Picosecond acoustic phonon pulse propagation in silicon

We report experimental and theoretical investigations of the behavior of coherent acoustic phonon pulses after propagation through millimeter-scale distances in crystalline Si. An ultrafast optical pump and probe technique is used to generate and detect the phonon pulses. The geometry of our experiment is such that we can make this measurement in either the far field or the near field of the acoustic source, allowing studies of diffraction effects in addition to dispersion and nonlinearity in the Si. We also present a rigorous derivation of the Korteweg-de Vries equation, which describes the behavior of these acoustic pulses in the nonlinear regime in one dimension. This one-dimensional (1D) model is combined with a 3D analysis of diffraction effects in anisotropic media in order to analyze far-field data.