Dipole selection rules in multiband semiconductors

Rigorous dipole selection rules are derived for an interacting electron-hole system in a multiband semiconductor. The electronic system is described by the Coulomb many-body Hamiltonian and the valence-band structure is modeled using the Luttinger Hamiltonian in the axial approximation. For the example of a third-order analysis of polarization dependent two- and three-beam four-wave-mixing experiments the polarizations of the mixing signals are computed. Besides situations with well-defined four-wave-mixing polarizations configurations are identified where the polarization state of the outgoing signal depends on the dynamic and coherent properties of the semiconductor.