  We report on the first optical characterization of both cubic and hexagonal
SrMnO$_3$. Room-temperature Raman spectra collected by means of a micro-Raman
spectrometer are shown. The spectrum of the cubic compound is characterized by
weak and broad bands in agreement with group-theory which predicts no
Raman-active phonons for this compound. On the other hand, the spectrum of the
hexagonal compound shows six narrow peaks ascribed to one-phonon processes. A
complete polarization analysis of the spectra collected from a single
crystallite allows us to completely assign the symmetries of the six observed
peaks. Atomic displacements for each phonon peaks are also proposed.
