Spatial dispersion contribution to second harmonic generation in inversion-symmetric materials

Abstract

It is well known that second harmonic generation (SHG) from dipoles within the bulk vanishes in inversion-symmetric semiconductor materials as a consequence of parity symmetry. Hence SHG is then ascribed in the form of either surface dipole effects or bulk-related electric quadrupole or magnetic dipole effects. By incorporating the redefined spatial dispersion into the simplified bond-hyperpolarizability model, we show that the SHG spatial dispersion contribution for Si(001) and Si(111) facet orientations can be reformulated by a third-rank tensor containing one independent parameter, namely, the complex SHG spatial dispersion hyperpolarizability. Our results show that certain unexplained rotational anisotropy SHG intensity features for different incoming light wavelengths or optical penetration depths can be well reproduced only if the contribution from spatial dispersion is incorporated.