ABSTRACT
InChap. 2,we have discussed at length the nonlinear polarization in amaterial and derived the nonlinear wave equation rigorously.We have also shown that a scalar nonlinear wave equation can be heuristically derived from the concept that the phase velocity of a wave is modified in the presence of nonlinearities. In this chapter, we will employ the more rigorous approach to investigate second harmonic generation (SHG) in quadratically nonlinear materials. We examine the effect of linear phase mismatch, and of the beam profile and crystal anisotropy on the conversion efficiency. We would like to point out that, in general, both quadratic and cubic nonlinearities may exist in a material. It turns out that ‘‘cascaded’’ quadratic nonlinearities can, in some cases, simulate an effective cubic nonlinearity. Spatial solitons commonly exist in a cubically nonlinear material, as will be shown in the following chapter.
