Here's the context; I'm studying biological tissues that are supposed to behave like dielectrics. Using the modified cole-cole equation for theoretical predictions:
$$\tilde{\varepsilon}_r (\omega )= \varepsilon_\infty + \sum\limits_n \frac{\Delta \varepsilon_n}{1 +(i \omega \tau_n)^{(1-\alpha_n)}} + \frac{\sigma_m }{i \omega \varepsilon_0 }$$
with $\varepsilon_\infty$ the one when $\omega \tau >>1$, $\varepsilon_s$ when $\omega \tau <<1$ and $\Delta \varepsilon_n$ the difference of the two previous. $\tau$ is the relaxation time (like the one in Debyes equation). $\sigma_m/(i \omega \varepsilon_0)$ is the ionic contribution with the ionic conductivity.
The problem I'm having as of right now is that the second term, $\sigma_m/(i\omega \varepsilon_0)$ has such a great weight that the imaginary part of $\tilde{\varepsilon}_r$ (usually written either $\varepsilon_r$" or $k$) makes it as great as the real part (usually written $\varepsilon_r$') (y axis- permittivity, x axis- light frequenc Hz). The real part datas are in good agreement with previous studies. From my understanding, the real part is the polarizability of the material, and how much a field is transmitted, and the imaginary part represents the absorption/loss of energy in the matter.
In parallel, since it is known that the tissues I'm studying are lossy, I've derived the following equations
$$n' = \sqrt{\frac{1}{2}\left(\sqrt{\varepsilon_r'^2 + \varepsilon_r"^2} +\varepsilon_r' \right)} \\
n'' = \sqrt{\frac{1}{2}\left(\sqrt{\varepsilon_r'^2 + \varepsilon_r"^2} -\varepsilon_r' \right)} $$
Using the results of the modified Cole-Cole equation in the expressions of refractive index above, the results for real and imaginary parts are almost identical (Y axis- diffraction axis, x axis, frequency of light) (orange is real and blue is imaginary here)
Here is the same graph, but with a log y-scale (good remark from a comment of
Jos Bergervoet, thank you)
I'm at a loss facing this. I thought that the sign change would've made a greater difference between the two parts and allowed me to better understand the matters behavior, but I'm more lost regarding it now than before. Any pointer/suggestion regarding this?