Abstract

We study the grating-assisted light-emitting diode, an LED design for high brightness based on a resonant cavity containing one- or two-dimensionally periodically corrugated layers (grating). We give in detail a generally applicable electromagnetic analysis based on the rigorous coupled-wave theory to calculate the extraction efficiency of spontaneous emission in a periodically corrugated layer structure. This general model is then specified on the grating-assisted resonant-cavity LED, showing simulated efficiencies of more than 40%.

© 2002 Optical Society of America

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  3. M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).
  4. I. Schnitzer, E. Yablonovitch, C. Carneau, T. J. Gmitter, A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  16. A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
    [CrossRef]
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  18. M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
    [CrossRef]
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  24. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation of stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  25. M. G. Moharam, D. A. Pommet, E. B. Grann, T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
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  26. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  27. P. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998).
    [CrossRef]
  28. D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

2001

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

M. G. Salt, P. Andrew, W. L. Barnes, “Microcavities, texture symmetry, and photonic bandgaps,” J. Opt. Soc. Am. B 18, 240–243 (2001).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

2000

M. G. Salt, W. L. Barnes, “Flat photonic bands in guided modes of textured metallic microcavities,” Phys. Rev. B 61, 11125–11135 (2000).
[CrossRef]

H. Rigneault, F. Lemarchand, A. Sentenac, “Dipole radiation into grating structures,” J. Opt. Soc. Am. A 17, 1048–1058 (2000).
[CrossRef]

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000).
[CrossRef]

1999

H. Rigneault, F. Lemarchand, A. Sentenac, H. Giovannini, “Extraction of light from source located inside waveguide grating structures,” Opt. Lett. 24, 148–150 (1999).
[CrossRef]

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
[CrossRef]

J. J. Wierer, D. A. Kellogg, N. Holonyak, “Tunnel contact junction native-oxide aperture and mirror vertical-cavity surface-emitting lasers and resonant-cavity light-emitting diodes,” Appl. Phys. Lett. 74, 926–928 (1999).
[CrossRef]

1998

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photonic bandgaps in metallic microcavities,” J. Appl. Phys. 84, 2399–2403 (1998).
[CrossRef]

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
[CrossRef]

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part II: selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

P. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998).
[CrossRef]

1997

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet–Bloch theory,” Appl. Phys. Lett. 13, 2301–2315 (1997).

1996

1995

1993

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

I. Schnitzer, E. Yablonovitch, C. Carneau, T. J. Gmitter, A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

Andrew, P.

Baets, R.

D. Delbeke, B. Dhoedt, R. Bockstaele, I. Moerman, P. Van Daele, T. F. Krauss, R. Baets, “Electrically pumped photonic crystal micro-cavity light emitting diodes,” in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 71–72.

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

Barnes, W. L.

M. G. Salt, P. Andrew, W. L. Barnes, “Microcavities, texture symmetry, and photonic bandgaps,” J. Opt. Soc. Am. B 18, 240–243 (2001).
[CrossRef]

M. G. Salt, W. L. Barnes, “Flat photonic bands in guided modes of textured metallic microcavities,” Phys. Rev. B 61, 11125–11135 (2000).
[CrossRef]

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000).
[CrossRef]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photonic bandgaps in metallic microcavities,” J. Appl. Phys. 84, 2399–2403 (1998).
[CrossRef]

Benisty, H.

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part II: selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
[CrossRef]

M. Rattier, H. Benisty, C. Weisbuch, “Photonic crystal extractor,” in Electromagnetic Crystal Structures: Proceedings of Workshop on Photonic and Electromagnetic Crystal Structures III (PECS3) (T. F. Krauss, University of St. Andrews, St. Andrews, UK, 2001).

Bhat, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
[CrossRef]

Bockstaele, R.

D. Delbeke, B. Dhoedt, R. Bockstaele, I. Moerman, P. Van Daele, T. F. Krauss, R. Baets, “Electrically pumped photonic crystal micro-cavity light emitting diodes,” in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 71–72.

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

Borghs, G.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Boroditsky, M.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
[CrossRef]

Butler, J. K.

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet–Bloch theory,” Appl. Phys. Lett. 13, 2301–2315 (1997).

Caneau, C.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

Carneau, C.

I. Schnitzer, E. Yablonovitch, C. Carneau, T. J. Gmitter, A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

Carter-Coman, C.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Chen, E.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Coccioli, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
[CrossRef]

Collins, D.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Congdon, P.

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet–Bloch theory,” Appl. Phys. Lett. 13, 2301–2315 (1997).

Craford, G. M.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

De Neve, H.

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
[CrossRef]

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part II: selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

H. De Neve, “Design and fabrication of light emitting diodes based on the microcavity effect,” Ph. D. dissertation (Ghent University, Ghent, Belgium), p. 110 (1997).

Delbeke, D.

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

D. Delbeke, B. Dhoedt, R. Bockstaele, I. Moerman, P. Van Daele, T. F. Krauss, R. Baets, “Electrically pumped photonic crystal micro-cavity light emitting diodes,” in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 71–72.

Dhoedt, B.

D. Delbeke, B. Dhoedt, R. Bockstaele, I. Moerman, P. Van Daele, T. F. Krauss, R. Baets, “Electrically pumped photonic crystal micro-cavity light emitting diodes,” in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 71–72.

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

Doehler, G. H.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Dutta, B.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Ebeling, K. J.

W. Schmid, F. Eberhard, R. Jäger, R. King, M. Miller, J. Joos, K. J. Ebeling, “45% quantum efficiency light-emitting diodes with radial outcoupling taper,” in Light-Emitting Diodes: Research, Manufacturing, and Applications IV, H. W. Yao, I. T. Ferguson, E. F. Schubert, eds., Proc. SPIE3938, 90–97 (2000).

Eberhard, F.

W. Schmid, F. Eberhard, R. Jäger, R. King, M. Miller, J. Joos, K. J. Ebeling, “45% quantum efficiency light-emitting diodes with radial outcoupling taper,” in Light-Emitting Diodes: Research, Manufacturing, and Applications IV, H. W. Yao, I. T. Ferguson, E. F. Schubert, eds., Proc. SPIE3938, 90–97 (2000).

Erchak, A. A.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Evans, G. A.

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet–Bloch theory,” Appl. Phys. Lett. 13, 2301–2315 (1997).

Fan, S.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Gardner, N. F.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Gaylord, T. K.

Gillessen, K.

K. Gillessen, W. Schairer, Light Emitting Diodes: an Introduction, (Prentice-Hall International, Cambridge, UK, 1987).

Giovannini, H.

Gmitter, T. J.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Carneau, T. J. Gmitter, A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

Grann, E. B.

Grillot, P.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Heremans, P.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Hofler, G. E.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Holcomb, M. O.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Holonyak, N.

J. J. Wierer, D. A. Kellogg, N. Holonyak, “Tunnel contact junction native-oxide aperture and mirror vertical-cavity surface-emitting lasers and resonant-cavity light-emitting diodes,” Appl. Phys. Lett. 74, 926–928 (1999).
[CrossRef]

Huang, J.-W.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Hueschen, M.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Ippen, E. P.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Jäger, R.

W. Schmid, F. Eberhard, R. Jäger, R. King, M. Miller, J. Joos, K. J. Ebeling, “45% quantum efficiency light-emitting diodes with radial outcoupling taper,” in Light-Emitting Diodes: Research, Manufacturing, and Applications IV, H. W. Yao, I. T. Ferguson, E. F. Schubert, eds., Proc. SPIE3938, 90–97 (2000).

Joannopoulos, J. D.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Joos, J.

W. Schmid, F. Eberhard, R. Jäger, R. King, M. Miller, J. Joos, K. J. Ebeling, “45% quantum efficiency light-emitting diodes with radial outcoupling taper,” in Light-Emitting Diodes: Research, Manufacturing, and Applications IV, H. W. Yao, I. T. Ferguson, E. F. Schubert, eds., Proc. SPIE3938, 90–97 (2000).

Jory, M. J.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000).
[CrossRef]

Kellogg, D. A.

J. J. Wierer, D. A. Kellogg, N. Holonyak, “Tunnel contact junction native-oxide aperture and mirror vertical-cavity surface-emitting lasers and resonant-cavity light-emitting diodes,” Appl. Phys. Lett. 74, 926–928 (1999).
[CrossRef]

Kiesel, P.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

King, R.

W. Schmid, F. Eberhard, R. Jäger, R. King, M. Miller, J. Joos, K. J. Ebeling, “45% quantum efficiency light-emitting diodes with radial outcoupling taper,” in Light-Emitting Diodes: Research, Manufacturing, and Applications IV, H. W. Yao, I. T. Ferguson, E. F. Schubert, eds., Proc. SPIE3938, 90–97 (2000).

Kish, F. A.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Kitson, S. C.

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photonic bandgaps in metallic microcavities,” J. Appl. Phys. 84, 2399–2403 (1998).
[CrossRef]

Kocot, C. P.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Kolodziejsk, L. A.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Krames, M. R.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Krauss, T. F.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
[CrossRef]

D. Delbeke, B. Dhoedt, R. Bockstaele, I. Moerman, P. Van Daele, T. F. Krauss, R. Baets, “Electrically pumped photonic crystal micro-cavity light emitting diodes,” in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 71–72.

Kuijk, M.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Lalanne, P.

P. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998).
[CrossRef]

Lemarchand, F.

Li, L.

Loewen, E. G.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Lupton, J. M.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000).
[CrossRef]

Matterson, B. J.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000).
[CrossRef]

Meinlschmidt, S.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Miller, M.

W. Schmid, F. Eberhard, R. Jäger, R. King, M. Miller, J. Joos, K. J. Ebeling, “45% quantum efficiency light-emitting diodes with radial outcoupling taper,” in Light-Emitting Diodes: Research, Manufacturing, and Applications IV, H. W. Yao, I. T. Ferguson, E. F. Schubert, eds., Proc. SPIE3938, 90–97 (2000).

Moerman, I.

D. Delbeke, B. Dhoedt, R. Bockstaele, I. Moerman, P. Van Daele, T. F. Krauss, R. Baets, “Electrically pumped photonic crystal micro-cavity light emitting diodes,” in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 71–72.

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

Moharam, M. G.

Pang, L.

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet–Bloch theory,” Appl. Phys. Lett. 13, 2301–2315 (1997).

Park, K.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Petrich, G. S.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Pommet, D. A.

Popov, E.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Posselt, J.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Rakich, P.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Rattier, M.

M. Rattier, H. Benisty, C. Weisbuch, “Photonic crystal extractor,” in Electromagnetic Crystal Structures: Proceedings of Workshop on Photonic and Electromagnetic Crystal Structures III (PECS3) (T. F. Krauss, University of St. Andrews, St. Andrews, UK, 2001).

Rigneault, H.

Ripin, D. J.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Rooman, C.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Salt, M. G.

M. G. Salt, P. Andrew, W. L. Barnes, “Microcavities, texture symmetry, and photonic bandgaps,” J. Opt. Soc. Am. B 18, 240–243 (2001).
[CrossRef]

M. G. Salt, W. L. Barnes, “Flat photonic bands in guided modes of textured metallic microcavities,” Phys. Rev. B 61, 11125–11135 (2000).
[CrossRef]

Sambles, J. R.

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photonic bandgaps in metallic microcavities,” J. Appl. Phys. 84, 2399–2403 (1998).
[CrossRef]

Samuel, I. D. W.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000).
[CrossRef]

Schairer, W.

K. Gillessen, W. Schairer, Light Emitting Diodes: an Introduction, (Prentice-Hall International, Cambridge, UK, 1987).

Scherer, A.

I. Schnitzer, E. Yablonovitch, C. Carneau, T. J. Gmitter, A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

Schmid, W.

W. Schmid, F. Eberhard, R. Jäger, R. King, M. Miller, J. Joos, K. J. Ebeling, “45% quantum efficiency light-emitting diodes with radial outcoupling taper,” in Light-Emitting Diodes: Research, Manufacturing, and Applications IV, H. W. Yao, I. T. Ferguson, E. F. Schubert, eds., Proc. SPIE3938, 90–97 (2000).

Schnitzer, I.

I. Schnitzer, E. Yablonovitch, C. Carneau, T. J. Gmitter, A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

Sentenac, A.

Stockman, S. A.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Sun, N. H.

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet–Bloch theory,” Appl. Phys. Lett. 13, 2301–2315 (1997).

Tamir, T.

Tan, I.-H.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Tan, T. S.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

Van Daele, P.

D. Delbeke, B. Dhoedt, R. Bockstaele, I. Moerman, P. Van Daele, T. F. Krauss, R. Baets, “Electrically pumped photonic crystal micro-cavity light emitting diodes,” in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 71–72.

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

Vandeputte, K.

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

Verstuyft, S.

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

Vrijen, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
[CrossRef]

Weisbuch, C.

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
[CrossRef]

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part II: selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

M. Rattier, H. Benisty, C. Weisbuch, “Photonic crystal extractor,” in Electromagnetic Crystal Structures: Proceedings of Workshop on Photonic and Electromagnetic Crystal Structures III (PECS3) (T. F. Krauss, University of St. Andrews, St. Andrews, UK, 2001).

Wierer, J. J.

J. J. Wierer, D. A. Kellogg, N. Holonyak, “Tunnel contact junction native-oxide aperture and mirror vertical-cavity surface-emitting lasers and resonant-cavity light-emitting diodes,” Appl. Phys. Lett. 74, 926–928 (1999).
[CrossRef]

Windisch, R.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Yablonovitch, E.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Carneau, T. J. Gmitter, A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

Zhang, S.

Zipperer, D.

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

Appl. Phys. Lett.

M. O. Holcomb, M. R. Krames, G. E. Hofler, C. Carter-Coman, E. Chen, P. Grillot, K. Park, N. F. Gardner, J.-W. Huang, J. Posselt, D. Collins, S. A. Stockman, G. M. Craford, F. A. Kish, I.-H. Tan, T. S. Tan, C. P. Kocot, M. Hueschen, “High power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P light-emitting diodes exhibiting >50% external quantum efficiency,” Appl. Phys. Lett. 75, 9365–9367 (1993).

I. Schnitzer, E. Yablonovitch, C. Carneau, T. J. Gmitter, A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174–2176 (1993).
[CrossRef]

R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H. Doehler, B. Dutta, M. Kuijk, G. Borghs, P. Heremans, “Impact of texture-enhanced transmission on high-effiency surface-textured light-emitting diodes,” Appl. Phys. Lett. 79, 2315–2317 (2001).
[CrossRef]

J. J. Wierer, D. A. Kellogg, N. Holonyak, “Tunnel contact junction native-oxide aperture and mirror vertical-cavity surface-emitting lasers and resonant-cavity light-emitting diodes,” Appl. Phys. Lett. 74, 926–928 (1999).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000).
[CrossRef]

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystal,” Appl. Phys. Lett. 75, 1036–1038 (1999).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejsk, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

N. H. Sun, J. K. Butler, G. A. Evans, L. Pang, P. Congdon, “Analysis of grating-assisted directional couplers using the Floquet–Bloch theory,” Appl. Phys. Lett. 13, 2301–2315 (1997).

IEEE J. Quantum Electron.

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
[CrossRef]

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction—part II: selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

J. Appl. Phys.

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photonic bandgaps in metallic microcavities,” J. Appl. Phys. 84, 2399–2403 (1998).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. B

P. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998).
[CrossRef]

M. G. Salt, W. L. Barnes, “Flat photonic bands in guided modes of textured metallic microcavities,” Phys. Rev. B 61, 11125–11135 (2000).
[CrossRef]

Other

D. Delbeke, B. Dhoedt, R. Bockstaele, I. Moerman, P. Van Daele, T. F. Krauss, R. Baets, “Electrically pumped photonic crystal micro-cavity light emitting diodes,” in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 71–72.

H. De Neve, “Design and fabrication of light emitting diodes based on the microcavity effect,” Ph. D. dissertation (Ghent University, Ghent, Belgium), p. 110 (1997).

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

K. Gillessen, W. Schairer, Light Emitting Diodes: an Introduction, (Prentice-Hall International, Cambridge, UK, 1987).

W. Schmid, F. Eberhard, R. Jäger, R. King, M. Miller, J. Joos, K. J. Ebeling, “45% quantum efficiency light-emitting diodes with radial outcoupling taper,” in Light-Emitting Diodes: Research, Manufacturing, and Applications IV, H. W. Yao, I. T. Ferguson, E. F. Schubert, eds., Proc. SPIE3938, 90–97 (2000).

D. Delbeke, K. Vandeputte, R. Baets, R. Bockstaele, B. Dhoedt, I. Moerman, P. Van Daele, S. Verstuyft, “Holographically defined grating assisted micro-cavity light emitting diodes,” in Proceedings of the IEEE/LEOS Benelux Symposium (Faculté Politechnique de Mons, Mons, Belgium, 1999), pp. 159–162.

M. Rattier, H. Benisty, C. Weisbuch, “Photonic crystal extractor,” in Electromagnetic Crystal Structures: Proceedings of Workshop on Photonic and Electromagnetic Crystal Structures III (PECS3) (T. F. Krauss, University of St. Andrews, St. Andrews, UK, 2001).

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Figures (11)

Fig. 1
Fig. 1

(a) k-space presentation of outside, leaky, and guided modes, (b) RCLED, (c) typical internal angular emission distribution in RCLED, with θ=arcsin(k/k).

Fig. 2
Fig. 2

Wave-vector diagram. (a) Top view of a 1D grating. (b) Extraction of guided mode with use of a 1D first-order grating (β=|Kx|) presented in the k plane: When the guided mode is projected toward the extraction cone, ec, the overlap of the diffracted light and the extraction cone can be extracted. This corresponds to a fraction of 22% of the guided mode. (c) Alternative graphic presentation to calculate the upper limit: projection of the extraction cone toward the guided mode by the Bragg vector. The overlap of the projected cone and the guided mode is limited to 22%. (d) Top view of a 2D grating (β=|Ki|, i=x, y). (e) Analog graphic presentation for a 2D first-order grating. (f) 2D second-order grating (β=2|Ki|).

Fig. 3
Fig. 3

Sketch of a GA-RCLED.

Fig. 4
Fig. 4

Plane-wave formalism in a multilayer periodically corrugated structure. Eint is defined in Eq. (8).

Fig. 5
Fig. 5

Solid-angle transformation due to refraction and diffraction.

Fig. 6
Fig. 6

Polarization-selective emission: surface-normal spectral data for TE and TM polarization.

Fig. 7
Fig. 7

Angle-resolved spectrum in the plane mounted by the Bragg vector and kz (azimuthal angle ϕ=0).

Fig. 8
Fig. 8

Simulated power per unit solid angle along the x axis as a function of the angle in the highest-index medium. Inset: contour plot of the simulated power per unit solid angle in k space.

Fig. 9
Fig. 9

Simulated power per unit solid angle along the x axis as a function of the angle for increasing period.

Fig. 10
Fig. 10

Simulated power per unit solid angle along the x axis as a function of the angle in the highest-index medium. Inset: contour plot of the simulated power per unit solid angle in k space. (a) 2D partially metallized air–semiconductor square lattice grating of depth 90 nm, fill factor 0.5, and period 300 nm; (b) 2D partially metallized air–semiconductor square lattice grating of depth 90 nm, fill factor 0.5, and period 390 nm.

Fig. 11
Fig. 11

(a) Extraction efficiency of a hybrid bottom-emitting cavity with a 2D partially metallized air–semiconductor square lattice grating with period 300 nm and wavelength 976 nm as a function of the grating depth, (b) corresponding power per unit solid angle along the x axis as a function of the angle in the highest-index medium, (c) extraction efficiency for a grating with depth 90 nm as a function of the emitted wavelength.

Tables (1)

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Table 1 Source Terms for Horizontal and Vertical Dipoles

Equations (25)

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e(x, y, z)=0π/2+π/2+i0π/2+isin θ dθ×02πdϕeF(θ, ϕ, z)exp(ikr),
e(e, y, z)=--dkxdkynk0kzeF(kx, ky, z)×exp(ikxx+ikyy).
kvw=kin+v2πΛx1x+w2πΛy1y,
e(x, y, z)=02π/Λx02π/Λydkxdkynk0kzKxy·EF,
EF[Wv+w]=eF(kxvw, kyvw, z),
Kxy[Wv+w]=exp(ikxvwx+ikyvwy),
kxvw=kx00+v2πΛx+w cos(ζ)2πΛy,
kyvw=ky00+w sin(ζ)2πΛy,
0v<V,0w<W,vandwinteger.
Eh/v=Eh/v,sEh/v,p,
Eh/v[Wv2+w]=1-v2VEh/v,s[Wv2+w]+v2VEh/v,p[W(v2-V)+w],
0v2<2V,0w<W,
Ah/v=Ah/v, sAh/v, p,
Euph/v(v2, w)=Tup(RdownSEv2wAh/v-SEv2wAh/v)I-RdownRup
=TupEintuph/v,
Edownh/v(v2, w)=Tdown(RupSEv2wAh/v-SEv2wAh/v)I-RdownRup
=TdownEintdownh/v,
Re(s·1z)=12Re(e×h*)·1z,
Re(szin)=12Re(kzin)ωμ0,
Re(szvw)=12Re(kzvw)wμ0tfvwtfvw*,
tpowvw=Re(szvw)Re(szin),
tpowvw=|tsfvw|2 Rekzvwkzin+|tpfvw|2 Rekzvw/nsur2kzin.
Ωs[Wv+w]=v2,w2V,W|Eh/v,s(v2, w)[Wv+w]|2×Rekzvwkzv2,w1nref k0kzν2w,
Ωp[Wv+w]=Σv2,w2V,W|Eh/v,p(v2, w)[Wv+w]|2×Rekzvw/nsur2kzv2,w1nref k0kzν2w,
ps,p=02π/Λx02π/Λy dkxdkyIrΩs,p,

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