Theory of time-domain Brillouin scattering for probe light and acoustic beams propagating at an arbitrary relative angle: Application to acousto-optic interaction near material interfaces

A simple theory is developed for an interpretation of the time-domain Brillouin scattering experiments where the coherent acoustic pulse and the probe light pulse beams are propagating at an angle to each other. The directivity pattern of their acousto-optic interaction in case of heterodyne detection of the acoustically scattered probe light (in nearly backward direction to the probe light) is predicted. The theory reveals the dependences of carrier frequency and duration of acoustically induced "wave packets" in the transient reflectivity signals, on the widths of light and sound beams, and on the angle of their relative propagation (interaction angle). It also describes the transient dynamics of these wave packets when the probe light and the coherent acoustic pulses are incident on material interfaces (inter-grain boundaries) and Brillouin scattering by incident acoustic field is transformed into Brillouin scattering by the reflected and transmitted (refracted) acoustic fields. In general, these transformations are accompanied by the modifications of the interaction angles between the coherent acoustic pulses and probe light beams. The sensitivities of the carrier frequencies and wave packet amplitudes in the reflected/transmitted beams to the angle of the beams incidence on the interface are evaluated and compared. The theory confirms the expected possibility of strong and dominant reduction in the time-domain Brillouin scattering amplitude following the reflection/transmission processes for large interaction angles.