ABSTRACT
The two principal assumptions are monochromatic plane-wave interactions and the small-signal approximation where the inputs are negligibly affected by the nonlinear interaction. This chapter discusses the coupled amplitude equations but with less restrictive assumptions regarding the changes in field amplitudes. This treatment shows the important result that nonlinear interactions exhibit exponential gain. Anything that reduces the exponential gain, such as absorption losses, has the potential to greatly reduce the conversion efficiency. A fundamental upper limit to the conversion efficiency is dictated by energy conservation, which the chapter discusses in the context of the Manley–Rowe relations. From the coupled amplitude equations, the chapter moves to work with the example of difference-frequency generation (DFG). The chapter ends by covering spontaneous parametric scattering (SPS), which is a three-wave mixing process: sum-frequency generation (SFG) and second-harmonic generation (SHG), that requires a different formalism.
