19 - Introduction to nonlinear processes

Summary

Introduction

In this chapter we shall begin our discussion of nonlinear phenomena that are important in optics. When one or more electromagnetic waves propagate through any medium they produce polarizations in the medium that, in principle, oscillate at all the possible sum and difference frequencies that can be generated from the incoming waves. These polarizations, which oscillate at these new frequencies, give rise to corresponding electromagnetic waves. Thus, we get phenomena such as harmonic generation, for example, when infrared light is converted into visible or ultraviolet light, and various other frequency-mixing processes. These nonlinear processes can be described by a series of nonlinear susceptibilities or mixing coefficients. These coefficients will be defined and their origin traced to the anharmonic character of the potential that describes the interaction of particles in the medium.

Anharmonic potentials and nonlinear polarization

When an electromagnetic wave propagates through a medium a total electric field acts on each particle of the medium. This total field contains components at all the frequencies contained in the input wave or waves. Each particle of the medium will be displaced from its equilibrium position by the action of this field. Positive ions and nuclei will be displaced in the direction of the field, while negative ions and electrons will be displaced in the opposite direction to that of the field. The resultant separation of centers of positive and negative charge creates dipoles in the medium.