Facet-dependent electric-field-induced second harmonic generation in silicon and zincblende

We discuss electric-field-induced second harmonic (EFISH) generation for silicon and zincblende facets (001), (011), and (111), employing the full fourth-rank tensor representation of the third-order susceptibility. Then we directly relate these 81 tensor elements with the contracted or Voigt matrix representation. Using group theory, we show that the number of independent elements is only two; however, at different facets, different linear combinations thereof appear. Also, specific expressions for the resulting s- and p-polarized second harmonic polarization are given for incident s- and p-polarizations, for the first time explaining the facet and angle of incidence dependence of EFISH. Finally, a classical oscillator model is used to explain the response of the electrons and the material combined with a direct physical interpretation of the breaking of the symmetry and thus the deformation of the electronic charge density along the bonds. Through this model we propose a connection between the strength parameter b for third harmonic generation and the second harmonic signal originated by EFISH mechanism. (C) 2017 Optical Society of America