Acoustic solitons: A robust tool to investigate the generation and detection of ultrafast acoustic waves

Solitons are self-preserving traveling waves of great interest in nonlinear physics but hard to observe experimentally. In this report an experimental setup is designed to observe and characterize acoustic solitons in a GaAs(001) substrate. It is based on careful temperature control of the sample and an interferometric detection scheme. Ultrashort acoustic solitons, such as the one predicted by the Korteweg–de Vries equation, are observed and fully characterized. Their particlelike nature is clearly evidenced and their unique properties are thoroughly checked. The spatial averaging of the soliton wave front is shown to account for the differences between the theoretical and experimental soliton profile. It appears that ultrafast acoustic experiments provide a precise measurement of the soliton velocity. It allows for absolute calibration of the setup as well as the response function analysis of the detection layer. Moreover, the temporal distribution of the solitons is also analyzed with the help of the inverse scattering method. It shows how the initial acoustic pulse profile which gives birth to solitons after nonlinear propagation can be retrieved. Such investigations provide a new tool to probe transient properties of highly excited matter through the study of the emitted acoustic pulse after laser excitation.

Figure 1

Pump-probe setup based on interferometric detection of acoustic pulses. AOM: acousto-optical modulator; SBC: Soleil-Babinet compensator; MO: microscope objective; $\lambda /2$: half wave plate. The sample is placed in a cold finger cryostat. Typical pump-probe signal (black line) obtained after photothermal generation in a 60 nm Ti film with 12.5 nJ/pulse, propagation through a $370\text{−}\mu \mathrm{m}$-thick GaAs(100) slab at 20 K, and detection in a 60-nm-thick Ti layer. The signal derivative (blue line) shows the train of solitons and the dispersive tail.

Figure 2

Strain profile (black triangle) measured at $\tau ={\tau }_{\mathrm{prop}}=77.4\text{ns}$ after linear propagation through GaAs(100) substrate at 20 K $(\text{DC}=50\%$ with 12.6 pJ/pulse). Initial strain pulse (blue dot) calculated by propagating back numerically at $\tau =0\text{ns}$ the strain profile. The initial strain pulse is well fitted (see text) by a Gaussian derivative (solid line) with $z_0=13\text{nm}$.

Figure 3

Example of laser heating in ultrafast acoustic experiment in the case of a $100\text{nm}$ chromium film as transducer on top of $370\text{−}\mu \text{m}$-thick GaAs cooled down to $T_0=30\text{K}$. The average power is changed while the energy per pulse is kept constant by controlling the duty cycle (DC). Average pump power is 1 W at $\text{DC}=100\%.$ (a) UAPs measured for different DC with a vertical offset applied for the purpose of clarity. (b) Measurements (black diamonds) and calculated values (dashed line) for the relative change of velocity $\frac{\mathrm{\Delta }{v}_s}{v_s}\left(\text{DC}\right)$ (black scale). The corresponding temperature is provided by Ref. [22] and is given by $\frac{\mathrm{\Delta }{v}_s}{v_s}\left(T\right)$ (gray curve, gray scale). (c) Acoustic power detected when varying the DC.

Figure 4

Trains of solitons observed at 20 K $\left(\text{DC}=10\%\right)$ for (a) different pump energies $E_{\mathrm{pump}}$ but same titanium film thickness $d_{\text{Ti}}=120$ nm and (b) different titanium film thicknesses $d_{\text{Ti}}$ but same pump energy $E_{\mathrm{pump}}=8.75$ nJ.

Figure 5

Zoom on the fastest soliton profile for $d_{\text{Ti}}=60$ nm and $E_p=12.5$ nJ as measured by the interferometric setup. Expected soliton profile (solid line) when averaging over the probe spot. The soliton profile at $r=0$ $\mu \mathrm{m}$ and $r=1.6$ $\mu \mathrm{m}$ are plotted (dotted and dashed curves, respectively) scaled down by 3.

Figure 6

(a) Ultrafast acoustics signal (black line) measured at 20 K $\left(\text{DC}=10\%\right)$ for $E_{\mathrm{pump}}=12.5$ nJ and $d_{\text{Ti}}=60$ nm and expected strain profile (blue line) computed with ${\eta }_0=1.083(\pm 0.006)\times {10}^{-3}$ and $z_0=19.5$ nm. (b) Corresponding pulse profiles at $r=0\mu \mathrm{m}$ before propagation $\left(\tau =0\text{ns}\right)$ and after propagation $\left(\tau =77.4\text{ns}\right)$ through the substrate.