  The magneto-optical properties of (Ga,Mn)As have been determined within
density functional theory using the highly precise full-potential linear
augmented plane wave (FLAPW) method. A detailed investigation of the electronic
and magnetic properties in connection to the magneto-optic effects is reported.
The spectral features of the optical tensor in the 0-10 eV energy range are
analyzed in terms of the band structure and density of states and the essential
role of the dipole matrix elements is highlighted by means of Brillouin zone
dissection. Using an explicit representation of the Kerr angle in terms of real
and imaginary parts of the tensor components, a careful analysis of the Kerr
spectra is also presented. The results of our study can be summarized as
follows: i) different types of interband transitions do contribute in shaping
the conductivity tensor; ii) the dipole matrix elements are important in
obtaining the correct optical spectra; iii) different regions in the
irreducible Brillouin zone contribute to the conductivity very differently; iv)
a minimum in the Re $\sigma_{xx}$ spectra can give rise to a large Kerr
rotation angle in the same energy region; and v) materials engineering via the
magneto-optical Kerr effect is possible provided that the electronic structure
of the material can be tuned in such a way as to \emph{enhance} the depth of
the minima of Re $\sigma_{xx}$.
