  The dielectric properties of La$_{1-x}$Sr$_{1+x}$MnO$_4$ single crystals with
x = 0, 0.125, 0.25, and 0.5 were studied by means of electron energy-loss
spectroscopy as a function of temperature and momentum transfer. A clear
signature of the doped holes is observed around 1.65 eV energy loss, where
spectral weight emerges with increasing x. For all $x \neq 0$, this
doping-induced excitation can propagate within the ab-plane, as revealed by a
clear upward dispersion of the corresponding loss peak with increasing momentum
transfer. The hole-induced excitation also shifts to higher energies with the
onset of magnetic correlations for x = 0.5, implying a strong coupling of
charge and spin dynamics. We conclude that (i) the loss feature at 1.65 eV is a
signature of electronic polarons, which are created around doped holes, and
that (ii) this low-energy excitation involves the charge transfer between
manganese and oxygen. The finite dispersion of these excitations further
indicates significant polaron-polaron interactions.
