if the susceptibility of materials A and B given by X1 and X2 (kappa), respectively, what will be the total refraction index if A be doped by B?
I have found some text. Especially the last one - Relation between nonlinear refractive index and third-order susceptibility in absorbing media - seems to be able to give answer to your question. There are of course some links which can be useful too.
https://www.osapublishing.org/viewmedia.cfm?uri=oe-18-21-21918&seq=0
www.uark.edu/misc/quantopt/gan2007.pdf
digital.csic.es/bitstream/10261/62047/1/Coso.pdf
Dear Bijan,
If you have a mixed material that is composed of two elements with the susceptibilities x1 and x2 strating from the definition of the polarisation, one can prove that the combined susceptibility x can be expressed by
x = ( N1/ Nt1) x1 + (N2/Nt2) x2 where,
Nt1 and Nt2 are the atomic concentrations of materials one and two in their elementary pure form. N1 and N2 are the atomic concentrations of material one and two in the mixer or the compound. It is assume that there is atomic polarization only other wise N represents the volume density the dipole moments.
After calculating the susceptibility x one can then calculates the relative dielectric constant epsilon r== 1 + x, and then the refractive index n = sqr root of epsilonr
wish you success
refractive index of doped material depends on the concentration of the constituents and on their individual susceptibilities. Detail calculation given in this journal. I think it is useful for you
Catunda, T., Cansian, A.M. and Castro, J.C., 1991. Saturation effects in degenerate four-wave mixing in ruby and GdAlO 3: Cr+ 3. JOSA B, 8(4), pp.820-823.
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