Advertisement

Quantization of the electromagnetic field at the presence of two dielectric slabs and application to the Casimir effect

  • Hossein FalinejadEmail author
Regular Article
  • 59 Downloads

Abstract

The three dimensional formalism of the Green function method of the electro-magnetic field quantization is extended to quantize the electromagnetic field, at the presence of two dispersive and dissipative dielectric slabs. It is shown that the system decomposes into a singlet and a doublet parts. The singlet system corresponds to the normal polarization state of the electric field and the doublet system corresponds to the sum of parallel and longitudinal polarization states. Each part is quantized separately and vector potential operator of the each part is derived in terms of rightward and leftwards annihilation and creation operators. By using the assuming commutation properties of the noise current density, the equal time canonical commutation relations between the vector potential operator and its conjugate generalized momentum are verified for each part. Finally as an application, the explicit form of field operators are used to obtain an expression for the Casimir force between the two slabs via Maxwell stress tensor.

Graphical abstract

Keywords

Quantum Optics 

References

  1. 1.
    W. Vogel, D.G. Welsh, S. Wallentowitz, Quantum Optics: An Introduction (Wiley-VCH, 2001)Google Scholar
  2. 2.
    I. Abram, Phys. Rev. A 35, 4661 (1987)ADSCrossRefGoogle Scholar
  3. 3.
    L. Koll, W. Vogel, D.G. Welsh, Phys. Rev. A 36, 3808 (1987)ADSGoogle Scholar
  4. 4.
    K.J. Blow, R. Loudon, S.J.D. Phonix, T.J. Shepherd, Phys. Rev. A 42, 4102 (1990)ADSCrossRefGoogle Scholar
  5. 5.
    D.J. Santon, R. Loudon, Phys. Rev. A 52, 1538 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    R. Matloob, G. Pooseh, Opt. Commun. 181, 109 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    S.M. Barnett, B.H. Huttner, R. Loudon, Phys. Rev. Lett. 68, 3698 (1992)ADSCrossRefGoogle Scholar
  8. 8.
    S.M. Barnett, B.H. Huttner, R. Loudon, R. Matloob, J. Phys. B 29, 3763 (1996)ADSCrossRefGoogle Scholar
  9. 9.
    A. Tip, Phys. Rev. A 56, 5022 (1997)ADSCrossRefGoogle Scholar
  10. 10.
    A. Tip, Phys. Rev. A 57, 4818 (1998)ADSCrossRefGoogle Scholar
  11. 11.
    D. Kupiszewska, J. Mostoveski, Phys. Rev. A 41, 4636 (1990)ADSCrossRefGoogle Scholar
  12. 12.
    D. Kupiszewska, Phys. Rev. A 46, 2286 (1992)ADSCrossRefGoogle Scholar
  13. 13.
    F. Kheirandish, M. Soltani, J. Sarabadani, Ann. Phys. 326, 657 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    B. Huttner, S. Barnett, Europhys. Lett. 16, 177 (1991)ADSCrossRefGoogle Scholar
  15. 15.
    B. Huttner, S. Barnett, Europhys. Lett. 18, 487 (1992)ADSCrossRefGoogle Scholar
  16. 16.
    B. Huttner, S. Barnett, Phys. Rev. A 46, 4306 (1992)ADSCrossRefGoogle Scholar
  17. 17.
    M. Amooshahi, B. Nasr Esfahani, Ann. Phys. 325, (2010) 1913–1930Google Scholar
  18. 18.
    S.A.R. Horsley, T.G. Philbin, New J. Phys. 16, 013030 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    R. Matloob, Opt. Commun. 192, 287 (2001)ADSCrossRefGoogle Scholar
  20. 20.
    S. Barnett, R. Matloob, R. Loudon, J. Mod. Opt. 42, 1165 (1995)ADSCrossRefGoogle Scholar
  21. 21.
    R. Matloob, R. Loudon, S. Barnett, J. Jeffers, Phys. Rev. A 52, 4823 (1995)ADSCrossRefGoogle Scholar
  22. 22.
    R. Matloob, R. Loudon, Phys. Rev. A 53, 4567 (1996)ADSCrossRefGoogle Scholar
  23. 23.
    T. Gurner, D.-G. Welsch, Phys. Rev. A 51, 3246 (1995)ADSCrossRefGoogle Scholar
  24. 24.
    T. Gurner, D.-G. Welsch, Phys. Rev. A 53, 1818 (1996)ADSCrossRefGoogle Scholar
  25. 25.
    H. Dung, L. Knoll, D.-G. Welsch, Phys. Rev. A 57, 3931 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    R. Matloob, Phys. Rev. A 60, 50 (1999)ADSCrossRefGoogle Scholar
  27. 27.
    R. Matloob, H. Safari, Opt. Commun. 214, 255 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    S. Scheel, L. Koll, D.-G. Welsch, Phys. Rev. A 58, 700 (1998)ADSCrossRefGoogle Scholar
  29. 29.
    A.A. Maradudin, D.L. Mills, Phys. Rev. B 11, 1392 (1975) 1392ADSCrossRefGoogle Scholar
  30. 30.
    R. Matloob, H. Falinejad, Phys. Rev. A 64, 042102 (2001)ADSCrossRefGoogle Scholar
  31. 31.
    S.M. Barnett, J. Jeffers, A. Gatti, R. Loudon, Phys. Rev. A 57, 2134 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    S.M. Barnett, C.R. Gilson, B. Huttner, N. Imoto, Phys. Rev. Lett. 77, 1739 (1996)ADSCrossRefGoogle Scholar
  33. 33.
    M. Ueda, N. Imoto, Phys. Rev. A 50, 89 (1994)ADSCrossRefGoogle Scholar
  34. 34.
    C. Cohen-Tannoudji, J. Dupont-Roc, G. Gryberg, Photons and Atoms (Wiley, New York, 1980)Google Scholar
  35. 35.
    L. Landau, E. Lifshitz, L. Pitaevskii, Electromagnetic of Continuous Media (Pergamon, Oxford, 1984)Google Scholar
  36. 36.
    A. Lambrecht, S. Reynaud, Eur. Phys. J. D 8, 309 (2000)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of PhysicsPersian Gulf UniversityBushehrIran

Personalised recommendations