Abstract

Modification of dipole emission that is due to its optical environment is calculated for planar layered structures. The layers are optically described by standard matrix techniques, and the dipole is included by using additive source terms for the electric field that depend on dipole orientation and wave polarization. These source terms also allow coupling through evanescent waves. We emphasize the applicability of this method to cases in which the power distribution into various modes is affected: dipole emission into guided modes and emission distribution into the various modes of structures that contain multilayer reflectors, such as microcavities.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
  2. J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
    [CrossRef]
  3. H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
    [CrossRef]
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    [CrossRef]
  20. Y. Yamamoto, S. Machida, K. Igeta, G. Björk, “Controlled spontaneous emission in microcavity semiconductor lasers,” in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), p. 561.
  21. Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solutions of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
    [CrossRef] [PubMed]
  22. H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye,” Appl. Phys. Lett. 58, 2598–2600 (1991).
    [CrossRef]
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    [CrossRef] [PubMed]
  27. P. Wittke, “Spontaneous emission rate alteration by dielectric and other waveguiding structures,” RCA Rev. 36, 655–660 (1975).
  28. S. T. Ho, D. Y. Chu, J.-P. Zhang, S. Wu, M. Chin, “Dielectric photonic wells and wires and spontaneous coupling efficiency of microdisk and photonic-wire semiconductor lasers,” in Optical Processes in Microcavities, Advanced Series in Applied Physics, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), p. 339.
    [CrossRef]
  29. W. N. Carr, “Photometric figures of merit for semiconductor luminescent sources operating in spontaneous mode,” in Semiconductor Devices Pioneering Papers, S. M. Sze, ed. (World Scientific, Singapore, 1991), pp. 919–937.
  30. R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, “Impurity modes in one-dimensional periodic-systems: the transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
    [CrossRef] [PubMed]

1997 (2)

1995 (2)

J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
[CrossRef]

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
[CrossRef]

1993 (2)

G. Björk, H. Heitmann, Y. Yamamoto, “Spontaneous-emission coupling factor and mode characteristics of planar dielectric microcavity lasers,” Phys. Rev. A 47, 4451–4463 (1993).
[CrossRef] [PubMed]

R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, “Impurity modes in one-dimensional periodic-systems: the transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

1991 (4)

D. G. Deppe, C. Lei, “Spontaneous emission from a dipole in a semiconductor microcavity,” J. Appl. Phys. 70, 3443–3448 (1991).
[CrossRef]

K. Ujihara, “Spontaneous emission and the concept of effective area in a very short optical cavity with plane parallel dielectric mirrors,” Jpn. J. Appl. Phys., Part 1 30, L901–L904 (1991).
[CrossRef]

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

1990 (1)

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solutions of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

1984 (1)

G. W. Ford, W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

1981 (1)

1980 (3)

W. Lukosz, “Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin layers,” Phys. Rev. B 22, 3030–3038 (1980).
[CrossRef]

R. E. Kunz, W. Lukosz, “Changes in fluorescence lifetime induced by variable optical environments,” Phys. Rev. B 21, 4814–4828 (1980).
[CrossRef]

W. H. Weber, G. W. Ford, “Enhanced Raman scattering by adsorbates including the nonlocal response of the metal and the excitation of nonradiative modes,” Phys. Rev. Lett. 44, 1774–1777 (1980).
[CrossRef]

1979 (1)

1977 (2)

1975 (1)

P. Wittke, “Spontaneous emission rate alteration by dielectric and other waveguiding structures,” RCA Rev. 36, 655–660 (1975).

1974 (1)

R. R. Chance, A. Prock, R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

Baets, R.

J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
[CrossRef]

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
[CrossRef]

Björk, G.

G. Björk, H. Heitmann, Y. Yamamoto, “Spontaneous-emission coupling factor and mode characteristics of planar dielectric microcavity lasers,” Phys. Rev. A 47, 4451–4463 (1993).
[CrossRef] [PubMed]

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, K. Igeta, G. Björk, “Controlled spontaneous emission in microcavity semiconductor lasers,” in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), p. 561.

Blondelle, J.

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
[CrossRef]

J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
[CrossRef]

Borghs, G.

J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
[CrossRef]

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Carr, W. N.

W. N. Carr, “Photometric figures of merit for semiconductor luminescent sources operating in spontaneous mode,” in Semiconductor Devices Pioneering Papers, S. M. Sze, ed. (World Scientific, Singapore, 1991), pp. 919–937.

Chance, R. R.

R. R. Chance, A. Prock, R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

R. R. Chance, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces?” in Advances in Chemical Physics, I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1978), pp. 1–65.

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1989).

Chin, M.

S. T. Ho, D. Y. Chu, J.-P. Zhang, S. Wu, M. Chin, “Dielectric photonic wells and wires and spontaneous coupling efficiency of microdisk and photonic-wire semiconductor lasers,” in Optical Processes in Microcavities, Advanced Series in Applied Physics, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), p. 339.
[CrossRef]

Cho, A. Y.

N. E. J. Hunt, E. F. Schubert, D. L. Sirco, A. Y. Cho, R. F. Kopf, R. A. Logan, G. L. Zydzjk, “High efficiency, narrow spectrum resonant-cavity light-emitting diodes,” in Confined Electrons and Photons, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995), pp. 703–714.

Chu, D. Y.

S. T. Ho, D. Y. Chu, J.-P. Zhang, S. Wu, M. Chin, “Dielectric photonic wells and wires and spontaneous coupling efficiency of microdisk and photonic-wire semiconductor lasers,” in Optical Processes in Microcavities, Advanced Series in Applied Physics, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), p. 339.
[CrossRef]

De Neve, H.

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
[CrossRef]

J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
[CrossRef]

Demeester, P.

J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
[CrossRef]

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
[CrossRef]

Deppe, D. G.

D. G. Deppe, C. Lei, “Spontaneous emission from a dipole in a semiconductor microcavity,” J. Appl. Phys. 70, 3443–3448 (1991).
[CrossRef]

Ford, G. W.

G. W. Ford, W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

W. H. Weber, G. W. Ford, “Enhanced Raman scattering by adsorbates including the nonlocal response of the metal and the excitation of nonradiative modes,” Phys. Rev. Lett. 44, 1774–1777 (1980).
[CrossRef]

Hall, D. G.

Heitmann, H.

G. Björk, H. Heitmann, Y. Yamamoto, “Spontaneous-emission coupling factor and mode characteristics of planar dielectric microcavity lasers,” Phys. Rev. A 47, 4451–4463 (1993).
[CrossRef] [PubMed]

Ho, S. T.

S. T. Ho, D. Y. Chu, J.-P. Zhang, S. Wu, M. Chin, “Dielectric photonic wells and wires and spontaneous coupling efficiency of microdisk and photonic-wire semiconductor lasers,” in Optical Processes in Microcavities, Advanced Series in Applied Physics, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), p. 339.
[CrossRef]

Houdré, R.

R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, “Impurity modes in one-dimensional periodic-systems: the transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

Hunt, N. E. J.

N. E. J. Hunt, E. F. Schubert, D. L. Sirco, A. Y. Cho, R. F. Kopf, R. A. Logan, G. L. Zydzjk, “High efficiency, narrow spectrum resonant-cavity light-emitting diodes,” in Confined Electrons and Photons, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995), pp. 703–714.

Igeta, K.

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, K. Igeta, G. Björk, “Controlled spontaneous emission in microcavity semiconductor lasers,” in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), p. 561.

Ilegems, M.

R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, “Impurity modes in one-dimensional periodic-systems: the transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

Kopf, R. F.

N. E. J. Hunt, E. F. Schubert, D. L. Sirco, A. Y. Cho, R. F. Kopf, R. A. Logan, G. L. Zydzjk, “High efficiency, narrow spectrum resonant-cavity light-emitting diodes,” in Confined Electrons and Photons, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995), pp. 703–714.

Kunz, R. E.

Lei, C.

D. G. Deppe, C. Lei, “Spontaneous emission from a dipole in a semiconductor microcavity,” J. Appl. Phys. 70, 3443–3448 (1991).
[CrossRef]

Logan, R. A.

N. E. J. Hunt, E. F. Schubert, D. L. Sirco, A. Y. Cho, R. F. Kopf, R. A. Logan, G. L. Zydzjk, “High efficiency, narrow spectrum resonant-cavity light-emitting diodes,” in Confined Electrons and Photons, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995), pp. 703–714.

Lukosz, W.

Machida, S.

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, K. Igeta, G. Björk, “Controlled spontaneous emission in microcavity semiconductor lasers,” in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), p. 561.

Nambu, Y.

H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Oesterle, U.

R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, “Impurity modes in one-dimensional periodic-systems: the transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

Prock, A.

R. R. Chance, A. Prock, R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

R. R. Chance, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces?” in Advances in Chemical Physics, I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1978), pp. 1–65.

Satpathy, S.

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solutions of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

Schubert, E. F.

N. E. J. Hunt, E. F. Schubert, D. L. Sirco, A. Y. Cho, R. F. Kopf, R. A. Logan, G. L. Zydzjk, “High efficiency, narrow spectrum resonant-cavity light-emitting diodes,” in Confined Electrons and Photons, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995), pp. 703–714.

Silbey, R.

R. R. Chance, A. Prock, R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

R. R. Chance, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces?” in Advances in Chemical Physics, I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1978), pp. 1–65.

Sirco, D. L.

N. E. J. Hunt, E. F. Schubert, D. L. Sirco, A. Y. Cho, R. F. Kopf, R. A. Logan, G. L. Zydzjk, “High efficiency, narrow spectrum resonant-cavity light-emitting diodes,” in Confined Electrons and Photons, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995), pp. 703–714.

Stanley, R. P.

R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, “Impurity modes in one-dimensional periodic-systems: the transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

Sullivan, K. G.

Suzuki, M.

H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Ujihara, K.

K. Ujihara, “Spontaneous emission and the concept of effective area in a very short optical cavity with plane parallel dielectric mirrors,” Jpn. J. Appl. Phys., Part 1 30, L901–L904 (1991).
[CrossRef]

Vandaele, P.

J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
[CrossRef]

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
[CrossRef]

Weber, W. H.

G. W. Ford, W. H. Weber, “Electromagnetic interaction of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

W. H. Weber, G. W. Ford, “Enhanced Raman scattering by adsorbates including the nonlocal response of the metal and the excitation of nonradiative modes,” Phys. Rev. Lett. 44, 1774–1777 (1980).
[CrossRef]

Wittke, P.

P. Wittke, “Spontaneous emission rate alteration by dielectric and other waveguiding structures,” RCA Rev. 36, 655–660 (1975).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Wu, S.

S. T. Ho, D. Y. Chu, J.-P. Zhang, S. Wu, M. Chin, “Dielectric photonic wells and wires and spontaneous coupling efficiency of microdisk and photonic-wire semiconductor lasers,” in Optical Processes in Microcavities, Advanced Series in Applied Physics, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), p. 339.
[CrossRef]

Yamamoto, Y.

G. Björk, H. Heitmann, Y. Yamamoto, “Spontaneous-emission coupling factor and mode characteristics of planar dielectric microcavity lasers,” Phys. Rev. A 47, 4451–4463 (1993).
[CrossRef] [PubMed]

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, K. Igeta, G. Björk, “Controlled spontaneous emission in microcavity semiconductor lasers,” in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), p. 561.

Yeh, P.

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

Yokoyama, H.

H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Zhang, J.-P.

S. T. Ho, D. Y. Chu, J.-P. Zhang, S. Wu, M. Chin, “Dielectric photonic wells and wires and spontaneous coupling efficiency of microdisk and photonic-wire semiconductor lasers,” in Optical Processes in Microcavities, Advanced Series in Applied Physics, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), p. 339.
[CrossRef]

Zhang, Z.

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solutions of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

Zydzjk, G. L.

N. E. J. Hunt, E. F. Schubert, D. L. Sirco, A. Y. Cho, R. F. Kopf, R. A. Logan, G. L. Zydzjk, “High efficiency, narrow spectrum resonant-cavity light-emitting diodes,” in Confined Electrons and Photons, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995), pp. 703–714.

Appl. Phys. Lett. (1)

H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Electron. Lett. (1)

J. Blondelle, H. De Neve, P. Demeester, P. Vandaele, G. Borghs, R. Baets, “16% external quantum efficiency from planar microcavity LEDs at 940 nm by precise matching of cavity wavelength,” Electron. Lett. 31, 1286–1287 (1995).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

H. De Neve, J. Blondelle, R. Baets, P. Demeester, P. Vandaele, G. Borghs, “High efficiency planar microcavity LEDs: comparison of design and experiments,” IEEE Photonics Technol. Lett. 7, 287–289 (1995).
[CrossRef]

J. Appl. Phys. (1)

D. G. Deppe, C. Lei, “Spontaneous emission from a dipole in a semiconductor microcavity,” J. Appl. Phys. 70, 3443–3448 (1991).
[CrossRef]

J. Chem. Phys. (1)

R. R. Chance, A. Prock, R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Bare emission pattern of (a) a vertical dipole in p (TM) modes, (b) a horizontal dipole in p (TM) modes, and (c) a horizontal dipole in s (TE) modes. The right inset sketches the azimuthal average for horizontal dipoles.

Fig. 2
Fig. 2

Sketch of a layered structure with a source plane inside and matrices describing the propagation of electric fields from the outside to the source. Only outgoing fields do not vanish if fields come only from the source.

Fig. 3
Fig. 3

(a) Power flux and the Poynting vector crossing a surface, (b) differential solid angle transfer from one layer to another.

Fig. 4
Fig. 4

Emission pattern for radiation of a vertical dipole at distances (a) z=0, (b) z=λ/4, and (c) z=λ/2 from the interface between vacuum and a medium of index n=3 (on the right).

Fig. 5
Fig. 5

(a) Solid curve, emission pattern of a layer of horizontal dipoles located in the center of a nonabsorbing slab of index n=3 (inset) in s (TE) modes for nd/λ=2.1; the internal angles are on the left, and the diagram in air is on the right. Dashed curve, same as the solid curve, but for p (TM) modes. (b) Same as (a), but for nd/λ=1.75.

Fig. 6
Fig. 6

(a) Lower solid curve, power extracted from a layer of horizontal dipoles located in the center of a nonabsorbing slab of index n=3 in s (TE) modes as a function of the slab reduced optical thickness nd/λ; upper solid curve, power in s (TE) guided modes; dashed curve, total emitted power in s (TE) modes. (b) Extracted and guided fraction of TE emitted power.

Fig. 7
Fig. 7

Emission from (h) dipoles in an n=3.5 cavity embedded between two DBR mirrors into s (TE, thick curve) and p (TM, thin curve) waves. Emission is at the stop-band center. DBR’s consists of five periods of n=2 and n=3 index of quarter-wave optical thickness, as depicted in the inset. The source is off the 5λ/4n cavity center to couple to all modes. The outside medium is of index n=3.5 as well. Regions of emission in outside, leaky, and quasi-guided modes are outlined.

Fig. 8
Fig. 8

Cumulated fractions of the emission from (h) dipoles into the four channels that it can feed (outside modes, metal absorption, leaky modes, guided modes) for the cavity pictured in the inset as a function of its reduced optical thickness nd/λ. The cavity and the substrate are of index n=3, as is the DBR high index; the DBR low index is n=2. There are five pairs. The source is located within a very small distance of the DBR.

Tables (1)

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Table 1 Source Terms for Horizontal and Vertical Dipoles

Equations (21)

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(E>)-(E<)=(sourceterms),
kz,j2+k2=ω2c2nj2.
γj2+neff2=nj2,
dPdΩ(v)=38πsin2 θ1,
dPdΩ(h),s=316π,dPdΩ(h),p=316πcos2 θ1.
A,(v),p=38π sin θ1=38πkk1,A,(v),s=0,
A,(h),s=±316π,
A,(h),p=±316π cos θ1=±316πkz,1k1.
E(z)=Ejs,p exp[ikz,j(z-zj)]+Ejs,p exp[-ikz,j(z-zj)]EjEjs,p
1=dPdP1dΩ1dΩ.
dPdS=S·dSdS=S cos θ=n|E|2 cos θ=|E|2kz/k,
dΩ1dΩ=n2 cos θn12 cos θ1=nkzn1kz,1
dPdΩdS=dPdP1dΩ1dΩdP1dΩ1dS=kz|E|2kz,1|E1|2×nkzn1kz,1×(sourceterms),
dPdΩdS=|E|2|E1|2×(sourceterms)×nkz2n1kz,12=|Eout|2 nkz2n1kz,12.
E12(θ1)E12(θ1)-E10(θ1)E10(θ1)=A(θ1)A(θ1),
a11a21a12a220E0(θ0)=E10E10,
b11b21b12b22E2(θ2)0=E12E12.
E0=b21A-b11Aa22b11-b21a12sourcetermsΔ;
E0=t0(r2A-A)1-r0r2,E2=t2(r0A-A)1-r0r2.
P(iso)=23P(h)+13P(v).
Pextrac=0π/22π(θ)sin θ dθ

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