Velocimetry of GHz elastic surface waves in quartz and fused silica based on full-field imaging of pump–probe reflectometry

This study reports an imaging method for gigahertz surface acoustic waves in transparent layers using infrared subpicosecond laser pulses in the ablation regime and an optical pump–probe technique. The reflectivity modulations due to the photoelastic effect of generated multimodal surface acoustic waves were imaged by an sCMOS camera illuminated by the time-delayed, frequency-doubled probe pulses. Moving the delay time between 6.0nsto11.5ns, image stacks of wave field propagation were created. Two representative samples were investigated: wafers of isotropic fused silica and anisotropic x-cut quartz. Rayleigh (SAW) and longitudinal dominant high-velocity pseudo-surface acoustic wave (HVPSAW) modes could be observed and tracked along a circular grid around the excitation center, allowing the extraction of angular profiles of the propagation velocity. In quartz, the folding of a PSAW was observed. A finite element simulation was developed to predict the measurement results. The simulation and measurement were in good agreement with a relative error of 2 % to 5 %. These results show the potential for fast and full-field imaging of laser-generated ultrasonic surface wave modes, which can be utilized for the characterization of thin transparent samples such as semiconductor wafers or optical crystals in the gigahertz frequency range.


Additional Figures
Figure 1 shows the comparison between unaveraged and averaged image quality for x-cut quartz at delay times of 11.5 ns.The SNR scales with the square root of the number of averages, leading to 3× improvements in our case which can be observed for the measurements along the line profiles at the bottom of Figure 1.  Figure 3 shows the calculated piezoelectric coupling K for x-cut quartz.
The maximum value is reached slightly offset from the material y-axis and the minimum is along the z-axis.The simulation was performed with a 20 nm Al film deposited on a 10 µm fused silica substrate.A finite difference element size of 2 nm was used, increasing to 10 nm within the SiO 2 substrate for depths exceeding 1 µm.
Substrate side laser irradiation was simulated with a fluence of 1.4 J cm −2 , wavelength of 1056 nm, and pulse duration of 0.7 ps.It should be noted that the SiO 2 substrate within the simulation does not interact with the laser pulse.Time delays up to 1 ns were investigated, with a particular focus on the ablation induced pressure within the SiO 2 substrate.We emphasize that the chosen method for simulating thin-film ultrafast laser ablation has been extensively validated, as demonstrated e.g. by Olbrich et al. [6] for thin gold films.The main limitation of the 1D simulation compared to experiments is that it may overestimate the pressure induced in the SiO 2 substrate, as already described in the main manuscript.This is because the 1D model does not account for 3D losses, which would tend to reduce the pressure buildup.
The pressure distribution over time is shown in Figure 4 for up to 100 ps (left) and 1 ns (right) after excitation.The temporal development of the pressure distribution after excitation at t = 0 ps is displayed.The interface between Al and fused silica is at z = 0 nm with the Al layer extending to z = −20 nm and the fused silica for z > 0 nm.The small yellow section in

Figure 2
Figure2shows the measurement software and data analysis.The red crosses show the detected wavefront positions for the HVPSAW at one delay time.At the bottom, a line profile along the selected angles is displayed.

4 2 .
Details of ablation simulationUltrafast laser ablation simulations were performed with one-dimensional two-temperature hydrodynamic code developed by Povarnitsyn et al.[1].For our simulations, we employed a layered system consisting of Al on SiO 2 in the form of fused silica.In addition to the transport and optical parameters of Al related to the two-temperature model (TTM)[2,3], the material response to ultrafast laser excitation is modeled within this framework by an equation of state (EOS).For Al, a two-temperature wide-range multi-phase EOS was utilized, developed by Khishchenko[4].For fused silica, an implemented simple thermal two-temperature EOS model based on the quasi-harmonic Debye model was used[5].This model is calibrated primarily using shock-wave data (shock Hugoniots, release isentropes, and sound speed measurements behind the shock front).The ideal Fermi-gas model was used for the electronic term.

Figure 4 :
Figure 4: Simulation of the generated pressure during ablative excitation within 100 ps (left) and up to 1 ns (right).Note the different color scale.

Figure 4 (
Figure 4 (left) shows the high pressures created during the ablation of the Al layer directly after excitation.The pressure pulse transmitted in the fused silica shows significant curvature, especially during the first 100 ps, indicating amplitude-dependent propagation velocities of the shock wave.Figure

4 (
right) shows the high attenuation of the pulse after 1 ns with pressure amplitudes reduced to ≈ 2 GPa.Note the different pressure scales of the