Electrical susceptibility, nonlinear light interaction

The nonlinear interaction of light with matter is useful both as an optical method for generating new radiation fields and as a spectroscopic means for probing the quantum-mechanical structure of molecules [1-5]. Light-matter interactions can be formally classified [5,6] as either active or passive processes and for electric field based interactions with ordinary molecules (electric dipole approximation), both may be described in terms of the familiar nonlinear electrical susceptibilities. The nonlinear electrical susceptibility represents the material response to incident CW radiation and its microscopic quantum-mechanical formalism can be found directly by diagrammatic techniques based on the perturbative density matrix approach including dephasing effects in their fast-modulation limit [7]. Since time-independent (DC) fields can only induce a... 

So far, in the description of the interaction of light with matter, we have assumed that the response of the material to an applied optical field was independent of its magnitude. This approximation is valid when the electric field amplitude is negligible compared with the internal electric fields in atoms and molecules. However, when lasers are used as light sources, the intensity of the optical field is usually strong and can drive the electronic response of a dielectric into a nonlinear regime. This nonlinear optical response is described by a field-dependent susceptibility that can be written as... 

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