  Excitonic effects in the linear optical response of semiconductors are
well-known and the subject of countless experimental and theoretical studies.
For the technologically important second order nonlinear response, however,
description of excitonic effects has proved to be difficult. In this work, a
simplified three-band Wannier exciton model of cubic semiconductors is applied
and a closed form expression for the complex second harmonic response function
including broadening is derived. Our calculated spectra are found to be in
excellent agreement with the measured response near the band edge. In addition,
a very substantial enhancement of the nonlinear response is predicted for the
transparency region.
