Abstract

The local-field correction experienced by an interstitial impurity in a crystal with cubic symmetry is derived by use of a rigorous, self-consistent, semimicroscopic description of spontaneous emission in a microcavity. We compute the local-field factor for various positions of the impurity inside the crystal. Furthermore, we demonstrate that the local-field factor can be computed from a simple electrostatic model as a rapidly converging lattice sum. We show that the agreement between the predictions of this simple model and the rigorous calculations is remarkable, opening the way to a simple, general theory of a local-field effect for an impurity in a crystal with arbitrary symmetry.

© 2002 Optical Society of America

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References

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  1. A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 0238-19 (2001).
    [CrossRef]
  2. G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
    [CrossRef]
  3. G. S. Agarwal, Phys. Rev. A 12, 1475 (1975).
    [CrossRef]
  4. E. M. Purcell and C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
    [CrossRef]
  5. B. T. Draine, Astrophys. J. 333, 848 (1988).
    [CrossRef]
  6. B. T. Draine and P. J. Flatau, J. Opt. Soc. Am. A 11, 1491 (1994), and references therein.
    [CrossRef]
  7. P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
    [CrossRef]
  8. P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 61, 141-19 (2000).
    [CrossRef]
  9. P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 62, 111-85 (2000).
    [CrossRef]
  10. P. C. Chaumet and M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000).
    [CrossRef]
  11. P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 0354-22 (2001).
    [CrossRef]
  12. A. Liu, A. Rahmani, G. W. Bryant, L. Richter, and S. Stranick, J. Opt. Soc. Am. A 18, 704 (2001).
    [CrossRef]
  13. A. Rahmani and G. W. Bryant, “Spontaneous emission in microcavity electrodynamics,” Phys. Rev. A (to be published).
  14. A. Rahmani and G. W. Bryant, Phys. Status Solidi B 224, 807 (2001).
    [CrossRef]
  15. H. Chew, J. Chem. Phys. 87, 1355 (1987).
  16. H. Chew, Phys. Rev. A 38, 3410 (1988).
    [CrossRef] [PubMed]
  17. B. R. A. Nijboer and F. W. De Wette, Physica 24, 422 (1958).
    [CrossRef]
  18. A. Rahmani and G. W. Bryant, Opt. Lett. 25, 433 (2000).
    [CrossRef]
  19. F. W. De Wette and G. E. Schacher, Phys. Rev. 137, A78 (1965).
    [CrossRef]

2001 (4)

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 0238-19 (2001).
[CrossRef]

A. Rahmani and G. W. Bryant, Phys. Status Solidi B 224, 807 (2001).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 0354-22 (2001).
[CrossRef]

A. Liu, A. Rahmani, G. W. Bryant, L. Richter, and S. Stranick, J. Opt. Soc. Am. A 18, 704 (2001).
[CrossRef]

2000 (4)

P. C. Chaumet and M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000).
[CrossRef]

A. Rahmani and G. W. Bryant, Opt. Lett. 25, 433 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 61, 141-19 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 62, 111-85 (2000).
[CrossRef]

1998 (1)

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

1994 (1)

1988 (2)

H. Chew, Phys. Rev. A 38, 3410 (1988).
[CrossRef] [PubMed]

B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

1987 (1)

H. Chew, J. Chem. Phys. 87, 1355 (1987).

1975 (2)

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

G. S. Agarwal, Phys. Rev. A 12, 1475 (1975).
[CrossRef]

1973 (1)

E. M. Purcell and C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[CrossRef]

1965 (1)

F. W. De Wette and G. E. Schacher, Phys. Rev. 137, A78 (1965).
[CrossRef]

1958 (1)

B. R. A. Nijboer and F. W. De Wette, Physica 24, 422 (1958).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. A 12, 1475 (1975).
[CrossRef]

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

Bryant, G. W.

A. Rahmani and G. W. Bryant, Phys. Status Solidi B 224, 807 (2001).
[CrossRef]

A. Liu, A. Rahmani, G. W. Bryant, L. Richter, and S. Stranick, J. Opt. Soc. Am. A 18, 704 (2001).
[CrossRef]

A. Rahmani and G. W. Bryant, Opt. Lett. 25, 433 (2000).
[CrossRef]

A. Rahmani and G. W. Bryant, “Spontaneous emission in microcavity electrodynamics,” Phys. Rev. A (to be published).

Chaumet, P. C.

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 0354-22 (2001).
[CrossRef]

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 0238-19 (2001).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 61, 141-19 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 62, 111-85 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000).
[CrossRef]

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

Chew, H.

H. Chew, Phys. Rev. A 38, 3410 (1988).
[CrossRef] [PubMed]

H. Chew, J. Chem. Phys. 87, 1355 (1987).

de Fornel, F.

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 0238-19 (2001).
[CrossRef]

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

De Wette, F. W.

F. W. De Wette and G. E. Schacher, Phys. Rev. 137, A78 (1965).
[CrossRef]

B. R. A. Nijboer and F. W. De Wette, Physica 24, 422 (1958).
[CrossRef]

Draine, B. T.

Dufour, J.-P.

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

Flatau, P. J.

Liu, A.

Nieto-Vesperinas, M.

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 0354-22 (2001).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 62, 111-85 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 61, 141-19 (2000).
[CrossRef]

Nijboer, B. R. A.

B. R. A. Nijboer and F. W. De Wette, Physica 24, 422 (1958).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[CrossRef]

Rahmani, A.

A. Rahmani and G. W. Bryant, Phys. Status Solidi B 224, 807 (2001).
[CrossRef]

A. Liu, A. Rahmani, G. W. Bryant, L. Richter, and S. Stranick, J. Opt. Soc. Am. A 18, 704 (2001).
[CrossRef]

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 0238-19 (2001).
[CrossRef]

A. Rahmani and G. W. Bryant, Opt. Lett. 25, 433 (2000).
[CrossRef]

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

A. Rahmani and G. W. Bryant, “Spontaneous emission in microcavity electrodynamics,” Phys. Rev. A (to be published).

Richter, L.

Schacher, G. E.

F. W. De Wette and G. E. Schacher, Phys. Rev. 137, A78 (1965).
[CrossRef]

Stranick, S.

Astrophys. J. (2)

E. M. Purcell and C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[CrossRef]

B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

J. Chem. Phys. (1)

H. Chew, J. Chem. Phys. 87, 1355 (1987).

J. Opt. Soc. Am. A (2)

Opt. Lett. (2)

Phys. Rev. (1)

F. W. De Wette and G. E. Schacher, Phys. Rev. 137, A78 (1965).
[CrossRef]

Phys. Rev. A (4)

H. Chew, Phys. Rev. A 38, 3410 (1988).
[CrossRef] [PubMed]

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 0238-19 (2001).
[CrossRef]

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

G. S. Agarwal, Phys. Rev. A 12, 1475 (1975).
[CrossRef]

Phys. Rev. B (4)

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 61, 141-19 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 62, 111-85 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 0354-22 (2001).
[CrossRef]

Phys. Status Solidi B (1)

A. Rahmani and G. W. Bryant, Phys. Status Solidi B 224, 807 (2001).
[CrossRef]

Physica (1)

B. R. A. Nijboer and F. W. De Wette, Physica 24, 422 (1958).
[CrossRef]

Other (1)

A. Rahmani and G. W. Bryant, “Spontaneous emission in microcavity electrodynamics,” Phys. Rev. A (to be published).

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Figures (3)

Fig. 1
Fig. 1

Absolute value of the local-field factor versus permittivity for an interstitial source: symbols, self-consistent CDM calculation; dashed curves, results from Table 1 [Eq. (13)]. The numbers in parentheses give the a,b,c coordinates of the source in the lattice. The transition moment of the source defines the z direction.

Fig. 2
Fig. 2

Same as Fig. 1 but at different locations in the lattice.

Fig. 3
Fig. 3

Same as Fig. 1 but here we have computed the solid curves by using the generalized local-field factor [Eq. (12)].

Tables (1)

Tables Icon

Table 1 Dipole Sum and Local-Field Factor at Various Locations in the Lattice

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

ΓσΓ0=1+22k03ImFσσr0,r0;ω,
Γ=L2Γcav+δΓ,
Eloc=Eext+Edip.
Edipr=iF0r,ri;0αd3Ediplocri,
Edip=αd3AEdiploc.
P=αd3Ediploc=-14πEmacro,
ηEmacro=Eext,
η=10001000,
Eloc=ηEmacro+-14πAEmacro.
Eloc=ΛEmacro.
Λ=-14πA+η.
Li=j=13Λij21/2.
LLz=-14πAzz+,
Azz=m=-3m+c2S5/2-S3/2,
Sn=k,l=-k+a2+l+b2+m+c2-n.

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