Raman transition - Index of refraction

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Main Question or Discussion Point

When one calculate the real part of the index of refraction for a specific multilevel atom one would use the following formula:
[tex] Re(n(\Delta))=1+\frac{N e^2}{8\pi \epsilon_0 m\omega} \sum_i \frac{\Delta_i}{\Delta_i^2+(\gamma/2)^2}K_i
[/tex]
Where [itex]K_i[/itex] is the C-G coefficient.

My question is as follow:
How can I calculate this index of refraction in the case of a Raman transition? a.e. in the case where there is a coupling between two fields to create an otherwise forbidden transition.
 

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