retrieval method and metamatrerials (please help me)

hi,
I work on the retrieval method using HFSS (D.Smith pulication) and I try to find the curve of the index of refraction n with:

n=A.acos(BD)
A=1/kd
B=1/2S21
D=1-(S11)(S11)+(S21)(S21)

I find the curve (a-Magnetude of S), (b-Phase of S) and (d-Impedance z) but the curve (c) poses a problem to me I believe that the arcosinus is the problem.
I join a file presenting the problem clearly with the diferents curves.

In the retrieval methods there are ususally ± roots and multiple branches. You should select the ones which are not violating the fundamental laws of physics. Imaginary n must be positive all the time. For example looking at your graph, I can say that you should select -n from 0 to 8.7GHz, +n from 8.7 to 9.2GHz, -n from 9.2 to 19.1GHz and +n from 19.1 to 20GHz. Retrieval methods are not as simple as they look. You should be very careful.