Skip to main content
SpringerLink
Log in

The molecular spontaneous emission rate evaluation in a dispersive and dissipative Fabry–Perot cavity, a field quantization approach

  • Regular Article – Quantum Optics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

By using the vector potential operator commutation relations, for a molecule (or generally an emitter) placed between two infinite identical dielectric slabs and with the given transition frequency and electric dipole moment, the spontaneous emission rate is evaluated via Fermi golden rule. Molecules with the electric dipole moment parallel and perpendicular to the slabs are considered separately, and for each orientation, a typical variation of the emission rate in the space of the cavity is demonstrated. In the used quantization scheme, the dielectric functions of the slabs can be an arbitrary complex function of frequency (satisfying Kramers–Kronig relations) and thus, slabs generally can be dissipative and dispersive. By showing the agreement of this quantization approach with two previous green function approaches, in evaluating the spontaneous emission rate in a Fabry–Perot cavity, the consistency between field quantization and Green function approaches is shown.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated date or data will not be deposited [Author’s comment: This is a theoretical study and no experimental data has been listed.]

References

  1. H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)

    Google Scholar 

  2. D. Kupiszewska, J. Mostoveski, Phys. Rev. A 41, 4636 (1990)

    Article  ADS  Google Scholar 

  3. M. ThierryJaekel, S. Reynaud, J. Phys. France 1, 1395–1409 (1991)

    Article  Google Scholar 

  4. D. Kupiszewska, Phys. Rev. A 46, 2286 (1992)

    Article  ADS  Google Scholar 

  5. R. Matloob, Phys. Rev. A 60, 3421 (1999)

    Article  ADS  Google Scholar 

  6. V. Hushwater, Am. J. Phys. 65, 5 (1997)

    Article  Google Scholar 

  7. R. Matloob, H. Falinejad, Phys. Rev. A 64, 042102 (2001)

    Article  ADS  Google Scholar 

  8. A.A. Saharian, Eur. Phys. J. C. 52, 721–733 (2007)

    Article  ADS  Google Scholar 

  9. F. Kheirandish, M. Soltani, J. Sarabadani, Ann. Phys. 326, 657–667 (2011)

    Article  ADS  Google Scholar 

  10. H. Falinejadand, F. Bayat, Int. J. Mod. Phys. B 28, 1450232 (2014)

    Article  ADS  Google Scholar 

  11. N.R. Khusnutdinov, R.N. Kashapov, Theor. Math. Phys. 183(1), 491–500 (2015)

    Article  Google Scholar 

  12. H. Falinejad, Eur. Phys. J. D. 71, 165 (2017)

    Article  ADS  Google Scholar 

  13. H.B.G. Casimir, D. Polder, Phys. Rev. 73, 360 (1948)

    Article  ADS  Google Scholar 

  14. P.W. Milonni, The Quantum Vacuum (Academic Press, New York, 1994)

    Book  Google Scholar 

  15. S.Y. Buhmann, H.T. Dung, T. Kampf, D.G. Welsch, Eur. Phys. J. D 35, 15–30 (2005)

    Article  ADS  Google Scholar 

  16. S. Spagnolo, R. Passante, L. Rizzuto, Phys. Rev. A 73, 062117 (2006)

    Article  ADS  Google Scholar 

  17. R. Vasile, R. Passante, Phys. Rev. A 78, 032108 (2008)

    Article  ADS  Google Scholar 

  18. F. Intravaia, C. Henkel, and M. Antezza, Casimir Phys. pp. 345–391 (2011)

  19. H. Falinejad, and N. Niknam, Int. J. Theor. Phys., (2020)

  20. R. Matloob, Phys. Rev. A 61, 06213 (2001)

    Google Scholar 

  21. H. Khosravi, R. Loudon, Proc. R. Soc. Lond. A 433, 337–352 (1991)

    Article  ADS  Google Scholar 

  22. H. Khosravi, R. Loudon, Proc. R. Soc. Lond. A 436, 373–389 (1992)

    Article  ADS  Google Scholar 

  23. R. Matloob, Phys. Rev. A 62, 022113 (2000)

    Article  ADS  Google Scholar 

  24. S.M. Barnett, B.H. Huttner, R. Loudon, Phys. Rev Lett. 68, 3698 (1992)

    Article  ADS  Google Scholar 

  25. S.M. Barnett, B.H. Huttner, R. Loudon, R. Matloob, J. Phys. B 29, 3763 (1996)

    Article  ADS  Google Scholar 

  26. A. Tip, Phys. Rev. A 56, 5022 (1997)

    Article  ADS  Google Scholar 

  27. A. Tip, Phys. Rev. A 57, 4818 (1998)

    Article  ADS  Google Scholar 

  28. B. Bloch, M. Ducloy, Adv. Atom. Mol. Opt. Phys. 50, 91–154 (2005)

    Article  ADS  Google Scholar 

  29. M. Amooshahi, B. Nasr, Esfahani. Ann. Phys. 325, 1913–1930 (2010)

    Article  ADS  Google Scholar 

  30. J.P. Dowling, Foundation Phys. 23, 6 (1993)

    Article  Google Scholar 

  31. K. Kakazu, Y.S. Kim, Phys. Rev. A 50, 1830 (1994)

    Article  ADS  Google Scholar 

  32. W. Zakowicz, A. Bledowski, Phys. Rev. A 52, 1640 (1995)

    Article  ADS  Google Scholar 

  33. K. Kakazu, Y.S. Kim, Prog. Theor. Phys. 96, 5 (1996)

    Article  Google Scholar 

  34. M.S. Yeung, T.K. Gustafson, Phys. Rev. A 54, 5227 (1996)

    Article  ADS  Google Scholar 

  35. H.P. Urbach, G.L.J.A. Rikken, Phys. Rev. A 57, 3913 (1998)

    Article  ADS  Google Scholar 

  36. C. Creatore, L.C. Andreani, Phys. Rev. A 78, 63825 (2008)

  37. H. Falinejad, S. Najafi, Ardekani. Appl. Phys. B 125, 208 (2019)

    Article  ADS  Google Scholar 

  38. J. P. Dowling, Foundation Phys. Vol. 23, No. 6, (1993)

  39. K. Kakazu, and Y. S. Kim, Prog. Theor. Phys., Vol. 96, No.5, (1996)

  40. J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1998)

    MATH  Google Scholar 

  41. N. Furtak-Wells, L.A. Clark, R. Purdy, A. Beige, Phys. Rev. A 97, 043827 (2018)

    Article  ADS  Google Scholar 

  42. B. Huttner, S. Barnett, Europhys. Lett. 16, 177 (1991)

    Article  ADS  Google Scholar 

  43. B. Huttner, S. Barnett, Europhys. Lett. 18, 487 (1992)

    Article  ADS  Google Scholar 

  44. R. Matloob, Opt. Com. 192, 287–297 (2001)

    Article  ADS  Google Scholar 

  45. B. Huttner, S. Barnett, Phys. Rev. A 46, 4306 (1992)

    Article  ADS  Google Scholar 

  46. S.A.R. Horsley, T.G. Philbin, New J. Phys. 16, 013030 (2014)

    Article  ADS  Google Scholar 

  47. S. Barnett, R. Matloob, R. Loudon, J. Mod. Opt. 42, 1165 (1995)

    Article  ADS  Google Scholar 

  48. R. Matloob, R. Loudon, S. Barnett, J. Jeffers, Phys. Rev. A 52, 4823 (1995)

    Article  ADS  Google Scholar 

  49. R. Matloob, R. Loudon, Phys. Rev. A 53, 4567 (1996)

  50. T. Gurner, D.G. Welsh, Phys. Rev. A 51, 3246 (1995)

    Article  ADS  Google Scholar 

  51. T. Gurner, D.G. Welsh, Phys. Rev. A 53, 1818 (1996)

  52. H. Dung, L. Knoll, D.G. Welsh, Phys. Rev. A 57, 3931 (1998)

    Article  ADS  Google Scholar 

  53. R. Matloob, Phys. Rev. A 60, 50 (1999)

    Article  ADS  Google Scholar 

  54. R. Matloob, H. Safari, Opt. Commun. 214, 255–270 (2002)

    Article  ADS  Google Scholar 

  55. H. Falinejad, Indian J. Phys., (2020)

  56. M.S. Tomas, Z. Lenac, Phys. Rev. A 56, 4197 (1997)

    Article  ADS  Google Scholar 

  57. M.S. Tomas, Z. Lenac, Phys. Rev. A 60, 2431 (1999)

    Article  ADS  Google Scholar 

  58. C. Cohen-Tannoudji, J. Dupont-Roc, G. Gryberg, Photons and Atoms (Wiley, New York, 1980)

    Google Scholar 

  59. L. Landau, E. Lifshitz, Statistical Physics Part 2 (Pergamon Press, Oxford, 1980)

    Google Scholar 

Download references

Acknowledgements

The author would like to thank the Persian Gulf university council for its support.

Author information

Authors and Affiliations

  1. Department of Physics, The Persian Gulf University, Bushehr, 75169, Iran

    Hossein Falinejad

Authors
  1. Hossein Falinejad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hossein Falinejad.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Falinejad, H. The molecular spontaneous emission rate evaluation in a dispersive and dissipative Fabry–Perot cavity, a field quantization approach. Eur. Phys. J. D 75, 244 (2021). https://doi.org/10.1140/epjd/s10053-021-00249-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-021-00249-7

Search

Navigation