ABSTRACT
Linear optics plays a crucial role in determining the performance and characteristics of nonlinear optical systems. Focusing, material dispersion, and birefringence are only a few examples of linear properties that strongly influence nonlinear behavior. This chapter introduces linear properties important to nonlinear optics as well as the framework of derivations common to both linear optics and nonlinear optics. It addresses the distinctions between linear and nonlinear systems. In linear optical systems, the different beams of light in a system do not "talk" to each other. In contrast, nonlinear optical systems have energy exchanges between the inputs. Understanding these nonlinear coupling phenomena is the focus of the chapter. The chapter explains this with the help of Poynting's theorem, Maxwell's Equations, and the concept of linearity. The wave equation provides a quantitative approach to determine the evolution of optical fields as well as their effect on each other in the presence of nonlinearities.
