Electromagnetic field propagation in any medium at high frequency I am trying to understand an important concept regarding the propagation of EM fields in materials at high frequencies, which is:

"At high frequencies any material behaves as a dielectric material. This is because the displacement current dominates the conduction current and the EM field propagates as a wave instead of being diffused"

Please, someone explain this statement in a detailed way or give me sources to understand it. This statement is from the following paper:
"Principles of Mine Detection by Ground-penetrating Radar" by Motoyuki Sato
 A: According to Maxwell's law $\textrm{curl}\textbf{H}=\textbf{J}+\frac{\partial \textbf{D}}{\partial t}$ always. If you assume harmonic time dependence then you can write that all terms will have a form such as $\textbf{F} = \hat {\textbf {F}} e^{\mathfrak{j} \omega t}$, in which case we have 
$$\textrm{curl}\hat {\textbf{H}}=\hat {\textbf{J}}+\mathfrak{j} \omega\hat {\textbf{D}}.$$
Now you can see that if you keep everything else the same but increase the frequency then eventually you will have $\left | {\hat {\textbf{J}}} \right | \ll \omega \left |\hat {\textbf{D}}\right | $. Since the displacement intensity $\hat {\textbf{D}}$ is the characteristic of a dielectric for a given electric field $\hat {\textbf{E}}$ the equation means that for large enough frequency the dominant current is by the displacement current that being the polarization current in matter.
Let us now look at the other limit that is when $\left | {\hat {\textbf{J}}} \right | \gg \omega \left |\hat {\textbf{D}}\right | $. Take the curl of Faraday's law $\textrm{curl}\textbf{E}=-\frac{\partial \textbf{B}}{\partial t}$, so now $\textrm{curl}\textrm{curl}\textbf{E}=-\frac{\partial \textrm{curl}\textbf{B}}{\partial t}= -\mu\frac{\partial \textrm{curl}\textbf{H}}{\partial t}=-\mu\frac{\partial \textbf{J}}{\partial t}$ and in a linear conducting medium $\textbf{J}=\sigma \textbf{E}$ so then $\textrm{curl}\textrm{curl}\textbf{E}= -\mu\sigma\frac{\partial \textbf{E}}{\partial t}$. Without free charges $\textrm{div} \textbf{E}=0$, and then $\textrm{curl}\textrm{curl}\textbf{E} = \textrm{grad div}\textbf{E} -\nabla^2 \textbf{E}=-\nabla^2 \textbf{E}$, and finally $$\nabla^2 \textbf{E} = \mu\sigma\frac{\partial \textbf{E}}{\partial t}.$$ This is the diffusion equation for the electric field intensity, see https://en.wikipedia.org/wiki/Diffusion_equation.
