Four-wave mixing theory at the excitonic resonance: Weakly interacting boson model

A theory of degenerate four-wave mixing (DFWM) in the low density excitatio n limit at the semiconductor band edge is developed on the basis of the bos onic representation of the electron-hole Hamiltonian. By accounting for the exciton-exciton interactions of the lowest order we arrive at the practica l few-level density matrix description of the third-order excitonic nonline arity. The developed theory accounts phenomenologically for the phase space filling, and excitation induced dephasing effects and well reproduces the results of the recent DFWM experiments in high- and low-fineness microcavit y. We show that polarization-sensitive four-wave mixing measurements enable to discriminate the contributions to the DFWM signal from the exciton-exci ton interactions of different symmetry.