  Transition metal dichalcogenides (TMDCs) combine both strong
light-matter-interaction and strong Coulomb-interaction for the formation of
optically excitable excitons. Through radiative feedback control, a mechanism
to control the linewidth can be applied, which modifies optical transition
spectra. Here, we extend these investigations to the absorption spectra of
TMDCs in a variety of geometries with respect to non-Markovian
exciton-phonon-scattering contributions. Our approach is based on the self
consistent solution of the microscopic Bloch equations and the macroscopic
solution of the wave equation. We discuss the formation of a phonon sideband
for MoSe$_2$ embedded in SiO$_2$, and two setups for enhancing or suppressing
the phonon sideband in the spectrum.
