Complement 7B: Nonlinear optics in optical Kerr media

Summary

In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity, known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system, when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons, which maintain their shape during propagation.

Examples of third-order nonlinearities

Nonlinear response of two-level atoms

We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.