17.1 INTRODUCTION

The subject of this chapter could well fill a textbook, and indeed the topic comprises a significant portion of the many books on nonlinear optics. A large (but by no means exhaustive or complete) list of texts that provide extensive discussion of high-order nonlinearities appears in Refs. 1 through 29. We have not attempted to write a review chapter nor mentioned or even listed every known third-order nonlinear optical phenomenon. Our aim is to illustrate important and representative third-order effects, emphasizing qualitative descriptions. Details can be found in the references. An exception is our discussion of the Kramers-Kronig relations in nonlinear optics. A fundamental premise of this transformation is the causal link between nonlinear refraction and nonlinear absorption, which is a key aspect of the third-order susceptibility. It has not been treated in most texts; some of the important mathematical steps are given here. Our treatment of third-order nonlinear optics assumes that the reader is familiar with electromagnetic theory, physical optics, and quantum mechanical energy level diagrams.

Any real, physical oscillating system will exhibit a nonlinear response when it is overdriven. In an optical system, a nonlinear response can occur when there is sufficiently intense illumination. The nonlinearity is exhibited in the polarization ( ) of the material, which is often represented by a power series expansion of...