^{1}, Christoph Klieber

^{2}, Thomas Pezeril

^{1}and Keith Nelson

^{2}

^{1}Université du Maine.

^{2}MIT.

Picosecond ultrasonic interferometry also called time-resolved Brillouin scattering, monitors the time evolution of the spatial Fourier components of an optically excited acoustic strain distribution with wave number. Here, is the modification of the optical light wavevector in the probed medium. In the small-amplitude limit, a picosecond acoustic pulse propagates at a constant velocity, without nonlinear changes to its shape. The detected time-domain signal of the optical probe transient reflectivity, which includes a constant reflection from a metal surface against which the Brillouin-scattered field is heterodyned, shows a sinusoidal oscillation at a constant cyclic frequency equal to the Brillouin cyclic frequency. With known, the measurement allows determination of the velocity of acoustic phonons at frequency.

We present an analytical theory describing how nonlinear reshaping of a propagating, finite amplitude picosecond acoustic pulse results in a time-dependence of the observed frequency. In particular, we establish the conditions under which where is time-evolving speed of the weak-shock front that can be formed through the nonlinear acoustic transformation of the picosecond strain pulse. Depending on the parameters of the initial picosecond strain pulse and the monitored time interval of its nonlinear transformation, our theory predicts the frequency to either be monotonically decreasing or oscillating in time. We present examples in which the theory is used for interpretation of available experimental data.

The nonlinear transformation of the acoustic pulse profile and formation of a weak shock front with subsequent time-dependent variation in its velocity are the results of nonlinear acoustic multi-scattering processes involving all spectral components of the wide-frequency-band picosecond acoustic pulse. Thus, in general, picosecond ultrasonic interferometry of nonlinear acoustic pulses provides access to the nonlinear acoustic properties of the medium in much of the GHz frequency range.