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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 18, Iss. 2 — Feb. 1, 2001
  • pp: 206–217

Optical tunneling: a fingerprint of the lack of photon localizability

Ole Keller  »View Author Affiliations

JOSA B, Vol. 18, Issue 2, pp. 206-217 (2001)

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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

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(270.5580) Quantum optics : Quantum electrodynamics

Ole Keller, "Optical tunneling: a fingerprint of the lack of photon localizability," J. Opt. Soc. Am. B 18, 206-217 (2001)

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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).
  6. O. Keller, “Propagator picture of the spatial confinement of quantized light emitted from an atom,” Phys. Rev. A 58, 3407–3425 (1998).
  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).
  10. O. Keller, “Near-field optics: the nightmare of the photon,” J. Chem. Phys. 112, 7856–7863 (2000).
  11. O. Keller, “Space–time description of photon emission from an atom,” Phys. Rev. A 62, 022111 (2000).
  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).
  16. R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling,” Physica B 175, 257–262 (1991).
  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).
  18. K. Hass and P. Busch, “Causality of superluminal barrier traversal,” Phys. Lett. A 185, 9–13 (1994).
  19. Y. Wang and D. Zhang, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52, 2597–2600 (1995).
  20. Y. Japha and G. Kurizki, “Superluminal delays of coherent pulses in nondissipative media: a universal mechanism,” Phys. Rev. A 53, 586–590 (1996).
  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).
  22. G. Nimtz, “Superluminal signal velocity,” Ann. Phys. (Leipzig) 7, 618–624 (1998).
  23. G. Nimtz, “Evanescent waves are not necessarily Einstein causal,” Eur. Phys. J. B 7, 523–525 (1999).
  24. G. Nimtz, “The special features of superluminal evanescent mode propagation,” Gen. Relativ. Gravitation 31, 737–751 (1999).
  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).
  26. A. Enders and G. Nimtz, “Evanescent-mode propagation and quantum tunneling,” Phys. Rev. E 48, 632–634 (1993).
  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).
  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).
  29. A. M. Steinberg and R. Y. Chiao, “Tunneling times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
  30. O. Keller, “Local fields in the electrodynamics of mesoscopic media,” Phys. Rep. 268, 85–262 (1996).
  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).
  33. L. Lorenz, “Ueber die Reflexion des Lichts an der Gränzfläche zweier isotropen, durchsichtigen Mittel,” Ann. Phys. (Leipzig) 111, 460–473 (1860).
  34. P. J. Feibelman, “Microscopic calculation of electromagnetic fields in refraction at a jellium–vacuum interface,” Phys. Rev. B 12, 1319–1336 (1975).
  35. P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
  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).
  37. J. R. Oppenheimer, “Note on light quanta and the electromagnetic field,” Phys. Rev. 38, 725–746 (1931).
  38. L. Silberstein, “Elektromagnetische Grundgleichungen in bivektorieller Behandlung,” Ann. Phys. (Leipzig) 22, 579–586 (1907).
  39. L. Silberstein, “Nachtrag zur Abhandlung über ‘Elektromagnetische Grundgleichungen in bivektorieller Behandlung, ’ ” Ann. Phys. (Leipzig) 24, 783–784 (1907).
  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).
  42. O. Keller, “Theory of spatial confinement of light,” Mater. Sci. Eng., B 48, 175–183 (1997).

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