  We study the optical conductivity in the III-V diluted magnetic semiconductor
GaMnAs and compare our calculations to available experimental data. Our model
study is able to reproduce both qualitatively and quantitatively the observed
measurements. We show that compensation (low carrier density) leads, in
agreement to the observed measurements to a red shift of the broad peak located
at approximately 200 meV for the optimally annealed sample. The non
perturbative treatment appears to be essential, otherwise a blueshift and an
incorrect amplitude would be obtained. By calculating the Drude weight (order
parameter) we establish the metal-insulator phase diagram. We indeed find that
Mn doped GaAs is close to the metal-insulator transition and that for 5$%$ and
7$%$ doped samples, 20$%$ of the carriers only are delocalized. We have found
that the optical mass is approximately 2 m$_{e}$. We have also interesting
results for overdoped samples which could be experimentally realized by Zn
codoping.
