Intraband polarization as the source of degenerate four-wave mixing signals in asymmetric semiconductor quantum well structures

We have developed a formalism for calculating the coherent response of asymmetric semiconductor quantum well structures to ultrashort optical pulses. We work in an excitonic basis and include exciton-exciton interactions via the long-wavelength portion of the excitonic intraband polarization. We apply this formalism to the calculation of degenerate four-wave mixing intensities of a biased semiconductor superlattice and find that many aspects of the four-wave mixing signals are most naturally interpreted as directly resulting from the scattering of excitons off of the intraband polarization grating. We furthermore develop an extremely accurate method of factoring the dynamical equations that does not suffer from the problem encountered by the semiconductor Bloch equations in the Hartree-Fock approximation.