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

Abstract

This chapter presents a general quantum-mechanical theory of the nonlinear optical susceptibility, and uses the laws of quantum mechanics to derive explicit expressions for the nonlinear optical susceptibility. The chapter presents a derivation of the nonlinear optical susceptibility based on quantum-mechanical perturbation theory of the atomic wavefunction. The expressions that are derived using this formalism can be used to make accurate predictions of the nonresonant response of atomic and molecular systems. The chapter discusses relaxation processes in connection with the density matrix formulation of the theory of the nonlinear optical susceptibility. Calculation of the nonlinear susceptibility based on the properties of the atomic wavefunction is also carried out in the chapter. The nonlinear optical susceptibility is calculated through use of the density matrix formulation of quantum mechanics. The chapter also shows that nonlinear effects become particularly large when one of the frequencies of the incident laser field, or when sums or differences of these frequencies, becomes equal to a transition frequency of the atomic system. Density matrix calculation of the second-order susceptibility, as well as the third-order susceptibility, is discussed in the chapter.