We discuss the time analysis of multiple internal reflections during one-dimensional tunneling of non-relativistic particles and photons with sub-barrier energies through potential barriers. The approach exploited is a simple analytic continuation from real (over-barrier) wave numbers to imaginary (sub-barrier) wave numbers. It is shown in particular that not only the general effective tunneling velocity, but also every effective transmission (tunneling) velocity for at least the first intermediate stage between successive internal reflections is superluminal. An interpretation of this seemingly strange fact is given in terms of an effective deformation of spacetime inside the barrier. The results obtained are interpreted with the help of the Fourier expansion over the virtual momentum space. A comparison with the instanton approach is also made.
Cardone, F., Maidanyuk, S.p., Mignani, R., Olkhovsky, V.s. (2006). Multiple internal reflections during particle and photon tunneling. FOUNDATIONS OF PHYSICS LETTERS, 19(5), 441-457 [10.1007/s10702-006-0903-y].