Nonlinear optical response of ferroelectric oxides: first-principles calculations within the time-domain and the frequency-domain

The second and third order nonlinear susceptibilities of the ferroelectric oxides LiNbO$_3$, LiTaO$_3$, and KNbO$_3$ are calculated from first principles. Two distinct methodologies are compared, one approach is based on a perturbative approach within the frequency-domain, another on the time-evolution of the electric polarization. The frequency dependence of the second harmonic coefficients of the ferroelectric phase of LiNbO$_3$ calculated within the two approaches is in excellent agreement. This is further validated by experimental data for LiNbO$_3$ and LiTaO$_3$, measured for an incident range of photon energies between 0.78 eV and 1.6 eV. The real-time based approach is furthermore employed to estimate the third order nonlinear susceptibilities of all investigated ferroelectric oxides. We further show that the quasiparticle effects, considered by means of a scissors-shift in combination with the the computationally efficient independent particle approximation, result in a shift all spectral features towards higher energies and decrease the magnitude of the optical nonlinearities. The energy of the main resonances in the hyperpolarizabilities suggests that the spectra can be understood by multi-photon adsorption within the fundamental bandgap for all investigated materials.