Fig. 4: Wavepacket propagation and phonon lifetime as simulated by finite element modeling.

a Sketch of the 3D finite element model of the nanophononic structure. A semi-infinite solid is constructed by applying Periodic Boundary Conditions (yellow sides) and Perfect Matched Layers (end of the sample on the right). The wavepacket is generated on the left side of the sample (red). The four x positions at which the time evolution of the wavepacket is reported in (b) and (c) are indicated with dashed lines. b, c report the time dependence of the instantaneous kinetic energy E_kin(x, t) at the 4 selected positions, identified by the different colors (blue, orange, yellow, magenta from 1 to 4), for λ = 84 nm and λ = 201 nm, respectively. Arrows indicate the first peak in time that reaches each of the four positions. The coherent phonon attenuation was calculated from the decay of this peak and is reported in (d) as a function of the wavelength λ_ph in a logarithmic scale. Simulated points at the experimental wavelengths are reported in red. The black dashed line is a guide for the eye. The green solid line is the incoherent boundary scattering lifetime τ_b. The neck (N) and periodicity (A) are indicated by arrows. Error bars come from the fitting uncertainties.