In this paper, we present a dielectric theory for polaritons in semico
nductor superlattices. The coherent optical field is classical, satisf
ying Maxwell's equations, while the carriers are treated fully quantum
-mechanically. The dielectric function is obtained through the solutio
ns of modified semiconductor Bloch equations for superlattices, descri
bed as an anisotropic medium. The equations combine the most relevant
many-body and effective dimensionality effects. Numerical results are
presented for GaAs/AlGaAs superlattices.