Nonlinear optics from ab-initio by means of the dynamical Berry-phase
Résumé
We present an ab-initio real-time based computational approach to nonlinear optical properties in Condensed Matter systems.The equation of motions, and in particular the coupling of the electrons with the external electric field, are derived from the Berry phase formulation of the dynamical polarization (Phys. Rev. B 69, 085106). The zero-field Hamiltonian includes crystal local field effects and the renormalization of the independent particle energy levels by correlation effects. We also discuss the possibility of accurately treating excitonic effects by adding a screened Hartree-Fock self-energy operator. The approach is validated by calculating the second-harmonic generation of SiC and AlAs bulk semiconductors: an excellent agreement is obtained with existing ab-initio calculations from response theory in frequency domain (Phys. Rev. B 82, 235201). We finally show applications to the second-harmonic generation of CdTe and the third-harmonic generation of Si.