Subterahertz Phonon Dynamics in Acoustic Nanocavities

We report a direct determination of the dynamic behavior of confined acoustic phonons in nanocavities by picosecond acoustics. We provide the broadband, high resolution transmission amplitude curve in the subterahertz range, and we give evidence of resonant transmission peaks in three successive stop bands, in quantitative agreement with acoustic simulations. We furthermore demonstrate transit times in the nanosecond range at the cavity peaks reflecting the strong confinement of resonant phonons within the cavity layer. On the other hand, picosecond transit times are measured in the stop band, shorter than in any of the constituting materials, a tunneling effect well known both in photonic crystals and in macroscopic phononic systems.

Figure 1

Scheme of the acoustic nanodevice and configuration of the picosecond acoustic measurement.

Figure 2

Time dependence of the acoustic displacement across the device shown for sample $M$ on the left and $C$ on the right after a Gaussian pulse centered at 100 GHz with a full width of 0.2 GHz is sent from the substrate into the device. The thick black line at position $z=0$ indicates the substrate-device interface.

Figure 3

(a) Imaginary part of the time resolved reflectivity on sample $C$. The brackets indicate successive pairs of echoes and the labels give the associated number of substrate traversals ($2n+1$). The vertical lines define the time window used for the data analysis and the inset magnifies the short time variation inside the ellipse. (b) Variation of the peak intensity at the cavity mode (solid circles) and the stop-band low energy edge (open squares) in partial FT windows with a constant length 500 ps and varying central time delays given in the abscissa. The arrows indicate the arrival of new echoes. The solid lines are exponential fits of the decays, and the inset shows the partial FT traces at three typical delays, when the center of the window is at 0.45, 0.85, and 1.85 ns, respectively.

Figure 4

Fourier transform amplitudes of the time derivative of the transient reflectivity signal ($E$) for both samples $M$ (left side) and $C$ (right side) compared to the respective calculated Fourier transform of the deformations at the surface ($T$), including the simulated incident phonon pulse spectrum. The energy range of the phonon stop bands are emphasized in red.

Figure 5

Group transit time deduced from numerical filtering of the signal on sample $C$ with Gaussian filters centered at various energies and with widths of 0.01 GHz (blue points). A constant time offset has been adjusted to fit the theoretical group transit time through the cavity device obtained with the same method (black line). The red dotted line shows the transit time calculated using an effective velocity as described in the text.