  We report on a theoretical study of the electronic, optical and
magneto-optical properties of digital ferromagnetic hetero-structures based on
$Mn$ $\delta$--doped $GaAs$. We consider different structures corresponding to
$Mn$ contents within the range 12-50\% and we study how the system changes as a
function of the doping concentration. Our first--principles approach includes
the spin-orbit interaction in a fully relativistic pseudopotential scheme and
the local fields effect in the description of the optical absorption. We show
that $Mn$ $\delta$-doped $GaAs$ shares many properties with the uniformly doped
$Ga_{1-x}Mn_xAs$ system, i.e. half-metallicity, similar absorption spectra, and
moderate Kerr rotation angles in the visible spectral region.
