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Physical Review Letters

Observation of Superluminal Behaviors in Wave Propagation

Daniela Mugnai, Anedio Ranfagni, R. Ruggeri

Published May 22, 2000• 328 citations
Publisher

Abstract

The possibility of observing superluminal behavior in the propagation of localized microwaves over distances of tens of wavelengths is experimentally demonstrated. These types of waves, better than the evanescent modes of tunneling, can contribute to answering the question on the luminal limit of the signal velocity.
DOI
10.1103/physrevlett.84.4830

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Though both theoretical and experimental investigations have revealed the superluminal behavior of evanescent electromagnetic waves, there are many disputes about the physical meaning and validity of such superluminal phenomenon, which is due to the fact that the traditional investigations are based on the theory of tunneling time and concerned with the problem of what the group velocity of evanescent waves means. In this paper, by studying the quantum probability amplitude for photons to propagate over a spacelike interval along an undersized waveguide, we present theoretical evidence for such superluminality.
Photonic tunnelling experiments have shown that i) the Einstein energy relation is violated, ii) the tunnelling process is non‐local, iii) the signal velocity is faster than light, i.e. superluminal, iv) the tunnelling signal is not observable, since photonic tunnelling is described by virtual photons, and v) according to the experimental results the signal velocity is infinite inside the barriers, implying that tunnelling instantaneously acts at a distance. We think these properties are not compatible with the claims of many text books on Special Relativity, see for instance Refs. [1].
The widespread belief, that energy and signal velocities are bounded by the speed of light in vacuum has been challenged in recent years by observations of superluminal propagation of classical evanescent modes in tunneling time experiments. These experiments thus provide a frame for testing the limits of transport velocities physically achievable. Obvious and hidden time-scales involved in tunneling time experiments are discussed focussing on optical tunneling in frustrated total internal reflection. A suggestion for a direct test of the energy transport velocity—also of interest in future hyper-fast space travel—is presented. Related questions touching our current understanding of some fundamental concepts in physics are addressed.
Much experimental evidence of superluminal phenomena has been available by electromagnetic wave propagation experiments, with the results showing that the phase time describes the barrier traversal time. Based on the extrapolated phase time approach and numerical methods, we show that, in contrast to the ordinary Bessel waves of real argument, the group velocities of modified Bessel waves are superluminal. We obtain the following results. The group velocities increase with the increase of propagation distance, which is similar to the evanescent plane-wave cases. For large wave numbers, the group velocities fall off as the wave numbers increase, which is similar to the evanescent plane-wave cases. For small wave numbers, the group velocities increase with the increase of wave numbers, this is different from the evanescent plane-wave cases.
Contrary to mechanical waves, the two-slit interference experiment of single photons shows that the behavior of classical electromagnetic waves corresponds to the quantum mechanical one of single photons, which is also different from the quantum-field-theory behavior such as the creations and annihilations of photons, the vacuum fluctuations, etc. Owing to a purely quantum effect, quantum tunneling particles including tunneling photons (evanescent modes) can propagate over a spacelike interval without destroying causality. With this picture we conclude that the superluminality of evanescent modes is a quantum mechanical rather than a classical phenomenon.