  The equations-of-motion for the density matrix are derived in a multiband
model to describe the response of semiconductors (bulk or quantum well
structures) under optical excitation with arbitrary polarization. The multiband
model used, comprising the twofold conduction band and the fourfold topmost
valence band (or heavy- and light-hole states), incorporates spin-splitting of
the single-particle states. The interaction terms include besides the direct
Coulomb coupling between carriers also the electron-hole exchange interaction,
which together with the spin-splitting terms is responsible for spin
relaxation. Applying the Hartree-Fock truncation scheme leads to a set of
coherent semiconductor Bloch equations for the multiband case. This concept
provides the theoretical frame for describing phenomena connected with optical
response under excitation with arbitrary light polarization and spin
relaxation: polarized optical response, polarization dynamics of VCSELs, spin
relaxation, and the circular photovoltaic effect.
