What is the physical cause behind a material having a negative real part of its dielectric function? Given the complex permittivity, ϵ(ω)=ϵ(ω)′+iϵ(ω)″, the Drude model gives \begin{align} \epsilon'=1-\frac{\omega_{P}^2}{\omega^2+\omega_{\tau}^2} \end{align} where \omega is the frequency of the incoming light, \omega_{P}=\sqrt{\frac{Ne^2}{m\epsilon_0}} is the plasma frequency, N is the electron density, m is the electron's mass, e is the electronic charge, and \omega_{\tau} is the frequency of collisions between conduction electrons and the ion lattice.
If \omega is small enough, then \epsilon'<0. But how does this physically happen?
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