ABSTRACT
We describe recent advances in condensed matter physics that make it possible to study non-linear optical properties of periodic solids from first-principles density functional theory. These methods are either based on perturbation theory in the framework of the 2n + 1 theorem, finite electric fields or effective hamiltonians. We apply them to the study of non-linear optical properties of various ferroelectric ABO3 compounds such as BaTiO3, PbTiO3 or LiNbO3.
