We present an ab-initio real-time based computational approach to nonlinear optical properties in Condensed Matter systems. The equation of mot ions, and in particular the coupling of the electrons with the external electric field, are derived from the Berry phase formulation of the dynamical polarization. The zero-field Hamiltonian includes crystal local field effects, the renormalization of the independent particle energy levels by correlation and excitonic effects within the 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 . We finally show applications to the second-harmonic generation of CdTe the third-harmonic generation of Si.
Real-time approach to the optical properties of solids and nanostructures : Time-dependent Bethe-alpeter equation Phys. Rev. B 84, 245110 (2011)
Nonlinear optics from ab-initio by means of the dynamical Berry-phase
C. Attaccalite and M. Gruning Phys. Rev. B 88 (23), 235113 (2013)