Nonlinear optical phenomena occur when the response of a material system to an applied optical

field depends nonlinearly on the strength of the applied field. The subsequent interaction of the

optical field with this nonlinear response generates a myriad of interesting physical processes. In some

applications, these nonlinear processes are merely limitations to the performance of linear systems,

whereas in photonics, nonlinear processes promise to be much more. Applications of nonlinear optics

include the frequency doubling of semiconductor lasers, the generation of ultrashort laser pulses,

dispersion compensation in communication systems, and all-optical switching. In this chapter, we

provide a brief summary of this field, emphasizing important results and qualitative features. A more

complete, pedagogical introduction to nonlinear optics is presented in Boyd (1992). The reader is also

directed to the textbooks by Shen (1984), Butcher and Cotter (1990), and Zernike and Midwinter

(1973).