Simplified bond-hyperpolarizability model of second harmonic generation

Abstract

We show that the anisotropies of second-harmonic-generation (SHG) intensities of vicinal (111) and $(001){\mathrm{S}\mathrm{i}\ensuremath{-}\mathrm{S}\mathrm{i}\mathrm{O}}_{2}$ interfaces can be described accurately as dipole radiation originating from the anharmonic motion of bond charges strictly along bond directions. This simplified bond-hyperpolarizability model not only substantially simplifies the description of SHG, but also provides a microscopically physical and mathematically more efficient picture of the process than those found in standard phenomenological treatments employing tensor or Fourier coefficients. Using this approach we obtain an analytic solution for the expected response of (111) terraces, and by comparing to data show that the effective angles of incidence and observation for the $(111){\mathrm{S}\mathrm{i}\ensuremath{-}\mathrm{S}\mathrm{i}\mathrm{O}}_{2}$ interface are not those measured in the laboratory but correspond to those refracted at the air-${\mathrm{SiO}}_{2}$ interface. For (111) vicinal interfaces at 765 nm SHG absorption is found to occur mainly for the step bond. The success of this formulation indicates that in many, if not most, cases the description of SHG may be simpler than that of the linear-optical response.