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SUPERLUMINAL VELOCITIES. ILLUSION OR REALITY

Pedro Pereyra, S. Pablo

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

We study the time-evolution of electromagnetic wave packets through optical superlattices. We follow the time evolution (described by Maxwell equations) of Gaussian packets with centroid in dieren t energy regions. The time spent by the wave packet inside an optical structure agrees extremely well with the superluminal experimental results and the phase time predictions.

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We study the time-evolution of electromagnetic wave packets through optical superlattices. We follow the time evolution (described by Maxwell equations) of Gaussian packets with centroid in dieren t energy regions. The time spent by the wave packet inside an optical structure agrees extremely well with the superluminal experimental results and the phase time predictions.
We report on microwave measurements of barrier traversal time of electromagnetic wave packets in an undersized waveguide. This time was significantly shorter than the ratio L/cL/cL/c, with LLL the barrier length and ccc the velocity of light in vacuum. Consequently the transport velocity for the wave packet inside the barrier has to be superluminal, i.e. larger than ccc.
Evanescent modes or the tunnelling process are characterized by an imaginary wave number. These special solutions of the Helmholtz and of the Schrödinger equations first noticed in connection with the total reflection were said to have no physical meaning about 200 years ago. Last century the tunnelling problem in quantum mechanics has been described by the phase time approach. The phase time approach yields the group velocity of a wave packet (see e.g. Hartman, 1962). Nowadays the phase time approach is used in network analyzers to determine the group velocity of an electromagnetic wave in devices. We have reported about superluminal signal velocities in photonic tunnelling. It was observed that the superluminal photonic tunnelling time data measured in the time domain are in agreement with the calculated phase time data. This result is also in agreement with the definition of the barrier transition time given in the Federal Standard 1037 C (NTIA, USA 2000). Thus we have added further credibility to the assumption that the photonic tunnelling results are representative for quantum mechanical tunnelling of particles.
We derive an exact analytical solution to the time-dependent Schrödinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet is sufficiently broad in momentum space to guarantee that the resonance structure of the system is included in the dynamical description. We demonstrate that the transmitted wave packet exhibits a transient behavior which at very large distances and long times may be written as the free evolving Gaussian wave packet solution times the transmission amplitude of the system and hence it reproduces the resonance spectra of the system. This is a novel result that predicts the ultimate fate of the transmitted Gaussian wave packet. We also prove that at a fixed distance and very long times the solution goes as t−3/2t^{-3/2}t−3/2 which extends to arbitrary finite range potentials previous analysis on this issue. Our results are exemplified for single and multibarrier systems.