Chapter 3 - Quantum-Mechanical Theory of the Nonlinear Optical Susceptibility

Abstract

In this chapter, we use the laws of quantum mechanics to derive explicit expressions for the nonlinear optical susceptibility. The motivation for obtaining these expressions is at least threefold: (1) these expressions display the functional form of the nonlinear optical susceptibility and hence show how the susceptibility depends on material parameters such as dipole transition moments and atomic energy levels, (2) these expressions display the internal symmetries of the susceptibility, and (3) these expressions can be used to make predictions of the numerical values of the nonlinear susceptibilities. These numerical predictions are particularly reliable for the case of atomic vapors, because the atomic parameters (such as atomic energy levels and dipole transition moments) that appear in the quantum-mechanical expressions are often known with high accuracy. In addition, since the energy levels of free atoms are very sharp (as opposed to the case of most solids, where allowed energies have the form of broad bands), it is possible to obtain very large values of the nonlinear susceptibility through the technique of resonance enhancement.