Fig. 1. Schematic of acoustic vibrations in metal nanoparticles. (a) Ultrafast electron dynamics in metal nanoparticles; (b) time domain acoustic vibration curves of metal nanoparticles in ultrafast optical measurement

Fig. 2. Principle of transient absorption microscopy (TAM)^[28]. (a) Generic experimental setup with high-frequency modulation; (b) temporal modulation behavior of input and output pump and probe pulse trains, and intensity of detection beam may experience gain or loss; (c) noise spectrum (log-log plot) of a typical laser source as a function of frequency f

Fig. 3. Acoustic vibrations of spherical Au nanoparticles. (a) Calculated fundamental breathing mode of Au nanoparticles; (b) transient absorption traces for ensemble measurement of (48±5) nm diameter Au nanoparticle solution recorded at 510 nm and 550 nm probe laser wavelengths^[8]. Inset shows absorption spectrum of Au nanoparticle solution, and arrows correspond to positions of plasma formant of probe wavelengths relative to Au nanoparticles; (c) acoustic vibration frequency of Au nanoparticles as a function of reciprocal of particle radius (1/R)^[8]. Solid line shows calculated frequency for breathing vibration mode of spherical nanoparticles using elastic constants of bulk gold

Fig. 4. Acoustic vibrations of Au nanorods. (a) Calculated fundamental breathing mode and extensional mode of Au nanorods; (b) transient absorption traces for a single Au nanorod^[41]. Inset highlights partial vibration curves at early 200 ps. Right side is power spectral density of acoustic vibrations after Fourier transform. Low-frequency peak corresponds to extensional mode of nanorods, and high-frequency peak (inset) corresponds to breathing mode of nanorods; (c) acoustic vibration breathing mode dependent on diameter of Au nanorods^[41]; (d) average vibrational period of extensional mode versus average length of Au nanorods with different growth directions^[8]

Fig. 5. Acoustic vibrations of Au nanoplates. (a) Calculated fundamental breathing mode of Au nanoplates; (b) transient absorption traces of a single suspended Au nanoplate^[95]. Inset is corresponding fast Fourier transform spectrum of oscillation signal; (c) nanoplate thickness-dependent acoustic vibrational period of Au nanoplates^[61]

Fig. 6. Distance dependence of surface-mediated acoustic vibrational coupling in plasmonic nanoclusters^{[99, 103]}. (a) Transient absorption traces and (b) fast Fourier transform spectra of acoustic vibrations of individual nanoclusters with different gap sizes. Corresponding SEM images for nanoclusters are shown on top of figures; (c) measured acoustic vibrational frequencies as a function of gap size; (d) transient absorption traces and (e) fast Fourier transform spectra of acoustic vibrations of individual nanoclusters with different central disk diameters. Corresponding SEM images for nanoclusters are shown on top of figures; (f) measured acoustic vibration frequencies as a function of acoustic vibrational frequencies of central disk

Fig. 7. Acoustic vibrational coupling in two Cu nanowires^[50]. (a) Transient absorption trace of acoustic vibrational coupling of Cu nanowires with a clear beating phenomenon. Inset is SEM image showing two nanowires with same diameter connected by MAKROFOL polymer; (b) corresponding fast Fourier transform spectrum with obvious splitting effect at frequencies of 15 GHz and 16 GHz due to coupling effect

Fig. 8. Strong acoustic vibrational coupling in stacked Au nanoplates^{[65, 68-69]}. (a) SEM image of stacked Au nanoplates^[68]; (b) diagram of two stacked Au nanoplates separated by a PVP-40K polymer layer; (c) acoustic vibrational spectra of first plate f1, second plate f2, and overlapping area. Acoustic vibrational coupling between plates creates new frequencies f+ and f-; (d) calculated vibrational coupling spectra between acoustic resonators with different coupling rates^[65]. Inset shows schematic model of coupled resonators; (e) polymer dependent acoustic vibrational coupling strength of stacked Au nanoplates^[69]; (f) frequency shift of coupled modes f+ and f- relative to uncoupled nanoplate frequency versus frequency detuning of uncoupled modes. Experimental data (dots) are fitted to coupled oscillator model (lines), showing anticrossing behavior characteristic of strong coupling

Fig. 9. Theoretical studies of acoustic vibrational coupling in stacked Au nanoplates^［102］. (a) Calculated vibrational frequencies in stacked Au nanoplates based on continuum mechanics model. Dot-dash lines are results of symmetric modes and solid lines are results of antisymmetric modes; (b) vibrational profiles (from left to right) that correspond to first three modes at d/h=0.1 marked with dashed box in (a) (from low to high). Modes are relative mode, f-, and f+ for stacked Au nanoplates as shown in Fig. 8(c); (c) finite element calculations of first five vibrational eigenfrequencies in three Au-polymer-Au-polymer-Au stacking structures; (d) vibrational profiles (from left to right) that correspond to first five modes at d/h=0.1 marked with dashed box in (c) (from low to high)

Fig. 10. Metal acoustic nanocavity used for studies on nanometer slip at solid-liquid interface and liquid viscoelastic properties^{[40, 78, 80, 95]}. (a) Acoustic vibrations of highly spherical Au nanoparticles in glycerol-water mixtures^[40]; (b) corresponding quality factors for acoustic vibrations of Au nanosparticles. Points correspond to experimental data, solid lines correspond to viscoelastic theory, and dashed lines correspond to Newtonian theory; (c) quality factor and (d) frequency of acoustic vibrations of Au bipyramids in glycerol-water mixtures^[78]; (e) quality factors Qliq of fundamental acoustic vibrations versus vibrational frequency for Au nanoplates in glycerol-water mixtures^[95]; Dashed and solid lines correspond to calculation results of inviscid and viscoelastic fluid models, respectively. Symbols show experimental data; (f) liquid relaxation time λliq determined from experiments (spots). Solid line shows relaxation time from reference