I missing some thing in this experiment, I have seen several papers they reported only Chi3, Chi5 and Chi7...all odd terms. If I have a sample by considering it is non-centro symmetric. That means it has Chi2 and Chi4 and so on..is it possible to measure these even terms by using Z-scan experiment?
No. Only the odd terms will have polarization at frequency ω for an input electric field at frequency ω. Please refer to Nonlinear Optics book by R. W. Boyd.
If the sample is symmetric, Chi2 and Chi4 so on.. all of them are zero
Z-scan can be used to measure second order susceptibilities (chi2), by observing what's referred to as cascaded second-order effects. For example, with imperfect phase matching, second harmonic light will be down converted back to the fundamental frequency, but with a phase shift. This intensity dependent phase shift appears similar to genuine (chi3) nonlinear refraction. See link below for details.
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-17-1-28
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