Second-Harmonic Generation in Bulk Centrosymmetric Media

Abstract

Until recently, the dependence on the crystal orientation in second-harmonic generation (SHG) by cubic centrosymmetric media had gone unnoticed.1 It is now known that a variety of such materials do in fact show appreciable anisotropies.2,3 The second-harmonic (SH) radiation arises from the polarization in the bulk, which is for bidden in the electric-dipole approximation, as well as from a layer of polarization at the surface, where the symmetry constraint is relaxed. The bulk nonlinear polarization is nonlocal, consisting of terms proportional to products of the pump electric field E and gradients of this field. We find for cubic symmetry that the (generalized) nonlinear polarization along the ith crystal axis can be expressed as © 1984 Optical Society of America