Transverse wave cutoff in a cold unmagnetized plasma

With immobile ions, negligible collisions and electron density $n_e$, the plasma frequency is ${\omega }_p^2=n_e{e}^2/(m_e{ϵ}_0)$. Combining inertial electron current with vacuum displacement current gives ${\omega }^2={\omega }_p^2+c^2{k}^2$. Transverse fields are evanescent below ${\omega }_p$ and propagate above it.