Exciton-exciton interaction and optical nonlinearity in biased semiconductor quantum wells

We investigate theoretically the excitonic optical nonlinearity in a semiconductor quantum well subject to an electrostatic field normal to the quantum-well plane, basing our calculation on the Hamiltonian of interacting bosons for the system of many quasi-two-dimensional excitons. It is pointed out that the dipole-dipole interaction between excitons plays an essential role in this optical nonlinearity. Numerical results of the third-order optical susceptibility for a GaAs quantum-well structure are also presented.