Introduction

Since graphene was discovered a decade ago1, its remarkable properties have been utilized for novel devices and technological applications2,3,4,Full size image

We first investigated the PTA process as a function of the excitation wavelength. We used both 800 nm and 400 nm laser pulses to examine the sound generation efficiency. The experimental results are shown in Fig. 2, which displays the temporal signal trace of the generated acoustic sound. The major peaks are separated by 1 ms, corresponding to the laser pulse repetition rate of 1 kHz, where the laser pulse width is 130 fs. Furthermore, higher frequency oscillations are observed between the major peaks. These faster oscillations correspond to the characteristic frequency of the acoustic sound wave, as we will discuss in the following. In Fig. 2 we show the frequency domain analysis of the corresponding time domain data within one period. It is evident that the time and frequency domain analyses show indistinguishable results for the 800 nm and 400 nm optical excitations. Moreover, the efficiency for sound generation is also independent of the laser wavelength, since the generated sound pressures have the same power dependence (Fig. 2). One can also quantitatively determine a sound generation efficiency of 0.012% (see SI3). This photon-energy-independent feature can be attributed to two factors—the photon-energy-independent absorption coefficient in the visible to the near IR range37,38, due to a large energy window of the Dirac-like electronic states; and a very efficient energy relaxation channel for the hot electrons (holes) to reach equilibrium with the lattice temperature—both of which have been regarded as hallmarks of the remarkable properties of graphene. The PTA conversion efficiency of 0.012% is nearly identical to the efficiency of the TA process investigated earlier using pure Joule heating (SI3), implying an almost ideal energy conversion efficiency of the photo-thermal process in the MLG sheet.

Subsequently, we investigated the effect of the laser pulse duration on the generation efficiency. Three laser beams with durations of 130 fs, 190 ps and 230 ns (see Methods) were employed, all at 1 kHz repetition rate. The microphone detection distance was 25 mm. The experimental results are shown in Fig. 3, which demonstrates that within two orders of magnitude dynamic range of the laser power, the slope and thus the sound generation efficiency, is nearly identical for the three pulse durations. Moreover, the line shape of the acoustic waves is independent of the excitation pulse duration. In Fig. 3b we show the Fourier transform of the time domain data (Fig. 3b inset) that is taken for exactly one period. A peak is clearly observed around 6 kHz. For all three pulse durations, the frequency components and their amplitudes are identical. Unlike the 1 kHz repetition rate observed in Fig. 2 lower right panel, this 6 kHz anharmonic signal is more interesting, which has never been reported before. One needs a pulsed excitation source to observe this anharmonic signal. We show that this 6 kHz characteristic frequency originates from the interaction between the sample and the ambient gas molecules. By changing the ambient condition (e.g. using Helium gas in an enclosure) we observed that this 6 kHz frequency changed to ~2 kHz (Figure S2 in SI4).

Considering the results shown in Fig. 3, we were able to ascribe the sound generation to a PTA mechanism, a two-step process comprising an ultrafast PT process followed by a slower TA process. First we eliminated the possibility of a direct photo-acoustic (PA) mechanism. In the PA mechanism, the photo-excited electrons interact directly with the ambient air molecules. The ultrafast dynamics of the free carriers, the phonons and their interactions all have their characteristic time scales, ranging from tens of femtoseconds to picoseconds to sub-nanoseconds (see SI1). If a direct PA mechanism was involved: (1) the generation efficiency will be higher for the 130 fs pulses, because for 190 ps and 230 ns pulses a prominent portion of the absorbed photon energies are inevitably dissipated through electron-phonon scattering (as thermal energy, instead of acoustic energy); (2) the peak width of the acoustic wave should be smaller for the 130 fs and 190 ps cases, since it is only limited by the ultrafast electron-air molecule scattering rate. This is contrary to our experimental results. The above two reasons are summarized in a table in the supplementary information (see SI5). Our careful experiment in both the temporal and the frequency domain with different pulse widths (Fig. 3) is a direct experimental proof of the PTA mechanism. Our method also applies to other systems of similar materials. The PTA mechanism that we found is in consonant with the photo-thermal-electric (PTE) rather than the photo-voltaic (PV) mechanism in the electronic transport properties of graphene39,40,41. The ultrafast time scale of the PT process effectively creates a delta-function like temperature pulse on the sample. This sharp (in time) temperature pulse generates sound waves at the air/graphene interface, which then propagate through the air and are detected in the far field.

Coherent phase-control of the PTA sound waves

An interesting aspect of these PTA generated acoustic waves is the well-defined frequency (~6 kHz, different than the laser repetition rate) and the well-defined phase in the time domain. This introduces the interesting prospect of coherently controlling the relative phase between acoustic pulses, leading to constructive or destructive interferences.

In order to investigate this thoroughly, we used laser pulses of 532 nm wavelength, 400 ns duration and a fixed energy, thus the average laser power increased linearly with the repetition rate. In Fig. 4a we show the time-resolved acoustic waves, which exhibit constructive and destructive interference effects, as a function of the laser repetition rate (for tuning the repetition rate, see Methods). The relative phase between two consecutive acoustic wave packets in the time domain is directly related to the repetition rate. In Fig. 4b we show a numerical simulation of such an interference effect, by taking the acoustic response of a single pulse and applying strictly the wave superposition according to the laser repetition rate. It is evident that the numerical simulations using wave superposition accurately reproduce the experimental results. In Fig. 4c we show the false color map** of the result in Fig. 4a to clearly illustrate the phase-control effect. Owing to the finite number of discrete values of repetition rates, the interpolation is implemented between the measured data. The phase tuning is marked by white dashed curves and the interference effect is manifested by the horizontal red and blue color stripes. At low repetition rates the interference effect is small and at relatively high repetition rates the interference becomes more pronounced. The quantitative analysis of such an interference effect is further described in the discussion section. As verified in additional experiment (results not shown here), tuning the repetition rate at much lower than 1000 Hz (for example, from 1 Hz to 1000 Hz) has very little effect on the sound amplitude. However, as the laser repetition rate increases, the sound amplitude displays a pronounced increase and decrease alternately (Fig. 4c,d). This modification can be constructive or destructive, depending on the relative phase between the consecutive acoustic wave packets. In Fig. 4c the red stripe corresponds to constructive interference and the blue stripe to destructive interference.