Acoustic Vibration of Metal Films and Nanoparticles

Cooling Dynamics of Individual Gold Nanodisks Deposited on Thick Substrates and Nanometric Membranes

The cooling dynamics of individual gold nanodisks synthesized using colloidal chemistry and deposited on solid substrates with different compositions and thicknesses were investigated using optical time-resolved spectroscopy and finite-element modeling. Experiments demonstrate a strong substrate-dependence of these cooling dynamics, which require the combination of heat transfer at the nanodisk/substrate interface and heat diffusion in the substrate. In the case of nanodisks deposited on a thick sapphire substrate, the dynamics are found to be mostly limited by the thermal resistance of the gold/sapphire interface, for which a value similar to that obtained in the context of previous experiments on sapphire-supported single gold nanodisks produced by electron beam lithography is deduced. In contrast, the cooling dynamics of nanodisks supported by nanometric silica and silicon nitride membranes are much slower and largely affected by heat diffusion in the membranes, whose efficiency is strongly reduced as compared to the thick sapphire case.

Surface plasmon-based detection for picosecond ultrasonics in planar gold-dielectric layer geometries

Longitudinal acoustic modes in planar thin gold films are excited and detected by a combination of ultrafast pump-probe photoacoustic spectroscopy and a surface plasmon resonance (SPR) technique. The resulting high sensitivity allows the detection of acoustic modes up to the 7th harmonic (258 GHz) with sub-pm amplitude sensing capabilities. This makes a comparison of damping times of individual modes possible. Further, the dynamics of the real and imaginary part of the dielectric function and the film's thickness variation are separated by using the dependence of the amplitudes of the acoustic modes on the detection angle and the surface plasmon resonance. We find that longitudinal acoustic modes in the gold films mainly affect the real part of the dielectric function and highlight the importance to consider thickness related effects in acousto-plasmonic sensing.

Vibroacoustic Characteristics of a Specific Patterned Polymer with Graphene for an Electrostatic Speaker

Graphene/polymer actuators were developed using bilayer graphene and various polymer substrates for use as transparent, flexible, and robust electrostatic speaker units. Additionally, a resonant frequency shift was induced using a polymer substrate on which various micropatterns were transferred to boost bass. The total sound pressure level (SPL) in the graphene/polymer actuator was measured by a sweep, and the frequency of the spectrum was confirmed to be one-third that of the octave band frequency. The change in the vibroacoustic characteristic with changes in Young's modulus and density was studied for the polymers of the same size and thickness. Particularly, the possibility of boosting bass was confirmed by inducing a resonant frequency shift and increasing the total SPL by adding micropatterns on a polymer substrate under the same conditions. The resonance frequency of 523 Hz and the SPL of 54 dBA in flat polymer film became 296 Hz and 69 dBA in a specific pattern, which produced a sound of >15 dB based on the same flat polymer. We expect that the design and information provided herein can provide the key parameters required to change the resonant frequency in small-size devices for the application of graphene/polymer thin-film actuators.

Low-Frequency Oscillations in Optical Measurements of Metal-Nanoparticle Vibrations

Time-resolved optical measurements of vibrating metal nanoparticles have been used extensively to probe the ultrafast mechanical properties of the nanoparticles and of the surrounding liquid, but nearly all investigations so far have been limited to the linear regime. Here, we report the observation of a low-frequency oscillating signal in transient-absorption measurements of nanoparticles with octahedral gold cores and cubic silver shells; the signal appears at the difference of two mechanical vibrational frequencies in the particles, suggesting a nonlinear mixing process. We tentatively attribute this proposed mixing to a nonlinear coupling between a vibrational mode of the nanoparticle and its optical-frequency plasmon resonance. The optimization of this nonlinear transduction may enable high-efficiency opto-mechanical frequency mixing in the GHz-THz frequency regime.

Polymer dependent acoustic mode coupling and Hooke's law spring constants in stacked gold nanoplates

Metal nanoparticles are excellent acoustic resonators and their vibrational spectroscopy has been widely investigated. However, the coupling between vibrational modes of different nanoparticles is less explored. For example, how the intervening medium affects the coupling strength is not known. Here, we investigate how different polymers affect coupling in Au nanoplate-polymer-Au nanoplate sandwich structures. The coupling between the breathing modes of the Au nanoplates was measured using single-particle pump-probe spectroscopy, and the polymer dependent coupling strength was determined experimentally. Analysis of the acoustic mode coupling gives the effective spring constant for the polymers. A relative motion mode was also observed for the stacked Au nanoplates. The frequency of this mode is strongly correlated with the coupling constant for the breathing modes. The breathing mode coupling and relative motion mode were analyzed using a coupled oscillator model. This model shows that both these effects can be described using the same spring constant for the polymer. Finally, we present a new type of mass balance using the strongly coupled resonators. We show that the resonators have a mass detection limit of a few femtograms. We envision that further understanding of the vibrational coupling in acoustic resonators will improve the coupling strength and expand their potential applications.

Ultrafast strain propagation and acoustic resonances in nanoscale bilayer systems

Ultrafast structural probing has greatly enhanced our understanding of the coupling of atomic motion to electronic and phononic degrees-of-freedom in quasi-bulk materials. In bi- and multilayer model systems, additionally, spatially inhomogeneous relaxation channels are accessible, often governed by pronounced interfacial couplings and local excitations in confined geometries. Here, we systematically explore the key dependencies of the low-frequency acoustic phonon spectrum in an elastically mismatched metal/semiconductor bilayer system optically excited by femtosecond laser pulses. We track the spatiotemporal strain wave propagation in the heterostructure employing a discrete numerical linear chain simulation and access acoustic wave reflections and interfacial couplings with a phonon mode description based on a continuum mechanics model. Due to the interplay of elastic properties and mass densities of the two materials, acoustic resonance frequencies of the heterostructure significantly differ from breathing modes in monolayer films. For large acoustic mismatch, the spatial localization of phonon eigenmodes is derived from analytical approximations and can be interpreted as harmonic oscillations in decoupled mechanical resonators.

Ultrafast acoustic vibrations of Au-Ag nanoparticles with varying elongated structures

Acoustic vibrations of Au and Ag elongated nano-objects with original morphologies, from Ag-Ag homodimers to Au@Ag-Ag heterodimers and Au@Ag eccentric core-shell spheroids, have been experimentally investigated by ultrafast time-resolved optical spectroscopy. Their frequencies, obtained by the analysis of time-dependent transient absorption changes, are compared with the results obtained from finite element modeling (FEM) numerical computations, which allow assignment of the detected oscillating signals to fundamental radial and extensional modes. FEM was further used to analyze the effects of morphology and composition on the vibrational dynamics. FEM computations indicate that (1) the central distance between particles forming the nanodimers has profound effects on the extensional mode frequencies and a negligible influence on the radial mode ones, in analogy with the case of monometallic nanorods, (2) coating Au with Ag also has a strong mass-loading-like effect on the dimer and core-shell stretching mode frequency, while (3) its influence on the radial breathing mode is smaller and analogous to the non-monotonic frequency dependence on the Au fraction previously observed in isotropic bimetallic spheres. These findings are significant for developing a predictive understanding of nanostructure mechanical properties and for designing new mechanical nanoresonators.

Understanding How Acoustic Vibrations Modulate the Optical Response of Plasmonic Metal Nanoparticles

Measurements of acoustic vibrations in nanoparticles provide an opportunity to study mechanical phenomena at nanometer length scales and picosecond time scales. Vibrations in noble-metal nanoparticles have attracted particular attention because they couple to plasmon resonances in the nanoparticles, leading to strong modulation of optical absorption and scattering. There are three mechanisms that transduce the mechanical oscillations into changes in the plasmon resonance: (1) changes in the nanoparticle geometry, (2) changes in electron density due to changes in the nanoparticle volume, and (3) changes in the interband transition energies due to compression/expansion of the nanoparticle (deformation potential). These mechanisms have been studied in the past to explain the origin of the experimental signals; however, a thorough quantitative connection between the coupling of phonon and plasmon modes has not yet been made, and the separate contribution of each coupling mechanism has not yet been quantified. Here, we present a numerical method to quantitatively determine the coupling between vibrational and plasmon modes in noble-metal nanoparticles of arbitrary geometries and apply it to silver and gold spheres, shells, rods, and cubes in the context of time-resolved measurements. We separately determine the parts of the optical response that are due to shape changes, changes in electron density, and changes in deformation potential. We further show that coupling is, in general, strongest when the regions of largest electric field (plasmon mode) and largest displacement (phonon mode) overlap. These results clarify reported experimental results and should help guide future experiments and potential applications.

Interrogating Nanojunctions Using Ultraconfined Acoustoplasmonic Coupling

Single nanoparticles are shown to develop a localized acoustic resonance, the bouncing mode, when placed on a substrate. If both substrate and nanoparticle are noble metals, plasmonic coupling of the nanoparticle to its image charges in the film induces tight light confinement in the nanogap. This yields ultrastrong "acoustoplasmonic" coupling with a figure of merit 7 orders of magnitude higher than conventional acousto-optic modulators. The plasmons thus act as a local vibrational probe of the contact geometry. A simple analytical mechanical model is found to describe the bouncing mode in terms of the nanoscale structure, allowing transient pump-probe spectroscopy to directly measure the contact area for individual nanoparticles.

Femtosecond single-electron diffraction

Ultrafast electron diffraction allows the tracking of atomic motion in real time, but space charge effects within dense electron packets are a problem for temporal resolution. Here, we report on time-resolved pump-probe diffraction using femtosecond single-electron pulses that are free from intra-pulse Coulomb interactions over the entire trajectory from the source to the detector. Sufficient average electron current is achieved at repetition rates of hundreds of kHz. Thermal load on the sample is avoided by minimizing the pump-probe area and by maximizing heat diffusion. Time-resolved diffraction from fibrous graphite polycrystals reveals coherent acoustic phonons in a nanometer-thick grain ensemble with a signal-to-noise level comparable to conventional multi-electron experiments. These results demonstrate the feasibility of pump-probe diffraction in the single-electron regime, where simulations indicate compressibility of the pulses down to few-femtosecond and attosecond duration.

Transient crystalline superlattice generated by a photoacoustic transducer

Designing an efficient and simple method for modulating the intensity of x-ray radiation on a picosecond time-scale has the potential to produce ultrafast pulses of hard x-rays. In this work, we generate a tunable transient superlattice, in an otherwise perfect crystal, by photoexciting a metal film on a crystalline substrate. The resulting transient strain has amplitudes approaching 1%, wavevectors greater than [Formula: see text], and lifetimes approaching 1 ns. This method has the potential to generate isolated picosecond x-ray bursts with scattering efficiencies in excess of 10%.

Acoustic vibrations of Au nano-bipyramids and their modification under Ag deposition: a perspective for the development of nanobalances

We investigated the acoustic vibrations of gold nanobipyramids and bimetallic gold-silver core-shell bipyramids, synthesized by wet chemistry techniques, using a high-sensitivity pump-probe femtosecond setup. Three modes were observed and characterized in the gold core particles for lengths varying from 49 to 170 nm and diameters varying from 20 to 40 nm. The two strongest modes have been associated with the fundamental extensional and its first harmonic, and a weak mode has been associated with the fundamental radial mode, in very good agreement with numerical simulations. We then derived linear laws linking the periods to the dimensions both experimentally and numerically. To go further, we investigated the evolution of these modes under silver deposition on gold core bipyramids. We studied the evolution of the periods of the extensional modes, which were found to be in good qualitative agreement with numerical simulations. Moreover, we observed a strong enhancement of the radial mode amplitude when silver is deposited: we are typically sensitive to the deposition of 40 attograms of silver per gold core particle. This opens up possible applications in the field of mass sensing, where metallic nanobalances have an important role to play, taking advantage of their robustness and versatility.

Damping of acoustic vibrations in gold nanoparticles

Studies of acoustic vibrations in nanometre-scale particles can provide fundamental insights into the mechanical properties of materials because it is possible to precisely characterize and control the crystallinity and geometry of such nanostructures. Metal nanoparticles are of particular interest because they allow the use of ultrafast laser pulses to generate and probe high-frequency acoustic vibrations, which have the potential to be used in a variety of sensing applications. So far, the decay of these vibrations has been dominated by dephasing due to variations in nanoparticle size. Such inhomogeneities can be eliminated by performing measurements on single nanoparticles deposited on a substrate, but unknown interactions between the nanoparticles and the substrate make it difficult to interpret the results of such experiments. Here, we show that the effects of inhomogeneous damping can be reduced by using bipyramidal gold nanoparticles with highly uniform sizes. The inferred homogeneous damping is due to the combination of damping intrinsic to the nanoparticles and the surrounding solvent; the latter is quantitatively described by a parameter-free model.

Time-domain control of ultrahigh-frequency nanomechanical systems

Nanoelectromechanical systems could have applications in fields as diverse as ultrasensitive mass detection and mechanical computation, and can also be used to explore fundamental phenomena such as quantized heat conductance and quantum-limited displacement. Most nanomechanical studies to date have been performed in the frequency domain. However, applications in computation and information storage will require transient excitation and high-speed time-domain operation of nanomechanical systems. Here we show a time-resolved optical approach to the transduction of ultrahigh-frequency nanoelectromechanical systems, and demonstrate that coherent control of nanomechanical oscillation is possible through appropriate pulse programming. A series of cantilevers with resonant frequencies ranging from less than 10 MHz to over 1 GHz are characterized using the same pulse parameters.

Detection of acoustic oscillations of single gold nanospheres by time-resolved interferometry

We measure the transient absorption of single gold particles with a common-path interferometer. The prompt electronic part of the signal provides images for diameters as small as 10 nm. Mechanical vibrations of single particles appear on a longer time scale (period of 16 ps for 50 nm diameter). They reveal the full heterogeneity of the ensemble, and the intrinsic damping of the vibration. We also observe a lower-frequency mode involving shear. Ultrafast pump-probe spectroscopy of individual particles opens new insight into mechanical properties of nanometer-sized objects.

Far-field optical microscopy of single metal nanoparticles

Individual noble-metal particles, with sizes ranging from a few tenths to some hundreds of nanometers, can now be detected by far-field optics. Single-particle microscopy gives access to inhomogeneity, distributions, and fluctuations, which were previously hidden in ensemble experiments. Scattering methods rely on dark-field illumination, spectral signatures of the metal particles, or both. More advanced techniques provide high sensitivity and improved selectivity with respect to other scatterers by isolating metal-specific signals, for example the refractive index change due to heating of the environment by a pump beam or the time-resolved optical response of the particle to a short pump pulse. We review and compare linear and nonlinear methods in far-field optical microscopy that have reached the single-particle regime by means of scattered light, thermal effects, photoluminescence, or nonlinear frequency generation.

Long lived acoustic vibrational modes of an embedded nanoparticle

Classical continuum elastic calculations show that the acoustic vibrational modes of an embedded nanoparticle can be lightly damped even when the longitudinal plane wave acoustic impedances Z(o)=rhov(L) of the nanoparticle and the matrix are the same. It is not necessary for the matrix to be less dense or softer than the nanoparticle in order to have long lived vibrational modes. A corrected formula for acoustic impedance is provided for the case of longitudinal spherical waves. Continuum boundary conditions do not always accurately reflect the microscopic nature of the interface between the nanoparticle and the matrix, and a multilayer model of the interface reveals the possibility of additional reduction of mode damping.

Vibrational Response of Nanorods to Ultrafast Laser Induced Heating: Theoretical and Experimental Analysis

In this paper, we elucidate the vibrational response of cylindrical nanorods to ultrafast laser-induced heating. A theoretical analysis of the expected behavior is first presented. This analysis predicts that both extensional and breathing vibrational modes of the rods should be excited by laser-induced heating. Analytical formulas are derived assuming that the heating/expansion process is instantaneous, and that the lengths of the rods are much greater than their radii. These results show that the breathing mode dominates the mechanical deformation of the rod. However, because the frequency of the extensional mode is much lower than that of the breathing mode, the extensional mode will dominate the response for a real experiment (a finite-time heating/expansion process). The results of this model are compared to data from transient absorption experiments performed on gold nanorods with average lengths between 30 and 110 nm. The transient absorption traces show pronounced modulations with periods between 40 and 120 ps, which are only observed when the probe laser is tuned to the longitudinal plasmon band. The measured periods are in good agreement with the expected values for the extensional modes of the rods. For rods wider than 20 nm, the breathing mode can also be observed and, again, the measured periods are in good agreement with the theoretical calculations. The breathing mode is not observed for thinner rods (<20 nm width) because, in this case, the period is comparable to the time scale for lattice heating.