ABSTRACT
A more complete description of nonlinear interactions includes the transformation of fields in the nonlinear medium. Maxwell's equations, including the nonlinear material response, provide such a description. This chapter considers simplified systems that shed light on some general trends in nonlinear optics. It first derives a wave equation for a low-efficiency (small-signal) three-wave interaction consisting of collinear plane waves. This interaction is characterized by two input beams and a generated output beam. In the small-signal regime, the amplitudes of the inputs do not change appreciably during the nonlinear interaction. The solution for the output in this small-signal regime introduces the important concept of phase matching, which determines how efficient the process can be. Finally, the chapter shows that phase matching also allows for a description of the system's tolerance to changes in temperature, frequency, and other parameters.
