General Nonlinear Polarization and Susceptibility

Mixed systems of units have been employed by various researchers as some of the numerical examples in the preceding chapters have demonstrated. A masteiy of these unit conversion techniques is almost a prerequisite in the study of liquid crystals and/or nonhnear optics. 

As we mentioned in the beginning of the chapter, in the electromagnetic approach to nonhnear optics, the nonlinear response of a medium to an applied electromagnetic field is described by a functional dependence of the form 

The nonlinear response at the space-time point (r,t) is due not only to the action of the applied fields at the same space-time point, but also of the fields at a different space-time point (r, t ). In other words, the response is a nonlocal function of time 

A more explicit form for P r,t) can be obtained if we make some simplifying assumptions. 

An approximation that is often made is the expression of the resulting polarization as a power series in the fields. We have 

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