Interaction of almost-collinear longitudinal phonons

The interaction of two longitudinal ultrasonic waves to produce sum- and difference-frequency waves has been studied experimentally and theoretically. These interactions are closely analogous to the type of threephonon interactions believed to be important in low-temperature ultrasonic attenuation. We have applied the coherent-state formalism to a description of these interactions and have discussed the similarities between coherent and incoherent processes. Experimentally we have measured the amplitude of the generated sum- or difference-frequency wave as a function of the angle between the input waves and of the amplitude and frequency of the input waves. The effect of crystalline anisotropy has also been observed. The change in amplitude of one of the input waves has been measured as a function of the parameters listed above. In all cases the experimental observations are in good agreement with theory.