Abstract

In this paper, we have made a clear differentiation among bandgap, diffraction, interference, and refraction effects in photonic crystal structures (PhCs). For observing bandgap, diffraction, and refraction effects, PhCs are considered on the top p-GaN surface of light emitting diodes (LEDs), whereas for interference effect, hole type PhCs are considered to be embedded within n-GaN layer of LED. From analysis, it is observed that at a particular lattice periodicity, for which bandgap lies within the wavelength of interest shows a significant light extraction due to inhibition of guided mode. Beyond a certain periodicity, diffraction effect starts dominating and light extraction improves further. The interference effect is observed in embedded photonic crystal LEDs, where depth of etching supports constructive interference of outward light waves. We have also shed light on refraction effects exhibited by the PhCs and whether negative refraction properties of PhCs may be useful in case of LED light extraction.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
    [CrossRef]
  4. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
    [CrossRef]
  5. E. Y. Schnitzer, C. Caneau, and T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from Al-GaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
    [CrossRef]
  6. D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
    [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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    [CrossRef]
  23. J. E. Lugo, R. Doti, and J. Faubert, “Negative refraction angular characterization in one-dimensional photonic crystals,” PLoS ONE 6, e17188 (2011).
    [CrossRef]
  24. Z. Y. Li and L. L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
    [CrossRef]
  25. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
    [CrossRef]
  26. M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
    [CrossRef]
  27. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013 (5)

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

S. Patra, S. Adhikari, and S. Pal, “Design and analysis of chess board like photonic crystal structure for light extraction enhancement in GaN/InGaN LEDs,” IEEE J. Disp. Tech. 9, 339–345 (2013).
[CrossRef]

X. X. Shen, Y. Z. Ren, G. Y. Dong, X. Z. Wang, and Z. W. Zhou, “Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED,” Superlattices Microstruct. 64, 303–310 (2013).
[CrossRef]

J. R. M-Salazar, “Optical properties of two-dimensional metamaterial photonic crystals,” J. Appl. Phys. 114, 223513 (2013).
[CrossRef]

L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevičius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38, 2376–2378 (2013).
[CrossRef]

2011 (1)

J. E. Lugo, R. Doti, and J. Faubert, “Negative refraction angular characterization in one-dimensional photonic crystals,” PLoS ONE 6, e17188 (2011).
[CrossRef]

2009 (4)

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15, 1257–1263 (2009).
[CrossRef]

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94, 123106 (2009).
[CrossRef]

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

C. Xiong, B. Zhang, X. N. Kang, T. Dai, and G. Zhang, “Diffracted transmission effects of GaN and polymer two-dimensional square-lattice photonic crystals,” Opt. Express 17, 23684–23689 (2009).
[CrossRef]

2008 (1)

K. Kim, J. Choi, J. B. Park, S. C. Jeon, J. S. Kim, and H. M. Lee, “Lattice constant effect of photonic crystals on the light output of blue light-emitting diodes,” IEEE Photon. Technol. Lett. 20, 1455–1457 (2008).
[CrossRef]

2007 (3)

F. García-Santamaría, E. C. Nelson, and P. V. Braun, “An optical surface resonance may render photonic crystals ineffective,” Phys. Rev. B 76, 075132 (2007).
[CrossRef]

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
[CrossRef]

2006 (1)

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

2005 (1)

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

2004 (4)

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[CrossRef]

K. Orita, S. Tamura, T. Takizawa, T. Yeda, M. Yuri, S. Takigawa, and D. Ueda, “High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal,” Jpn. J. Appl. Phys. 43, 5809–5813 (2004).
[CrossRef]

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

2003 (3)

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

Z. Y. Li and L. L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[CrossRef]

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, “Wave propagation through a photonic crystal in a negative phase refractive-index region,” IEEE J. Sel. Top. Quantum Electron. 9, 106–110 (2003).
[CrossRef]

2002 (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

2000 (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

1997 (1)

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

1993 (1)

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

Adhikari, S.

S. Patra, S. Adhikari, and S. Pal, “Design and analysis of chess board like photonic crystal structure for light extraction enhancement in GaN/InGaN LEDs,” IEEE J. Disp. Tech. 9, 339–345 (2013).
[CrossRef]

Alcubilla, R.

Z. Kral, J. Ferre-Borrull, L. F. Marsal, J. Pallarès, T. Trifonov, A. Rodriguez, and R. Alcubilla, “Reflection analysis of 2D-photonic crystal lattice using Bragg-diffraction phenomena,” in 2007 Spanish Conference on Electron Devices (IEEE, 2007), pp. 293–295.

Bergenek, K.

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

Braun, P. V.

F. García-Santamaría, E. C. Nelson, and P. V. Braun, “An optical surface resonance may render photonic crystals ineffective,” Phys. Rev. B 76, 075132 (2007).
[CrossRef]

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Caneau, C.

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

Chao, C. H.

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94, 123106 (2009).
[CrossRef]

Chen, C. M.

C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
[CrossRef]

Chi, G. C.

C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
[CrossRef]

Choi, J.

K. Kim, J. Choi, J. B. Park, S. C. Jeon, J. S. Kim, and H. M. Lee, “Lattice constant effect of photonic crystals on the light output of blue light-emitting diodes,” IEEE Photon. Technol. Lett. 20, 1455–1457 (2008).
[CrossRef]

Chong, K. K.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

Cojocaru, C.

Craford, M. G.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

Dai, T.

Dong, G. Y.

X. X. Shen, Y. Z. Ren, G. Y. Dong, X. Z. Wang, and Z. W. Zhou, “Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED,” Superlattices Microstruct. 64, 303–310 (2013).
[CrossRef]

Doti, R.

J. E. Lugo, R. Doti, and J. Faubert, “Negative refraction angular characterization in one-dimensional photonic crystals,” PLoS ONE 6, e17188 (2011).
[CrossRef]

Epler, J. E.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

Fan, S.

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

Faubert, J.

J. E. Lugo, R. Doti, and J. Faubert, “Negative refraction angular characterization in one-dimensional photonic crystals,” PLoS ONE 6, e17188 (2011).
[CrossRef]

Feng, H. C.

C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
[CrossRef]

Ferre-Borrull, J.

Z. Kral, J. Ferre-Borrull, L. F. Marsal, J. Pallarès, T. Trifonov, A. Rodriguez, and R. Alcubilla, “Reflection analysis of 2D-photonic crystal lattice using Bragg-diffraction phenomena,” in 2007 Spanish Conference on Electron Devices (IEEE, 2007), pp. 293–295.

Gailevicius, D.

Galisteo-López, J. F.

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

García-Santamaría, F.

F. García-Santamaría, E. C. Nelson, and P. V. Braun, “An optical surface resonance may render photonic crystals ineffective,” Phys. Rev. B 76, 075132 (2007).
[CrossRef]

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Gardner, N. F.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

Gmitter, T. J.

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

Hascik, S.

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

Houng, M. P.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

Hung, C. I.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

Hwang, I. K.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15, 1257–1263 (2009).
[CrossRef]

Jaskorzynska, B.

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, “Wave propagation through a photonic crystal in a negative phase refractive-index region,” IEEE J. Sel. Top. Quantum Electron. 9, 106–110 (2003).
[CrossRef]

Jeon, S. C.

K. Kim, J. Choi, J. B. Park, S. C. Jeon, J. S. Kim, and H. M. Lee, “Lattice constant effect of photonic crystals on the light output of blue light-emitting diodes,” IEEE Photon. Technol. Lett. 20, 1455–1457 (2008).
[CrossRef]

Jiang, H. X.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[CrossRef]

Joannopoulos, J. D.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

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

Johnson, S. G.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Kang, X. N.

Kim, J. S.

K. Kim, J. Choi, J. B. Park, S. C. Jeon, J. S. Kim, and H. M. Lee, “Lattice constant effect of photonic crystals on the light output of blue light-emitting diodes,” IEEE Photon. Technol. Lett. 20, 1455–1457 (2008).
[CrossRef]

Kim, K.

K. Kim, J. Choi, J. B. Park, S. C. Jeon, J. S. Kim, and H. M. Lee, “Lattice constant effect of photonic crystals on the light output of blue light-emitting diodes,” IEEE Photon. Technol. Lett. 20, 1455–1457 (2008).
[CrossRef]

Kim, K. H.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[CrossRef]

Kovac, J.

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

Kral, Z.

Z. Kral, J. Ferre-Borrull, L. F. Marsal, J. Pallarès, T. Trifonov, A. Rodriguez, and R. Alcubilla, “Reflection analysis of 2D-photonic crystal lattice using Bragg-diffraction phenomena,” in 2007 Spanish Conference on Electron Devices (IEEE, 2007), pp. 293–295.

Krames, M. R.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

Krauss, T. F.

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

Ku, H.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

Kubicova, I.

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

Kuo, C. H.

C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
[CrossRef]

Kuo, C. W.

C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
[CrossRef]

Kuo, H. C.

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94, 123106 (2009).
[CrossRef]

Lai, C. F.

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94, 123106 (2009).
[CrossRef]

Lee, C. E.

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94, 123106 (2009).
[CrossRef]

Lee, H. M.

K. Kim, J. Choi, J. B. Park, S. C. Jeon, J. S. Kim, and H. M. Lee, “Lattice constant effect of photonic crystals on the light output of blue light-emitting diodes,” IEEE Photon. Technol. Lett. 20, 1455–1457 (2008).
[CrossRef]

Li, Z. Y.

Z. Y. Li and L. L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[CrossRef]

Lin, J. Y.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[CrossRef]

Lin, L. L.

Z. Y. Li and L. L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[CrossRef]

Linder, N.

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

Liu, C. C.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

Long, D. H.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15, 1257–1263 (2009).
[CrossRef]

López, C.

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Lugo, J. E.

J. E. Lugo, R. Doti, and J. Faubert, “Negative refraction angular characterization in one-dimensional photonic crystals,” PLoS ONE 6, e17188 (2011).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Maigyte, L.

Malinauskas, M.

Marsal, L. F.

Z. Kral, J. Ferre-Borrull, L. F. Marsal, J. Pallarès, T. Trifonov, A. Rodriguez, and R. Alcubilla, “Reflection analysis of 2D-photonic crystal lattice using Bragg-diffraction phenomena,” in 2007 Spanish Conference on Electron Devices (IEEE, 2007), pp. 293–295.

Martincek, I.

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

M-Salazar, J. R.

J. R. M-Salazar, “Optical properties of two-dimensional metamaterial photonic crystals,” J. Appl. Phys. 114, 223513 (2013).
[CrossRef]

Nelson, E. C.

F. García-Santamaría, E. C. Nelson, and P. V. Braun, “An optical surface resonance may render photonic crystals ineffective,” Phys. Rev. B 76, 075132 (2007).
[CrossRef]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

Oder, T. N.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[CrossRef]

Orita, K.

K. Orita, S. Tamura, T. Takizawa, T. Yeda, M. Yuri, S. Takigawa, and D. Ueda, “High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal,” Jpn. J. Appl. Phys. 43, 5809–5813 (2004).
[CrossRef]

Pal, S.

S. Patra, S. Adhikari, and S. Pal, “Design and analysis of chess board like photonic crystal structure for light extraction enhancement in GaN/InGaN LEDs,” IEEE J. Disp. Tech. 9, 339–345 (2013).
[CrossRef]

Pallarès, J.

Z. Kral, J. Ferre-Borrull, L. F. Marsal, J. Pallarès, T. Trifonov, A. Rodriguez, and R. Alcubilla, “Reflection analysis of 2D-photonic crystal lattice using Bragg-diffraction phenomena,” in 2007 Spanish Conference on Electron Devices (IEEE, 2007), pp. 293–295.

Park, J. B.

K. Kim, J. Choi, J. B. Park, S. C. Jeon, J. S. Kim, and H. M. Lee, “Lattice constant effect of photonic crystals on the light output of blue light-emitting diodes,” IEEE Photon. Technol. Lett. 20, 1455–1457 (2008).
[CrossRef]

Patela, S.

K. Ptasi and S. Patela, “Numerical investigation of negative refraction effect in two-dimensional photonic crystal fabricated in gallium nitride,” International Students and Young Scientists Workshop on Photonics and Microsystems (IEEE, 2009).

Patra, S.

S. Patra, S. Adhikari, and S. Pal, “Design and analysis of chess board like photonic crystal structure for light extraction enhancement in GaN/InGaN LEDs,” IEEE J. Disp. Tech. 9, 339–345 (2013).
[CrossRef]

Peckus, M.

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

Ptasi, K.

K. Ptasi and S. Patela, “Numerical investigation of negative refraction effect in two-dimensional photonic crystal fabricated in gallium nitride,” International Students and Young Scientists Workshop on Photonics and Microsystems (IEEE, 2009).

Pudis, D.

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

Purlys, V.

Qin, Z. X.

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

Qiu, M.

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, “Wave propagation through a photonic crystal in a negative phase refractive-index region,” IEEE J. Sel. Top. Quantum Electron. 9, 106–110 (2003).
[CrossRef]

Ren, Y. Z.

X. X. Shen, Y. Z. Ren, G. Y. Dong, X. Z. Wang, and Z. W. Zhou, “Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED,” Superlattices Microstruct. 64, 303–310 (2013).
[CrossRef]

Rodriguez, A.

Z. Kral, J. Ferre-Borrull, L. F. Marsal, J. Pallarès, T. Trifonov, A. Rodriguez, and R. Alcubilla, “Reflection analysis of 2D-photonic crystal lattice using Bragg-diffraction phenomena,” in 2007 Spanish Conference on Electron Devices (IEEE, 2007), pp. 293–295.

Rumbolz, C.

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

Ryu, S. W.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15, 1257–1263 (2009).
[CrossRef]

Schaaf, P.

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

Schnitzer, E. Y.

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

Schubert, E. F.

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

Shen, X. X.

X. X. Shen, Y. Z. Ren, G. Y. Dong, X. Z. Wang, and Z. W. Zhou, “Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED,” Superlattices Microstruct. 64, 303–310 (2013).
[CrossRef]

Sigalas, M. M.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

Simmons, J. A.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

Skriniarova, J.

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

Staliunas, K.

Streubel, K.

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

Suslik, L.

D. Pudis, L. Suslik, J. Skriniarova, J. Kovac, J. Kovac, I. Kubicova, I. Martincek, S. Hascik, and P. Schaaf, “Effect of 2D photonic structure patterned in the LED surface on emission properties,” Appl. Surf. Sci. 269, 161–165 (2013).
[CrossRef]

Swillo, M.

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, “Wave propagation through a photonic crystal in a negative phase refractive-index region,” IEEE J. Sel. Top. Quantum Electron. 9, 106–110 (2003).
[CrossRef]

Takigawa, S.

K. Orita, S. Tamura, T. Takizawa, T. Yeda, M. Yuri, S. Takigawa, and D. Ueda, “High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal,” Jpn. J. Appl. Phys. 43, 5809–5813 (2004).
[CrossRef]

Takizawa, T.

K. Orita, S. Tamura, T. Takizawa, T. Yeda, M. Yuri, S. Takigawa, and D. Ueda, “High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal,” Jpn. J. Appl. Phys. 43, 5809–5813 (2004).
[CrossRef]

Tamura, S.

K. Orita, S. Tamura, T. Takizawa, T. Yeda, M. Yuri, S. Takigawa, and D. Ueda, “High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal,” Jpn. J. Appl. Phys. 43, 5809–5813 (2004).
[CrossRef]

Thylén, L.

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, “Wave propagation through a photonic crystal in a negative phase refractive-index region,” IEEE J. Sel. Top. Quantum Electron. 9, 106–110 (2003).
[CrossRef]

Trifonov, T.

Z. Kral, J. Ferre-Borrull, L. F. Marsal, J. Pallarès, T. Trifonov, A. Rodriguez, and R. Alcubilla, “Reflection analysis of 2D-photonic crystal lattice using Bragg-diffraction phenomena,” in 2007 Spanish Conference on Electron Devices (IEEE, 2007), pp. 293–295.

Trull, J.

Ueda, D.

K. Orita, S. Tamura, T. Takizawa, T. Yeda, M. Yuri, S. Takigawa, and D. Ueda, “High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal,” Jpn. J. Appl. Phys. 43, 5809–5813 (2004).
[CrossRef]

Villeneuve, P. R.

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

Wang, C. C.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

Wang, X. Z.

X. X. Shen, Y. Z. Ren, G. Y. Dong, X. Z. Wang, and Z. W. Zhou, “Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED,” Superlattices Microstruct. 64, 303–310 (2013).
[CrossRef]

Wang, Y. H.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

Wendt, J. R.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

Wierer, J. J.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

Wiesmann, Ch.

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

Wirth, R.

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

Wu, L. W.

C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
[CrossRef]

Xiong, C.

Xu, J.

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

Xu, K.

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

Yang, Z. J.

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

Yeda, T.

K. Orita, S. Tamura, T. Takizawa, T. Yeda, M. Yuri, S. Takigawa, and D. Ueda, “High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal,” Jpn. J. Appl. Phys. 43, 5809–5813 (2004).
[CrossRef]

Yeh, W. Y.

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94, 123106 (2009).
[CrossRef]

Yen, H. H.

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94, 123106 (2009).
[CrossRef]

Yu, D. P.

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

Yu, T. J.

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

Yuri, M.

K. Orita, S. Tamura, T. Takizawa, T. Yeda, M. Yuri, S. Takigawa, and D. Ueda, “High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal,” Jpn. J. Appl. Phys. 43, 5809–5813 (2004).
[CrossRef]

Zhang, B.

C. Xiong, B. Zhang, X. N. Kang, T. Dai, and G. Zhang, “Diffracted transmission effects of GaN and polymer two-dimensional square-lattice photonic crystals,” Opt. Express 17, 23684–23689 (2009).
[CrossRef]

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

Zhang, G.

Zhang, Z. S.

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

Zhou, Z. W.

X. X. Shen, Y. Z. Ren, G. Y. Dong, X. Z. Wang, and Z. W. Zhou, “Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED,” Superlattices Microstruct. 64, 303–310 (2013).
[CrossRef]

Zull, H.

K. Bergenek, Ch. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Beamshaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals,” Proc. SPIE 7231, 72310C (2009).

Appl. Phys. Lett. (8)

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887 (2004).
[CrossRef]

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91, 121109 (2007).
[CrossRef]

C. H. Kuo, H. C. Feng, C. W. Kuo, C. M. Chen, L. W. Wu, and G. C. Chi, “Nitride-based near-ultraviolet light emitting diodes with meshed pGaN,” Appl. Phys. Lett. 90, 142115 (2007).
[CrossRef]

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

Z. S. Zhang, B. Zhang, J. Xu, K. Xu, Z. J. Yang, Z. X. Qin, T. J. Yu, and D. P. Yu, “Effects of symmetry of GaNbased two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction,” Appl. Phys. Lett. 88, 171103 (2006).
[CrossRef]

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[CrossRef]

C. F. Lai, C. H. Chao, H. C. Kuo, H. H. Yen, C. E. Lee, and W. Y. Yeh, “Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes,” Appl. Phys. Lett. 94, 123106 (2009).
[CrossRef]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

Appl. Surf. Sci. (1)

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Figures (11)

Fig. 1.
Fig. 1.

Schematics for the cross-sections of photonic crystal structures (a) on top of p-GaN layer of LED for analysis of bandgap, diffraction, and refraction effects and (b) within n-GaN layer as embedded PhCs for analysis of the interference effect.

Fig. 2.
Fig. 2.

Band diagram of 2D photonic crystal structure of circular hole etched in GaN having hexagonal lattice for a hole radius, r=0.3*a (a: lattice constant).

Fig. 3.
Fig. 3.

Plot for the variation of light extraction efficiency with periodicity for different etch depths considering both TE and TM polarizations.

Fig. 4.
Fig. 4.

Comparison of output light intensity for LED having PhCs of different etch-depth (d) with respect to that of the LED without PhC (etch-depth=0).

Fig. 5.
Fig. 5.

Wave-vector diagram of PhC.

Fig. 6.
Fig. 6.

Light extraction efficiency with the variation of etch depth for period of 0.4 μm.

Fig. 7.
Fig. 7.

Equi-frequency contours for the first TM band.

Fig. 8.
Fig. 8.

Equi-frequency contours for second TM band.

Fig. 9.
Fig. 9.

TM band diagram for an air-hole PhC structure embedded in GaN with hexagonal lattice with r/a=0.3.

Fig. 10.
Fig. 10.

Plot of effective indices versus normalized frequency for second TM band.

Fig. 11.
Fig. 11.

Demonstration of negative refraction. (a) Focused light with negative refraction for wavelength 0.465 μm. (b) Scattered light without negative refraction for 0.400 μm.

Equations (3)

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f=(Area occupied by atoms in a unitcell)(Total area of unitcell)f=πr23a2/2.
neff=fnair2+(1f)nGaN2,
d=(m+1/2)λ/(2neff),

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