About the envelope of the wave packet (pulse)

Background and Objectives: The methodological work considers the issues of the velocities and times of propagation of wave packets (pulses) through a medium layer of thickness $d$ with dispersion. Methods: The spectral method of numerical calculation of the wave packet is used, taking into account the dispersion of the dielectric constant. Results: It has been shown that the output pulse appears no earlier than after time $d/c$, while it weakens and expands with the formation of a tail. Tunneling through a plasma layer has been numerically investigated, while no Hartmann-type tunneling paradoxes have been observed.