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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Time diffraction of evanescent waves

Mufei Xiao

Published Nov 1, 1999• 12 citations
Publisher

Abstract

The concept of time diffraction of evanescent electromagnetic waves is proposed. Transient propagation of electromagnetic waves is studied in two forms: propagating and evanescent waves. Differences and similarities between quantum particle tunneling and photon tunneling are clearly demonstrated. Traversal time cannot be accurately defined due to diffraction in time. Nevertheless, a delay time is defined as the difference between the time of flight and the peak time of the transient light. The delay time is found to increase linearly and slowly with the traversal distance. Superluminal tunneling is found possible only for evanescent waves, and Einstein causality is not violated.

DOI
10.1103/physreve.60.6226

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The concept of time diffraction of evanescent electromagnetic waves is proposed. Transient propagation of electromagnetic waves is studied in two forms: propagating and evanescent waves. Differences and similarities between quantum particle tunneling and photon tunneling are clearly demonstrated. Traversal time cannot be accurately defined due to diffraction in time. Nevertheless, a delay time is defined as the difference between the time of flight and the peak time of the transient light. The delay time is found to increase linearly and slowly with the traversal distance. Superluminal tunneling is found possible only for evanescent waves, and Einstein causality is not violated.
The analogy between quantum tunneling of particles and evanescent electromagnetic waves can be used to study particle tunneling. Possibilities for the measurement of the time delay resulting from the transmission of waves through an evanescent region, say with lower dielectric constant, are discussed. In contrast to particle tunneling, an electromagnetic pulse can consist of many photons and can be probed in a noninvasive way. We emphasize the delay of the centroid of an electromagnetic pulse transmitted below cutoff through a portion of a waveguide with the same cross section as the adjacent propagating guides. The boundary conditions at the interface between the propagating and the evanescent region lead to the same transmission and reflection coefficients as for a square-barrier tunneling problem. For a pulse restricted to a narrow frequency range, the time delay depends only on the frequency derivative of the phase shift associated with transmission. The delay of a centroid is just that; there is no deeper physical sense which links the incoming centroid to the outgoing centroid. For sufficiently long evanescent regions, the delay is independent of thickness.
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.
Measures of pulse delay in microwave propagation, in open air and for short distances (not much greater than 1 m), were made by using launcher and receiver horns. When these are facing each other we observe a delay time corresponding to a speed equal to c while, if the receiver horn is shifted or tilted with respect to the launcher horn, the delay time decreases showing a superluminal behavior. In other words the modulation phase shift, interpreted as a propagation time, turns out to be surprisingly smaller than the one relative to the light speed. This effect, which disappears for longer distances, is here interpreted on the basis of the existence of a special kind of evanescent waves (leaky waves). Just the presence of evanescent waves allows one to make a comparison with the tunneling processes where superluminal transport properties have been theoretically predicted.
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.
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.
Abstract 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. With this picture we conclude that the superluminality of evanescent modes is a quantum mechanical rather than a classical phenomenon.