Abstract

This paper proposes a polarization-selective light emitter that can enhance preferentially the spontaneous emission rate of one desired polarization state using a one-dimensional metal grating mirror. Systematic numerical simulations were performed to determine the optimized structural parameters of the metal grating mirror consisting of ITO/silver, in which the two orthogonally polarized lights reflected from the grating mirror undergo completely opposite phases. This metal grating mirror was incorporated into a GaN medium, and the spontaneous emission rate of one linearly polarized light was 1.3 times higher than that of the other at a specific distance between the light source and mirror. In addition, the polarization ratio can be increased to 15:1 by considering the extracted power in a practical vertical GaN slab light-emitting diode structure. This study will be useful for demonstrating high-efficiency polarization-selective light-emitting diodes without using additional optical components, such as a polarizer.

© 2011 OSA

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  1. A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007).
    [CrossRef]
  2. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
    [CrossRef]
  3. S. Noda and M. Fujita, “Light-emitting diodes: Photonic crystal efficiency boost,” Nat. Photonics 3(3), 129–130 (2009).
    [CrossRef]
  4. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
    [CrossRef]
  5. K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
    [CrossRef]
  6. S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
    [CrossRef]
  7. S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
    [CrossRef]
  8. Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
    [CrossRef]
  9. S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
    [CrossRef] [PubMed]
  10. H. Kawamoto, “The History of Liquid-Crystal Displays,” Proc. IEEE 90(4), 460–500 (2002).
    [CrossRef]
  11. R. E. Smith, M. E. Warren, J. R. Wendt, and G. A. Vawter, “Polarization-sensitive subwavelength antireflection surfaces on a semiconductor for 975 nm,” Opt. Lett. 21(15), 1201–1203 (1996).
    [CrossRef] [PubMed]
  12. L. Zhang, J. H. Teng, S. J. Chua, and E. A. Fitzgerald, “Linearly polarized light emission from InGaN light emitting diode with subwavelength metallic nanograting,” Appl. Phys. Lett. 95(26), 261110 (2009).
    [CrossRef]
  13. G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
    [CrossRef] [PubMed]
  14. J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
    [CrossRef]
  15. Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
    [CrossRef]
  16. 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(7), 4688–4695 (1999).
    [CrossRef]
  17. The spontaneous emission enhancement rate is defined by the spontaneous emission rate of a dipole source in a structure of interest which is divided by that in a homogeneous medium, as described in refs. [15] and [16].
  18. We used a home-made FDTD code using Drude model, which is accurate in narrow visible spectral range (400 - 500 nm).
  19. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  20. D. R. Lide, CRC handbook of chemistry and physics: a ready-reference book of chemical and physical data, 88th ed. (CRC Press, 2008).
  21. FDTD simulation with a higher resolution of 0.75 nm also provides identical results.
  22. A. Taflove, and S. C. Hagness, Computational electrodynamics: The finite-difference time-domain method, 3rd ed. (Norwood, MA: Artech House, 2005), Chap. 5.
  23. A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
    [CrossRef]
  24. We tried different values of a and obtained similar h’s although the TE/TM ratios are slightly smaller than the ratio at a = 140 nm.
  25. J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
    [CrossRef]
  26. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
    [CrossRef] [PubMed]
  27. Similar results were obtained for other values of a, showing slightly smaller polarization ratios.

2010 (2)

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

2009 (6)

J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
[CrossRef]

L. Zhang, J. H. Teng, S. J. Chua, and E. A. Fitzgerald, “Linearly polarized light emission from InGaN light emitting diode with subwavelength metallic nanograting,” Appl. Phys. Lett. 95(26), 261110 (2009).
[CrossRef]

S. Noda and M. Fujita, “Light-emitting diodes: Photonic crystal efficiency boost,” Nat. Photonics 3(3), 129–130 (2009).
[CrossRef]

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[CrossRef]

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[CrossRef]

2008 (2)

S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[CrossRef]

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
[CrossRef]

2007 (2)

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007).
[CrossRef]

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

2004 (1)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

2003 (1)

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

2002 (1)

H. Kawamoto, “The History of Liquid-Crystal Displays,” Proc. IEEE 90(4), 460–500 (2002).
[CrossRef]

2000 (1)

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[CrossRef]

1999 (2)

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
[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(7), 4688–4695 (1999).
[CrossRef]

1996 (1)

R. E. Smith, M. E. Warren, J. R. Wendt, and G. A. Vawter, “Polarization-sensitive subwavelength antireflection surfaces on a semiconductor for 975 nm,” Opt. Lett. 21(15), 1201–1203 (1996).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Ahmed, F.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Ahn, S.

J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
[CrossRef]

Bae, D.-K.

S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[CrossRef]

Benisty, H.

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007).
[CrossRef]

Bergenek, K.

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

Bhat, J. C.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Cao, B.

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

Chang, H.

J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
[CrossRef]

Cho, H.-K.

S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Chua, S. J.

L. Zhang, J. H. Teng, S. J. Chua, and E. A. Fitzgerald, “Linearly polarized light emission from InGaN light emitting diode with subwavelength metallic nanograting,” Appl. Phys. Lett. 95(26), 261110 (2009).
[CrossRef]

Craford, M. G.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

David, A.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[CrossRef]

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
[CrossRef]

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007).
[CrossRef]

DenBaars, S. P.

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[CrossRef]

Ee, H.-S.

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

Fitzgerald, E. A.

L. Zhang, J. H. Teng, S. J. Chua, and E. A. Fitzgerald, “Linearly polarized light emission from InGaN light emitting diode with subwavelength metallic nanograting,” Appl. Phys. Lett. 95(26), 261110 (2009).
[CrossRef]

Fujita, M.

S. Noda and M. Fujita, “Light-emitting diodes: Photonic crystal efficiency boost,” Nat. Photonics 3(3), 129–130 (2009).
[CrossRef]

Gardner, N. F.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
[CrossRef]

Grundmann, M. J.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
[CrossRef]

Harbers, G.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

Huang, Z.

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

Hwang, J. K.

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(7), 4688–4695 (1999).
[CrossRef]

Jeon, H.

J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kaeding, J. F.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
[CrossRef]

Kawamoto, H.

H. Kawamoto, “The History of Liquid-Crystal Displays,” Proc. IEEE 90(4), 460–500 (2002).
[CrossRef]

Kim, A. Y.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Kim, J.

J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
[CrossRef]

Kim, S.-K.

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[CrossRef]

Krames, M. R.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
[CrossRef]

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Krauss, T. F.

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

Kwon, H.

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

Kwon, S.-H.

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

Lee, J.

J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
[CrossRef]

Lee, J.-S.

S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[CrossRef]

Lee, J.-W.

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

Lee, R. K.

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
[CrossRef]

Lee, Y. H.

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(7), 4688–4695 (1999).
[CrossRef]

Lee, Y.-H.

S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[CrossRef]

Linder, N.

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

Loncar, M.

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[CrossRef]

Ludowise, M. J.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Martin, P. S.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Megens, M. M.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[CrossRef]

Mihopoulos, T. G.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
[CrossRef]

Misra, M. S.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Moon, Y.-T.

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

Mueller, G. O.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Mueller-Mach, R.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

Mukai, T.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Nakamura, S.

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[CrossRef]

Narukawa, Y.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Niki, I.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Noda, S.

S. Noda and M. Fujita, “Light-emitting diodes: Photonic crystal efficiency boost,” Nat. Photonics 3(3), 129–130 (2009).
[CrossRef]

Okamoto, K.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Painter, O. J.

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
[CrossRef]

Park, H.-G.

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[CrossRef]

Park, Y.

J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
[CrossRef]

Pimputkar, S.

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[CrossRef]

Rumbolz, C.

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

Ryu, H. Y.

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(7), 4688–4695 (1999).
[CrossRef]

Scherer, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[CrossRef]

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
[CrossRef]

Shchekin, O. B.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

Shen, Y. C.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Shvartser, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Smith, R. E.

R. E. Smith, M. E. Warren, J. R. Wendt, and G. A. Vawter, “Polarization-sensitive subwavelength antireflection surfaces on a semiconductor for 975 nm,” Opt. Lett. 21(15), 1201–1203 (1996).
[CrossRef] [PubMed]

Speck, J. S.

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[CrossRef]

Stockman, S. A.

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Streubel, K.

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

Teng, J. H.

L. Zhang, J. H. Teng, S. J. Chua, and E. A. Fitzgerald, “Linearly polarized light emission from InGaN light emitting diode with subwavelength metallic nanograting,” Appl. Phys. Lett. 95(26), 261110 (2009).
[CrossRef]

Vawter, G. A.

R. E. Smith, M. E. Warren, J. R. Wendt, and G. A. Vawter, “Polarization-sensitive subwavelength antireflection surfaces on a semiconductor for 975 nm,” Opt. Lett. 21(15), 1201–1203 (1996).
[CrossRef] [PubMed]

Vuckovic, J.

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[CrossRef]

Vuckovic, J. S.

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
[CrossRef]

Wang, C.

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

Wang, J.

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

Warren, M. E.

R. E. Smith, M. E. Warren, J. R. Wendt, and G. A. Vawter, “Polarization-sensitive subwavelength antireflection surfaces on a semiconductor for 975 nm,” Opt. Lett. 21(15), 1201–1203 (1996).
[CrossRef] [PubMed]

Weisbuch, C.

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007).
[CrossRef]

Wendt, J. R.

R. E. Smith, M. E. Warren, J. R. Wendt, and G. A. Vawter, “Polarization-sensitive subwavelength antireflection surfaces on a semiconductor for 975 nm,” Opt. Lett. 21(15), 1201–1203 (1996).
[CrossRef] [PubMed]

Wierer, J. J.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[CrossRef]

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

Wiesmann, C.

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

Wirth, R.

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

Xu, K.

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

Xu, Y.

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
[CrossRef]

Yariv, A.

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
[CrossRef]

Zhang, B.

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

Zhang, G.

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

Zhang, L.

L. Zhang, J. H. Teng, S. J. Chua, and E. A. Fitzgerald, “Linearly polarized light emission from InGaN light emitting diode with subwavelength metallic nanograting,” Appl. Phys. Lett. 95(26), 261110 (2009).
[CrossRef]

Zhou, L.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

Zull, H.

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

Appl. Phys. Lett. (4)

S.-K. Kim, H.-K. Cho, D.-K. Bae, J.-S. Lee, H.-G. Park, and Y.-H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[CrossRef]

Y. C. Shen, J. J. Wierer, M. R. Krames, M. J. Ludowise, M. S. Misra, F. Ahmed, A. Y. Kim, G. O. Mueller, J. C. Bhat, S. A. Stockman, and P. S. Martin, “Optical cavity effects in InGaN/GaN quantum-well-heterostructure flip-chip light-emitting diodes,” Appl. Phys. Lett. 82(14), 2221 (2003).
[CrossRef]

L. Zhang, J. H. Teng, S. J. Chua, and E. A. Fitzgerald, “Linearly polarized light emission from InGaN light emitting diode with subwavelength metallic nanograting,” Appl. Phys. Lett. 95(26), 261110 (2009).
[CrossRef]

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[CrossRef]

K. Bergenek, C. Wiesmann, H. Zull, C. Rumbolz, R. Wirth, N. Linder, K. Streubel, and T. F. Krauss, “Strong high order diffraction of guided modes in micro-cavity light-emitting diodes with hexagonal photonic crystals,” IEEE J. Quantum Electron. 45(12), 1517–1523 (2009).
[CrossRef]

J. Display Tech. (2)

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Display Tech. 3(2), 133–148 (2007).
[CrossRef]

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Tech. 3(2), 160–175 (2007).
[CrossRef]

J. Opt. Soc. Am. B (1)

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Painter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16(3), 465–474 (1999).
[CrossRef]

Nat. Mater. (1)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Nat. Photonics (3)

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[CrossRef]

S. Noda and M. Fujita, “Light-emitting diodes: Photonic crystal efficiency boost,” Nat. Photonics 3(3), 129–130 (2009).
[CrossRef]

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[CrossRef]

Opt. Express (3)

S.-K. Kim, J.-W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, “High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters,” Opt. Express 18(11), 11025–11032 (2010).
[CrossRef] [PubMed]

G. Zhang, C. Wang, B. Cao, Z. Huang, J. Wang, B. Zhang, and K. Xu, “Polarized GaN-based LED with an integrated multi-layer subwavelength structure,” Opt. Express 18(7), 7019–7030 (2010).
[CrossRef] [PubMed]

J. Lee, S. Ahn, H. Chang, J. Kim, Y. Park, and H. Jeon, “Polarization-dependent GaN surface grating reflector for short wavelength applications,” Opt. Express 17(25), 22535–22542 (2009).
[CrossRef]

Opt. Lett. (1)

R. E. Smith, M. E. Warren, J. R. Wendt, and G. A. Vawter, “Polarization-sensitive subwavelength antireflection surfaces on a semiconductor for 975 nm,” Opt. Lett. 21(15), 1201–1203 (1996).
[CrossRef] [PubMed]

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[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(7), 4688–4695 (1999).
[CrossRef]

Proc. IEEE (1)

H. Kawamoto, “The History of Liquid-Crystal Displays,” Proc. IEEE 90(4), 460–500 (2002).
[CrossRef]

Other (7)

The spontaneous emission enhancement rate is defined by the spontaneous emission rate of a dipole source in a structure of interest which is divided by that in a homogeneous medium, as described in refs. [15] and [16].

We used a home-made FDTD code using Drude model, which is accurate in narrow visible spectral range (400 - 500 nm).

D. R. Lide, CRC handbook of chemistry and physics: a ready-reference book of chemical and physical data, 88th ed. (CRC Press, 2008).

FDTD simulation with a higher resolution of 0.75 nm also provides identical results.

A. Taflove, and S. C. Hagness, Computational electrodynamics: The finite-difference time-domain method, 3rd ed. (Norwood, MA: Artech House, 2005), Chap. 5.

Similar results were obtained for other values of a, showing slightly smaller polarization ratios.

We tried different values of a and obtained similar h’s although the TE/TM ratios are slightly smaller than the ratio at a = 140 nm.

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic diagram of an electric dipole located at a distance of h from a metal mirror. (b) Spontaneous emission enhancements were calculated as a function of h using a 3-D FDTD simulation. (c) The electric field intensity profiles calculated using 1-D FDTD simulation as planewave is normally incident to the mirror. In (b) and (c), perfect metal, aluminum and silver were used as a mirror.

Fig. 2
Fig. 2

(a) Schematic diagram of an ITO/silver grating mirror and TE and TM planewaves incident to the grating mirror. The pitch, width and depth of the grating are a, w and d, respectively. (b), (c), and (d) The TE and TM electric field profiles reflected from the ITO/silver grating mirror were calculated at a = 180 nm, d = 85 nm as a function of w, using a 2-D FDTD simulation. The calculated phase differences between TE and TM are (b) π/4 at w = 170 nm, (c) π/2 at w = 155 nm, and (d) π at w = 115 nm, respectively.

Fig. 3
Fig. 3

Calculated phase differences between the TE and TM waves reflected from the ITO/silver grating mirror with (a) a = 120 nm, (b) a = 180 nm, and (c) a = 240 nm. These graphs are plotted as a function of w and d of the grating. The white dashed circles indicate the widest regions of the phase difference of π. (d) Optimal w and d that maximize the phase difference of the reflected light are plotted as a function of a. The data is from (a), (b), and (c).

Fig. 4
Fig. 4

(a) Schematic diagram of a GaN LED structure with the QWs and ITO/silver grating mirror. The distance between the QWs and mirror is h. A single electric dipole is excited at (x, h) with changing x from 0 to a/2. (b) Spontaneous emission enhancement rates of the incoherent TE (red line) and TM (blue line) dipoles in the QWs were calculated as a function of h using a 3-D FDTD simulation. The structural parameters of the grating were set to a = 140 nm, w = 100 nm, and d = 95 nm. (c) The TE/TM ratios of the spontaneous emission enhancement rates are plotted as a function of h at w = 90 nm (magenta), w = 100 nm (black), and w = 110 nm (cyan). In the case of w = 100 nm, data was obtained from (b).

Fig. 5
Fig. 5

(a) Schematic diagram of a vertical GaN slab LED structure. The background is air and the thickness and lateral size of the GaN slab are 1 μm and 2 μm, respectively. The distance between the QWs and mirror is h. A single electric dipole was excited at (x, h) with changing x from 0 to a/2. (b) The normalized extracted powers with the TE (red line) and TM (blue line) polarization directions were calculated as a function of h at a = 200 nm, w = 120 nm, and d = 85 nm, using 3-D FDTD simulation. The TE/TM ratio was also plotted (green dashed line). (c) The field profiles of the TE part of Sz . Vertical emission is clearly shown. (d) The field profiles of the TM part of Sz . The field profiles in (c) and (d) are calculated at h = 75 nm.

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