Full Vector Theory of Fundamental and Second-Harmonic CW Waves

Abstract

Second-harmonic generation (SHG) is explained in terms of linear phase matching and deploys in non-centrosymmetric crystals. The classification of the SHG processes into type I and type II are well known but the more general vector case has not been studied. Type II SHG is a vector process involving two electric field components at the fundamental frequency and one component at the second-harmonic frequency. It is assumed in the literature that only one component of the second-harmonic field is phase matched but this argument is based upon the magnitude of the linear phases only. For a situation in which linear phase matching is absent the nonlinear phases are important and will balance the linear phases. The full vector theory needs to be investigated therefore.