Abstract

A “superperiodic” photonic-crystal (PhC) light-emitting diode (LED) design exhibiting high-luminance patterns is proposed for applications that require highly directive vertical light extraction. The superperiodic design employs a periodic arrangement of defective missing holes on an otherwise perfect periodic pattern of holes for the basic two-dimensional PhC structure. Avoiding the fragile semiconductor membrane structure that is popular in current PhC laser designs, the design utilizes a thick epitaxy structure with electromagnetic density-of-mode singularity. This singularity is created by the defect mode in a three-dimensional frequency versus wave vector relation within the band matched with the gain spectrum of the LED that is placed on top of the base reflector plate material. The superperiodic structure of this design is shown to provide an effective means for sharpening the vertical beam in the far field, based on discrete-Fourier transformation theory. Subsequent simulations based on the finite-difference time-domain analysis verify the effectiveness of the design principle on GaN epitaxy structures with various bottom layers.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2006 (2)

C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
[CrossRef]

C. H. Chao, S. L. Chuang, and T. L. Wu, “Theoretical demonstration of enhancement of light extraction of flip-chip GaN light-emitting diodes with photonic crystals,” Appl. Phys. Lett. 89, 091116 (2006).
[CrossRef]

2005 (6)

A. David, C. Meier, R. Sharma, F. S. Diana, S. P. Denbaars, E. Hu, S. Nakamura, and C. Weisbuch, “Photonic bands in two-dimensionally patterned multimode GaN waveguide for light extraction,” Appl. Phys. Lett. 87, 101107 (2005).
[CrossRef]

D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, and Y. S. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87, 203508 (2005).
[CrossRef]

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202-1215 (2005).
[CrossRef] [PubMed]

Y. J. Lee, S. H. Kim, G. H. Kim, Y. H. Lee, S. H. Cho, Y. W. Song, Y. C. Kim, and Y. R. Do, “Far-field radiation of photonic crystal organic light-emitting diode,” Opt. Express 13, 5864-5870 (2005).
[CrossRef] [PubMed]

H. Altug and J. Vučković, “Photonic crystal nanocavity array laser,” Opt. Express 13, 8819-8828 (2005).
[CrossRef] [PubMed]

2004 (1)

H. Altug and J. Vučković, “Two-dimensional coupled photonic crystal resonator arrays,” Appl. Phys. Lett. 84, 161-163 (2004).
[CrossRef]

2003 (1)

2002 (2)

2001 (2)

H. Y. Ryu, J. K. Hwang, Y. J. Lee, and Y. H. Lee, “Enhancement of light extraction from two-dimensional photonic crystal slab structure,” IEEE J. Sel. Top. Quantum Electron. 8, 231-241 (2001).
[CrossRef]

A. L. Fehrembach, S. Enoch, and A. Sentenac, “Highly directive light sources using two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 4280-4282 (2001).
[CrossRef]

1999 (2)

1997 (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

1996 (2)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

W. J. Fan, M. F. Li, and T. C. Chong, “Valence hole subbands and optical gain spectra of GaN/Ga1−xAlxN strained quantum wells,” J. Appl. Phys. 80, 3471-3478 (1996).
[CrossRef]

1995 (1)

A. C. Dutta, A. Suzuki, K. Kurihara, F. Miyasaka, H. Hotta, and K. Sugita, “High-brightness, AlGaInP-based, visible light-emitting diode for efficient coupling with POF,” IEEE Photon. Technol. Lett. 7, 1134-1136 (1995).
[CrossRef]

Akahane, Y.

Altug, H.

H. Altug and J. Vučković, “Photonic crystal nanocavity array laser,” Opt. Express 13, 8819-8828 (2005).
[CrossRef] [PubMed]

H. Altug and J. Vučković, “Two-dimensional coupled photonic crystal resonator arrays,” Appl. Phys. Lett. 84, 161-163 (2004).
[CrossRef]

Asano, T.

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Thomson Learning, 1976), p. 145.

Baets, R.

Bhat, R.

Bienstman, P.

Bockstaele, R.

Boroditsky, M.

Chao, C. H.

C. H. Chao, S. L. Chuang, and T. L. Wu, “Theoretical demonstration of enhancement of light extraction of flip-chip GaN light-emitting diodes with photonic crystals,” Appl. Phys. Lett. 89, 091116 (2006).
[CrossRef]

Cheng, C. C.

C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
[CrossRef]

Cheng, H. C.

C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
[CrossRef]

Cho, C. O.

D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, and Y. S. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87, 203508 (2005).
[CrossRef]

Cho, S. H.

Choi, Y. S.

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

Chong, T. C.

W. J. Fan, M. F. Li, and T. C. Chong, “Valence hole subbands and optical gain spectra of GaN/Ga1−xAlxN strained quantum wells,” J. Appl. Phys. 80, 3471-3478 (1996).
[CrossRef]

Chu, C. F.

C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
[CrossRef]

Chu, J. Y.

C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
[CrossRef]

Chuang, S. L.

C. H. Chao, S. L. Chuang, and T. L. Wu, “Theoretical demonstration of enhancement of light extraction of flip-chip GaN light-emitting diodes with photonic crystals,” Appl. Phys. Lett. 89, 091116 (2006).
[CrossRef]

Coccioli, R.

Craford, M. G.

M. G. Craford, “Nanoscience and solid state lighting,” Presented at Nanosummit2004, Washington, D.C., June 23-24, 2004.

David, A.

A. David, C. Meier, R. Sharma, F. S. Diana, S. P. Denbaars, E. Hu, S. Nakamura, and C. Weisbuch, “Photonic bands in two-dimensionally patterned multimode GaN waveguide for light extraction,” Appl. Phys. Lett. 87, 101107 (2005).
[CrossRef]

Delbeke, D.

Denbaars, S. P.

A. David, C. Meier, R. Sharma, F. S. Diana, S. P. Denbaars, E. Hu, S. Nakamura, and C. Weisbuch, “Photonic bands in two-dimensionally patterned multimode GaN waveguide for light extraction,” Appl. Phys. Lett. 87, 101107 (2005).
[CrossRef]

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

Diana, F. S.

A. David, C. Meier, R. Sharma, F. S. Diana, S. P. Denbaars, E. Hu, S. Nakamura, and C. Weisbuch, “Photonic bands in two-dimensionally patterned multimode GaN waveguide for light extraction,” Appl. Phys. Lett. 87, 101107 (2005).
[CrossRef]

Do, Y. R.

Doan, T.

C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
[CrossRef]

Dutta, A. C.

A. C. Dutta, A. Suzuki, K. Kurihara, F. Miyasaka, H. Hotta, and K. Sugita, “High-brightness, AlGaInP-based, visible light-emitting diode for efficient coupling with POF,” IEEE Photon. Technol. Lett. 7, 1134-1136 (1995).
[CrossRef]

Enoch, S.

A. L. Fehrembach, S. Enoch, and A. Sentenac, “Highly directive light sources using two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 4280-4282 (2001).
[CrossRef]

Fan, F. H.

C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

Fan, W. J.

W. J. Fan, M. F. Li, and T. C. Chong, “Valence hole subbands and optical gain spectra of GaN/Ga1−xAlxN strained quantum wells,” J. Appl. Phys. 80, 3471-3478 (1996).
[CrossRef]

Fehrembach, A. L.

A. L. Fehrembach, S. Enoch, and A. Sentenac, “Highly directive light sources using two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 4280-4282 (2001).
[CrossRef]

Gao, Y.

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

Haberer, E.

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

Hennessy, K.

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

Hotta, H.

A. C. Dutta, A. Suzuki, K. Kurihara, F. Miyasaka, H. Hotta, and K. Sugita, “High-brightness, AlGaInP-based, visible light-emitting diode for efficient coupling with POF,” IEEE Photon. Technol. Lett. 7, 1134-1136 (1995).
[CrossRef]

Hu, E.

A. David, C. Meier, R. Sharma, F. S. Diana, S. P. Denbaars, E. Hu, S. Nakamura, and C. Weisbuch, “Photonic bands in two-dimensionally patterned multimode GaN waveguide for light extraction,” Appl. Phys. Lett. 87, 101107 (2005).
[CrossRef]

Hu, E. L.

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

Hwang, J. K.

H. Y. Ryu, J. K. Hwang, Y. J. Lee, and Y. H. Lee, “Enhancement of light extraction from two-dimensional photonic crystal slab structure,” IEEE J. Sel. Top. Quantum Electron. 8, 231-241 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, and Y. H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60, 4688-4695 (1999).
[CrossRef]

Jeon, H.

D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, and Y. S. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87, 203508 (2005).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

Joung, H.

C. M. Lim, H. Joung, and G. H. Song, “Highly controlled luminescence angle-profile from light-emitting diodes with super-periodic photonic-crystal patterns on the PMMA film,” in Proceedings of Photonic and Electromagnetic Crystal Structures PECS-VII (2007), p. B-9.

Kim, D. H.

D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, and Y. S. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87, 203508 (2005).
[CrossRef]

Kim, G. H.

Kim, S. H.

Kim, Y. C.

Krauss, T. F.

Kurihara, K.

A. C. Dutta, A. Suzuki, K. Kurihara, F. Miyasaka, H. Hotta, and K. Sugita, “High-brightness, AlGaInP-based, visible light-emitting diode for efficient coupling with POF,” IEEE Photon. Technol. Lett. 7, 1134-1136 (1995).
[CrossRef]

Lee, Y. H.

Y. J. Lee, S. H. Kim, G. H. Kim, Y. H. Lee, S. H. Cho, Y. W. Song, Y. C. Kim, and Y. R. Do, “Far-field radiation of photonic crystal organic light-emitting diode,” Opt. Express 13, 5864-5870 (2005).
[CrossRef] [PubMed]

H. Y. Ryu, J. K. Hwang, Y. J. Lee, and Y. H. Lee, “Enhancement of light extraction from two-dimensional photonic crystal slab structure,” IEEE J. Sel. Top. Quantum Electron. 8, 231-241 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, and Y. H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60, 4688-4695 (1999).
[CrossRef]

Lee, Y. J.

Y. J. Lee, S. H. Kim, G. H. Kim, Y. H. Lee, S. H. Cho, Y. W. Song, Y. C. Kim, and Y. R. Do, “Far-field radiation of photonic crystal organic light-emitting diode,” Opt. Express 13, 5864-5870 (2005).
[CrossRef] [PubMed]

H. Y. Ryu, J. K. Hwang, Y. J. Lee, and Y. H. Lee, “Enhancement of light extraction from two-dimensional photonic crystal slab structure,” IEEE J. Sel. Top. Quantum Electron. 8, 231-241 (2001).
[CrossRef]

Li, M. F.

W. J. Fan, M. F. Li, and T. C. Chong, “Valence hole subbands and optical gain spectra of GaN/Ga1−xAlxN strained quantum wells,” J. Appl. Phys. 80, 3471-3478 (1996).
[CrossRef]

Lim, C. M.

C. M. Lim, H. Joung, and G. H. Song, “Highly controlled luminescence angle-profile from light-emitting diodes with super-periodic photonic-crystal patterns on the PMMA film,” in Proceedings of Photonic and Electromagnetic Crystal Structures PECS-VII (2007), p. B-9.

Liu, W. H.

C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
[CrossRef]

Loncar, M.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850-856 (2002).
[CrossRef]

Mabuchi, H.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850-856 (2002).
[CrossRef]

Meier, C.

A. David, C. Meier, R. Sharma, F. S. Diana, S. P. Denbaars, E. Hu, S. Nakamura, and C. Weisbuch, “Photonic bands in two-dimensionally patterned multimode GaN waveguide for light extraction,” Appl. Phys. Lett. 87, 101107 (2005).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Thomson Learning, 1976), p. 145.

Miyasaka, F.

A. C. Dutta, A. Suzuki, K. Kurihara, F. Miyasaka, H. Hotta, and K. Sugita, “High-brightness, AlGaInP-based, visible light-emitting diode for efficient coupling with POF,” IEEE Photon. Technol. Lett. 7, 1134-1136 (1995).
[CrossRef]

Nakamura, S.

A. David, C. Meier, R. Sharma, F. S. Diana, S. P. Denbaars, E. Hu, S. Nakamura, and C. Weisbuch, “Photonic bands in two-dimensionally patterned multimode GaN waveguide for light extraction,” Appl. Phys. Lett. 87, 101107 (2005).
[CrossRef]

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

Noda, S.

Painter, O.

Park, Y. S.

D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, and Y. S. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87, 203508 (2005).
[CrossRef]

Roh, Y. G.

D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, and Y. S. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. 87, 203508 (2005).
[CrossRef]

Ryu, H. Y.

H. Y. Ryu, J. K. Hwang, Y. J. Lee, and Y. H. Lee, “Enhancement of light extraction from two-dimensional photonic crystal slab structure,” IEEE J. Sel. Top. Quantum Electron. 8, 231-241 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, and Y. H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60, 4688-4695 (1999).
[CrossRef]

Scherer, A.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850-856 (2002).
[CrossRef]

Sentenac, A.

A. L. Fehrembach, S. Enoch, and A. Sentenac, “Highly directive light sources using two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 4280-4282 (2001).
[CrossRef]

Sharma, R.

Y. S. Choi, K. Hennessy, R. Sharma, E. Haberer, Y. Gao, S. P. Denbaars, S. Nakamura, and E. L. Hu, “GaN blue photonic crystal membrane nanocavities,” Appl. Phys. Lett. 87, 243101 (2005).
[CrossRef]

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Song, G. H.

C. M. Lim, H. Joung, and G. H. Song, “Highly controlled luminescence angle-profile from light-emitting diodes with super-periodic photonic-crystal patterns on the PMMA film,” in Proceedings of Photonic and Electromagnetic Crystal Structures PECS-VII (2007), p. B-9.

Song, Y. W.

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A. C. Dutta, A. Suzuki, K. Kurihara, F. Miyasaka, H. Hotta, and K. Sugita, “High-brightness, AlGaInP-based, visible light-emitting diode for efficient coupling with POF,” IEEE Photon. Technol. Lett. 7, 1134-1136 (1995).
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C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
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[CrossRef]

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A. David, C. Meier, R. Sharma, F. S. Diana, S. P. Denbaars, E. Hu, S. Nakamura, and C. Weisbuch, “Photonic bands in two-dimensionally patterned multimode GaN waveguide for light extraction,” Appl. Phys. Lett. 87, 101107 (2005).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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C. C. Cheng, C. F. Chu, W. H. Liu, J. Y. Chu, H. C. Cheng, F. H. Fan, J. K. Yen, C. A. Tran, and T. Doan, “Highly efficient GaN vertical light emitting diodes on metal alloy substarate from near UV to green color for solid state lightning application,” Proc. SPIE 6337, 633703 (2006).
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C. M. Lim, H. Joung, and G. H. Song, “Highly controlled luminescence angle-profile from light-emitting diodes with super-periodic photonic-crystal patterns on the PMMA film,” in Proceedings of Photonic and Electromagnetic Crystal Structures PECS-VII (2007), p. B-9.

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Figures (17)

Fig. 1
Fig. 1

Design schematics for (a) the proposed superperiodic PhC LED, and (b) its in-plane unit supercell. Radius ρ of the etched periodic holes is normally set at 0.4 a except for the six holes around the defect cell, where a is the basic period of the holes in the triangular PhC structure. The figure shows the case of d c = 6 a for the superperiodic distance between the adjacent defects.

Fig. 2
Fig. 2

Schematic of the domain used for the 3D-FDTD calculations. The shadowed regions represent the anisotropic perfectly matched layers (APMLs). The dielectric structure penetrates into the APML layers for impedance matching. The white solid line on the bottom of the GaN layer represents an artificial perfect reflection layer for the type-1 structure, approximating a metal base. Type-2 is terminated by air, whereas type-3 is terminated by a sapphire layer.

Fig. 3
Fig. 3

Plots for the H z component of the mode profile inside the slab in detection layer B of Fig. 2; (a) for the DD1 mode and (b) for the DD2 mode. A type-1 structure with ρ m = 0.15 a and ω a 2 π c = 0.290 was chosen for the FDTD simulation.

Fig. 4
Fig. 4

In-plane field components of the DD1 mode. (a) Internal-field profile measured at detection layer B in Fig. 2. (b) Near-field profile measured at the upper detection layer A. A type-1 structure with ρ m = 0.15 a and ω a 2 π c = 0.290 was chosen for the FDTD simulation.

Fig. 5
Fig. 5

Range of overlapped concentration between E y 2 and H x 2 in the k space for a type-1 structure with ρ m = 0.15 a and ω a 2 π c = 0.290 in the case of the DD1 mode of Fig. 3a. (a) Top and bottom pictures are plotted along k x and k y , respectively. Shadowed ranges of k x and k y represent the inside of the light cone. (b) Logarithmic plot for the power distribution in k space. The dashed circle represents the light cone for ω a 2 π c = 0.290 .

Fig. 6
Fig. 6

Solid curves and dashed lines correspond to the dispersion curves of the Bloch-modes and the localized H z -dipole modes for a type-1 structure, respectively. The dispersion curves for the Bloch-modes in the PhC-slab without any defect may still be considered as approximate curves in the presence of a single defect as a perturbation. Additionally, the frequencies of the localized H z -dipole modes are calculated for the PhC structure with a single defect using the FDTD program. The shadowed region represents the light-cone for the PhC-slab. The frequency of the localized H z -dipole modes is lowered as ρ m is reduced. The curves are obtained using a three dimensional plane-wave expansion method within the supercell.

Fig. 7
Fig. 7

Time-averaged intensity plots in the k space. Powers are measured at detection layer B in Fig. 2. Hexagons represent the the first Brillouin-zone. (a) Power concentration at the zone-boundary, especially M-points, is due to excitation of Bloch-modes for the structure with ρ m = 0.40 a . (b) Power concentration around k x = k y = 0 is mainly from excitation of H z -dipole modes for the structure tuned with ρ m = 0.15 a .

Fig. 8
Fig. 8

Time-averaged far-field intensity plots for the radiated beam from a single point-defect for a type-1 structure with ρ m = 0.4 a and ω a 2 π c = 0.310 . The current is randomly generated on a sheet randomized dipoles in a unit supercell of the super-PhC structure shown in Fig. 1b. (a) Plots of luminance for all solid angles in the logarithmic scale. The dashed circle represents the escape light cone. (b) Top and bottom polar-plots are obtained by scanning the luminance in the linear scale along the vertical and horizontal lines of (a), respectively.

Fig. 9
Fig. 9

Time-averaged far-field intensity plots for the radiated beam from a tuned single point-defect for a type-1 structure with ρ m = 0.15 a and ω a 2 π c = 0.290 . (a) Plots of luminance for all solid angles in the logarithmic scale. The dashed circle represents the escape light cone. (b) Top and bottom polar-plots are obtained by scanning the luminance in the linear scale along ther vertical and horizontal lines of (a), respectively. Spectral isolation of the H z -dipole mode let the excitation of the Bloch-mode be suppressed. The intensity toward the normal direction is about 5.5 times greater than that for Fig. 8.

Fig. 10
Fig. 10

Schematic for explaining the principle of optimizing the far-field luminance pattern with the super-PhC structure. d c is the distance between the adjacent point-defects. Excitation of the fundamental mode has been optimally enhanced by tuning ρ m . Note that (c) and (d) represent the absolute magnitude of the power spectral density.

Fig. 11
Fig. 11

Time-averaged far-field intensity plots for the radiated beam from the super-PhC structure of a type-1 structure with ρ m = 0.4 a , ω a 2 π c = 0.310 , and d c = 6 a . The area of the current sheet for field excitation is set to cover a unit supercell of the super-PhC structure, as shown in Fig. 1b. The random current simultaneously excites the H z -dipole and the Bloch-modes. (a) Luminance is plotted for all solid angles in the logarithmic scale. The dashed circle represents the escape light cone. (b) Top and bottom polar-plots are obtained by scanning the luminance in the linear scale along vertical and horizontal lines of (a), respectively. The center peak and the other six peaks surrounding the center one together represent the luminance pattern of the seven beams inside the escape light cone for this untuned structure. The k-space distance between the neighboring peaks is found to be 4 π 3 d c .

Fig. 12
Fig. 12

Time-averaged far-field intensity plots for the radiated beam from the super-PhC structure for a type-1 structure with ρ m = 0.15 a , ω a 2 π c = 0.296 , and d c = 6 a . The random current predomonantly excites the H z -dipole mode. (a) Luminance is plotted for all solid angles in the logarithmic scale. The dashed circle represents the escape light cone. (b) Top and bottom polar-plots are obtained by scanning the luminance in the linear scale along the vertical and horizontal lines of (a), respectively. For this optimized structure, side peaks are subdued, leaving only the center peak within the escape light cone.

Fig. 13
Fig. 13

Time-averaged far-field intensity plots for the radiated beam from the super-PhC structure for a type-2 structure with ρ m = 0.33 a , ω a 2 π c = 0.3365 , and d c = 5 a . (a) Plots of luminance for all solid angles in the logarithmic scale. The dashed circle represents the escape light cone. (b) Top and bottom polar-plots are obtained by scanning the luminance in the linear scale along vertical and horizontal lines of (a), respectively.

Fig. 14
Fig. 14

Time-averaged far-field intensity plots for the radiated beam from the super-PhC structure for a type-3 structure with ρ m = 0.25 a , ω a 2 π c = 0.3350 , and d c = 5 a . (a) Plots of luminance for all solid angles in the logarithmic scale. The dashed circle represents the escape light cone. (b) Top and bottom polar-plots are obtained by scanning the luminance in the linear scale along vertical and horizontal lines of (a), respectively.

Fig. 15
Fig. 15

Plot of extraction efficiency as a function of normalized frequency with holes of various sizes (radius ρ m ). The points marked with an × correspond to frequencies of the dipole-mode.

Fig. 16
Fig. 16

Factors of extraction efficiency enhancement are plotted for three types of structures optimally designed to obtain highly directional radiation. The solid, dashed, and dotted curves correspond to the results of the type-1, type-2, and type-3 structures, respectively. The points marked with a × denote the frequencies of the defect-modes. The extraction efficiency enhancement is defined as the ratio between the extraction efficiency of the nonpatterned structure and that of the patterned-structure. The enhancement factors are shown to be about 40 for optimally designed structures. The points marked with a × correspond to frequencies of the dipole-mode.

Fig. 17
Fig. 17

(a) Polar-plots of highly directional far-field pattern from optimized structures with ρ = 0.3 a . (b) Time-averaged intensity plot in k-space. The power is measured at the detection layer B. Hexagons represents the first Brillouin-zone. The significant difference is noticed in comparison with Fig. 7b. The degradation of efficiency is due to the increased power concentration at the zone-boundary for the smaller hole radius of ρ = 0.3 a due to increased excitation of the inescapable Bloch-mode. ρ m is set at 0.35 a and the normalized frequency is 0.2910.

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