Nonlinear optical response of ferroelectric oxides: First-principles calculations within the time and frequency domains

Abstract

The second- and third-order nonlinear susceptibilities of the ferroelectric oxides ${\mathrm{LiNbO}}_{3}$, ${\mathrm{LiTaO}}_{3}$, and ${\mathrm{KNbO}}_{3}$ 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 ${\mathrm{LiNbO}}_{3}$ calculated within the two approaches is in excellent agreement. This is further validated by experimental data for ${\mathrm{LiNbO}}_{3}$ and ${\mathrm{LiTaO}}_{3}$, measured for an incident range of photon energies between 0.78 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 show that the quasiparticle effects, considered by means of a scissors shift in combination with the computationally efficient independent particle approximation, result in a shift of 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 multiphoton absorption within the fundamental band gap for all investigated materials.