Communications: Ab initio second-order nonlinear optics in solids.

We present a first-principles theory for the calculation of the macroscopic second-order susceptibility chi((2)), based on the time-dependent density-functional theory approach. Our method allows to include straightforwardly the many-body effects, such as crystal local fields and excitons. We apply the theory to the computation of the second-harmonic generation spectroscopy. In order to demonstrate the accuracy of this approach we present spectra for the cubic semiconductor GaAs for which we obtain a very good agreement with the experimental results. We point out that crystal local fields are not sufficient to reproduce the experimental results. Only when we account for the excitonic effects we obtain a very good agreement with the experimental second-harmonic generation spectrum.