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

The radiation at the boundary of an isotropic or cubic medium by a polarization at $2\omega$, the amplitude of which is proportional to the product of the incident laser field at $\omega$ 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.