  Enabling the light-control of complex systems on ultra-short timescales gives
rise to rich physics with promising applications. While crucial, the
quantitative determination of both the longitudinal and shear photo-induced
strains still remains challenging. Here, by scrutinizing asymmetric Bragg peaks
pairs $(\pm h01)$ using picosecond time-resolved X-ray diffraction experiments
in BiFeO$_3$, we simultaneously determine the longitudinal and shear strains.
The relative amplitude of those strains can be explained only if both thermal
and non-thermal processes contribute to the acoustic phonon photogeneration
process. Importantly, we also reveal a difference of the dynamical response of
the longitudinal strain with respect to the shear one due to an interplay of
quasi-longitudinal and quasi-transverse acoustic modes, well reproduced by our
model.
