Skip to main content
SpringerLink
Log in

On photonic tunnelling and the possibility of superluminal transport of electromagnetic energy

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Motivated by the increased interest in experiments in which light appears to propagate by tunnelling at superluminal velocity, the Lorentz invariant theory proposed by Partha Ghose to explain these surprising effects is revisited. This theory is based on the Harish-Chandra formalism, which describes the relativistic dynamics of a massless spin-1 boson, like a photon. By this formalism, the Bohmian average transport velocity of the electromagnetic energy is formulated. It is proved that this velocity can be superluminal if the dielectric making the waveguide is non-absorptive and non-dispersive. This result is validated in the framework of quantum electrodynamics, demonstrating that the average velocity of the photon inside the waveguide is given by the contribution of instantaneous superluminal velocities. This theory, therefore, suggests the optimal conditions for designing the optical devices capable of locally transporting electromagnetic energy at superluminal velocities mitigating signal attenuation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N H Liu, S Y Zhu, H Chen and X Wu, Phys. Rev. E. 65, 046607 (2002)

    Article  ADS  Google Scholar 

  2. L G Wang, A Kuzmich and A Dogariu, Nature 117, 610 (2000)

    Google Scholar 

  3. L G Wang, N H Liu, Q Lin and S Y Zhu, Phys. Rev. E 68, 066606 (2003)

    Article  ADS  Google Scholar 

  4. A H Dorrah, A Ramakrishnan and M Mojahedi, Phys. Rev. E 91, 033206 (2015)

    Article  ADS  Google Scholar 

  5. D Mugnai, A Ranfagni and R Ruggeri, Phys. Rev. Lett. 84, 4830 (2000)

    Article  ADS  Google Scholar 

  6. A Enders and G Nimtz, Phys. Rev. B 47, 9605 (1993)

    Article  ADS  Google Scholar 

  7. H M Brodowsky, W Heitmann and G Nimtz, Phys. Lett. A 222, 125 (1996)

    Article  ADS  Google Scholar 

  8. W Heitmann and G Nimtz, Prog. Quantum Electron. 21, 81 (1997)

    Article  ADS  Google Scholar 

  9. S Longhi, P Laporta, M Belmonte and E Recami, Phys. Rev. E 65, 046610 (2002)

    Article  ADS  Google Scholar 

  10. R Y Chiao and A M Steinberg, Prog. Opt. 37, 345 (1997)

    Article  ADS  Google Scholar 

  11. G Nimtz and A A Stahlofen, Ann. Phys. 17, 374 (2008)

    Article  Google Scholar 

  12. G Nimtz, Found. Phys. 34, 1889 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  13. G Nimtz and A Haibel, Ann. Phys. 11, 163 (2002)

    Article  Google Scholar 

  14. R Dumont, T Rivlin and E Pollak, New J. Phys. 22, 093060 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  15. R Ramos, D Spierings, I Racicot and A M Steinberg, Nature 583, 529 (2020)

    Article  ADS  Google Scholar 

  16. K W Kark, Frequenzy 59, 51 (2005)

    ADS  Google Scholar 

  17. E Recami, M Zamboni-Rached, K Z Nobrega, C A Dartora and H E Hernandez, IEEE J. ST Quant. Electron. 9, 59 (2003)

    Google Scholar 

  18. V S Olkhovsky, E Recami and J Jakiel, Phys. Rep. 398, 133 (2004)

    Article  ADS  Google Scholar 

  19. G Nimtz, Eur. Phys. J. B 7, 523 (1999)

    Article  ADS  Google Scholar 

  20. G Nimtz, Found. Phys. 41, 1193 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  21. S Cialdi, I Boscolo, F Castelli and V Petrillo, New J. Phys. 11, 023036 (2009)

    Article  ADS  Google Scholar 

  22. G Feinberg, Phys. Rev. D 17, 1651 (1978)

    Article  ADS  Google Scholar 

  23. S K Bose, J. Phys.: Conf. Ser. 196, 012022 (2009)

    Google Scholar 

  24. R-G Cai, Phys. Lett. B 517, 457 (2001)

    Article  ADS  Google Scholar 

  25. D Bortman-Arbiv, A D Wilson-Gordon and H Friedmann, Phys. Rev. A 63, 043818 (2001)

    Article  ADS  Google Scholar 

  26. A Sommerfeld, Pure Appl. Phys. 8, 17 (1960)

    Google Scholar 

  27. M J Lazarus, Phys. Today 56, 14 (2003)

    Article  Google Scholar 

  28. M Bertolotti, C Sibilia and A M Guzman, Evanescent waves in optics (Springer AG, Heidelberg, 2017)

    Book  Google Scholar 

  29. G Nimtz, A Haibel and A A Stahlhofen, On superluminal photonic tunneling, in: Ultra-wideband, short-pulse electromagnetics (Springer, Boston, 2002)

  30. V S Olkhovsky, Int. J. Mod. Phys. E 23, 1460006 (2014)

    Article  ADS  Google Scholar 

  31. P Ghose and M K Samal, Phys. Rev. E 64, 036620 (2001)

    Article  ADS  Google Scholar 

  32. Harish-Chandra, Proc. R. Soc. A 186, 502 (1946)

    ADS  Google Scholar 

  33. D Sokolovski and E Akhmatskaya, Commun. Phys. 1, 47 (2018)

    Article  Google Scholar 

  34. N Kemmer, Proc. R. Soc. A 173, 91 (1939)

    ADS  MathSciNet  Google Scholar 

  35. W Struyve and A Valentini, J. Phys. A: Math. Theor. 42, 035301 (2008)

    Article  ADS  Google Scholar 

  36. F de Fornel, Evanescent waves: From Newtonian optics to atomic optics (Springer-Verlag, Berlin, Heidelberg, 2001)

    Book  Google Scholar 

  37. G Fan, Z Wang, Z Wei, Y Liu and R Fan, Compos. Part A: Appl. Sci. Manuf. 139, 106132 (2020)

    Article  Google Scholar 

  38. W Cai and V Shalaev, Optical properties of metal-dielectric composites, in: Optical metamaterials (Springer, New York, 2010)

  39. A Cannas da Silva, Lectures on symplectic geometry, Lecture notes in mathematics (Springer, Berlin, Heidelberg, 2001) Vol. 1764

  40. E T Newman, J. Math. Phys. 14, 102 (1973)

    Article  ADS  Google Scholar 

  41. E Recami, Physica A 252, 586 (1988)

    Article  ADS  Google Scholar 

  42. M Davidson, J. Phys.: Conf. Ser. 361, 012005 (2011)

    Google Scholar 

  43. P Yu and M Cadorna, Fundamentals of semiconductors (Springer Science, Berlin, 2005) Vol. 3

    Book  Google Scholar 

  44. R W Boyd, Physics and applications of epsilon-near-zero materials, Proc. SPIE 10922, Smart Photonic and Optoelectronic Integrated Circuits XXI, 1092207 (2019)

  45. M Silveirinha and N Engheta, Phys. Rev. Lett. 97, 157403 (2006)

    Article  ADS  Google Scholar 

  46. M H Javani and M I Stockman, Phys. Rev. Lett. 117, 107404 (2016)

    Article  ADS  Google Scholar 

  47. H Lobato-Morales, A Corona-Chavez, D V B Murthy, J Martinez-Brito and L G Guerrero-Ojeda, IEEE MTT-S International Microwave Symposium 2010, 1644 (2010)

    Google Scholar 

  48. V B Novikov, A P Leontiev, K S Napolskii and T V Murzina, Opt. Lett. 10, 2276 (2021)

    Article  ADS  Google Scholar 

  49. E Recami, J. Mod. Opt. 51, 913 (2004)

    ADS  Google Scholar 

  50. H G Winful, Phys. Rep. 436, 1 (2006)

    Article  ADS  Google Scholar 

  51. G Nimtz, AIP Conf. Proc. 461, 14 (1999)

    Google Scholar 

  52. G Feinberg, Phys. Rev. 159, 1089 (1967)

    Article  ADS  Google Scholar 

  53. E Recami, Fund. Phys. 17, 239 (1987)

    Article  ADS  Google Scholar 

  54. E F Schubert, J K Kim and J Q Xi, Phys. Status Solidi B 244, 3002 (2007)

    Article  ADS  Google Scholar 

  55. A Goodarzi, M Ghanaatshoar and M Mozafari, Sci. Rep. 8, 15340 (2018)

    Article  ADS  Google Scholar 

  56. M Ware, S A Glasgow and J Peatross, Opt. Express 9, 519 (2001)

    Article  ADS  Google Scholar 

  57. R Y Chiao, Phys. Rev. A 48, R34 (1993)

    Article  ADS  Google Scholar 

  58. J P Dowling and C M Bowden, J. Mod. Opt. 41, 345 (1994)

    Article  ADS  Google Scholar 

  59. P M Visser and G Nienhuis, Opt. Commun. 136, 470 (1997)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Natural Science, University of Ferrara, 44122, Ferrara, Italy

    Luca Nanni

Authors
  1. Luca Nanni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luca Nanni.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nanni, L. On photonic tunnelling and the possibility of superluminal transport of electromagnetic energy. Pramana - J Phys 97, 37 (2023). https://doi.org/10.1007/s12043-022-02511-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-022-02511-y

Keywords

PACS Nos

Search

Navigation