electromagnetism - Physical cause of Negative Permittivity

What is the physical cause behind a material having a negative real part of its dielectric function? Given the complex permittivity, $\epsilon(\omega)=\epsilon(\omega)'+i\epsilon(\omega)''$, 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?