contributions from electron-phonon scattering γ el−ph and energy-dependent electronelectron scattering where E F = 5.51 eV is the Fermi energy, Γ = 0.55 is the scattering probability averaged over the Fermi surface and ∆ = 0.77 is the fractional umklapp scattering. 7,8 The interband transmission coefficients A X /A L + 4 = 1 and A X /A L + 5+6 = 0.4 related to the values of the corresponding transition dipole moments, and broadening coefficient b = 2.5 were set to fit the Johnson-Cristy data for the permittivity of gold at room temperature. 3,6,9,10 The real part of the interband permittivity Re [ inter (ω, T e )] was found from its imaginary part Im [ inter (ω, T e )] using the Kramers-Kronig relations and an approach based on the Hilbert transform described in Ref. 11 The intraband component of the permittivity is given by the Drude formula where inf = 3 was set to fit the Johnson-Cristy data for the permittivity of gold at room temperature ? and ω p = 9.02 eV is the gold plasma frequency.

Calculations of natural vibration frequencies.
Free vibrations in vacuum of a core, a shell and a complete multishell nanoparticle can be easily obtained following Erdinger and Suhubi. 12 For spheroidal vibrations at frequency Ω, with l = 0, that are of interest in this work, in the absence of dissipation, the displacements and tractions can be expressed in spherical coordinates as u r (r) = Aqz 1 (qr)e −iΩt , where C L and C T are the longitudinal and transverse speeds of sound in the material, respectively, q = Ω/C L , Q = Ω/C T , µ L is the Lame parameter of material, A is the vibration mode amplitude, and z 0,1 are the linear combinations of spherical Bessel functions j 0,1 and y 0,1 in all regions except for the one that contains the origin, where only j 0,1 are used. Note that we omitted here u φ and t rφ as these components are related to torsional modes only, and are not of interest in this work as they cannot be optically excited. The free vibrations can be obtained by setting the appropriate boundary conditions for the displacement and traction: continuity on internal boundaries and the absence of traction on free boundaries.
This method produces a system of 2, 4, and 10 linear equations for the cases of a sphere, a spherical shell and a hetero-particle, respectively. The frequencies of the free vibrations can be obtained by setting the determinant of the system matrix to zero and obtaining the roots numerically. The frequencies quoted in the main text are obtained with this method, using a custom numerical solver written in Python.
Separately, we used an extended version of this approach as proposed in Ref. 13 to evaluate the damping of mechanical vibrations due to the presence of water. The method consists of searching for the solution in the surrounding medium as decaying spherical waves propagating at speeds where λ and µ are the viscosity coefficients of the surrounding medium, and λ L , µ L are its Lame parameters, related to the transversal/longitudinal speeds of sound, and the Bessel functions for the displacement given by a set of equations S8, are replaced with the Hankel functions of the second kind in order to fulfil the correct asymptotic behaviour at infinity.
The calculation may then proceed in a similar manner to the one mentioned above, with the exception that solutions are now searched with complex frequencies.
For the considered geometries, we have evaluated the damping and the shift of the real part of the frequency for the hetero-nanoparticle in water, as well as a gold spherical shell either having water both on the inside and outside or possessing a free surface on the inside and surrounded by water on the outside. In all cases, the damping was shown to have a minor effect (within few percent) on the real part of the normal frequency, which justified the use of the model without damping, the linewidths around 0.3 GHz were obtained from the imaginary part of the normal frequencies in all cases. Figure S2 shows the transient absorption spectra recorded under the 1028 nm excitation in a cuvette filled with pure deionised water, obtained under similar conditions as in Fig. 2.

Coherent cubic nonlinearity in water
While the long-lived induced transient absorption/bleaching signal, indicative of hot carrier dynamics in gold, is absent in pure water, the short-lived positive signal is still present.
Assuming that this coherent nonlinearity arises from efficient pumping into a vibrational level of water molecules with the difference frequency Ω = ω probe − ω pump , a good agreement with the known spectral features of the absorption spectra of water is obtained. 14,15