Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry

TLDR

The study examines second‑harmonic radiation at the boundary of isotropic or cubic media, where the reflected 2ω field scales with the incident field and its spatial derivative, and notes that this bound‑electron nonlinearity is comparable in magnitude to that of conduction electrons in metals. The authors aim to derive a complete expression for the intensity and polarization of reflected second‑harmonic radiation as functions of incidence angle and incident polarization state. They analytically relate the reflected 2ω field to the incident field and its spatial derivative, incorporating angle of incidence and polarization to predict intensity and polarization. The predicted angular dependences agree with measurements on Si, Ge, and Ag, additional experimental results are reported, and the bound‑electron nonlinearity magnitude scales with the square of the linear susceptibility, matching observations in Si, Ge, and alkali halides.

Abstract

The radiation at the boundary of an isotropic or cubic medium by a polarization at $2\ensuremath{\omega}$, the amplitude of which is proportional to the product of the incident laser field at $\ensuremath{\omega}$ and a spatial derivative of this field, is examined theoretically. A complete expression for the intensity and polarization of the reflected harmonic radiation as a function of the angle of incidence and state of polarization of the incident laser beam is derived. The angular dependences are in good agreement with observations on Si, Ge, and Ag. Some additional experimental results, not previously reported, are described. The magnitude of the nonlinearity due to bound electrons in these cubic materials is related to the square of the linear susceptibility, and agrees qualitatively with observations in Si, Ge, and alkali halides. This nonlinearity has the same order of magnitude as that caused by conduction electrons in metals, which has been extensively discussed in the literature. The influence of absorbed surface layers is considered.