Contra-intuitive features of time-domain Brillouin scattering in collinear paraxial sound and light beams

Time-domain Brillouin scattering is an opto-acousto-optical probe technique for the evaluation of transparent materials. Via optoacoustic conversion, ultrashort pump laser pulses launch coherent acoustic pulses in the sample. Time-delayed ultrashort probe laser pulses monitor the propagation of the coherent acoustic pulses via the photo-elastic effect, which induces light scattering. A photodetector collects both the acoustically scattered light and the probe light reflected by the sample structure for the heterodyning. The scattered probe light carries information on the acoustical, optical and acousto-optical parameters of the material for the current position of the coherent acoustic pulse. Thus, among other applications, time-domain Brillouin scattering is a technique for three-dimensional imaging. Sharp focusing of coherent acoustic pulses and probe laser pulses could increase lateral spatial resolution of imaging, but could potentially diminish the depth of imaging. However, the theoretical analysis presented in this manuscript contra-intuitively demonstrates that the depth and spectral resolution of the time-domain Brillouin scattering imaging, with collinearly propagating paraxial sound and light beams, do not depend on the focusing/diffraction of sound. The variations of the amplitude of the time-domain Brillouin scattering signal are only due to the variations of the probe light amplitude caused by light focusing/diffraction. Although the amplitude of the acoustically scattered light is proportional to the product of the local acoustical and probe light field amplitudes, the temporal dynamics of the time-domain Brillouin scattering signal amplitude is independent of the dynamics of the coherent acoustic pulse amplitude.