Nonlinear Optics

Throughout the long history of optics, and indeed until relatively recently, it was thought that all optical media were linear. The assumption of linearity of the optical medium has far-reaching consequences. The invention of the laser in 1960 enabled us to examine the behavior of light in optical materials at higher intensities than previously possible. Many of the experiments carried out made it clear that optical media do in fact exhibit nonlinear behavior. The field of nonlinear optics comprises many fascinating phenomena. Linearity or nonlinearity is a property of the medium through which light travels, rather than a property of the light itself. Nonlinear behavior is not exhibited when light travels in free space. Light interacts with light via the medium. The presence of an optical field modifies the properties of the medium which, in turn, modify another optical field or even the original field itself. In Chapter 5, dielectric media were further classified with respect to their homogeneity, isotropy, and dispersiveness. To focus on the principal effect of interest in this chapter—nonlinearity—the medium is initially assumed to be homogeneous, isotropic, and nondispersive. In this chapter we provide brief discussions of anisotropic and dispersive nonlinear optical media. The theory of nonlinear optics and its applications is presented at two levels. A simplified approach is provided. This is followed by a more detailed analysis of the same phenomena. Light propagation in media characterized by a second-order (quadratic) nonlinear relation between 𝒫 and ℰ is described. Applications include the frequency doubling of a monochromatic wave (second-harmonic generation), the mixing of two monochromatic waves to generate a third wave whose frequency is the sum or difference of the frequencies of the original waves (frequency conversion), the use of two monochromatic waves to amplify a third wave (parametric amplification), and the addition of feedback to a parametric amplifier to create an oscillator (parametric oscillation). Wave propagation in a medium with a third-order 𝒫−ℰ relation is discussed. Applications include third-harmonic generation, self-phase modulation, self-focusing, four-wave mixing, optical amplification, and optical phase conjugation. Optical solitons are discussed. These are optical pulses that propagate in a nonlinear dispersive medium without changing their shape. Changes in the pulse profile caused by the dispersive and nonlinear effects just compensate each other, so that the pulse shape is maintained for long propagation distances. Optical bistability is discussed in Chap. 21.