Abstract

It is argued that the photon tunneling process originates in an inability to localize photons completely in space. Seen in this perspective, optical tunneling experiments might allow one to obtain rich information on the photon localizability problem, that until now has been studied mainly theoretically. A rigorous analysis of the electrodynamics in the near-field zone of matter enables us to identify the transverse vector field and subsequently to use it to construct a first-quantized space–time theory for the photon birth process and to determine the source region of the photon. The present theory shows that optical tunneling never appears outside the photon’s source domain, and it is shown that an apparently superluminal response occurs as a consequence of the lack of complete photon localizability. No fundamental velocity is attached to this effect, which stems solely from quantum nonlocality. Starting from the Riemann–Silberstein vectors, which permit the introduction of a space–time description of a free polychromatic photon’s so-called energy wave function, a theoretical investigation of the near-field scattering of a single photon from a mesoscopic or microscopic (molecular, atomic) particle is presented. Inasmuch as the photon tunneling phenomenon appears to be an indispensable part of the near-field scattering process, it might be possible to establish a rigorous first-quantized theory of one-photon tunneling between macroscopic molecular solids by adding the tunneling contributions from the individual molecules.

© 2001 Optical Society of America

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References

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  1. F. Grass, Relativistic Quantum Mechanics and Field Theory (Wiley Interscience, New York, 1993).
  2. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms, Introduction to Quantum Electrodynamics (Wiley Interscience, New York, 1989).
  3. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1992).
  4. R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1997), Vol. XXXVII, pp. 345–405, and references therein.
  5. O. Keller, “Relation between spatial confinement of light and optical tunneling,” Phys. Rev. A 60, 1652–1671 (1999).
    [Crossref]
  6. O. Keller, “Propagator picture of the spatial confinement of quantized light emitted from an atom,” Phys. Rev. A 58, 3407–3425 (1998).
    [Crossref]
  7. I. Bialynicki-Birula, “Photon wave function,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), Vol. XXXVI, pp. 245–294, and references therein.
  8. I. Bialynicki-Birula, “On the wave function of the photon,” Acta Phys. Pol. A 86, 97–111 (1994).
  9. J. E. Sipe, “Photon wave functions,” Phys. Rev. A 52, 1875–1883 (1995).
    [Crossref] [PubMed]
  10. O. Keller, “Near-field optics: the nightmare of the photon,” J. Chem. Phys. 112, 7856–7863 (2000).
    [Crossref]
  11. O. Keller, “Space–time description of photon emission from an atom,” Phys. Rev. A 62, 022111 (2000).
    [Crossref]
  12. A. Otto, “Spectroscopy of surface polaritons by attenuated total reflection,” in Optical Properties of Solids—New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 677–729.
  13. A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, Chichester, UK, 1982).
  14. V. M. Agranovich and D. L. Mills, eds., Surface Polaritons, Electromagnetic Waves at Surfaces and Interfaces (North-Holland, Amsterdam, 1982).
  15. A. Ghatak and S. Banerjee, “Temporal delay of a pulse undergoing frustrated total internal reflection,” Appl. Opt. 28, 1960–1961 (1989).
    [Crossref] [PubMed]
  16. R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling,” Physica B 175, 257–262 (1991).
    [Crossref]
  17. Th. Martin and R. Landauer, “Time delay of evanescent electromagnetic waves and the analogy to particle tunneling,” Phys. Rev. A 45, 2611–2617 (1992).
    [Crossref] [PubMed]
  18. K. Hass and P. Busch, “Causality of superluminal barrier traversal,” Phys. Lett. A 185, 9–13 (1994).
    [Crossref]
  19. Y. Wang and D. Zhang, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52, 2597–2600 (1995).
    [Crossref]
  20. Y. Japha and G. Kurizki, “Superluminal delays of coherent pulses in nondissipative media: a universal mechanism,” Phys. Rev. A 53, 586–590 (1996).
    [Crossref] [PubMed]
  21. D. van Labeke, J. M. Vigoureux, and G. Parent, “Photon tunneling time. Superluminal velocity for 1-D tunneling through a metallic barrier,” Ultramicroscopy 71, 11–20 (1998).
    [Crossref]
  22. G. Nimtz, “Superluminal signal velocity,” Ann. Phys. (Leipzig) 7, 618–624 (1998).
    [Crossref]
  23. G. Nimtz, “Evanescent waves are not necessarily Einstein causal,” Eur. Phys. J. B 7, 523–525 (1999).
    [Crossref]
  24. G. Nimtz, “The special features of superluminal evanescent mode propagation,” Gen. Relativ. Gravitation 31, 737–751 (1999).
    [Crossref]
  25. A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774–776 (1991).
    [Crossref]
  26. A. Enders and G. Nimtz, “Evanescent-mode propagation and quantum tunneling,” Phys. Rev. E 48, 632–634 (1993).
    [Crossref]
  27. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurements of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
    [Crossref] [PubMed]
  28. Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
    [Crossref] [PubMed]
  29. A. M. Steinberg and R. Y. Chiao, “Tunneling times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
    [Crossref] [PubMed]
  30. O. Keller, “Local fields in the electrodynamics of mesoscopic media,” Phys. Rep. 268, 85–262 (1996).
    [Crossref]
  31. O. Keller, “Local fields in linear and nonlinear optics of mesoscopic systems,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1997), Vol. XXXVII, pp. 257–343.
  32. R. Fuchs and K. L. Kliewer, “Surface plasmons in a semi-infinite free-electron gas,” Phys. Rev. B 3, 2270–2278 (1971).
    [Crossref]
  33. L. Lorenz, “Ueber die Reflexion des Lichts an der Gränzfläche zweier isotropen, durchsichtigen Mittel,” Ann. Phys. (Leipzig) 111, 460–473 (1860).
    [Crossref]
  34. P. J. Feibelman, “Microscopic calculation of electromagnetic fields in refraction at a jellium–vacuum interface,” Phys. Rev. B 12, 1319–1336 (1975).
    [Crossref]
  35. P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
    [Crossref]
  36. F. Forstmann and R. R. Gerhardts, Metal Optics Near the Plasma Frequency Vol. 109 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1986).
    [Crossref]
  37. J. R. Oppenheimer, “Note on light quanta and the electromagnetic field,” Phys. Rev. 38, 725–746 (1931).
    [Crossref]
  38. L. Silberstein, “Elektromagnetische Grundgleichungen in bivektorieller Behandlung,” Ann. Phys. (Leipzig) 22, 579–586 (1907).
    [Crossref]
  39. L. Silberstein, “Nachtrag zur Abhandlung über ‘Elektromagnetische Grundgleichungen in bivektorieller Behandlung,’” Ann. Phys. (Leipzig) 24, 783–784 (1907).
    [Crossref]
  40. L. I. Schiff, Quantum Mechanics (McGraw-Hill, Tokyo, 1968).
  41. I. Bialynicki-Birula, “Exponential localization of photons,” Phys. Rev. Lett. 80, 5247–5250 (1998).
    [Crossref]
  42. O. Keller, “Theory of spatial confinement of light,” Mater. Sci. Eng., B 48, 175–183 (1997).
    [Crossref]

2000 (2)

O. Keller, “Near-field optics: the nightmare of the photon,” J. Chem. Phys. 112, 7856–7863 (2000).
[Crossref]

O. Keller, “Space–time description of photon emission from an atom,” Phys. Rev. A 62, 022111 (2000).
[Crossref]

1999 (3)

O. Keller, “Relation between spatial confinement of light and optical tunneling,” Phys. Rev. A 60, 1652–1671 (1999).
[Crossref]

G. Nimtz, “Evanescent waves are not necessarily Einstein causal,” Eur. Phys. J. B 7, 523–525 (1999).
[Crossref]

G. Nimtz, “The special features of superluminal evanescent mode propagation,” Gen. Relativ. Gravitation 31, 737–751 (1999).
[Crossref]

1998 (4)

D. van Labeke, J. M. Vigoureux, and G. Parent, “Photon tunneling time. Superluminal velocity for 1-D tunneling through a metallic barrier,” Ultramicroscopy 71, 11–20 (1998).
[Crossref]

G. Nimtz, “Superluminal signal velocity,” Ann. Phys. (Leipzig) 7, 618–624 (1998).
[Crossref]

O. Keller, “Propagator picture of the spatial confinement of quantized light emitted from an atom,” Phys. Rev. A 58, 3407–3425 (1998).
[Crossref]

I. Bialynicki-Birula, “Exponential localization of photons,” Phys. Rev. Lett. 80, 5247–5250 (1998).
[Crossref]

1997 (1)

O. Keller, “Theory of spatial confinement of light,” Mater. Sci. Eng., B 48, 175–183 (1997).
[Crossref]

1996 (2)

O. Keller, “Local fields in the electrodynamics of mesoscopic media,” Phys. Rep. 268, 85–262 (1996).
[Crossref]

Y. Japha and G. Kurizki, “Superluminal delays of coherent pulses in nondissipative media: a universal mechanism,” Phys. Rev. A 53, 586–590 (1996).
[Crossref] [PubMed]

1995 (2)

Y. Wang and D. Zhang, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52, 2597–2600 (1995).
[Crossref]

J. E. Sipe, “Photon wave functions,” Phys. Rev. A 52, 1875–1883 (1995).
[Crossref] [PubMed]

1994 (4)

K. Hass and P. Busch, “Causality of superluminal barrier traversal,” Phys. Lett. A 185, 9–13 (1994).
[Crossref]

I. Bialynicki-Birula, “On the wave function of the photon,” Acta Phys. Pol. A 86, 97–111 (1994).

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[Crossref] [PubMed]

A. M. Steinberg and R. Y. Chiao, “Tunneling times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
[Crossref] [PubMed]

1993 (2)

A. Enders and G. Nimtz, “Evanescent-mode propagation and quantum tunneling,” Phys. Rev. E 48, 632–634 (1993).
[Crossref]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurements of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[Crossref] [PubMed]

1992 (1)

Th. Martin and R. Landauer, “Time delay of evanescent electromagnetic waves and the analogy to particle tunneling,” Phys. Rev. A 45, 2611–2617 (1992).
[Crossref] [PubMed]

1991 (2)

R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling,” Physica B 175, 257–262 (1991).
[Crossref]

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774–776 (1991).
[Crossref]

1989 (1)

1982 (1)

P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
[Crossref]

1975 (1)

P. J. Feibelman, “Microscopic calculation of electromagnetic fields in refraction at a jellium–vacuum interface,” Phys. Rev. B 12, 1319–1336 (1975).
[Crossref]

1971 (1)

R. Fuchs and K. L. Kliewer, “Surface plasmons in a semi-infinite free-electron gas,” Phys. Rev. B 3, 2270–2278 (1971).
[Crossref]

1931 (1)

J. R. Oppenheimer, “Note on light quanta and the electromagnetic field,” Phys. Rev. 38, 725–746 (1931).
[Crossref]

1907 (2)

L. Silberstein, “Elektromagnetische Grundgleichungen in bivektorieller Behandlung,” Ann. Phys. (Leipzig) 22, 579–586 (1907).
[Crossref]

L. Silberstein, “Nachtrag zur Abhandlung über ‘Elektromagnetische Grundgleichungen in bivektorieller Behandlung,’” Ann. Phys. (Leipzig) 24, 783–784 (1907).
[Crossref]

1860 (1)

L. Lorenz, “Ueber die Reflexion des Lichts an der Gränzfläche zweier isotropen, durchsichtigen Mittel,” Ann. Phys. (Leipzig) 111, 460–473 (1860).
[Crossref]

Banerjee, S.

Bialynicki-Birula, I.

I. Bialynicki-Birula, “Exponential localization of photons,” Phys. Rev. Lett. 80, 5247–5250 (1998).
[Crossref]

I. Bialynicki-Birula, “On the wave function of the photon,” Acta Phys. Pol. A 86, 97–111 (1994).

I. Bialynicki-Birula, “Photon wave function,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), Vol. XXXVI, pp. 245–294, and references therein.

Busch, P.

K. Hass and P. Busch, “Causality of superluminal barrier traversal,” Phys. Lett. A 185, 9–13 (1994).
[Crossref]

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, “Tunneling times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
[Crossref] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurements of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[Crossref] [PubMed]

R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling,” Physica B 175, 257–262 (1991).
[Crossref]

R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1997), Vol. XXXVII, pp. 345–405, and references therein.

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms, Introduction to Quantum Electrodynamics (Wiley Interscience, New York, 1989).

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms, Introduction to Quantum Electrodynamics (Wiley Interscience, New York, 1989).

Enders, A.

A. Enders and G. Nimtz, “Evanescent-mode propagation and quantum tunneling,” Phys. Rev. E 48, 632–634 (1993).
[Crossref]

Fabeni, P.

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774–776 (1991).
[Crossref]

Feibelman, P. J.

P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
[Crossref]

P. J. Feibelman, “Microscopic calculation of electromagnetic fields in refraction at a jellium–vacuum interface,” Phys. Rev. B 12, 1319–1336 (1975).
[Crossref]

Forstmann, F.

F. Forstmann and R. R. Gerhardts, Metal Optics Near the Plasma Frequency Vol. 109 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1986).
[Crossref]

Fuchs, R.

R. Fuchs and K. L. Kliewer, “Surface plasmons in a semi-infinite free-electron gas,” Phys. Rev. B 3, 2270–2278 (1971).
[Crossref]

Gerhardts, R. R.

F. Forstmann and R. R. Gerhardts, Metal Optics Near the Plasma Frequency Vol. 109 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1986).
[Crossref]

Ghatak, A.

Grass, F.

F. Grass, Relativistic Quantum Mechanics and Field Theory (Wiley Interscience, New York, 1993).

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms, Introduction to Quantum Electrodynamics (Wiley Interscience, New York, 1989).

Hass, K.

K. Hass and P. Busch, “Causality of superluminal barrier traversal,” Phys. Lett. A 185, 9–13 (1994).
[Crossref]

Japha, Y.

Y. Japha and G. Kurizki, “Superluminal delays of coherent pulses in nondissipative media: a universal mechanism,” Phys. Rev. A 53, 586–590 (1996).
[Crossref] [PubMed]

Keller, O.

O. Keller, “Near-field optics: the nightmare of the photon,” J. Chem. Phys. 112, 7856–7863 (2000).
[Crossref]

O. Keller, “Space–time description of photon emission from an atom,” Phys. Rev. A 62, 022111 (2000).
[Crossref]

O. Keller, “Relation between spatial confinement of light and optical tunneling,” Phys. Rev. A 60, 1652–1671 (1999).
[Crossref]

O. Keller, “Propagator picture of the spatial confinement of quantized light emitted from an atom,” Phys. Rev. A 58, 3407–3425 (1998).
[Crossref]

O. Keller, “Theory of spatial confinement of light,” Mater. Sci. Eng., B 48, 175–183 (1997).
[Crossref]

O. Keller, “Local fields in the electrodynamics of mesoscopic media,” Phys. Rep. 268, 85–262 (1996).
[Crossref]

O. Keller, “Local fields in linear and nonlinear optics of mesoscopic systems,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1997), Vol. XXXVII, pp. 257–343.

Kliewer, K. L.

R. Fuchs and K. L. Kliewer, “Surface plasmons in a semi-infinite free-electron gas,” Phys. Rev. B 3, 2270–2278 (1971).
[Crossref]

Krausz, F.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[Crossref] [PubMed]

Kurizki, G.

Y. Japha and G. Kurizki, “Superluminal delays of coherent pulses in nondissipative media: a universal mechanism,” Phys. Rev. A 53, 586–590 (1996).
[Crossref] [PubMed]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurements of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[Crossref] [PubMed]

R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling,” Physica B 175, 257–262 (1991).
[Crossref]

Landauer, R.

Th. Martin and R. Landauer, “Time delay of evanescent electromagnetic waves and the analogy to particle tunneling,” Phys. Rev. A 45, 2611–2617 (1992).
[Crossref] [PubMed]

Lorenz, L.

L. Lorenz, “Ueber die Reflexion des Lichts an der Gränzfläche zweier isotropen, durchsichtigen Mittel,” Ann. Phys. (Leipzig) 111, 460–473 (1860).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1992).

Martin, Th.

Th. Martin and R. Landauer, “Time delay of evanescent electromagnetic waves and the analogy to particle tunneling,” Phys. Rev. A 45, 2611–2617 (1992).
[Crossref] [PubMed]

Mugnai, D.

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774–776 (1991).
[Crossref]

Nimtz, G.

G. Nimtz, “Evanescent waves are not necessarily Einstein causal,” Eur. Phys. J. B 7, 523–525 (1999).
[Crossref]

G. Nimtz, “The special features of superluminal evanescent mode propagation,” Gen. Relativ. Gravitation 31, 737–751 (1999).
[Crossref]

G. Nimtz, “Superluminal signal velocity,” Ann. Phys. (Leipzig) 7, 618–624 (1998).
[Crossref]

A. Enders and G. Nimtz, “Evanescent-mode propagation and quantum tunneling,” Phys. Rev. E 48, 632–634 (1993).
[Crossref]

Oppenheimer, J. R.

J. R. Oppenheimer, “Note on light quanta and the electromagnetic field,” Phys. Rev. 38, 725–746 (1931).
[Crossref]

Otto, A.

A. Otto, “Spectroscopy of surface polaritons by attenuated total reflection,” in Optical Properties of Solids—New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 677–729.

Parent, G.

D. van Labeke, J. M. Vigoureux, and G. Parent, “Photon tunneling time. Superluminal velocity for 1-D tunneling through a metallic barrier,” Ultramicroscopy 71, 11–20 (1998).
[Crossref]

Pazzi, G. P.

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774–776 (1991).
[Crossref]

Ranfagni, A.

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774–776 (1991).
[Crossref]

Schiff, L. I.

L. I. Schiff, Quantum Mechanics (McGraw-Hill, Tokyo, 1968).

Silberstein, L.

L. Silberstein, “Elektromagnetische Grundgleichungen in bivektorieller Behandlung,” Ann. Phys. (Leipzig) 22, 579–586 (1907).
[Crossref]

L. Silberstein, “Nachtrag zur Abhandlung über ‘Elektromagnetische Grundgleichungen in bivektorieller Behandlung,’” Ann. Phys. (Leipzig) 24, 783–784 (1907).
[Crossref]

Sipe, J. E.

J. E. Sipe, “Photon wave functions,” Phys. Rev. A 52, 1875–1883 (1995).
[Crossref] [PubMed]

Spielmann, Ch.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[Crossref] [PubMed]

Steinberg, A. M.

A. M. Steinberg and R. Y. Chiao, “Tunneling times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
[Crossref] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurements of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[Crossref] [PubMed]

R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling,” Physica B 175, 257–262 (1991).
[Crossref]

R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1997), Vol. XXXVII, pp. 345–405, and references therein.

Stingl, A.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[Crossref] [PubMed]

Szipöcs, R.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[Crossref] [PubMed]

van Labeke, D.

D. van Labeke, J. M. Vigoureux, and G. Parent, “Photon tunneling time. Superluminal velocity for 1-D tunneling through a metallic barrier,” Ultramicroscopy 71, 11–20 (1998).
[Crossref]

Vigoureux, J. M.

D. van Labeke, J. M. Vigoureux, and G. Parent, “Photon tunneling time. Superluminal velocity for 1-D tunneling through a metallic barrier,” Ultramicroscopy 71, 11–20 (1998).
[Crossref]

Wang, Y.

Y. Wang and D. Zhang, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52, 2597–2600 (1995).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1992).

Zhang, D.

Y. Wang and D. Zhang, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52, 2597–2600 (1995).
[Crossref]

Acta Phys. Pol. A (1)

I. Bialynicki-Birula, “On the wave function of the photon,” Acta Phys. Pol. A 86, 97–111 (1994).

Ann. Phys. (Leipzig) (4)

L. Lorenz, “Ueber die Reflexion des Lichts an der Gränzfläche zweier isotropen, durchsichtigen Mittel,” Ann. Phys. (Leipzig) 111, 460–473 (1860).
[Crossref]

L. Silberstein, “Elektromagnetische Grundgleichungen in bivektorieller Behandlung,” Ann. Phys. (Leipzig) 22, 579–586 (1907).
[Crossref]

L. Silberstein, “Nachtrag zur Abhandlung über ‘Elektromagnetische Grundgleichungen in bivektorieller Behandlung,’” Ann. Phys. (Leipzig) 24, 783–784 (1907).
[Crossref]

G. Nimtz, “Superluminal signal velocity,” Ann. Phys. (Leipzig) 7, 618–624 (1998).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774–776 (1991).
[Crossref]

Eur. Phys. J. B (1)

G. Nimtz, “Evanescent waves are not necessarily Einstein causal,” Eur. Phys. J. B 7, 523–525 (1999).
[Crossref]

Gen. Relativ. Gravitation (1)

G. Nimtz, “The special features of superluminal evanescent mode propagation,” Gen. Relativ. Gravitation 31, 737–751 (1999).
[Crossref]

J. Chem. Phys. (1)

O. Keller, “Near-field optics: the nightmare of the photon,” J. Chem. Phys. 112, 7856–7863 (2000).
[Crossref]

Mater. Sci. Eng., B (1)

O. Keller, “Theory of spatial confinement of light,” Mater. Sci. Eng., B 48, 175–183 (1997).
[Crossref]

Phys. Lett. A (1)

K. Hass and P. Busch, “Causality of superluminal barrier traversal,” Phys. Lett. A 185, 9–13 (1994).
[Crossref]

Phys. Rep. (1)

O. Keller, “Local fields in the electrodynamics of mesoscopic media,” Phys. Rep. 268, 85–262 (1996).
[Crossref]

Phys. Rev. (1)

J. R. Oppenheimer, “Note on light quanta and the electromagnetic field,” Phys. Rev. 38, 725–746 (1931).
[Crossref]

Phys. Rev. A (8)

J. E. Sipe, “Photon wave functions,” Phys. Rev. A 52, 1875–1883 (1995).
[Crossref] [PubMed]

O. Keller, “Relation between spatial confinement of light and optical tunneling,” Phys. Rev. A 60, 1652–1671 (1999).
[Crossref]

O. Keller, “Propagator picture of the spatial confinement of quantized light emitted from an atom,” Phys. Rev. A 58, 3407–3425 (1998).
[Crossref]

A. M. Steinberg and R. Y. Chiao, “Tunneling times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
[Crossref] [PubMed]

Y. Wang and D. Zhang, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52, 2597–2600 (1995).
[Crossref]

Y. Japha and G. Kurizki, “Superluminal delays of coherent pulses in nondissipative media: a universal mechanism,” Phys. Rev. A 53, 586–590 (1996).
[Crossref] [PubMed]

Th. Martin and R. Landauer, “Time delay of evanescent electromagnetic waves and the analogy to particle tunneling,” Phys. Rev. A 45, 2611–2617 (1992).
[Crossref] [PubMed]

O. Keller, “Space–time description of photon emission from an atom,” Phys. Rev. A 62, 022111 (2000).
[Crossref]

Phys. Rev. B (2)

R. Fuchs and K. L. Kliewer, “Surface plasmons in a semi-infinite free-electron gas,” Phys. Rev. B 3, 2270–2278 (1971).
[Crossref]

P. J. Feibelman, “Microscopic calculation of electromagnetic fields in refraction at a jellium–vacuum interface,” Phys. Rev. B 12, 1319–1336 (1975).
[Crossref]

Phys. Rev. E (1)

A. Enders and G. Nimtz, “Evanescent-mode propagation and quantum tunneling,” Phys. Rev. E 48, 632–634 (1993).
[Crossref]

Phys. Rev. Lett. (3)

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurements of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[Crossref] [PubMed]

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[Crossref] [PubMed]

I. Bialynicki-Birula, “Exponential localization of photons,” Phys. Rev. Lett. 80, 5247–5250 (1998).
[Crossref]

Physica B (1)

R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling,” Physica B 175, 257–262 (1991).
[Crossref]

Prog. Surf. Sci. (1)

P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
[Crossref]

Ultramicroscopy (1)

D. van Labeke, J. M. Vigoureux, and G. Parent, “Photon tunneling time. Superluminal velocity for 1-D tunneling through a metallic barrier,” Ultramicroscopy 71, 11–20 (1998).
[Crossref]

Other (11)

O. Keller, “Local fields in linear and nonlinear optics of mesoscopic systems,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1997), Vol. XXXVII, pp. 257–343.

F. Forstmann and R. R. Gerhardts, Metal Optics Near the Plasma Frequency Vol. 109 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1986).
[Crossref]

L. I. Schiff, Quantum Mechanics (McGraw-Hill, Tokyo, 1968).

I. Bialynicki-Birula, “Photon wave function,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), Vol. XXXVI, pp. 245–294, and references therein.

F. Grass, Relativistic Quantum Mechanics and Field Theory (Wiley Interscience, New York, 1993).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms, Introduction to Quantum Electrodynamics (Wiley Interscience, New York, 1989).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1992).

R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1997), Vol. XXXVII, pp. 345–405, and references therein.

A. Otto, “Spectroscopy of surface polaritons by attenuated total reflection,” in Optical Properties of Solids—New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 677–729.

A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, Chichester, UK, 1982).

V. M. Agranovich and D. L. Mills, eds., Surface Polaritons, Electromagnetic Waves at Surfaces and Interfaces (North-Holland, Amsterdam, 1982).

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Figures (2)

Fig. 1
Fig. 1

For photon tunneling to occur between a source and a detector (observer) the transverse parts [JTsource(r, t), JTobs(r, t)] of the respective particle (electron) current density distributions [Jsource(r, t), Jobs(r, t)] must overlap in space, as indicated.

Fig. 2
Fig. 2

Schematic illustration showing a pointlike photon detector D (e.g., a two-level atom) placed in the transverse current density domain VT of a photon source generated by an electron distribution in the spatial domain V. The shortest distance between V and D is denoted R0. A pure superluminal response, arising from our inability to localize photons completely in space, occurs in the detector at such early times that no photons (statistically) generated inside V, and thereafter propagating toward the detector with the vacuum speed of light (c0), can have reached D. If the source starts to be electrodynamically active at time t=0, only a purely superluminal response can occur in the detector for times 0<t<R0/c0.

Equations (93)

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2E(r, t)=0,
·E(r, t)=0.
·B(r, t)=0.
×E(r, t)=0.
E(r; ω)=E0(xˆ+izˆ)exp(iq x)exp(-q z).
×ET(r, t)=-B(r, t)t,
×B(r, t)=μ0JT(r, t)+c0-2 ET(r, t)t,
·ET(r, t)=0,
2ET(r, t)=μ0 JT(r, t)t
JT(r, t)=- δT(r-r)·J(r, t)d3r,
2ET(r, t)=μ0 -δT(r-r)·J(r, t)t d3r.
δ(R)=23δ(R)U-14πR3(U-3RˆRˆ),
2ET(r, t)=2μ03 J(r, t)t-μ04π - 1R3×(U-3RˆRˆ)·J(r, t)t d3r.
E(r, t)=ET(r, t)+EL(r, t).
EL(r, t)=-10 -t JL(r, t)dt,
δL(R)=13δ(R)U+14πR3(U-3RˆRˆ),
EL(r, t)=-130 -t J(r, t)dt-14π0 - 1R3(U-3RˆRˆ)·-t J(r, t)dtd3r.
·U-3RˆRˆ4πR3=×U-3RˆRˆ4πR3=0,R0,
2E(r, t)=·E(r, t)+μ0 J(r, t)t
[2+(ω/c0)2]E(r; ω)
=·E(r; ω)-iμ0ωJ(r; ω),
J(r; ω)=i0ω[1-(r; ω)]E(r; ω),
[2+(ω/c0)2n2(r; ω)]E(r; ω)=·E(r; ω),
[2+(ω/c0)2n2(r; ω)]E(r; ω)=0,
n(r; ω)c0ω{2m[E-V(r)]}1/2,
(r; ω)=0,
2E(r, t)=μ0 J(r, t)t,
Jind(r; ω)=σMB(r, r; ω)·[ET(r; ω)+ELext(r; ω)]d3r,
Jind(r, ω)= σ(r, rω)·E(r; ω)d3r.
Jind(q, ω)=σ(q, ω)·E(q, ω)
σ(q, ω)=σT(q, ω)(U-qˆqˆ)+σL(q, ω)qˆqˆ,
JLext(q, ω)+JLint(q, ω)=i0ωEL(q, ω),
JL(q, ω)=i-1μ0ωσL(q, ω)NL-1(q, ω)JLext(q, ω),
NL(q, ω)=ωc021+iσL(q, ω)0ω.
iπ - 1q2 q2NL(q, ω)+q2NT(q, ω)exp(iq0+)dq
=c0ω2q0
NT(q, ω)=ωc021+iσT(q, ω)0ω-q2,
EL(r, t)=-14π0 S 1RS3(U-3RˆSRˆS)·-t JS(rS, t)dtd2rS,
ET(r, t)=ETSF(r, t)+ETR(r, t),
ETSF(r, t)=-130 -t JT(r, t)dt
ETR(r, t)=μ0 - D0T(r-r, t-t)·J(r, t)t dtd3r
D0T(R, τ)=-14πR(U-RˆRˆ)δRc0-τ+c02τ4πR3(U-3RˆRˆ)θ(τ)θRc0-τ,
ETR,NF(r, t)=14π0 - 1R3(U-3RˆRˆ)·t-R/c0t(t-t) J(r, t)t dtd3r,
ETR,NF(r, t)=14π0 - 1R3(U-3RˆRˆ)·-Rc0 Jr, t-Rc0+P(r, t)-Pr, t-Rc0d3r,
J(r, t)P(r, t)t.
EL(r, t)=130[P(r,-)-P(r, t)]+14π0 - 1R3(U-3RˆRˆ)·[P(r,-)-P(r, t)]d3r,
ETR,NF(r, t)+EL(r, t)
=130[P(r,-)-P(r, t)]+14π0 - 1R3(U-3RˆRˆ)·P(r,-)-Pr, t-Rc0-Rc0 Jr, t-Rc0d3r.
ETR,NF(r, t)+EL(r, t)=130[P(r,-)-P(r, t)]
ETSF(r, t)=-130 -t J(r, t)dt-13 EL(r, t),
ETSF(r, t)=290[P(r,-)-P(r, t)]+112π0 - 1R3(U-3RˆRˆ)·[P(r, t)-P(r,-)]d3r.
ESUPERLUM(r, t)=ETSF(r, t)=112π0 - 1R3(U-3RˆRˆ)·[P(r, t)-P(r,-)]d3r,
rVT-V
·ETFF(r; ω)=μ0ω2πi - 1R2 expi ωc0RRˆ·J(r; ω)d3r,
f±(r, t)=0/2[eT(r, t)±ic0b(r, t)],
i t f±(r, t)=±c0×f±(r, t),
·f±(r, t)=0.
sx=00000-i0i0,sy=00i000-i00,
sz=0-i0i00000,
i t f±(r, t)=H±f±(r, t),
H±=±c0s·i
f±(p, t)=F±(p)exp(-iωt)
±c0s·pF±=ωF±(p).
(s·p)·U-ppp2=s·p,
±c0s·pF±T(p)=ωF±T(p),
F±T(p)=U-ppp2·F±(p).
ω=c0 p,ω>0;
F±T(pzˆ)=12 1±i0
f±(+)(r, t)=0/2 0[eT(r; ω)±ic0b(r; ω)]×exp(-iωt)dω.
Φ(r, t)=f+(+)(r, t)f-(+)(r, t).
E=-Φ(r, t)·Φ(r, t)d3r
f±(+)(p, t)c0 pg±(p, t)ˆ±(pˆ)=-f±(+)(r, t)exp(-ip·r/)d3r,
Φ(p, t)=h-3/2g+(p, t)g-(p, t)
- Φ(p, t)·Φ(p, t)d3p=1
E=- c0 pΦ(p, t)·Φ(p, t)d3p,
eT(r; ω)=eTi(r; ω)-iμ0ω - d(r-r; ω)·JT(r; ω)d3r,
d(R; ω)=-14πR expi ωc0RU
b(r; ω)=bi(r; ω)-iμ0ωc0 - m(r-r; ω)·JT(r; ω)d3r,
m(R; ω)=-14πR expi ωc0R×U+ic0ωR[Φˆ(Rˆ)Θˆ(Rˆ)-Θˆ(Rˆ)Φˆ(Rˆ)].
f±(r; ω)=f±i(r; ω)-iμ0ω0/2-[d(R; ω)±im(R; ω)]·JT(r; ω)d3r,
0[d(R; ω)±im(R; ω)]·JT(r; ω)exp(-iωt)dω
=-[d(R; ω)±im(R; ω)]·JT(+)(r; ω)exp(-iωt)dω,
JT(+)(r; ω)=JT(r; ω)ω00ω<0
f±(+)(r, t)=f±(+),i(r, t)+μ00/2- [d(r-r, t-t)±im(r-r, t-t)]·JT(+)(r, t)t d3rdt,
Ψ(r, t)f+(+)(r, t)f-(+)(r, t).
Φi(r, t)=f+(+),i(r, t)f-(+),i(r, t),
Ψ(r, t)=Φi(r, t)+μ002×-[d(R, τ)+im(R, τ)]·J˙T(+)(r, t)[d(R, τ)-im(R, τ)]·J˙T(+)(r, t)×d3rdt,
d(R, τ)=-14πRδRc0-τU,
m(R, τ)=-14πRδRc0-τ-c04πR2θτ-Rc0×[Φˆ(Rˆ)Θˆ(Rˆ)-Θˆ(Rˆ)Φˆ(Rˆ)].
Ψs(r, t)=Ψ(r, t)-Φi(r, t),
JT(+)(r, t)=-δT(r-r)·J(+)(r, t)d3r
limt Φf(r, t)=Φi(r, t)-μ04π 02 - 1R×[U+i(ΦˆΘˆ-ΘˆΦˆ)]·J˙T(+)(r,[t])[U-i(ΦˆΘˆ-ΘˆΦˆ)]·J˙T(+)(r,[t])×d3r,
JT(r; ω)=- σTTMB(r, r; ω)·ET(r; ω)d3r,

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