No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Superluminal Behaviors of Electromagnetic Near-fields
Abstract
Superluminal phenomena have been reported in many experiments of electromagnetic wave propagation, where the superluminal behaviors of evanescent waves are the most interesting ones with the important physical significances. Consider that evanescent waves are related to the near-zone fields of electromagnetic sources, based on the first principles, we study the group velocities of electromagnetic fields in near-field region, and show that they can be superluminal, which can provide a heuristic interpretation for the superluminal properties of evanescent waves.
ResearchGate has not been able to resolve any citations for this publication.
We demonstrate a bandpass amplifier which can be constructed from common electronic components and has the surprising property that the group delay is negative in most spectral regions. A pulse propagating through a chain of such amplifiers is advanced by several milliseconds: the output waveform precedes the input waveform. Although striking, this behavior is not in conflict with causality, as demonstrated by experiments with pulses which start or end abruptly. (C) 1998 American Association of Physics Teachers.
Over sixty years ago, it was suggested that there is a time associated with the passage of a particle under a tunneling barrier. The existence of such a time is now well accepted; in fact the time has been measured experimentally. There is no clear consensus, however, about the existence of a simple expression for this time, and the exact nature of that expression. The proposed expressions fall into three main classes. The authors argue that expressions based on following a feature of a wave packet through the barrier have little physical significance. A second class tries to identify a set of classical paths associated with the quantum-mechanical motion and then tries to average over these. This class is too diverse to permit assessment as a single entity. The third class invokes a physical clock involving degrees of freedom in addition to that involved in tunneling. This not only is a prescription for the derivation of expressions for the traversal time but also leads to a direct relationship to experiment.
In this paper we critically review and analyse the main theoretical definitions and calculations of the sub-barrier tunnelling and reflection times. Moreover, we propose a new, physically sensible definition of such durations, on the basis of a recent general formalism (already tested for other types of quantum collisions). Finally, we discuss some surprising results regarding the temporal evolution of the tunnelling processes.
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.
Einstein's theory of special relativity and the principle of causality imply that the speed of any moving object cannot exceed that of light in a vacuum (c). Nevertheless, there exist various proposals for observing faster-than-c propagation of light pulses, using anomalous dispersion near an absorption line, nonlinear and linear gain lines, or tunnelling barriers. However, in all previous experimental demonstrations, the light pulses experienced either very large absorption or severe reshaping, resulting in controversies over the interpretation. Here we use gain-assisted linear anomalous dispersion to demonstrate superluminal light propagation in atomic caesium gas. The group velocity of a laser pulse in this region exceeds c and can even become negative, while the shape of the pulse is preserved. We measure a group-velocity index of n(g) = -310(+/- 5); in practice, this means that a light pulse propagating through the atomic vapour cell appears at the exit side so much earlier than if it had propagated the same distance in a vacuum that the peak of the pulse appears to leave the cell before entering it. The observed superluminal light pulse propagation is not at odds with causality, being a direct consequence of classical interference between its different frequency components in an anomalous dispersion region.
The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points is shown to consist of two parts: a spectral superposition of group delays (inverse of group velocity) and a delay due to spectral reshaping via absorption or amplification. The result provides a context wherein group velocity is always meaningful even for broad band pulses and when the group velocity is superluminal or negative. The result imposes luminality on sharply defined pulses.
We consider pulse propagation in a linear anomalously dispersive medium where the group velocity exceeds the speed of light in vacuum ( c) or even becomes negative. A signal velocity is defined operationally based on the optical signal-to-noise ratio, and is computed for cases appropriate to the recent experiment where such a negative group velocity was observed. It is found that quantum fluctuations limit the signal velocity to values less than c.
The superluminal group velocity of an ultrashort optical Bessel beam pulse is measured over its entire depth of field, corresponding to approximately 2x10(4) optical wavelengths. The method used is to measure the traveling ionization front induced by the pulse.
We have observed both superluminal and ultraslow light propagation in an alexandrite crystal at room temperature. Group velocities as slow as 91 meters per second to as fast as -800 meters per second were measured and attributed to the influence of coherent population oscillations involving chromium ions in either mirror or inversion sites within the crystal lattice. Namely, ions in mirror sites are inversely saturable and cause superluminal light propagation, whereas ions in inversion sites experience conventional saturable absorption and produce slow light. This technique for producing large group indices is considerably easier than the existing methods to implement and is therefore suitable for diverse applications.
We present an experimental and theoretical study of a simple, passive system consisting of a birefringent, two-dimensional photonic crystal and a polarizer in series, and show that superluminal dispersive effects can arise even though no incident radiation is absorbed or reflected. We demonstrate that a vector formulation of the Kramers-Kronig dispersion relations facilitates an understanding of these counterintuitive effects.
Delay-time measurements in a diffraction experiment with microwaves have been performed both for the phase delay and for the group delay in the range of a few picoseconds to hundreds of picoseconds. The results obtained demonstrate that for evanescent modes below the cutoff frequency superluminal behavior was attained.
The old question of "How long does it take to tunnel through a barrier?" has acquired new urgency with the advent of techniques for the fabrication of semiconductor structures in the nanometer range. For the restricted problem of tunneling in a scattering configuration, a coherent picture is now emerging. The dwell time tauD has the status of an exact statement of the time spent in a region of space, averaged over all incoming particles. The phase times tauvarphiT and tauvarphiR are defined separately for transmitted and reflected particles. They are asymptotic statements on completed scattering events and include self-interference delays as well as the time spent in the barrier. Consequently, neither the dwell time nor the phase times can answer the question of how much time a transmitted (alternatively, reflected) particle spent in the barrier region. Our discussion of this question relies on a few simple criteria: (1) The average duration of a physical process must be real. (2) Since transmission and reflection are mutually exclusive events, the times tauT and tauR spent in the barrier region are, if they exist, conditional averages. Consequently, they must obey the identity tauD=TtauT+RtauR, where T and R are the transmission and reflection probabilities, respectively. The existence of this identity distinguishes tunneling in a scattering configuration from tunneling out of a metastable state. (3) Any proposed tauT and tauR must meet every requirement that can be constructed from tauD. On the basis of (2), the naively extrapolated phase times, as well as the Büttiker-Landauer time, must be rejected. The local Larmor times, as introduced by Baz', satisfy (2), but not every criterion of type (3). The local Larmor clock is therefore unreliable. The asymptotic Larmor clock shows the phase times, as it should. Finally, the inverse characteristic frequency of an oscillating barrier cannot always be defined. It is shown not to represent the duration of the tunneling process. This leaves the dwell time and the phase times as the only well-established times in this context. It also leaves open the question of the length of time a transmitted particle spends in the barrier region. It is not clear that a generally valid answer to this question exists.
Delay-time measurements in a two-prism experiment, at microwave scale, have been performed, both for phase- and group-delay, in the range of picoseconds. The results are interpreted within the scheme of an electromagnetic theory, and compared with quantum mechanical models, suitably adapted to the electromagnetic framework.
We investigate experimentally the optical tunneling times associated with frustrated total internal reflection of a light beam. Using as physical clocks the lateral shifts and angular deviations suffered by the transmitted and reflected beams, we measure both components of a complex tunneling time: the phase time and a semiclassical time. The phase time is shown to imply superluminal velocities and to depend strongly on boundary conditions not linked to the tunneling process. By contrast, the semiclassical time yields subluminal velocities and is related solely to tunneling.
The phenomenon of tunneling is a well-known fundamental consequence of quantum mechanics. All particles can in principle tunnel. In particular, both electrons and photons can tunnel through classically forbidden regions of space known as “barriers”. However, there have been numerous controversies over how long it takes a particle to cross a barrier. Exploiting an analogy between electrons and photons, we suggest an experiment to infer the characteristics of an electron's barrier-traversal time by measuring the time it takes a photon to traverse a similar barrier. Electron tunneling experiments are in general much more difficult to perform than analogous optical ones. With an optical technique one can construct optical barriers on the scale of microns, in contrast to theångstrom-scale barriers required for electron tunneling. Our experiment may help settle the controversies over tunneling times.By means of a newly developed quantum optical technique, we should be able to measure the tunneling times of individual photons with sub-picosecond resolution. In our experiments we are using a two-photon light source, in which a pair of tightly correlated photons is generated by the process of spontaneous parametric down-conversion. Hong, Ou and Mandel have already achieved a sub-picosecond comparison between the arrival times of two such photons at a beam splitter placed at the intersection of their paths. In our geometry, one member of the photon pair tunnels through a barrier, while the other does not. Then coincidence detection of this photon pair constitutes the detection of an individual tunneling event. The particle aspect of photon tunneling can thus be clearly observed. We propose to use the Hong-Ou-Mandel technique to measure the tunneling time. We have chosen for our tunneling barrier two glass prisms placed in close proximity, utilizing the phenomenon of frustrated total internal reflection.
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.
- Th
- Hartman Th
Th. Hartman Th 1962 J. Appl. Phys.33 3427.
- J Peatross
- S Glasgow
- M Ware
Peatross J, Glasgow S A and Ware M 2000 Phys. Rev. Lett. 84 2370.
- A Enders
- G Nimtz
Enders A and Nimtz G 1992 J. Phys. I (France) 2 1693.
- M S Bigelow
- N Lepeshkin
- R W Boyd
Bigelow M S, Lepeshkin N N and Boyd R W 2003 Science 301 200.
- M Büttiker
- R Landauer
Büttiker M and Landauer R 1982 Phys. Rev. Lett. 49 1739.
- R P Feynman
- R Leighton
- M Sands
Feynman R P, Leighton R B and Sands M 1964 Feynman Lectures on Physics Vol. (New York:
Addison-Wesley Publishing Company), Chapter 7-5 and Chapter 24-8.
- D Mugnai
- A Ranfagni
- L S Schulman
Mugnai D, Ranfagni A and Schulman L S 1997 Phys. Rev. E 55 3593.
- A M Steinberg
- P Kwiat
- R Y Chiao
Steinberg A M, Kwiat P G and Chiao R Y 1993 Phys. Rev. Lett.71 708.
- V S Olkhovsky
- E Recami
Olkhovsky V S and Recami E 1992 Phys. Reports 214 339.
- G Nimtz
- W Heitmann
Nimtz G and Heitmann W 1997 Prog. Quant. Electr. 21 81.
- J D Jackson
J. D. Jackson J D 1975 Classical Electrodynamics (New York: John Wiley & Sons, Inc.) pp
391-395.
- L J Wang
- Kuzmich A Dogariu
Wang L J, Kuzmich A and Dogariu A 2000 Nature 406 277.
- A Enders
- G Nimtz
Enders A and Nimtz G 1993 Phys. Rev. E 48 632.