  In recent years, the manipulation of Fano resonances in the time domain has
unlocked deep insights into a broad spectrum of systems' coherent dynamics.
Here, inelastic scattering of light with coherent acoustic phonons is harnessed
to achieve complex Fano resonances. The sudden change of phonon momentum during
reflection leads to a transition from anti-Stokes to Stokes light scattering,
producing two different resonances that interfere in the measurement process.
We highlight the conditions necessary to achieve such interference, revealing
an underlying symmetry between photons and phonons, and verify the theory
experimentally. Then, we demonstrate the possibility to characterize energy and
coherence losses at rough interfaces, thus providing a mechanism for
nondestructive testing of interface quality. Our results describe numerous
unexplained observations in ultrafast acoustics and can be generalized to the
scattering of light with any waves.
