  We investigated multilayer plates made by exfoliation from a high-quality
MoS$_2$ crystal and reveal that they represent a new object - van der Waals
homostructure consisting of a bulk core and a few detached monolayers on its
surface. This architecture comprising elements with different electron band
structure leads to specific luminescence, when the broad emission band from the
core is cut by the absorption peaks of strong exciton resonances in the surface
monolayers. The exfoliated flakes exhibit strong optical anisotropy. We have
observed a conversion of normally incident light polarization to $15\%$ in
transmission geometry. This background effect is due to fluctuations of the c
axis relative to the normal, whereas the pronounced resonance contribution is
explained by the polarization anisotropy of excitons localized in the stripes
of dissected surface monolayers.
