Fig. 6: Envelope of the kinetic energy simulated by finite element modeling.
From: The effect of echoes interference on phonon attenuation in a nanophononic membrane

a We report in a semi-logarithmic scale the envelope of the kinetic energy for λph=55 (black), 83 (red), 109 (blue), 201 (green) and 502 nm (magenta). In this scale, the linear dependence on the position x corresponds to a propagative behavior with a mean free path given by the inverse of the slope. b The mean free path calculated for the envelope (ℓenv, magenta circles) is reported and compared with the one of the main pulse, calculated following its propagation (ℓcoh, blue squares), as a function of the wavelength in a logarithmic scale. Red stars correspond to this latter, for the experimental wavelengths. The two mean free paths depart from each other between 102 and 502 nm, due to an increased importance of coherent constructive interference between multiply scattered peaks in this wavelength range. Vertical dashed lines highlight this interference-dominated region. Note that the value for λph = 502 nm has been devided by 1.5 for a better visibility of all points. Error bars come from the fit of the mean free path for the envelope and of the lifetime for the main pulse.