Chapter 2 - Wave-Equation Description of Nonlinear Optical Interactions

Abstract

This chapter discusses the basics of nonlinear optical interactions and presents derivation of the most general form of the wave equation in nonlinear optics. Nonlinearity in the response of a material system to an intense laser field can cause the polarization of the medium to develop new frequency components not present in the incident radiation field. These new frequency components of the polarization act as sources of new frequency components of the electromagnetic field. This chapter examines how Maxwell's equations describe the generation of these new components of the field, and explores how the various frequency components of the field become coupled by the nonlinear interaction. This chapter develops the mathematical theory of these effects and presents a simple physical picture of how these frequency components are generated. The chapter also discusses how nonlinear optical wave equation can be used to describe specific nonlinear optical interactions. One of the sections treats the process of sum-frequency generation in the simple limit in which the two input fields are undepleted by the nonlinear interaction. The chapter describes techniques that utilize the birefringence of an optical material to achieve the phase-matching condition of nonlinear optics.