I naively thought that most materials were transparent to radiation of frequencies above their plasma frequency, and opaque to radiation below it. The most intuitive (and analyzed lightly in Griffiths' E&M book) reason I've heard is that opaqueness is caused by electrons in the material responding to the incident radiation by getting oscillated by it, in which they produce their own radiation that cancels the incident radiation. However, when the incident radiation is above the plasma frequency, they can't respond quickly enough and it can start to penetrate the material.
Mathematically, $\epsilon(\omega) > 0$ for $\omega < \omega_{plasma}$ and $\epsilon(\omega) < 0$ for $\omega > \omega_{plasma}$, and the wave vector $k \propto n \propto \sqrt{\epsilon}$, so when $\omega$ is above $\omega_{plasma}$, $k$ is imaginary and $e^{i \vec k \cdot \vec r}$ decays quickly in the material.
But I was recently told that as the frequency keeps rising, the material again at some point becomes opaque to it. What is this called, and what's the physical reason for it?
