Formula for Coulomb effect on the nonlinear optical responses in quantum wells

In this paper I have derived a formula for the Coulomb effect on the nonlinear intersubband optical responses in quantum wells by introducing a collective dipole moment in the recursion relation. A square potential well with finite barrier is assumed for quantum wells biased by an electric field. The self-consistent screened Hartree-Fock approximation is used to calculate the Coulomb renormalization of the electron kinetic energy. The random-phase and ladder approximations are used to study the screening and excitonic interaction effects on the linear optical response in the intersubband optical absorption coefficient and refractive index function. Also, the nonparabolic electron energy dispersion and the z-dependent electron effective mass are considered. The formula could be used to calculate the nonlinear optical response to all orders. © 1996 The American Physical Society.