I'm having some problems with the definition of the real and imaginary parts of the Lorentz model, we start from the definition of the permitivity $$\chi=\chi'+i\chi''=\frac{\omega_p^2}{\omega^2-\omega^2-i\omega \gamma}=\omega_p^2\frac{\omega_0^2-\omega^2}{(\omega_0^2-\omega^2)^2+(\omega \gamma)^2}+i\omega_p^2\frac{\omega \gamma}{(\omega_0^2-\omega^2)^2+(\omega \gamma)^2}$$
So we have,
\begin{align} \chi'=\omega_p^2\frac{\omega_0^2-\omega^2}{(\omega_0^2-\omega^2)^2+(\omega \gamma)^2} \quad \xrightarrow{} \quad \text{Refractive index}\\ \chi''=\omega_p^2\frac{\omega \gamma}{(\omega_0^2-\omega^2)^2+(\omega \gamma)^2}\quad \xrightarrow{} \quad \text{Absorption} \qquad \, \end{align}
This results are correct, you can see them in different sites for example MIT-Lorentz-Oscillator, and as we expect, for the absorption we get a Lorentzian, and for the refractive index we get a dispersive distribution, as is illustrated at the image,
In the image are represented the permeabilities but are proportional. My doubt comes when if you plot the before expressions $\chi(\omega)$ you don't get the Lorentzian or the dispersive plots, in fact $\chi'$ is a even function, and $\chi''$ is a odd function, that doesnt match with the linked image... And I don't know what I'm doing wrong
