1. INTRODUCTION

Although metallic nanoparticles have been synthesized and widely used since ancient times due to their striking colors, the physicochemical properties of these nanostructures have been the subject of intense study only since the end of the past century. Optical fields drive the metal nanoparticle conduction electrons in collective oscillations known as localized surface plasmon resonances (LSPRs), producing a strong extinction cross section at specific wavelengths and optical responses that differ significantly from their bulk counterparts. The extensive interest in the properties of these materials gave birth to a name for this field as plasmonics or nanoplasmonics [1,2]. Later, and mainly due to their key functionality, metal nanoparticles started to be called nanoantennas [3,4] since these nanoobjects act as transductors of propagation into local electromagnetic fields and vice versa. Indeed, two fundamental properties made nanoantennas singular: the control and shaping of the electromagnetic landscape at nanoscale with tailored optoelectronic responses—by generating strong near-field enhancements and altering the local density of optical states (LDOS)—and the manipulation of scattered fields in the radiation zone. Many reviews have been written about the fundamentals and vast number of applications related to the nanoantennas’ capabilities to control the electromagnetic field (see, for example, Refs. [5–8]). Within the enormous extent of effects produced by the resonant and ultrafast optical excitation of plasmonic nanoantennas, in this review, we will focus on their ability to act as efficient local transducers of far-field electromagnetic radiation into mechanical energy, a topic on which there are only a few but excellent reviews [9–12]. They are, however, relatively old and do not address the most recent progress in the field.

Light interaction with mechanical systems leads to several exciting physical effects, from the ultrasensitive detection of mechanical motion down to the cooling of matter, driving it into the quantum regime [13–15]. Furthermore, optomechanical microcavities working at tens of GHz are promising devices to push the detection of quantum phenomena to higher temperatures [16] since the ground state temperature scales with the resonator frequency.

The ultrafast optical excitation and subsequent plasmon decay into coherent acoustic phonons convert nanoantennas into mechanical nanoresonators, showing a strong and periodic modulation of their optical properties at the GHz regime. In addition, the detection of these extremely small and fast movements can be done with remarkable sensitivity allowing their exploitation as exquisitely sensitive mechanical probes of their local environment. We will explore in this review the physics of these mechanical nanoresonators, and we will discuss from the first pioneer works carried out in ensembles, generally in the form of colloids, up to the recent studies where they become efficient transductors of energy at nanoscale when incorporated in phononic–plasmonic hybrid systems and probed individually. The work is organized to give a brief historical overview of the field in Section 2 with the mention of the physical processes involved in the generation and detection of coherent acoustic phonons, which have already been extensively reviewed, for example, in Ref. [9]. We then will carefully review the use of the finite element method (FEM) to solve the mechanical equations that describe the behavior of nanomechanical systems in Section 3, including a discussion of the phonon–plasmon coupling problem that leads to the dynamic modulation of the optical response. Section 4 gives insight into the experimental techniques to fabricate platforms where nanomechanical experiments have been done. The importance of the accurate measurement of frequency and quality factor ($Q$) of the nanoresonator is discussed, from both the fundamental point of view and novel applications, in Sections 5 and 6, respectively. The review explores in Section 7 the generation, propagation, and detection of surface acoustic waves (SAWs) with plasmonic nanoresonators, highlighting their importance for manipulating acoustic waves at nanoscale and the potential relevance for integration into hybrid devices. Finally, the conclusions and perspectives of the field are addressed in Section 8.

2. COHERENT ACOUSTIC PHONONS IN TIME DOMAIN EXPERIMENTS WITH PLASMONIC NANOANTENNAS

The development of ultrafast lasers in the early 1980s, together with the experimental schemes for their amplification and tunability, allowed the development of time-resolved spectroscopies in material science, particularly the optical generation of lattice vibrations in solids with spatial and temporal coherence called coherent phonons. Early experimental realizations of impulsive heating excitation of coherent acoustic phonons and SAWs in molecular crystals [17,18] were done using the transient grating technique, in which the interference of two pulsed lasers creates a standing wave of laser light that scatters a probe pulse carrying the material information. Shortly after, the first demonstration of the impulsive generation of coherent optical phonons in an organic molecular crystal [19] was performed using the same experimental method but with femtosecond lasers, which started an intense research field in condensed matter. We will not focus on coherent optical phonons in this review, although we recommend reading the exciting discussions about the underlying mechanisms for its generation [20–22]. Also, the development of today’s well-established picosecond acoustic technique [23–25] allowed the early study of coherent acoustic phonon propagation in thin films. Indeed, the interaction of ultrafast optical pulses with the surface of the films or with an intermediate material (generally a metal), based on the thermoelastic effect, produces a strain pulse probed with a second optical pulse as it propagates coherently back and forth into the film, making this method a powerful technique for thin film characterization [26].

In plasmonic nanoantennas, absorption of light pulses generates a population of energetic (hot) electrons that the resonant excitation of surface plasmons can further enhance. Electrons relax by Landau damping within the first few femtoseconds and then by electron–electron scattering in the next few hundred femtoseconds to picoseconds [27]. These processes are followed by thermal equilibrium with lattice ions also within a few picoseconds, thus originating mechanical oscillations of the nanostructure at the frequencies of its normal modes that are compatible with a symmetric excitation [9]. These coherent oscillations produce periodic disturbances in the dielectric constant that can be detected as a probe pulse’s transmission, reflection, or scattering changes in a typical pump–probe experiment. For modes with periods of the order of a few to few tens of picoseconds, the main driving mechanism comes from the dilation of the lattice produced by its rapid and homogeneous heating with a concomitant change in the equilibrium position of the oscillator [9]. This modulation of the size and shape of the nanoantenna will periodically modify the plasmon resonance at the phonon rhythm. As a result, the probe pulse transmission/reflection will show an oscillatory behavior [28]. Figure 1(a) depicts a typical non-degenerated pump–probe experiment. The sample, in this case, is a single gold nanorod (GNR) of around 100 nm in length fabricated by wet chemistry and deposited onto a glass substrate. A Ti:sapphire oscillator with a 95 MHz repetition rate and a few tens of nJ of energy per pulse is doubled and used as the pump to excite the gold interband transitions at 400 nm. The delayed probe at 800 nm is tuned at the LSPR. The plasmon resonance shift produced by the periodic mechanical deformation of the nanoparticle, shown in Fig. 1(b), results in efficient modulation of the probe transmission signal, $\Delta {\rm{T}}/{\rm{T}}$, as seen in Fig. 1(c). Besides the slow exponential decay, related to the thermal cooling of the sample, two vibrational resonances are detected: the extensional (9 GHz) and breathing (75 GHz) modes, both easily distinguishable in the fast Fourier transform (FFT), shown in Fig. 1(d). The deformation geometry associated with these two modes is represented in Fig. 1(e) (extensional mode at the top and breathing mode at the bottom), where the displacement patterns for the two fundamental modes of an isolated (free boundary conditions) nanocylinder resulting from the analytical solution of the elastic equations of motion are displayed [29].

 

Fig. 1. Coherent acoustic phonon dynamics in time domain experiments. (a) Schematics of the experiment for generating and detecting coherent acoustic phonons in plasmonic nanoantennas. The probe differential transmission is recorded in a typical non-degenerated pump–probe experiment (pump at 400 nm to excite hot electrons through interband transitions and probe at 800 nm, tuned at the LSPR) with lock-in detection. (b) Simulated absorption cross section of a single gold nanorod 117 nm in length and 32 nm in width (solid line). The dashed line shows schematically the plasmon resonance shift, mainly due to changes in the aspect ratio of the GNR. (c) Top: experimental differential probe transmission signal ($\Delta {\rm{T}}/{\rm{T}}$) for the gold nanorod shown in the SEM image in the inset (100 nm scalebar). Bottom: subtraction of the exponential decay and later decomposition into the two modes: extensional (low frequency) and breathing (high frequency) (d) Normalized amplitude of the fast Fourier transform of the signal shown in (c), after the exponential decay subtraction. (e) Diagram of the analytical solution for an isolated (without any contact) nanocylinder, displaying the deformation pattern associated with the two fundamental modes. Reprinted with permission from Hu et al., J. Am. Chem. Soc. 125, 14925–14933 (2003) [29]. Copyright 2003 American Chemical Society, https://doi.org/10.1021/ja037443y.

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The first observation of coherent acoustic phonons in metal nanoparticles using a pump–probe experiment was done for tin and gallium, fabricated by evaporation–condensation in an ultrahigh vacuum [30]. However, most of the pioneer early works [31–36] performed ensemble measurements using colloidal noble metal nanoparticles fabricated by chemical synthesis, immersed in liquid (cuvette), or embedded in a matrix. Indeed, coherent vibrations have been detected since then in many different geometries, such as nanorods and nanospheres [33,37,38], ellipsoids [31], bipyramids and nanojavelins [39–42], nanopolyhedrons [43], and bimetallic alloyed and core–shell nanoparticles [44–47].

Note that each mechanical oscillation normal mode of the nanoresonators inside the ensemble is characterized by two relevant parameters: frequency $f$ and $Q$. The frequency of each eigenmode assigned to an individual nanoantenna is determined by the size, shape, and material (density, elasticity, crystallinity) and by the boundary conditions. In an ensemble, the frequency measurement will not only be affected by the size and shape dispersion of the sample but also will lose the local environment sensitivity because of the ensemble averaging. In the same way, the $Q$ of the nanoresonator, which accounts for the internal and external losses and is related to the phonon decay time $\tau$ by $Q = \pi f\tau$, will naturally not reflect the interactions appropriately in ensemble measurements [11]. Both for the fundamental studies of the underlying physics that describes the mechanics of nanoantennas and the environment and to move towards applications, single-particle experiments are mandatory. That is why in recent years, measurements have moved to schemes in which the nanoantennas are incorporated into photonic platforms, typically deposited or grown on substrates with the possibility of accessing individual objects [48].

3. MECHANICAL SIMULATIONS IN SPECTRAL AND TIME DOMAIN REGIMES USING FINITE ELEMENT METHOD

Accurate numerical calculation of the oscillation modes of nanoantennas is a fundamental tool for interpreting the experimental results of increasingly complex nanoresonator systems interacting with the environment and for designing required properties. Only a few geometries (isotropic spheres, long cylinders, and plates) can be solved by analytical methods (see Ref. [9] for complete formulas), and consequently, simulations should solve all the rest. The continuum mechanics theory has proven to be a reliable tool to validate and predict the acoustic response of structures even with sizes down to a few nanometers [49,50]. Since the displacement amplitudes at reasonably low pump powers are expected to be much smaller than the geometric length scale of the nanoparticles, it is assumed that the linear elasticity theory can describe these systems.

The mechanical response of a solid continuum material [51] is given by the Cauchy momentum equation

 

Fig. 2. Frequency domain simulations of the mechanical response of a (a) ${{140}} \times {{35}}\;{\rm{nm}}$ disk and (c) ${{140}} \times {{60}} \times {{35}}\;{\rm{nm}}$ rod, both structures supported by a quartz substrate with a 2 nm thick Cr adhesion layer. (a), (c) Designs used for FEM simulations in COMSOL Multiphysics. (b), (d) Left: eigenmode spectrum of the average displacement for 100 K increase in the lattice temperature. Right: displacement map for the main acoustic resonances (${{20}} \times$ scale factor applied to highlight deformation) marked with symbols in the left panels. An isotropic loss factor $\eta = {0.1}$ was used in the gold domain to account for internal losses.

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This set of equations [Eqs. (1) and (2) plus Hooke’s law], together with the boundary conditions, can be solved by the FEM, in which the space dimensions are discretized by creating a mesh with a finite number of points that constitutes the solution domain. Given the finite computational resources, perfectly matched layers (PMLs)—non-reflecting domains used to truncate the physical domain (e.g., the thickness or lateral boundaries of the glass substrate)—are used to simulate an infinite medium by absorbing propagating acoustic waves traveling out of the computational domain. Continuity of stress and displacement are usually considered at all boundaries, where defects are neglected and perfect coupling between different materials is assumed.

Given a homogeneous illumination and a fast diffusion of hot electrons in the nanoantenna lattice, an isotropic thermal expansion strain proportional to the increase in lattice temperature following plasmon decay is considered as the initial excitation that sets the particle in motion after pulsed laser excitation [52,53]:

For describing losses in the material, a viscous stress component according to the Kelvin–Voigt model (elastic and viscous mechanism acting in parallel) can be considered [56]:

On the other hand, for simulations in the frequency domain, the harmonic time dependence of the displacement field and the external forces can be explicitly expressed as follows [9,57]:

To account for intrinsic damping mechanisms in the metal in a frequency domain analysis, viscous stress proportional to the stiffness tensor is usually considered [53,56]:

The free vibrational modes can also be easily obtained through an eigenfrequency study, solving the equation of motion in the absence of any external force: ${{\boldsymbol F}_{\rm{V}}} = 0$. Harmonic solutions of this analysis provide the deformation shape of each eigenmode, but not the amplitude, for which it is required to know the excitation and damping processes. However, a difficulty of this method that arises when simulating nanoresonators coupled to a medium is that it is necessary to distinguish the true nanostructure eigenmodes from those spurious eigenmodes that result from having truncated the size of the environment domain. For a thorough description of this type of analysis, see Ref. [57].

Figure 2 shows, as an example, a frequency domain study of the vibrational response of two different nanostructures, a nanorod and a nanodisk, supported by a substrate. Simulations were carried out using the Structural Mechanics module of the commercially available FEM solver software COMSOL Multiphysics, exploiting the symmetry of each geometry (and the excitation mechanism) to reduce the simulated volume and, thus, the computation time. Figures 2(a) and 2(c) show the models that were implemented in the simulations: the mechanical response of the nanodisk was calculated via 2D axisymmetric calculations using the geometry displayed in Fig. 2(a), while in the case of the rod, the reflection symmetries were exploited to reduce the size of the model, simulating only a quarter of the complete geometry, shown in Fig. 2(c). The phonon spectra can be quantified by integrating the absolute value of the displacement field components in the nanoparticle volume, as shown in Figs. 2(b) and 2(d), where three resonances in the 0–50 GHz range are noted. The corresponding deformation maps can be found in the right panels of Figs. 2(b) and 2(d).

 

Fig. 3. Phonon–plasmon coupling. (a) Left: displacement spectra of a free gold nanorod 61 nm long and 22 nm wide, sampled at one end (green) and at a midpoint of the surface (magenta). Right: deformation shapes corresponding to the main mechanical modes: extensional (17 GHz) and breathing-like (117 GHz). (b) Changes in extinction cross section in response to the vibrational modes for extensional (left) and breathing (right) modes. Upper (lower) panels show the differential (total) extinction cross section as a function of wavelength. Spectra of the expanded, nondeformed, and contracted structures are shown in the lower panels by blue, black, and red curves, respectively. Adapted with permission from Ahmed et al., ACS Nano 11, 9360–9369 (2017) [28]. Copyright 2017 American Chemical Society, https://doi.org/10.1021/acsnano.7b04789. (c) LSPR shifts in response to extensional (left) and breathing (right) modes of a gold nanorod of the same dimensions as in (a), (b), separating each one of the mechanism contributions to the phonon–plasmon coupling. ED, electron density; DP, deformation potential. Adapted with permission from Saison-Francioso et al., J. 1046 Phys. Chem. C 124, 12120–12133 (2020) [60]. Copyright 2020 American Chemical Society, https://doi.org/10.1021/acs.jpcc.0c00874.

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There are many different approaches to describe and quantify the mechanical response of these nanosystems, such as sampling the displacement at a given point of the geometry [28,59] or integrating the displacement amplitude in a surface or volume [as exemplified in Fig. 2(b) and 2(d)] [53]. In most studies, the transient transmission/reflection change is assumed to be proportional to the mechanical displacement amplitude, and then only mechanical simulations are performed. Nevertheless, the link between the acoustic vibration and the dynamic modulation of the optical response of the system is not straightforward. A more complete and accurate description should contemplate the phonon–plasmon coupling mechanisms that lead to dynamic modulation of the optical response of plasmonic nanoparticles [28,60]. Ahmed et al. [28] developed a numerical method to predict the changes in the plasmonic response of a vibrating metal nanoparticle based on three different contributions: changes in the nanoparticle shape, modifications in the free electron density due to changes in its volume, and changes in the interband transition energies through the deformation potential. First, the frequency and shape of the acoustic modes are calculated through FEM calculations, as described above, and then the optical response of the deformed geometry is computed using the finite-difference time domain (FDTD) method. The authors show that the strongest phonon–plasmon coupling occurs when regions of the largest electric field overlap regions of the largest displacement. Figure 3 shows the changes in the optical response of a GNR when the two main mechanical modes are excited: extension-like and breathing-like. Figure 3(a) shows the displacement as a function of the vibrational frequency of two points at the nanostructure’s surface (marked with colored arrows in the right panel), which are relevant to follow one or the other mode movement. Figure 3(b) shows the changes in the extinction spectra of the expanded and contracted structures with respect to the nondeformed nanorod. These results show in a straightforward way that the amplitude and phase of the time domain signal will depend on the wavelength for each one of the modes. Furthermore, Saison-Francioso et al. [60] simulate how acoustic vibrations modulate the optical response of a GNR for the three separate contributions due to the different acousto-plasmonic coupling mechanisms. A linear relation between the LSPR shift and the mechanical deformation amplitude is found for all cases, as shown in Fig. 3(c).

The coupling of optical and mechanical modes in several different devices is a continuously rising research topic addressed by cavity optomechanics [13]. In this field, the leading concept is that via a complex coefficient that governs dispersive and dissipative coupling, light frequency and linewidth can be modulated through mechanical action. Plasmonic nanoantennas are certainly dissipative optomechanical systems with the ubiquitous presence of internal vibrational degrees of freedom, so theoretical tools of cavity optomechanics may apply. Indeed, simulations would benefit from developing theoretical frameworks for a deeper understanding of the underlying physics and saving computational time. This approach is especially attractive when optimizing a deformed system to obtain a predetermined optical response requires working within a large parameter space. However, there are only a few attempts to model sole nanoplasmonic systems as such Refs. [61,62]. In contrast, in their interaction with molecular vibrational modes, as in surface enhanced Raman scattering (SERS), the framework of cavity optomechanics in which the molecular vibration and the plasmon are coupled has been shown to apply [63–65].

 

Fig. 4. Phononic–plasmonic platforms for single-particle and ensemble measurements. (a) Colloidal gold nanoparticles with an average diameter of 80 nm, spin-coated on top of a glass substrate patterned with a polymer grid fabricated by electron beam lithography (EBL). Several nanoparticles and aggregates are marked, and the corresponding enlarged scanning electron microscope (SEM) images are shown in the right panels. Tchebotareva et al., ChemPhysChem 10, 111–114 (2009) [72]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission. (b) Array of 35 nm thick gold Swiss-cross nanostructures with horizontal and vertical arm lengths of 120 and 90 nm, respectively, fabricated by EBL on a quartz substrate. Adapted by permission from Nature Publishing Group: Springer Nature, Nature Communications [52], “Tailored hyper-sound generation in single plasmonic nanoantennas,” O’Brien et al., COPYRIGHT 2014. (c) Pairs of gold nanocuboids periodically patterned on a quartz substrate with a separation of 600 nm. Adapted with permission from Wang et al., J. Phys. Chem. C 116, 17838–17846 (2012) [75]. Copyright 2012 American Chemical Society, https://doi.org/10.1021/jp305813w. (d) Gold nanorings fabricated using a colloidal-lithographic technique distributed on a silica substrate. The structures have an average outer diameter of 120 nm, wall thickness of 10 nm, and height of 35 nm. Adapted with permission from Kelf et al., Nano Lett. 1098 11, 3893–3898 (2011) [76]. Copyright 2011 American Chemical Society, https://doi.org/10.1021/nl202045z. (e) Plasmonic molecules to study near-field acoustic coupling. Gold nanostructures with 35 nm thickness were fabricated with a 2 nm Ti adhesion layer on a glass substrate by EBL. The top panels show individual decamers with different gap sizes, while the bottom panels show oligomers with central disks of different diameters. Adapted from Ref. [77]. (f) Mechanically constrained nanoantennas fabricated by two-step EBL. The top panels show SEM images of a gold nanorod with silica patches selectively positioned on top of it. The bottom panels show the corresponding 3D design implemented in the simulations. Adapted with permission from della Picca et al., Nano Lett. 16, 1428–1434 (2016) [53]. Copyright 2016 American Chemical Society, https://doi.org/10.1021/acs.nanolett.5b04991.

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A theoretical calculation of the optical modes in highly dissipative deformed nanoresonators has been done by Yan et al. [66], who developed a formalism based on the quasinormal-mode (QNM) perturbation theory [67]. They predicted the optical responses of arbitrarily large static boundary-deformed resonators obtaining exact formulas for both first- and high-order perturbation of the initial unperturbed modes. However, there is a lack of a theoretical framework that interprets the time domain experimental results that incorporate the dynamics of the time-dependent deformations that appear due to the vibrations of the nanoantenna in a similar way to what was done in Ref. [64] on plasmon–molecule coupling.

4. PHONONIC–PLASMONIC PLATFORMS DESIGN

The field of phononics with plasmonic nanoantennas has gained renewed energy, starting from experiments on nanoantennas deposited or grown onto substrates or photonic–plasmonic platforms. Indeed, careful analysis needs to be done because a vibrating nanoantenna is an extremely sensitive mechanical sensor of the environment, and mere interaction with the surface introduces variability in both frequency and $Q$, even for single-particle measurements, due to possible differences in the local mechanical contact. Nevertheless, these experimental arrangements allow single-particle, meta-atoms, or metasurface measurements with remarkable control and straightforward access to applications. However, before going into that, let us do a rapid overview of the techniques used and potentially valuable for fabricating these platforms that, somehow arbitrarily, can be separated into chemical, lithographic, and hybrid methods.

Working with nanoantennas fabricated by wet chemistry and then deposited onto substrates assures that the nanoparticles have a high degree of crystallinity and shape repeatability beyond size dispersion. The first idea for going from colloidal nanoparticles in solution to a plasmonic platform is to drop-cast the solution on a substrate [68]. However, this simple method produces an inhomogeneous concentration throughout the sample, with little control over the mechanical attachment of the nanoantennas to the substrates. A better strategy for creating homogeneous and ultra-low concentrations of nanoparticles is by spin-coating drops of the solution, producing isolated particles or small clusters throughout the substrate. In this way, and with the help of markers on the substrates and electron microscopy images to locate them, it has been possible to measure coherent acoustic phonons in individual particles [48,69–74] [Fig. 4(a)]. Also, a technique based on adding molecular modifiers over the substrate allows fine control of the concentration, aggregation [78], and mechanical contact, enabling selective access to a single particle, dimers, trimers, and higher-order aggregates, only by tuning the wavelength [79]. Another chemical route has been used to generate coherent acoustic phonons in gold nanoparticle superlattices by packing them onto a silicon substrate to a hexagonal structure by encapsulation with molecular chains [80].

Phononic–plasmonic platforms fabricated by electron beam lithography (EBL) came into use about a decade ago [81]. Usually, gold nanoantennas made by EBL are grown on a substrate with an intermediate adhesion layer, typically titanium or chromium. A vast number of geometries were probed experimentally with EBL platforms: gold nanorings [81], nanocuboids [75], nanodisks [82–84], nanorods [85], Swiss crosses [52], and aluminum nanodisks [86], among others; see Fig. 4. Also, it was possible to position hydrogen silsesquioxane (HSQ) patches, chemically similar to silica once exposed to the e-beam, at defined locations on top of the nanoantennas using two-step EBL, as seen in Fig. 4(f). Using this approach, the mechanical constraints imposed on GNRs modify the vibrational frequencies, allowing tuning of the acoustic phonons in the GHz range [53].

 

Fig. 5. Mass sensor. (a) Differential transmission signal from a single gold nanorod (taken from an ensemble average size of ${{54}}\;{{\pm}}\;{{3}}\;{\rm{nm}}$ in length and ${{25}}\;{{\pm}}\;{{3}}\;{\rm{nm}}$ in width) during the coating with a silver shell with thickness varying from 0 nm (bottom) to ${4.8}\;{{\pm}}\;{0.8}\;{\rm{nm}}$ (upper). Two modes are clearly seen: breathing (high frequency) and extensional (low frequency). (b) FFT of the signal in (a). The extensional mode is insensitive to increasing silver thickness, while the breathing mode frequency decreases, as indicated by the arrow. Adapted with permission from Yu et al., Nano Lett. 14, 915–922 (2014) [95]. Copyright 2014 American Chemical Society, https://doi.org/10.1021/nl404304h.

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The nanosphere lithography (NSL) method is a colloidal-lithographic approach where nanospheres are electrostatically self-assembled onto silica. In a second step, metal is sputtered on top of the colloidal assembly, and then the nanospheres are removed. Using this method, coherent acoustic phonons have been measured on gold nanorings [76] [Fig. 4(d)], gold nanoprism pairs [87], and gold prismatic nanoparticles [88]. Other methods are suitable for preparing phononic–plasmonic platforms for nanomechanical experiments, combining the best of two worlds: crystallinity of the chemically synthesized colloids and periodicity of predesigned patterns. Among them, we can mention optical printing [89–91], single colloids patterning [92,93], and photoinduced growth [94].

5. DETERMINATION OF OSCILLATION FREQUENCIES AND THEIR APPLICATIONS

Typically, a pump–probe experiment easily gives a frequency sensitivity of about 0.1 GHz. This high accuracy in the determination of single-particle oscillation frequencies allows using these mechanical nanoresonators as precise and exquisite sensors of their own elastic properties and of the presence of the local material environment.

By testing their use as mass sensors, Yu et al. [95] detected the nanometer thickness of silver coating onto GNRs by measuring single-particle acoustic vibrations. They introduced the GNR platform into a flow cell containing the proper reaction solution, allowing silver deposition to be controlled by the reaction time. The recording of the differential transmission signal is shown in Fig. 5(a) for different silver shell thicknesses. By choosing the right probe wavelength, they could detect both breathing and extensional modes, although they realized that only the breathing mode is sensitive to the silver shell, as seen in Fig. 5(b). Indeed, its frequency decreases as the shell thickness increases, whereas the extensional mode has no sensitivity since the increase in stiffness is exactly balanced by a commensurate increase in mass that lowers the frequency.

Thin films are at the center of many sensing and control devices that must work at micro- and nanoscale. Their operation requires detailed knowledge of their mechanical properties determined on spatial scales such as the physical sizes and in operando conditions at frequencies of GHz. Boggiano et al. [96] introduced a new method to assess the mechanical moduli of polymer films at GHz frequencies based on sensing the coherent acoustic phonons generated by individual plasmonic nanoantennas. Every GNR made by EBL is excited in a two-color pump–probe experiment before and after covering the phononic–plasmonic platform with amorphous polymer film. The top panel of Fig. 6(a) depicts schematically the experimental proposal, whereas the bottom panel shows the before (cyan) and after (red) differential transmission signals at a given individual nanoantenna; Fig. 6(b) is the FFT of the signals in Fig. 6(a). The comparison among the before/after frequency shift measurements [Fig. 6(c)] and FEM simulations considering several different values of the film’s mechanical moduli [Fig. 6(f)] allows the determination of the shear modulus $G$ and the Young’s modulus $E$ of the local environment, as seen in Fig. 6(g). Furthermore, the method can give statistical values by averaging the results over several different nanoantennas, as shown in Fig. 6, or local values by choosing the one for a given nanoantenna.

 

Fig. 6. Plasmonic antennas as nanomechanical sensors. (a) Differential probe transmission signals of a single gold nanorod, with nominal dimensions of ${{140}} \times {{60}} \times {{35}}\;{\rm{nm}}$, in air (cyan) and when covered with a thin polymer film (red). (b) Fast Fourier transform of the experimental signals in (a), showing the frequency shift introduced by the polymer. (c), (d) Frequency and $Q$ measurements on several individual nanorods first surrounded by air and then coated with the polymer. Dashed lines indicate the average values in air (cyan), with the polymer film (red), and the average increment (black), while the solid line corresponds to the identity. (e) Deformation fields associated with the extensional mode of a gold nanorod attached to a substrate. (f) Frequency domain simulations of the average displacement along the main rod axis in air and surrounded by the polymer with different values of the shear modulus, G. The inset shows the frequency shift of the extensional mode as a function of the shear modulus for antennas of different sizes. (g) Correlation between the measured frequency shifts and the elastic modulus of the polymer. Adapted with permission from Boggiano et al., ACS Photon. 7, 1403–1409 (2020) [96]. Copyright 2020 American Chemical Society, https://doi.org/10.1021/acsphotonics.0c00631.

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Sensitive measurements of the oscillation frequencies of single nanoantennas have also been used for high-resolution imaging through the accurate location of the nanoparticle centroid position [97] and determination of its shape through polarization-sensitive measurements. Guillet et al. [98] developed an ultrafast microscopy technique based on an asynchronous optical sampling (ASOPS) [99] pump–probe experiment that allows a high-speed acquisition rate. The whole vibrational spectrum with spatial and temporal resolution is recorded by raster-scanning the sample over a micrometer square area and detecting the transient reflectivity, $\Delta {\rm{R}}/{\rm{R}}$, over 20 ns in each pixel. Figure 7(a) (left panel) shows a typical spatiotemporal mapping recorded for a gold nanosphere at a given probe delay (882 ps in this case). The complete time trace can be seen in the top right panel for three different pixels (green, blue, and red), whereas the bottom panel shows the FFT for the red pixel signal. This mechanical spectrum shows a well-defined peak below 1 GHz [Fig. 7(b)] and a few noisy features above 1 GHz [Figs. 7(c)–7(f), for which the signal is multiplied by six]. Besides having high-resolution imaging, taking advantage of the spatially resolved recording of the spectrum, shown in Figs. 7(b)–7(f), makes it possible to decide whether a peak of the same order corresponds to a true vibration, as can be seen, for example, by comparing Figs. 7(d) and 7(f). Furthermore, polarization-sensitive high-resolution phononic reconstruction has been demonstrated by Fuentes-Domínguez et al. [100] by using a similar setup. In their work, shown in Figs. 7(g)–7(l), they identify each nanostructure through its vibrational frequencies [Figs. 7(j)–7(l)] and get the complete reconstruction of the size, shape, position, and orientation of nanospheres and nanorods, overcoming the optical diffraction limit.

 

Fig. 7. Ultrafast vibrational microscopy. Reprinted with permission from Guillet et al., Appl. Phys. Lett. 114, 091904 (2019) [98]. Copyright 2019, AIP Publishing LLC. (a) Snapshot of the transient reflectivity video for a gold nanoantenna in contact with a substrate at the probe delay of 882 ps. ΔR/R gives the amplitude of each image pixel at the correspondent delay. The time traces containing the vibrational response for three pixels (green, blue, and red) and the FFT for the red one are shown. FFT shows several modes present in the spectrum: 0.47, 5.90, 2.25, 3.29, and 5.01 GHz, for which the spectro-image is recorded in (b)–(f). Polarization-sensitive high-resolution phononic reconstruction, adapted from Ref. [100]. (g) Frequency map and (h) SEM image show three particles with mechanical spectra (j)–(l), two of them spherical (red and green) and one anisotropic rod (purple). The latter shows two modes and is sensitive to the linear light polarization angle, as shown in (i).

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6. $Q$ FACTOR: COUPLING AMONG NANOANTENNAS AND TO THE SURROUNDING MEDIUM

The damping of coherent phonon oscillations launched within a plasmonic nanostructure after optical excitation arises from both internal losses and the transfer of elastic energy from the metal–medium interface to the environment. Dissipation out of the structure is largely determined by acoustic impedance mismatch and mechanical contact quality between the metal and the surrounding medium, while crystal defects and surface roughness govern internal losses. A useful figure of merit that describes the rate of energy loss of an excited mode is the $Q$ of the mechanical resonance, which follows the relationship $\frac{1}{Q} = \frac{1}{{{Q_{\rm{int}}}}} + \frac{1}{{{Q_{\rm{ext}}}}}$, where ${Q_{\rm{int}}}$ and ${Q_{\rm{ext}}}$ correspond to the internal and external dissipation channels, respectively.

Several groups have studied the effect of the crystallinity of metallic resonators on the $Q$. Ostovar et al. [73] showed that chemically synthesized Al nanoparticles deposited on glass can yield $Q$ values as low as three or above 30, depending on the crystalline quality, as presented in Fig. 8(a). Much higher $Q$s, greater than 100, have been obtained by reducing the acoustic coupling to the environment by suspending a crystalline Au nanowire over a trench [103]. In contrast, top-down fabrication of nanostructured Au resonators has been shown to produce a nearly universal $Q$ of around 11 [Fig. 8(b)], independent of the size, shape, mechanical mode, or surface adhesion, due to the inherent lattice defects of the polycrystalline material. This was demonstrated by Yi et al. [82], who investigated the influence of resonator dimensions and morphology, the supporting substrate (glass or sapphire), and the thickness of the adhesion layer, on the mechanical modes, by analyzing more than 100 lithographically prepared nanodisks and nanorods. They found that the $Q$ did not change with the contact area, surface-to-volume ratio, substrate type, or binding strength, revealing that internal damping dominated the acoustic energy dissipation, while the mechanical energy flowing to the substrate, as well as the contribution from surface defects, could be neglected. The investigation also showed that photothermal treatment increased the $Q$s by 30% to 40% due to the partial removal of the crystal imperfections.

 

Fig. 8. (a) Acoustic vibrations of two colloidal Al nanoparticles on glass with similar diameters of 161 nm (blue) and 167 nm (red), presenting different crystalline qualities. The insets show the corresponding normalized Fourier transforms and SEM images. Adapted with permission from Ostovar et al., J. Phys. Chem. A 124, 3924–3934 (2020) [73]. Copyright 2020 American Chemical Society, https://doi.org/10.1021/acs.jpca.0c01190. (b) Quality factor histogram for 104 lithography-fabricated Au nanodisks with diameters varying from 120 to 240 nm, and 43 Au nanorods with lengths from 80 to 160 nm and a width of 35 nm. The thickness of the Ti adhesion layer varied between 0 and 4 nm. The thickness of all nanoantennas is 35 nm. The average $Q$ value is ${11.3} \pm {2.5}$. Adapted with permission from Yi et al., Nano Lett. 18, 3494–3501 (2018) [82]. Copyright 2018 American Chemical Society, https://doi.org/10.1021/acs.nanolett.8b00559. (c) Breathing mode frequencies of 35 nm high, 176 nm diameter Au nanodisks on glass as a function of the Ti adhesion layer thickness. The experimental data are compared with FEM simulations considering a free surface model (blue diamonds and solid line) and a fixed surface model (red squares and solid line). (d) Corresponding FEM calculations of the frequency spectra of acoustic modes when varying the stiffness of an intermediate layer added to model the binding strength between the nanoantenna and the substrate. The color of the plot represents the magnitude of the volume change in the bimetallic nanodisk schematized in the inset (red, maximum; blue, minimum). (e) Displacement profiles associated with the modes with the maximal volume change at three different values of the coupling layer stiffness, referenced in the contour plot of (d). Nature Publishing Group: Springer Nature, Nature Communications [83], “Tuning the acoustic frequency of a gold nanodisk through its adhesion layer,” Chang et al., COPYRIGHT 2015. (f) Measured quality factors of acoustic modes in Au nanodisks on sapphire for different aspect ratios $\eta$. The inset illustrates the variation in the acoustic coupling to the substrate for nanoantennas of different sizes. Adapted with permission from Medeghini et al., Nano Lett. 18, 5159–5166 (2018) [101]. Copyright 2018 American Chemical Society, https://doi.org/10.1021/acs.nanolett.8b02096. (g) Quality factor of the breathing mode measured for different single-crystal Au nanoplates on glass and Lacey carbon. The inset exhibits a representative optical image of two nanoplates. Adapted from Ref. [102].

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Although the binding strength of a resonator to the substrate may not affect the $Q$ of the resonance in polycrystalline metallic nanostructures, it has been shown to significantly modify the frequency of the eigenmodes. Chang et al. [83] demonstrated that the mechanical coupling of an Au nanodisk to a glass substrate can be controlled between the two extreme cases of a nanostructure that is (effectively) suspended or rigidly attached to the substrate, just by varying the thickness of a Ti adhesion layer. When having no adhesion layer, the experimental vibration frequency of the breathing mode of the resonator matched the theoretical value of the free structure, which can be understood from the characteristic poor adhesion of Au to glass. However, the frequency increased when increasing the Ti thickness, reaching the value for a structure with a fixed bottom surface at a Ti thickness of 3 nm [see Fig. 8(c)]. Moreover, for this thickness and above, the vibrational mode was found to split into two due to the strong coupling to the substrate, as evidenced by numerical simulations considering a varying stiffness underneath the disk [Fig. 8(d)]. Specifically, at ${{1}}{{{0}}^{4\:}}{\rm{GPa}}\;{\rm{n}}{{\rm{m}}^{- 1}}$, the two dominant modes [see profiles 5 and 6 in Fig. 8(e)] show either close to null or nearly maximum displacement next to the substrate, explaining why their frequencies approach those of the fixed or free surface models, respectively.

An alternative way to effectively decouple the resonator from the substrate has been proven by Medeghini et al. [101], who studied in detail the performance of single Au nanodisks of different diameters on a sapphire substrate. For a specific aspect ratio of the nanoantenna, they found a quasi-localized vibrational mode with negligible acoustic radiation efficiency to the surroundings. The effect was explained as a substrate-mediated hybridization between normal modes that effectively isolated the resonator from the substrate, giving rise to $Q$s as large as 70, as shown in Fig. 8(f). For a detailed description of this phenomenon, see Ref. [57]. Another approach by Wang et al. [102] used a porous Lacey carbon film to support single-crystal Au nanoplates. Record-breaking $Q$s exceeding 200 were obtained, as compared to values around 10 for the case of the nanoplate on a glass substrate, as can be seen in Fig. 8(g). Moreover, they further realized strong vibrational coupling by stacking two nanoplates and observed the distinctive avoided crossing.

Another degree of control on acoustic nanoresonators emerges when considering meta-molecules formed by multiple nanosized elements. In this regard, Yi et al. [77] investigated the intramolecular coupling of closely packed nanodisks in different arrangements. Figure 9(b) compares the frequency spectra of two nanodisks of different diameters in monomer, homodimer, and heterodimer configurations. The results could be well described by a coupled oscillator model [mass-spring schematic in Fig. 9(a)], where the vibrational coupling between meta-atoms is mediated by coherent phonons with low energies through the underlying substrate, explaining the frequency shift observed for the high-frequency mode in heterodimer design. We note that the presence of such a frequency shift indicates unusually strong coupling between particles, given their largely different eigenfrequencies. Significantly, the model also predicts the appearance of a blueshifted frequency mode for an out-of-phase oscillation in the homodimers, which is not observed in Fig. 9(b) as inhibited by the in-phase character of the impulsive launching of acoustic vibrations. The same also occurs for larger arrays of equally sized nanodisks. This does not apply, however, to the heterodimer design, and hence the shift can be optically generated and observed, revealing the importance of having differently sized elements to operate in the vibrational coupling regime. Interestingly, unlike single-component antennas, FEM simulations using classical continuum elastic theory fail to reproduce the experimental trends of plasmonic molecular systems. The reason seems to be the noncrystalline nature of the substrate and the low energy of the participating phonons, as the Debye approximation in glasses breaks down in the meV to sub-meV energy range, when the acoustic wavelengths become comparable to the local disorder [104].

 

Fig. 9. (a) Illustration of the frequency spectra of two independent oscillators (left) and the resulting frequency shifts when they are coupled (right). (b) Experimental acoustic mode frequencies of single Au nanodisks of 178 and 78 nm diameters on glass, their homodimers, and heterodimer. The size of the SEM images is ${{640}} \times {{550}}\;{\rm{nm}}$. (c) Frequency of the high-frequency (HF) mode when varying the interparticle gap size in a decamer Au nanodisk cluster on glass. The size of the SEM images is ${{640}} \times {{550}}\;{\rm{nm}}$. (d) Frequency of the HF mode of the plasmonic molecule when varying the diameter of the central disk. The size of the SEM images is ${{640}} \times {{550}}\;{\rm{nm}}$. Adapted from Ref. [77].

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To enhance the optical response of the system while keeping the same mechanical nature of the modes, the authors realized a configuration consisting of a large central disk surrounded by smaller nanodisks, as in Fig. 4(e). As only two different diameters are involved, the response of the bigger molecule should be the same as the corresponding heterodimer, but with an amplified optical signal given the larger number of elements. As a result, the predicted redshift of the low-frequency mode—not detected in Fig. 9(b) for the heterodimer—was registered in the lower-noise measurements of the decamer antenna. Also, as expected, the blueshifted high-frequency mode of the molecule redshifted when increasing the inter-particle distance until it reached the level of decoupled resonators, as shown in Fig. 9(c). On the other hand, changing the size of the central disk at a fixed gap distance revealed a maximum shift of the higher-frequency mode when its frequency doubled that of the slower mode [see Fig. 9(d)], suggesting the appearance of a Fermi resonance, as in real molecular systems. These results provide insights into the behavior of plasmonic molecules and the optomechanical selection rules for the excitation of vibrational modes.

7. SURFACE ACOUSTIC WAVES AND DEVICES

Electromagnetic wave transduction into hypersonic waves entails five orders of magnitude reduction in wavelength at the same frequency due to their intrinsically different phase velocities. This extreme shrinking in wavelength opens the doors to using nanoscale acoustic elements as mediators between optical signals in integrated circuits operating in the range of GHz, such as in telecommunication devices. Other possible applications include sensing and metrology. However, the manipulation of acoustic waves at nanometer scale is still challenging, with investigations in the miniaturization of GHz surface phonon generation, detection, and phase control underway.

When an optically excited vibrating plasmonic nanoantenna mechanically disturbs its local environment, it also launches acoustic waves through the embedding matrix or underlying substrate. The nature of the emitted waves is determined by the excited vibrational modes of the resonator and their coupling to the surroundings. As acoustic waves can travel for distances orders of magnitude longer than the characteristic deformation displacements of the source, placing a second nanoantenna in the far field, it can be mechanically stimulated by the propagating phonons. The excited eigenmodes are now constrained by the symmetry of the forces exerted by the arriving acoustic waves and their frequency spectra. This phenomenon was first demonstrated by Berté et al. [54], who optically studied the mechanical coupling between plasmonic particles placed apart by distances in the 1–3 µm range on a glass substrate. The experiment used a two-color pump–probe technique, where an emitter rod is pumped to generate SAWs, which travel along the substrate and excite a second receiver rod, which is evaluated with the probe beam. Since the oscillating receiver also synchronically modulates its optical response, the probe can indirectly read its mechanical distortions. Figure 10(a) shows the obtained pump–probe results for rod receptors placed at different distances from the source. The farther away the receiver is from the emitter, the longer the arrival time of the wave and the lower the amplitude of the signal, due to the attenuation of the SAW. A propagation speed of 3400 m/s was determined, in agreement with the expected value for the fused silica substrate. The measured frequency at the receptor corresponded to the extensional mode of the resonator, which matched the excited mode of the emitter. The simulated displacement pattern of the acoustic wave through the substrate can be seen in Fig. 10(b), revealing Rayleigh waves with an elliptical polarization confined to the surface.

 

Fig. 10. (a) Transient probe transmission curves for gold nanorod receptors (R) placed at varying distances (d) from a gold nanorod source (S). (b) $Xz$-plane view of the displacement pattern generated by a ${{140}} \times {{60}} \times {{35}}\;{\rm{nm}}$ Au rod on glass at its extensional mode (8.3 GHz). The rod is located at the top-left of the image. Adapted from Ref. [54]. (c) Illustration of a gold nanowire surface phonon emitter and gold nanorod receivers (L is not to scale). (d) Fourier spectra of the $x$ and $z$ displacement components of the nanowire emitter (65 nm wide and 50 nm high) calculated at the sampling point shown by the red dot in the sketch on the right. The inset shows the frequency spectra of the substrate displacement components at a distance of 5 µm from the source. (e) Snapshots of the motion of the nanowire at the principal resonance frequencies shown in (d). (f) Differential reflectivity measured by probing the receivers (${{210}} \times {{65}} \times {{50}}\;{\rm{nm}}$ rods), positioned at a distance ${\rm{L}} = {{10}}\;\unicode{x00B5}{\rm m}$ from the emitter. (g) Fourier spectrum of the measured Rayleigh phonon wave packet. The inset shows snapshots of the motion of a nanorod receptor at the peak resonance frequency. Adapted with permission from Imade et al., Nano Lett. 21, 6261–6267 (2021) [59]. Copyright 2021 American Chemical Society, https://doi.org/10.1021/acs.nanolett.1c02070.

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Fig. 11. (a) Illustration of the generation and detection of surface acoustic waves (SAW) using a V-shaped antenna emitter and a disk receptor. The inset displays SEM images of different emitter–receptor relative orientations. Source and receiver are located 1.5 µm apart. (b) Comparison between the amplitude of the Fourier transform of the pump–probe signal of the emitter–receptor configuration (${\cal F}[{{S_{\rm{SAW}}}}]$, dashed curve) and the product of the Fourier transforms of the signals of a V-shaped antenna and a single disk (${\cal F}[{{S_s}}] \cdot {\cal F}[{{S_r}}]$, solid curve) measured separately. The individual components of the product are shown as filled curves. (c) The left panel displays a top view of the substrate displacement pattern at the main mechanical frequency of the source antenna. The right panel exhibits the mean amplitude of the pump–probe signal of the receptor disk as a function of the relative orientation angle with respect to the V-shaped source antenna. The solid line is a guide to the eyes. Adapted with permission from Poblet et al., ACS Photon. 8, 2846–2852 (2021) [105]. Copyright 2021 American Chemical Society, https://doi.org/10.1021/acsphotonics.1c00741.

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Imade et al. [59] later explored the configuration depicted in Fig. 10(c), where instead of using a small nanorod as the source, they employed a long nanowire of 50 µm length, so as to produce a stronger response on a series of rod receivers. Figure 10(d) exhibits the computed Fourier spectra of the $x$ and $z$ components of the displacement field at the excited nanowire, showing two main peaks corresponding to a piston-like vertical motion ($\alpha$) and a flexural mode ($\beta$), as can be appreciated in Fig. 10(e). Noticeably, while the flexural mode is dominant in the nanowire response, it only poorly couples to the substrate, as can be seen in the inset of Fig. 10(d). The receiver, placed 10 µm apart from the emitter, selects a small frequency range from the incoming wave following its own mechanical impulse response. However, as not all mechanical motion translates into an optical change, the acousto-optic coupling also needs to be considered. Simulations and experiments indicate that the acousto-optic coupling is especially less sensitive to higher-order vibrational modes, where the effect of positively and negatively directed portions of the deformation fields cancel each other out. In this investigation, the main frequency identified from the optical measurement corresponded to that of a quasi-longitudinal mode of the nanorod [see Fig. 10(g)]. Moreover, as shown in Fig. 10(f), not only the Rayleigh wave packet was registered, but also the faster surface-skimming longitudinal (SSL) bulk phonons. It should be mentioned that positioning the rod receivers parallel to the emitter nanowires resulted in a weaker response, as the nanorod extent along the SAW propagation direction represented a shorter fraction of the acoustic wavelength.

Poblet et al. [105] went one step forward and studied the directionality of the SAWs emitted by a more complex V-shaped nanoantenna [see Fig. 11(a)]. To that end, they placed nanodisk receptors at different relative angular positions around the emitter, as seen in the SEM image in the inset of Fig. 11(a). The disk shape was selected because of its circular symmetry, yielding a response that is independent of the arriving direction of the phonon wave. The disk size was chosen to have a mechanical resonance spectrum with a reasonable contribution at the main vibrational frequency of the source, as well as an electromagnetic response that enabled good acousto-optic coupling at the probe wavelength. Figure 11(b) shows the measured Fourier spectra when pumping and probing over the same element (V-shaped nanoantenna or nanodisk) as filled curves, as well as the result obtained in the source–receptor scheme (dashed line). Noticeably, the latter can be reasonably described by the product of the curves characterizing the separate elements (solid line), as the impulse response of the combined system is, in essence, the convolution of the mechanical responses of the individual components. Figure 11(c) finally compares the simulated displacement field of the generated SAWs with the amplitude of the pump–probe signals measured for all explored positions of the receptor around the emitter, where a highly anisotropic pattern can be distinguished.

8. CONCLUSIONS AND PERSPECTIVES

In conclusion, in this work, we have critically reviewed the bibliography of plasmonic nanoantennas acting as mechanical nanoresonators after being perturbed by an incident resonant pulsed light field. The significance of ultrafast optical methods to generate coherent lattice vibrations and read them with great sensitivity has been highlighted in the review. We have discussed from the first pioneering experiments in which coherent phonons were generated in metal colloids of different shapes and sizes to those in which minute movements of individual objects are detected at the time that their coupling with the substrate produces acoustic wave fields. Additionally, we emphasized that all experimental studies must be complemented with simulations to extract quantitative values from them, whose accuracy depends on the number of approximations done, which has to be kept to a minimum.

Nanoantennas, as mechanical resonators, detect with great sensitivity their own mechanical properties and those of the environment, as well as the presence of contact surfaces. Indeed, this information is not generally accessible with measurements on the optical response of the plasmonic system and would allow, for instance, to evaluate the degree of adhesion of different materials in a hybrid arrangement. Moreover, nanoantennas acting as mechanical sensors have two main advantages when compared with other methods; first, their oscillation frequencies in the GHz range allow the evaluation of the mechanical properties of materials at frequencies relevant to the operation of many current devices. And second, even though measurements in many positions can give an average value of mechanical properties, they are essentially local sensors due to their size at nanoscale.

Given the ability to calculate the oscillation modes of plasmonic systems for almost any geometry, the facilities for fabrication of increased complexity and the mature sensitivity of the optical experiments for both measuring frequencies and detecting their changes suggest that the next generation of experiments will tend to include plasmonic nanoresonators in multiple hybrid platforms. For example, the dynamic interaction of these nanoresonators with 2D optical materials has not yet been explored. Although the size of the movements is sub-nanometric, ultrafast optics have proven to be sensitive enough to detect small modulations of optical properties, such as those occurring in 2D materials under strain [106,107]. Another example for which there have not yet been reports is the combination of these nanoresonators with films of magnetic materials, where their magnetostriction properties may be relevant for applications in the field of spintronics [108,109].

Finally, we emphasize that these nanoresonators produce an all-optical generation of SAWs with wavelengths of tens to a few hundred nanometers that travel through the underlying substrate. Unlike the interdigital transducer technology [110] generally used to generate SAWs, piezoelectric materials do not need to be used. Depending on the application, this can be an advantage or a disadvantage since a modulated electric field could enhance or screen the effect to measure. However, there is still a lot of work to be done in choosing the correct substrate for the desired application. From changing the materials to nanostructuring them, those proposals are yet to come. These waves, whose direction can be controlled, can carry the optical information of incident light and be detected optically in a place different from where the light pulse arrived. Furthermore, by engineering the nanoantennas and substrates, it may be possible to focus, interact with, or disperse this acoustic energy, allowing optical information processing in a micrometer-sized device.