HAL Id: jpa-00247035
https://hal.archives-ouvertes.fr/jpa-00247035
Submitted on 1 Jan 1994
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Reply on the Comment on “Photonic Tunneling Times”
by A.M. Steinberg
G. Nimtz
To cite this version:
G. Nimtz. Reply on the Comment on “Photonic Tunneling Times” by A.M. Steinberg. Journal de
Physique I, EDP Sciences, 1994, 4 (12), pp.1817-1818. �10.1051/jp1:1994223�. �jpa-00247035�
J. Phys. I £Yonce 4 (1994) 1817-1818 DECEMBER 1994, PAGE 1817
Classification Physics Abstracts
42.50 03.658 73.40G
Reply on the Comment on "Photonic Tunneling Times"
by A.M. Steinberg
G Nimtz
II Physikalisches Institut, Universitàt zu Kôln, D-50923 Kôln, Germany
(Received 15 August 1994, accepted 23 August 1994)
It bas been our opinion ail trie time that trie result of trie single-photon tunneling time exper- iment by Steinberg et ai. [Ii agrees with that of our previous microwave tunneling experiments [2-4j. But there is still disagreement with trie following statements given in Steinberg's Com-
ment. At first we can't accept trie daim, that Steinberg et ai. [Ii bave measured trie tunneling
time of a single photon. Steinberg et ai. did net carry eut
a direct measurement, instead they
bave measured trie destructive interference at different long delay patins. For each length of delay patin, which is proportional to trie phase difference, they bave measured trie detection
probability. TO determine trie delay time they were forced to measure at many different path lengths, and thus to combine the results of different experimental arrangements. The procedure results in a mean delay time of a large photon ensemble eventually and so equals trie classical
wave packet experiments of Enders and Nimtz [2-4].
Therefore the experimental results of Steinberg et ai. are quantitatively described by trie
propagation of Gaussian wave packets as was shown by Spieker [Si. The transmission function of the investigated tunneling barrier is calculated (eleven quarter wave layers, corresponding
to a stopping band, which has a quite different dispersion relation than a potential bottier or
a subcut-off wavegmde [2]) with the continuity conditions for E- and H-fields at the barrier interfaces. Trie computed absolute value and phase of the transmission function fit the theo- retical data of transmission probability and group delay presented in figure 1 of reference [Ii for the single-photon tunnehng time. In addition trie tunnehng time of Gaussian wave packets was
calculated from the transmission function. Agoni trie results agree with trie experimental mean single-photon delay time, thus trie "single-photon experiment" of reference [Ii is described by
a completely classical method.
Secondly, so far ail the photonic tunneling experiments are understood at a classical level.
However, a puise reshaping does trot necessarily describe the observed superluminal tunnel- mg of wave packets [2-4]. For instance a puise reshaping does net play a rote m trie case of
a symmetrical stopping band dispersion, when transmitting a frequency-band limited signal
with frequency components in trie evanescent regime only [2, 7j. In this special case of our experiments a frequency limited signal, either frequency modulated (FM) or amplitude mod- ulated (AM) crosses an opaque barrier at a superlummal speed I?i On trie other hand we are
Q Les Editions de Physique 1994
1818 JOURNAL DE PHYSIQUE I N°12
questioning, how a puise reshaping in trie case of a surgie photon can be evidenced, as was proposed by Steinberg et ai. [6] in order to avoid a violation of causahty.
Thirdly, we also think, that there is much confusion about causality. Particularly some
theoretical proofs are irrelevant for frequency band limited signais as bas been discussed by
Heitmann and Nimtz recently [7]. Most of trie theoretical proofs are carried out with a Gaussian function as signal [9, 8, 10, iii. Such a signal bas no front. However, it is trie front velocity,
which should not exceed trie velocity of light to preserve causality [12j. Trie signais studied in
the microwave experiments are frequency-band limited as ail the technical signais, Accordingly
they don't bave a sharp front in trie sense of Einstein causality. From trie experimental point
of view, it is not possible to test trie classical causality: an ideal front cannot be generated
due to the frequency band limitation in any real experiment. The new aspect revealed in the
microwave experiments is that electromagnetic wave packets (center of mass and rising edge)
are tunneling at a superluminal speed. Such a superluminal wave packet propagation is not observed in vacuum or in any medium descnbed by the general Lorentz-Lorenz dispersion.
References
[il Steinberg A., Kwiat P. and Chiao R, Phys. Reu. Lent 71 (1993) 708.
[2] Nimtz G., Enders A. and Spieker H., J. Phys. I France 4 (1994) 565 [3] Enders A. and Nimtz G., J. Phys. I France 2 (1992)1693.
[4] Enders A. and Nimtz G., Phys. Reu. E 48 (1993) 632.
[5] Spieker H., pnvate communication
[fil Chiao R., Kwiat P. and Steinberg A., SC~. Am. (August 1993) p. 38 [7] Heitmann W. and Nimtz G., submitted Phys. Lent. A.
[8] Deutsch J-M- and Low F., Ann. Phys. (NY) 228 (1993) 184.
[9] Hass K. and Busch P., Phys. Lett. A 185 (1994) 9.
[10] Azbel'M.Ya., Sand State Commun. 91 (1994) 439
[Ill Landauer R. and Martin Th., Reu Mod. Phys. 66 (1994) 217.
[12] Brillouin L
,
