The four-wave mixing (FWM) signal of a semiconductor superlattice with
an external electric field is evaluated using the semiconductor Bloch
equations. It is found that the FWM signal for a GaAs/AlGaAs-semicond
uctor superlattices with a lattice constant d has a deep valley when t
he electric field is around eFd = 1 meV. It is also found that the dee
p valley comes mainly from the broken inversion symmetry caused by the
exteral electric field and that the field intensity determines the si
gn and the magnitude of the Coulomb-induced optical nonlinearities.