Hyperpolarizabilities of LiNbO $$_3$$ 3 , LiTaO $$_3$$ 3 and KNbO $$_3$$ 3 calculated from First Principles

LiNbO $$_3$$ 3 , LiTaO $$_3$$ 3 , and KNbO $$_3$$ 3 are ferroelectric oxides that are largely employed in technological applications due to their strong nonlinear optical response. In this manuscript, we calculate their second and third order nonlinear susceptibilities from first principles. Two different approaches are employed, based on the perturbative estimate of the optical response in the frequency-domain, and on the time-evolution of the electric polarization, respectively. The two approaches predict second harmonic coefficients for LiNbO $$_3$$ 3 which are in excellent agreement with each other. We furthermore calculate second and third order nonlinear susceptibilities of all investigated materials. Quasiparticle effects, accounted for by means of a scissors-shift, blue-shift the calculated spectral features and reduce their intensity. A comparison of the linear and nonlinear optical response suggests that the spectra can be understood by multi-photon adsorption within the fundamental bandgap of the modeled ferroelectric oxides.