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arXiv:physics/0504160 · Chinese Physics Letters

Superluminal Behaviour of Modified Bessel Waves

Wang Zhi-Yong, Xiong Cai-Dong

Published Sep 1, 2006• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0256-307x/23/9/020

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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.
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.
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.
An explanation for superluminal phenomena based on wave-particle duality of photons is suggested. A single photon may be regarded as a wave packet, whose spatial extension is its coherence volume. As a photon propagates as a wave train in vacuum, its velocity is just the speed of light. When it tunnels through a barrier as a particle, its wave function collapses and it will travel faster than light. Superluminal motion can occur only within the coherence length and the time constrained by uncertainty principle. A massive particle cannot be superluminal during the tunneling process. So superluminality does not violate causality. As for the superluminal and negative group velocities in anomalously dispersive medium, they are merely reshaping effect of the pulse, and they will become subluminal at large distances. A couple of experiments are proposed to test the superluminal phenomena.
The tunneling of particles is in direct analogy with the transmission of evanescent electromagnetic waveguide modes as has been shown quite recently. We compare experimental data of an electromagnetic wave packet traversing an evanescent waveguide region with theoretical values derived for particle tunneling through a rectangular potential barrier. The transmission time was deduced by transformation of the experimental frequency data to the time domain. The data are in agreement and reveal superluminal wave-packet velocities for opaque evanescent regions.
In last decade,faster-than-light(superluminal) propagation of short waves,microwaves,light waves and THz waves has been studied experimentally in several countries.Many of the attempts to send pulses faster than the speed of light involved a phonomenon called negative-velocities wave propagation.In this paper,we give a bird-eye view of the theoretical and experimental research work on negative-velocities wave propagation.For example and experimentally,a light pulse propagating through the atomic vapor cell has its peak reaching the exit side before entering it,resulting in a negative transit time,and negative group velocity.So that the group velocity vg can be greater than the velocity of light c,can be infinite and even negative.In recent years,many superluminal phenomena of negative-velocities have been discovered in experiments and observations,so we say it is a new frontier in sciences research.