Hartman effect and frequency-independent asymptote for the tunneling time of electromagnetic pulses through a plasma layer

Electromagnetic pulse propagation through a plasma layer below the plasma frequency is a genuine classical wave tunneling phenomenon strongly differing from tunneling in dielectric structures due to the specific dispersion of plasma. We consistently examine this phenomenon using direct numerical simulations of a time-dependent wave equation and show that in the low-frequency limit the tunneling time has the frequency-independent asymptotic $2/{\ensuremath{\omega}}_{p}$ with ${\ensuremath{\omega}}_{p}$ being the plasma frequency, in good correspondence with the analysis in stationary approximation. These results prove that radiation tunneling for plasma principally differs from the other electromagnetic tunneling phenomena which supposedly obey the inverse proportional dependence of the tunneling time on radiation frequency. The Hartman effect (saturation of the tunneling time with layer thickness) is demonstrated for pulse propagation as well with the saturated time getting closer to the asymptotic value as we move deeper into the tunneling regime. We also show that the reflected wave packet build-up gives an efficient tool for the tunneling problem and that reflection develops synchronously with transmission. Our theoretical calculations are supported by experiments with microwave tunneling through the electromagnetic band gap structure (electromagnetic crystal) based on gas discharge plasmas.