Abstract

We present a three-dimensional quantum theory of light scattering, absorption, and emission in arbitrary planar dielectric systems. The theory is based on a scheme for quantization of the electromagnetic field in dispersive and lossy arbitrary planar dielectrics that takes explicitly into account the finite extent of the medium. We present general quantum-optical input–output relations of the output TE and TM photon operators to the corresponding input photon operators and to the reservoir noise operators. These three-dimensional input–output relations are uniquely determined by knowledge of the classical light modes of the planar dielectric structure.

© 2002 Optical Society of America

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  1. E. M. Purcell, “Spontaneous emission probabilities of radio frequencies,” Phys. Rev. 69, 681 (1946).
  2. G. S. Agarwal, “Coherence in spontaneous emission in the presence of a dielectric,” Phys. Rev. Lett. 32, 703–706 (1974).
    [CrossRef]
  3. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  4. S. M. Barnett, B. Huttner, and R. Loudon, “Spontaneous emission in absorbing dielectric media,” Phys. Rev. Lett. 68, 3698–3701 (1992).
    [CrossRef] [PubMed]
  5. S. Scheel, L. Knöll, D.-G. Welsch, and S. M. Barnett, “Quantum local-field corrections and spontaneous decay,” Phys. Rev. A 60, 1590–1597 (1999).
    [CrossRef]
  6. Milloni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic, San Diego, Calif., 1994).
  7. M. Artoni and R. Loudon, “Propagation of nonclassical light through an absorbing and dispersive slab,” Phys. Rev. A 59, 2279–2290 (1999).
    [CrossRef]
  8. E. Schmidt, L. Knöll, and D.-G. Welsch, “Propagation of squeezed-light pulses in dispersive and absorbing linear dielectrics,” Phys. Rev. A 54, 843–855 (1996).
    [CrossRef] [PubMed]
  9. L. Knöll, E. Schmidt, D.-G. Welsh, and A. V. Chizhov, “Quantum-state transformation by dispersive and absorbing four-port devices,” Phys. Rev. A 59, 4716–4726 (1999).
    [CrossRef]
  10. C. H. Henry and F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
    [CrossRef]
  11. B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46, 4306–4322 (1992).
    [CrossRef] [PubMed]
  12. L. Knöll and U. Leonhardt, “Quantum optics in oscillator media,” J. Mod. Opt. 39, 1253 (1992).
    [CrossRef]
  13. R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, “Electromagnetic field quantization in absorbing dielectrics,” Phys. Rev. A 52, 4823–4838 (1995).
    [CrossRef] [PubMed]
  14. R. Matloob and R. Loudon, “Electromagnetic field quantization in absorbing dielectrics. II,” Phys. Rev. A 53, 4567–4582 (1996).
    [CrossRef] [PubMed]
  15. T. Gruner and D. G. Welsh, “Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 53, 1818–1829 (1996).
    [CrossRef] [PubMed]
  16. U. Leonhardt, “Influence of a dispersive and dissipative medium on spectral squeezing,” J. Mod. Opt. 40, 1123–1130 (1993).
    [CrossRef]
  17. D. Kupiszewska, “Casimir effect in absorbing media,” Phys. Rev. A 46, 2286–2294 (1992).
    [CrossRef] [PubMed]
  18. M. Artoni and R. Loudon, “Quantum theory of optical pulse propagation through an absorbing and dispersive slab,” Phys. Rev. A 55, 1347–1357 (1997).
    [CrossRef]
  19. T. Gruner and D. G. Welsch, “Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates,” Phys. Rev. A 54, 1661–1677 (1996).
    [CrossRef] [PubMed]
  20. O. Di Stefano, S. Savasta, and R. Girlanda, “Mode expansion and photon operators in dispersive and absorbing dielectrics,” J. Mod. Opt. 48, 67–84 (2001).
    [CrossRef]
  21. O. Di Stefano, S. Savasta, and R. Girlanda, “Electromagnetic-field quantization in absorbing confined systems,” Phys. Rev. A 60, 1614–1625 (1999).
    [CrossRef]
  22. H. T. Dung, L. Knöll, and D. G. Welsh, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A 57, 3931–3942 (1998).
    [CrossRef]
  23. S. Scheel, L. Knöll, and D.-G. Welsch, “QED commutation relations for inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 58, 700–706 (1998).
    [CrossRef]
  24. A. Tip, “Linear absorptive dielectrics,” Phys. Rev. A 57, 4818–4841 (1998).
    [CrossRef]
  25. A. Tip, L. Knöll, S. Scheel, and D.-G. Welsch, “Equivalence of the Langevin and auxiliary-field quantization methods for absorbing dielectrics,” Phys. Rev. A 63, 043806 (7 pages) (2001).
    [CrossRef]
  26. O. Di Stefano, S. Savasta, and R. Girlanda, “Three-dimensional electromagnetic field quantization in absorbing and dispersive bounded dielectrics,” Phys. Rev. A 61, 023803 (12 pages) (2000).
    [CrossRef]
  27. H. A. Mcleod, Thin Film Optical Filters (Elsevier, New York, 1969).
  28. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  29. M. S. Tomaš, “Green function for multilayers: Light scattering in planar cavities,” Phys. Rev. A 51, 2545–2559 (1995).
    [CrossRef] [PubMed]
  30. D. L. Mills and A. A. Maradudin, “Surface roughness and the optical properties of a semi-infinite material: the effect of a dielectric overlayer,” Phys. Rev. B 12, 2943–2958 (1975).
    [CrossRef]
  31. J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
    [CrossRef]

2001 (2)

O. Di Stefano, S. Savasta, and R. Girlanda, “Mode expansion and photon operators in dispersive and absorbing dielectrics,” J. Mod. Opt. 48, 67–84 (2001).
[CrossRef]

A. Tip, L. Knöll, S. Scheel, and D.-G. Welsch, “Equivalence of the Langevin and auxiliary-field quantization methods for absorbing dielectrics,” Phys. Rev. A 63, 043806 (7 pages) (2001).
[CrossRef]

2000 (1)

O. Di Stefano, S. Savasta, and R. Girlanda, “Three-dimensional electromagnetic field quantization in absorbing and dispersive bounded dielectrics,” Phys. Rev. A 61, 023803 (12 pages) (2000).
[CrossRef]

1999 (4)

O. Di Stefano, S. Savasta, and R. Girlanda, “Electromagnetic-field quantization in absorbing confined systems,” Phys. Rev. A 60, 1614–1625 (1999).
[CrossRef]

L. Knöll, E. Schmidt, D.-G. Welsh, and A. V. Chizhov, “Quantum-state transformation by dispersive and absorbing four-port devices,” Phys. Rev. A 59, 4716–4726 (1999).
[CrossRef]

S. Scheel, L. Knöll, D.-G. Welsch, and S. M. Barnett, “Quantum local-field corrections and spontaneous decay,” Phys. Rev. A 60, 1590–1597 (1999).
[CrossRef]

M. Artoni and R. Loudon, “Propagation of nonclassical light through an absorbing and dispersive slab,” Phys. Rev. A 59, 2279–2290 (1999).
[CrossRef]

1998 (3)

H. T. Dung, L. Knöll, and D. G. Welsh, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A 57, 3931–3942 (1998).
[CrossRef]

S. Scheel, L. Knöll, and D.-G. Welsch, “QED commutation relations for inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 58, 700–706 (1998).
[CrossRef]

A. Tip, “Linear absorptive dielectrics,” Phys. Rev. A 57, 4818–4841 (1998).
[CrossRef]

1997 (1)

M. Artoni and R. Loudon, “Quantum theory of optical pulse propagation through an absorbing and dispersive slab,” Phys. Rev. A 55, 1347–1357 (1997).
[CrossRef]

1996 (5)

T. Gruner and D. G. Welsch, “Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates,” Phys. Rev. A 54, 1661–1677 (1996).
[CrossRef] [PubMed]

E. Schmidt, L. Knöll, and D.-G. Welsch, “Propagation of squeezed-light pulses in dispersive and absorbing linear dielectrics,” Phys. Rev. A 54, 843–855 (1996).
[CrossRef] [PubMed]

R. Matloob and R. Loudon, “Electromagnetic field quantization in absorbing dielectrics. II,” Phys. Rev. A 53, 4567–4582 (1996).
[CrossRef] [PubMed]

T. Gruner and D. G. Welsh, “Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 53, 1818–1829 (1996).
[CrossRef] [PubMed]

C. H. Henry and F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
[CrossRef]

1995 (2)

M. S. Tomaš, “Green function for multilayers: Light scattering in planar cavities,” Phys. Rev. A 51, 2545–2559 (1995).
[CrossRef] [PubMed]

R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, “Electromagnetic field quantization in absorbing dielectrics,” Phys. Rev. A 52, 4823–4838 (1995).
[CrossRef] [PubMed]

1993 (1)

U. Leonhardt, “Influence of a dispersive and dissipative medium on spectral squeezing,” J. Mod. Opt. 40, 1123–1130 (1993).
[CrossRef]

1992 (4)

D. Kupiszewska, “Casimir effect in absorbing media,” Phys. Rev. A 46, 2286–2294 (1992).
[CrossRef] [PubMed]

B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46, 4306–4322 (1992).
[CrossRef] [PubMed]

L. Knöll and U. Leonhardt, “Quantum optics in oscillator media,” J. Mod. Opt. 39, 1253 (1992).
[CrossRef]

S. M. Barnett, B. Huttner, and R. Loudon, “Spontaneous emission in absorbing dielectric media,” Phys. Rev. Lett. 68, 3698–3701 (1992).
[CrossRef] [PubMed]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
[CrossRef]

1975 (1)

D. L. Mills and A. A. Maradudin, “Surface roughness and the optical properties of a semi-infinite material: the effect of a dielectric overlayer,” Phys. Rev. B 12, 2943–2958 (1975).
[CrossRef]

1974 (1)

G. S. Agarwal, “Coherence in spontaneous emission in the presence of a dielectric,” Phys. Rev. Lett. 32, 703–706 (1974).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities of radio frequencies,” Phys. Rev. 69, 681 (1946).

Agarwal, G. S.

G. S. Agarwal, “Coherence in spontaneous emission in the presence of a dielectric,” Phys. Rev. Lett. 32, 703–706 (1974).
[CrossRef]

Artoni, M.

M. Artoni and R. Loudon, “Propagation of nonclassical light through an absorbing and dispersive slab,” Phys. Rev. A 59, 2279–2290 (1999).
[CrossRef]

M. Artoni and R. Loudon, “Quantum theory of optical pulse propagation through an absorbing and dispersive slab,” Phys. Rev. A 55, 1347–1357 (1997).
[CrossRef]

Barnett, S. M.

S. Scheel, L. Knöll, D.-G. Welsch, and S. M. Barnett, “Quantum local-field corrections and spontaneous decay,” Phys. Rev. A 60, 1590–1597 (1999).
[CrossRef]

R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, “Electromagnetic field quantization in absorbing dielectrics,” Phys. Rev. A 52, 4823–4838 (1995).
[CrossRef] [PubMed]

S. M. Barnett, B. Huttner, and R. Loudon, “Spontaneous emission in absorbing dielectric media,” Phys. Rev. Lett. 68, 3698–3701 (1992).
[CrossRef] [PubMed]

B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46, 4306–4322 (1992).
[CrossRef] [PubMed]

Chizhov, A. V.

L. Knöll, E. Schmidt, D.-G. Welsh, and A. V. Chizhov, “Quantum-state transformation by dispersive and absorbing four-port devices,” Phys. Rev. A 59, 4716–4726 (1999).
[CrossRef]

Di Stefano, O.

O. Di Stefano, S. Savasta, and R. Girlanda, “Mode expansion and photon operators in dispersive and absorbing dielectrics,” J. Mod. Opt. 48, 67–84 (2001).
[CrossRef]

O. Di Stefano, S. Savasta, and R. Girlanda, “Three-dimensional electromagnetic field quantization in absorbing and dispersive bounded dielectrics,” Phys. Rev. A 61, 023803 (12 pages) (2000).
[CrossRef]

O. Di Stefano, S. Savasta, and R. Girlanda, “Electromagnetic-field quantization in absorbing confined systems,” Phys. Rev. A 60, 1614–1625 (1999).
[CrossRef]

Dung, H. T.

H. T. Dung, L. Knöll, and D. G. Welsh, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A 57, 3931–3942 (1998).
[CrossRef]

Girlanda, R.

O. Di Stefano, S. Savasta, and R. Girlanda, “Mode expansion and photon operators in dispersive and absorbing dielectrics,” J. Mod. Opt. 48, 67–84 (2001).
[CrossRef]

O. Di Stefano, S. Savasta, and R. Girlanda, “Three-dimensional electromagnetic field quantization in absorbing and dispersive bounded dielectrics,” Phys. Rev. A 61, 023803 (12 pages) (2000).
[CrossRef]

O. Di Stefano, S. Savasta, and R. Girlanda, “Electromagnetic-field quantization in absorbing confined systems,” Phys. Rev. A 60, 1614–1625 (1999).
[CrossRef]

Gruner, T.

T. Gruner and D. G. Welsch, “Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates,” Phys. Rev. A 54, 1661–1677 (1996).
[CrossRef] [PubMed]

T. Gruner and D. G. Welsh, “Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 53, 1818–1829 (1996).
[CrossRef] [PubMed]

Henry, C. H.

C. H. Henry and F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
[CrossRef]

Huttner, B.

B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46, 4306–4322 (1992).
[CrossRef] [PubMed]

S. M. Barnett, B. Huttner, and R. Loudon, “Spontaneous emission in absorbing dielectric media,” Phys. Rev. Lett. 68, 3698–3701 (1992).
[CrossRef] [PubMed]

Jeffers, J.

R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, “Electromagnetic field quantization in absorbing dielectrics,” Phys. Rev. A 52, 4823–4838 (1995).
[CrossRef] [PubMed]

Kazarinov, F.

C. H. Henry and F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
[CrossRef]

Knöll, L.

A. Tip, L. Knöll, S. Scheel, and D.-G. Welsch, “Equivalence of the Langevin and auxiliary-field quantization methods for absorbing dielectrics,” Phys. Rev. A 63, 043806 (7 pages) (2001).
[CrossRef]

S. Scheel, L. Knöll, D.-G. Welsch, and S. M. Barnett, “Quantum local-field corrections and spontaneous decay,” Phys. Rev. A 60, 1590–1597 (1999).
[CrossRef]

L. Knöll, E. Schmidt, D.-G. Welsh, and A. V. Chizhov, “Quantum-state transformation by dispersive and absorbing four-port devices,” Phys. Rev. A 59, 4716–4726 (1999).
[CrossRef]

H. T. Dung, L. Knöll, and D. G. Welsh, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A 57, 3931–3942 (1998).
[CrossRef]

S. Scheel, L. Knöll, and D.-G. Welsch, “QED commutation relations for inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 58, 700–706 (1998).
[CrossRef]

E. Schmidt, L. Knöll, and D.-G. Welsch, “Propagation of squeezed-light pulses in dispersive and absorbing linear dielectrics,” Phys. Rev. A 54, 843–855 (1996).
[CrossRef] [PubMed]

L. Knöll and U. Leonhardt, “Quantum optics in oscillator media,” J. Mod. Opt. 39, 1253 (1992).
[CrossRef]

Kupiszewska, D.

D. Kupiszewska, “Casimir effect in absorbing media,” Phys. Rev. A 46, 2286–2294 (1992).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, “Influence of a dispersive and dissipative medium on spectral squeezing,” J. Mod. Opt. 40, 1123–1130 (1993).
[CrossRef]

L. Knöll and U. Leonhardt, “Quantum optics in oscillator media,” J. Mod. Opt. 39, 1253 (1992).
[CrossRef]

Loudon, R.

M. Artoni and R. Loudon, “Propagation of nonclassical light through an absorbing and dispersive slab,” Phys. Rev. A 59, 2279–2290 (1999).
[CrossRef]

M. Artoni and R. Loudon, “Quantum theory of optical pulse propagation through an absorbing and dispersive slab,” Phys. Rev. A 55, 1347–1357 (1997).
[CrossRef]

R. Matloob and R. Loudon, “Electromagnetic field quantization in absorbing dielectrics. II,” Phys. Rev. A 53, 4567–4582 (1996).
[CrossRef] [PubMed]

R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, “Electromagnetic field quantization in absorbing dielectrics,” Phys. Rev. A 52, 4823–4838 (1995).
[CrossRef] [PubMed]

S. M. Barnett, B. Huttner, and R. Loudon, “Spontaneous emission in absorbing dielectric media,” Phys. Rev. Lett. 68, 3698–3701 (1992).
[CrossRef] [PubMed]

Maradudin, A. A.

D. L. Mills and A. A. Maradudin, “Surface roughness and the optical properties of a semi-infinite material: the effect of a dielectric overlayer,” Phys. Rev. B 12, 2943–2958 (1975).
[CrossRef]

Matloob, R.

R. Matloob and R. Loudon, “Electromagnetic field quantization in absorbing dielectrics. II,” Phys. Rev. A 53, 4567–4582 (1996).
[CrossRef] [PubMed]

R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, “Electromagnetic field quantization in absorbing dielectrics,” Phys. Rev. A 52, 4823–4838 (1995).
[CrossRef] [PubMed]

Mills, D. L.

D. L. Mills and A. A. Maradudin, “Surface roughness and the optical properties of a semi-infinite material: the effect of a dielectric overlayer,” Phys. Rev. B 12, 2943–2958 (1975).
[CrossRef]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities of radio frequencies,” Phys. Rev. 69, 681 (1946).

Savasta, S.

O. Di Stefano, S. Savasta, and R. Girlanda, “Mode expansion and photon operators in dispersive and absorbing dielectrics,” J. Mod. Opt. 48, 67–84 (2001).
[CrossRef]

O. Di Stefano, S. Savasta, and R. Girlanda, “Three-dimensional electromagnetic field quantization in absorbing and dispersive bounded dielectrics,” Phys. Rev. A 61, 023803 (12 pages) (2000).
[CrossRef]

O. Di Stefano, S. Savasta, and R. Girlanda, “Electromagnetic-field quantization in absorbing confined systems,” Phys. Rev. A 60, 1614–1625 (1999).
[CrossRef]

Scheel, S.

A. Tip, L. Knöll, S. Scheel, and D.-G. Welsch, “Equivalence of the Langevin and auxiliary-field quantization methods for absorbing dielectrics,” Phys. Rev. A 63, 043806 (7 pages) (2001).
[CrossRef]

S. Scheel, L. Knöll, D.-G. Welsch, and S. M. Barnett, “Quantum local-field corrections and spontaneous decay,” Phys. Rev. A 60, 1590–1597 (1999).
[CrossRef]

S. Scheel, L. Knöll, and D.-G. Welsch, “QED commutation relations for inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 58, 700–706 (1998).
[CrossRef]

Schmidt, E.

L. Knöll, E. Schmidt, D.-G. Welsh, and A. V. Chizhov, “Quantum-state transformation by dispersive and absorbing four-port devices,” Phys. Rev. A 59, 4716–4726 (1999).
[CrossRef]

E. Schmidt, L. Knöll, and D.-G. Welsch, “Propagation of squeezed-light pulses in dispersive and absorbing linear dielectrics,” Phys. Rev. A 54, 843–855 (1996).
[CrossRef] [PubMed]

Sipe, J. E.

Tip, A.

A. Tip, L. Knöll, S. Scheel, and D.-G. Welsch, “Equivalence of the Langevin and auxiliary-field quantization methods for absorbing dielectrics,” Phys. Rev. A 63, 043806 (7 pages) (2001).
[CrossRef]

A. Tip, “Linear absorptive dielectrics,” Phys. Rev. A 57, 4818–4841 (1998).
[CrossRef]

Tomaš, M. S.

M. S. Tomaš, “Green function for multilayers: Light scattering in planar cavities,” Phys. Rev. A 51, 2545–2559 (1995).
[CrossRef] [PubMed]

Welsch, D. G.

T. Gruner and D. G. Welsch, “Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates,” Phys. Rev. A 54, 1661–1677 (1996).
[CrossRef] [PubMed]

Welsch, D.-G.

A. Tip, L. Knöll, S. Scheel, and D.-G. Welsch, “Equivalence of the Langevin and auxiliary-field quantization methods for absorbing dielectrics,” Phys. Rev. A 63, 043806 (7 pages) (2001).
[CrossRef]

S. Scheel, L. Knöll, D.-G. Welsch, and S. M. Barnett, “Quantum local-field corrections and spontaneous decay,” Phys. Rev. A 60, 1590–1597 (1999).
[CrossRef]

S. Scheel, L. Knöll, and D.-G. Welsch, “QED commutation relations for inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 58, 700–706 (1998).
[CrossRef]

E. Schmidt, L. Knöll, and D.-G. Welsch, “Propagation of squeezed-light pulses in dispersive and absorbing linear dielectrics,” Phys. Rev. A 54, 843–855 (1996).
[CrossRef] [PubMed]

Welsh, D. G.

H. T. Dung, L. Knöll, and D. G. Welsh, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A 57, 3931–3942 (1998).
[CrossRef]

T. Gruner and D. G. Welsh, “Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 53, 1818–1829 (1996).
[CrossRef] [PubMed]

Welsh, D.-G.

L. Knöll, E. Schmidt, D.-G. Welsh, and A. V. Chizhov, “Quantum-state transformation by dispersive and absorbing four-port devices,” Phys. Rev. A 59, 4716–4726 (1999).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

J. Mod. Opt. (3)

L. Knöll and U. Leonhardt, “Quantum optics in oscillator media,” J. Mod. Opt. 39, 1253 (1992).
[CrossRef]

U. Leonhardt, “Influence of a dispersive and dissipative medium on spectral squeezing,” J. Mod. Opt. 40, 1123–1130 (1993).
[CrossRef]

O. Di Stefano, S. Savasta, and R. Girlanda, “Mode expansion and photon operators in dispersive and absorbing dielectrics,” J. Mod. Opt. 48, 67–84 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities of radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (18)

M. Artoni and R. Loudon, “Propagation of nonclassical light through an absorbing and dispersive slab,” Phys. Rev. A 59, 2279–2290 (1999).
[CrossRef]

E. Schmidt, L. Knöll, and D.-G. Welsch, “Propagation of squeezed-light pulses in dispersive and absorbing linear dielectrics,” Phys. Rev. A 54, 843–855 (1996).
[CrossRef] [PubMed]

L. Knöll, E. Schmidt, D.-G. Welsh, and A. V. Chizhov, “Quantum-state transformation by dispersive and absorbing four-port devices,” Phys. Rev. A 59, 4716–4726 (1999).
[CrossRef]

D. Kupiszewska, “Casimir effect in absorbing media,” Phys. Rev. A 46, 2286–2294 (1992).
[CrossRef] [PubMed]

M. Artoni and R. Loudon, “Quantum theory of optical pulse propagation through an absorbing and dispersive slab,” Phys. Rev. A 55, 1347–1357 (1997).
[CrossRef]

T. Gruner and D. G. Welsch, “Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates,” Phys. Rev. A 54, 1661–1677 (1996).
[CrossRef] [PubMed]

R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, “Electromagnetic field quantization in absorbing dielectrics,” Phys. Rev. A 52, 4823–4838 (1995).
[CrossRef] [PubMed]

R. Matloob and R. Loudon, “Electromagnetic field quantization in absorbing dielectrics. II,” Phys. Rev. A 53, 4567–4582 (1996).
[CrossRef] [PubMed]

T. Gruner and D. G. Welsh, “Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 53, 1818–1829 (1996).
[CrossRef] [PubMed]

B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46, 4306–4322 (1992).
[CrossRef] [PubMed]

S. Scheel, L. Knöll, D.-G. Welsch, and S. M. Barnett, “Quantum local-field corrections and spontaneous decay,” Phys. Rev. A 60, 1590–1597 (1999).
[CrossRef]

M. S. Tomaš, “Green function for multilayers: Light scattering in planar cavities,” Phys. Rev. A 51, 2545–2559 (1995).
[CrossRef] [PubMed]

O. Di Stefano, S. Savasta, and R. Girlanda, “Electromagnetic-field quantization in absorbing confined systems,” Phys. Rev. A 60, 1614–1625 (1999).
[CrossRef]

H. T. Dung, L. Knöll, and D. G. Welsh, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A 57, 3931–3942 (1998).
[CrossRef]

S. Scheel, L. Knöll, and D.-G. Welsch, “QED commutation relations for inhomogeneous Kramers–Kronig dielectrics,” Phys. Rev. A 58, 700–706 (1998).
[CrossRef]

A. Tip, “Linear absorptive dielectrics,” Phys. Rev. A 57, 4818–4841 (1998).
[CrossRef]

A. Tip, L. Knöll, S. Scheel, and D.-G. Welsch, “Equivalence of the Langevin and auxiliary-field quantization methods for absorbing dielectrics,” Phys. Rev. A 63, 043806 (7 pages) (2001).
[CrossRef]

O. Di Stefano, S. Savasta, and R. Girlanda, “Three-dimensional electromagnetic field quantization in absorbing and dispersive bounded dielectrics,” Phys. Rev. A 61, 023803 (12 pages) (2000).
[CrossRef]

Phys. Rev. B (1)

D. L. Mills and A. A. Maradudin, “Surface roughness and the optical properties of a semi-infinite material: the effect of a dielectric overlayer,” Phys. Rev. B 12, 2943–2958 (1975).
[CrossRef]

Phys. Rev. Lett. (3)

G. S. Agarwal, “Coherence in spontaneous emission in the presence of a dielectric,” Phys. Rev. Lett. 32, 703–706 (1974).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. M. Barnett, B. Huttner, and R. Loudon, “Spontaneous emission in absorbing dielectric media,” Phys. Rev. Lett. 68, 3698–3701 (1992).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

C. H. Henry and F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
[CrossRef]

Other (3)

Milloni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic, San Diego, Calif., 1994).

H. A. Mcleod, Thin Film Optical Filters (Elsevier, New York, 1969).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

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Figures (2)

Fig. 1
Fig. 1

Schematic representation of the light modes in the regions external to a bounded planar dielectric structure: (a) leftward modes, (b) rightward modes.

Fig. 2
Fig. 2

Notation for the annihilation operators used in the three-dimensional quantum-optical input–output relations.

Equations (75)

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vˆ(r, t)=-  dwvˆ(r, ω)exp(-iωt).
vˆ+(r, t)=0  dωvˆ+(r, ω)exp(-iωt).
vˆ(r, ω)=1A K  exp(iK·R)vˆK(z, ω),
vˆ(r)=1V σˆ,k  exp(ik·r)e˜σ˜,kvˆσ˜,k,
×Eˆ+(r, ω)-iωBˆ+(r, ω)=0,
×Bˆ+(r, ω)-iωμ0[ε0Eˆ+(r, ω)+Pˆ+(r, ω)]=0,
·[ε0Eˆ+(r, ω)+Pˆ+(r, ω)]=0,
·Bˆ+(r, ω)=0.
Pˆ+(r, ω)=ε0χ(r, ω)Eˆ+(r, ω)+i[ε0χI(r, ω)/π]1/2f+(r, ω),
[fˆi+(r, ω), fˆj-(r, ω)]=δi,jδ(r-r)δ(ω-ω),
[fˆi±(r, ω), fˆj±(r, ω)]=0,
Pˆ+(r, ω)=ε0χ(r, ω)Eˆ+(r, ω)+i[ε0χI(r, ω)/π]1/2fˆ+(r, ω),
[fˆK,i+(z, ω),fˆK,j-(z, ω)]=δK,Kδi,jδ(z-z)δ(ω-ω),
[fˆK,i±(z, ω), fˆK,j±(z, ω)]=0
[-××+ω2c2ε(r, ω)]Eˆ(r, ω)=-iωμ0ĵ+(r, ω),
ĵ+(r, ω)=ωμ0c2 ε0πχI(r, ω)1/2fˆ(r, ω).
Eˆ+(r, ω)=iωAˆh+(r, ω)+iωμ0  d3rG(r, r)·ĵ+(r, ω),
-××+ω2c2ε(r, ω)G(r, r, ω)=1δ(r-r),
×E(r, ω)-iωB(r, ω)=0,
×B+(r, ω)-iωμ0[ε0E(r, ω)+P(r, ω)]=0
·ε0E(r, ω)+P(r, ω)]=0,
·B(r, ω)=0.
P(r, ω)=ε0χ(r, ω)E(r, ω).
E(r, ω)=σ,K  exp(iK·R)[C,σ,KUσ,K(z, ω)+C,σ,KUσ,K(z, ω),
Uσ,K(z, ω)=exp(iw0z)η¯σ,0+exp(-iw0z)rση¯σ,0(intheleftvacuum),
Uσ,K(z, ω)=tσ  exp(iw0z)η˜σ,0(intherightvacuum),
Uσ,K(z, ω)=tσ  exp(-iw0z)η˜σ,0(intheleftvacuum),
Uσ,K(z, ω)=exp(-iw0z)η¯σ,0+exp(iw0z)rση˜σ,0(intherightvacuum),
μ-2rμrλ+2δλμ+w2c2δλμ(z, ω)Gμν(r, r, ω)
=δλνδ(r-r).
G(r, r, ω)=(1/A)K  exp[iK·(R-R)]GK(z, z, ω).
GK,x,x(z, z, ω)
=-1Wp,K(ω)[Ux,K(z, ω)Ux,K(z, ω)Θ(z-z)+Ux,K(z, ω)Ux,K(z, ω)Θ(z-z)],
GK,z,x(z, z, ω)
=-1Wp,K(ω)[Uz,K(z, ω)Ux,K(z, ω)Θ(z-z)+Uz,K(z, ω)Ux,K(z, ω)Θ(z-z)],
GK,x,z(z, z, ω)
=1Wp,K(ω)[Ux,K(z, ω)Uz,K(z, ω)Θ(z-z)+Uz,K(z, ω)Uz,K(z, ω)Θ(z-z)],
GK,z,z(z, z, ω)
=1Wp,K(ω)[Uz,K(z, ω)Uz,K(z, ω)Θ(z-z)+Uz,K(z, ω)Uz,K(z, ω)Θ(z-z)]+c2δ(z-z)ω2(z, ω),
GK,y,y(z, z, ω)
=1Ws,K(ω)[Uy,K(z, ω)Uy,K(z, ω)Θ(z-z)+Uy,K(z, ω)Uy,K(z, ω)Θ(z-z)],
UK,xi/(z, ω)=σ  Uσ,K/(z, ω)·xˆi.
Ws,K(ω)=Wyy,K(ω),
Wp,K(ω)=Wzz,K(ω)-Wxx,K(ω),
Wjj,K(ω)=Uj,K(z, ω) zUj,K(z, ω)-Uj,K(z, ω) zUj,K(z, ω).
Eˆ+(r, ω)=iωAˆh+(r, ω)+iωμ0d3rG(r, r)·ĵ(r, ω).
Aˆh+(r, ω)=σ,K  exp(iK·R)[Cˆσ,K(ω)Uσ,K(z, ω)+Cˆσ,K(ω)Uσ,K(z, ω).
iω[Cˆs,K(ω)exp(iw1z)s˜+Cˆp,K(ω)exp(iw1z)p˜1+].
Cˆs(p),K/(ω)=αK(ω)aˆs(p),K/(ω),
[aˆσ,Kτ(ω),aˆσ,Kτ(ω)]=δK,Kδσ,σδτ,τδ(ω-ω),
[aˆσ,Kτ(ω),aˆσ,Kτ(ω)]=0.
Eˆ(r, t)=Eˆ+(r, t)+Eˆ-(r, t),
Eˆ+(r, t)=0  dω exp(-iωt)Eˆ+(r, ω)
Eˆ+(r, ω)=1A K  exp(iK·R)EˆK+(z, ω),
EˆK+(z, ω)=iωαK(ω)τ,σ  Uσ,Kτ(z, ω)aˆσ,Kτ+iωμ0  -  dzGK(z, z, ω)·ĵK(z, ω).
EˆK+(z, ω)=iωαK(ω)[aˆs,K(ω)s˜  exp(iw1z)+bˆs,K(ω)s˜  exp(-iw1z)+aˆp,K(ω)p˜1+  exp(iw1z)+bˆp,K(ω)p˜1-  exp(-iw1z)],
bˆσ,K(ω)=rσaˆσ,K(ω)+tσaˆσ,K(ω)+FK,σ(ω),
FK,στ(ω)=μ02iw0αK(ω) -  dzU˜σ,Kτ(z, ω)·ĵK(z, ω).
[FK, στ(ω), FKτ,(ω)]=δ(ω-ω)×δK,Kδσ,σ(1-|rστ|2-|tσ|2).
EˆK+(z, ω)=iωαK(ω)[aˆs,K(ω)s˜  exp(-iw0z)+bˆs,K(ω)s˜  exp(iw0z)+aˆp,K(ω)p˜1-  exp(-iw0z)+bˆp,K(ω)p˜1+  exp(iw0z)],
bˆσ,K(ω)=rσaˆσ,K(ω)+tσaˆσ,K(ω)+FK,σ(ω).
EK+(z, ω)=iωμ0  c2ω2(z, ω)jˆz(z, ω)z˜+iωαK(ω)[Uσ,K(z, ω)cσ,K(z, ω)+Uσ,K(z, ω)cσ,K(z, ω)],
cσ,K(z, ω)=aσ,K(ω)+μ0Wσ,KαK -z  U˜σ,K(z, ω)·ĵK+(z, ω),
cσ,K(z, ω)=aσ,K(ω)+μ0Wσ,KαK z+  U˜σ,K(z, ω)·ĵK+(z, ω),
[bˆσ,Kτ(ω),bˆσ,Kτ,(ω)]=δK,Kδσ,σδτ,τδ(ω-ω),
[bˆσ,Kτ(ω),bˆσ,Kτ(ω)]=0.
[bˆσ,K(ω),bˆσ,K,(ω)]=δ(ω-ω)δK,Kδσ,σ×[|rσ|2+|tσ|2+AK(ω),
[bˆσ,K(ω),bˆσ,K,(ω)]=δ(ω-ω)δK,Kδσ,σ×[|rσ|2+|tσ|2+AK(ω),
[bˆσ,K(ω),bˆσ,K,(ω)=δ(ω-ω)δK,Kδσ,σ×[rσtσ*+rσ*tσ+AK(ω),
AKτ,τ(ω)
=ω2w1c2 j  -dzI(z, ω)Uj,Kτ(z, ω)Uj,Kτ*(z, ω).
ω2c2 -LL  dzI(z, ω)UK,iτ(z, ω)UK,jτ*(z, ω)
=i2[UK,jτ*(z, ω) zUK,στ(z, ω)-UK,iτ(z, ω) zUK,jτ*(z, ω)]-LL,
[bˆσ,K(ω), aˆσ,K(ω)]=[bˆσ,K(ω),aˆσ,K(ω)]=tσδK,Kδσ,σδ(ω-ω),
[bˆσ,K(,)(ω), aˆσ,K,(ω)]=rσ/δK,Kδσ,σδ(ω-ω).

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