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　The motivation for obtaining expression for the nonlinear optical susceptibility.
　　
　　(1) We wanna show how the susceptibility depends on material parameter.

　　(2) These expressions display the internal symmetries of susceptibility.

　　(3) These expressions can be used to obtain predictions of the numerical values of the nonlinear susceptibility.

　　This expressions is much better approximation for Atomic vapors than for solid state.


　　　　　Reasons

• Atomic parameter are often known with high accuracy.
• It is possible to obtain very large values of nonlinear susceptibility through the technique of resonance enhancement, because Atomic energy levels of free atoms are very sharp

　There are three possible strategies for enhancing the efficiency of third-harmonic generation through the technique of resonance enhancement.


　　　(a)
　　　　　　　　　　　　　　
　　　　　　　　　　
　　　　　　　 　　The one photon transition is nearly resonance.
　　　　　　　　　 The incident field experiences linear absorption and is rapidly attenuated.
　　　　　　　　　　

　　　(b)
　　　　　　　　　　　　　
　　　　　　　　　　　　　　
　　　　
　　　　　　　　　The two photon transition is nearly resonance.
　　　　　　　　　The two photon transition is usually prefered way in which to
　　　　　　　 　generated the third harmonic field with highi efficiency.


　　 (ｃ)

　　　　　　　　　　　　　　

　　　　　　　　　　The three photon transition is nearly resonance.
　　　　　　　　　　The generated field experiences linear absorption and is attenuated.


　But,all three procedures are equally effective at increasing the third nonlinear susceptibility.