Abstract

This study proposes a one-dimensional sub-wavelength grating structure on GaN surface which behaves as a reflector for transverse-electric polarized light in the blue wavelength range. The rigorous coupled-wave analysis method was used to analyze the effects of various structural parameters on the reflectance spectra of the grating. Based on the optimal design, a GaN surface grating reflector (SGR) was fabricated using holographic lithography and dry etching processes. It showed reflectance that exceeded 90% over a 60-nm bandwidth. The obtained experimental results were in good agreement with simulated ones. The SGR has an advantage of structural simplicity, which should greatly facilitate the fabrication and integration of high reflectors on GaN-based short-wavelength photonic devices.

© 2009 OSA

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References

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  1. G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
    [Crossref]
  2. S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
    [Crossref]
  3. M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 ( 2007).
    [Crossref]
  4. J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
    [Crossref]
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    [Crossref] [PubMed]
  9. Y. Ding and R. Magnusson, “Band gaps and leaky-wave effects in resonant photonic-crystal waveguides,” Opt. Express 15(2), 680–694 ( 2007).
    [Crossref] [PubMed]
  10. S. Boutami, B. Benbakir, X. Letartre, J. L. Leclercq, P. Regreny, and P. Viktorovitch, “Ultimate vertical Fabry-Perot cavity based on single-layer photonic crystal mirrors,” Opt. Express 15(19), 12443–12449 ( 2007).
    [Crossref] [PubMed]
  11. R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 ( 2008).
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  14. L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 ( 1907).
  15. E. Popov, M. Neviere, B. Gralak, and G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A 19(1), 33–42 ( 2002).
    [Crossref]
  16. C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
    [Crossref]
  17. C.-O. Cho, J. Lee, Y. Park, Y. Roh, H. Jeon, and I. Kim, “Photonic Crystal Cavity Lasers Patterned by a Combination of Holography and Photolithography,” IEEE Photon. Technol. Lett. 19(8), 556–558 ( 2007).
    [Crossref]
  18. J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
    [Crossref]

2009 (2)

J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
[Crossref]

J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
[Crossref]

2008 (1)

2007 (4)

C.-O. Cho, J. Lee, Y. Park, Y. Roh, H. Jeon, and I. Kim, “Photonic Crystal Cavity Lasers Patterned by a Combination of Holography and Photolithography,” IEEE Photon. Technol. Lett. 19(8), 556–558 ( 2007).
[Crossref]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 ( 2007).
[Crossref]

Y. Ding and R. Magnusson, “Band gaps and leaky-wave effects in resonant photonic-crystal waveguides,” Opt. Express 15(2), 680–694 ( 2007).
[Crossref] [PubMed]

S. Boutami, B. Benbakir, X. Letartre, J. L. Leclercq, P. Regreny, and P. Viktorovitch, “Ultimate vertical Fabry-Perot cavity based on single-layer photonic crystal mirrors,” Opt. Express 15(19), 12443–12449 ( 2007).
[Crossref] [PubMed]

2006 (2)

G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
[Crossref]

E. Bisaillon, D. Tan, B. Faraji, A. Kirk, L. Chrowstowski, and D. V. Plant, “High reflectivity air-bridge subwavelength grating reflector and Fabry-Perot cavity in AlGaAs/GaAs,” Opt. Express 14(7), 2573–2582 ( 2006).
[Crossref] [PubMed]

2005 (1)

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

2003 (1)

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

2002 (1)

1998 (1)

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 ( 1998).
[Crossref]

1995 (1)

1981 (1)

1907 (1)

L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 ( 1907).

1902 (1)

R. Wood, “On a remarkable case of uneven distribution of light in diffraction grating problems,” Philos. Mag. 4, 396–402 ( 1902).

Ahn, S.

J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
[Crossref]

Baek, J. H.

J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
[Crossref]

Baets, R.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 ( 1998).
[Crossref]

Benbakir, B.

Bisaillon, E.

Boons, S.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 ( 1998).
[Crossref]

Boutami, S.

Caekebeke, K.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 ( 1998).
[Crossref]

Chae, S.

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Chang, L.

G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
[Crossref]

Chang-Hasnain, C. J.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 ( 2007).
[Crossref]

Cho, C.-O.

C.-O. Cho, J. Lee, Y. Park, Y. Roh, H. Jeon, and I. Kim, “Photonic Crystal Cavity Lasers Patterned by a Combination of Holography and Photolithography,” IEEE Photon. Technol. Lett. 19(8), 556–558 ( 2007).
[Crossref]

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

Cho, Y.

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Choi, Y.

J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
[Crossref]

Chrowstowski, L.

Dhoedt, B.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 ( 1998).
[Crossref]

Ding, Y.

Faraji, B.

Gaylord, T. K.

Goeman, S.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 ( 1998).
[Crossref]

Gralak, B.

Grann, E. B.

Huang, G.

G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
[Crossref]

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 ( 2007).
[Crossref]

Jang, D.

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

Jeon, H.

J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
[Crossref]

J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
[Crossref]

C.-O. Cho, J. Lee, Y. Park, Y. Roh, H. Jeon, and I. Kim, “Photonic Crystal Cavity Lasers Patterned by a Combination of Holography and Photolithography,” IEEE Photon. Technol. Lett. 19(8), 556–558 ( 2007).
[Crossref]

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Jeong, C.

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Jeong, J.

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

Kim, D.

J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
[Crossref]

Kim, D. U.

J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
[Crossref]

Kim, I.

C.-O. Cho, J. Lee, Y. Park, Y. Roh, H. Jeon, and I. Kim, “Photonic Crystal Cavity Lasers Patterned by a Combination of Holography and Photolithography,” IEEE Photon. Technol. Lett. 19(8), 556–558 ( 2007).
[Crossref]

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

Kim, J.

J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
[Crossref]

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Kim, S.

J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
[Crossref]

Kirk, A.

Kuo, H.

G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
[Crossref]

Leclercq, J. L.

Lee, J.

J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
[Crossref]

J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
[Crossref]

C.-O. Cho, J. Lee, Y. Park, Y. Roh, H. Jeon, and I. Kim, “Photonic Crystal Cavity Lasers Patterned by a Combination of Holography and Photolithography,” IEEE Photon. Technol. Lett. 19(8), 556–558 ( 2007).
[Crossref]

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

Lee, S.

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Lee, S. J.

J. Lee, S. Ahn, S. Kim, D. U. Kim, H. Jeon, S. J. Lee, and J. H. Baek, “GaN light-emitting diode with monolithically integrated photonic crystals and angled sidewall deflectors for efficient surface emission,” Appl. Phys. Lett. 94(10), 101105 ( 2009).
[Crossref]

Letartre, X.

Lin, C.

G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
[Crossref]

Lu, T.

G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
[Crossref]

Magnusson, R.

Moharam, M. G.

Neviere, M.

Park, S.

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Park, Y.

J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
[Crossref]

C.-O. Cho, J. Lee, Y. Park, Y. Roh, H. Jeon, and I. Kim, “Photonic Crystal Cavity Lasers Patterned by a Combination of Holography and Photolithography,” IEEE Photon. Technol. Lett. 19(8), 556–558 ( 2007).
[Crossref]

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Plant, D. V.

Pommet, D. A.

Popov, E.

Rayleigh, L.

L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 ( 1907).

Regreny, P.

Roh, Y.

C.-O. Cho, J. Lee, Y. Park, Y. Roh, H. Jeon, and I. Kim, “Photonic Crystal Cavity Lasers Patterned by a Combination of Holography and Photolithography,” IEEE Photon. Technol. Lett. 19(8), 556–558 ( 2007).
[Crossref]

Sakong, T.

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Shokooh-Saremi, M.

Tan, D.

Tayeb, G.

Van Daele, P.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 ( 1998).
[Crossref]

Vandeputte, K.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photon. Technol. Lett. 10(9), 1205–1207 ( 1998).
[Crossref]

Viktorovitch, P.

Wang, S.

G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
[Crossref]

Woo, J.

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. Jang, Y. Park, and J. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 ( 2005).
[Crossref]

Wood, R.

R. Wood, “On a remarkable case of uneven distribution of light in diffraction grating problems,” Philos. Mag. 4, 396–402 ( 1902).

Yao, H.

G. Huang, T. Lu, H. Yao, H. Kuo, S. Wang, C. Lin, and L. Chang, “Crack-free GaN/AlN distributed Bragg reflectors incorporated with GaN/AlN superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 88(6), 061904 ( 2006).
[Crossref]

Yeom, G.

S. Park, J. Kim, H. Jeon, T. Sakong, S. Lee, S. Chae, Y. Park, C. Jeong, G. Yeom, and Y. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 ( 2003).
[Crossref]

Zhou, Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 ( 2007).
[Crossref]

Appl. Phys. Lett. (5)

J. Kim, D. Kim, J. Lee, H. Jeon, Y. Park, and Y. Choi, “AlGaN membrane grating reflector,” Appl. Phys. Lett. 95(2), 021102 ( 2009).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a 1D GaN SGR.

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Fig. 2
Fig. 2

Calculated diffraction efficiency spectra of a GaN SGR (optimized for λ = 450 nm and TE-polarization) for all the allowed diffraction orders in both reflection and transmission: (a) TE-polarization and (b) TM-polarization. Light is incident in the normal direction from the GaN side. (c) Electric field distribution in the vicinity of the SGR for the λ = 450 nm TE-polarized light. (d) Electric field profiles integrated over a grating peak (red line) and over a grating trough (blue line), and their sum (black line). Shaded is the grating region.

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Fig. 3
Fig. 3

Contour plots of the GaN SGR (optimized for λ = 450 nm TE-polarization) for various structural parameters: (a) period, (b) height, (c) filling factor, and (d) slanted angle of the grating.

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Fig. 4
Fig. 4

(a) Schematic diagram of the holographic lithography setup used in the experiments. SEM images of the fabricated GaN SGR: (b) cross-section and (c) plan-view.

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Fig. 5
Fig. 5

(a) Schematic of the reflectance spectrum measurement setup, where the Xe lamp is used as a white light source. (b) Experimental and calculated reflectance spectra of the SGR (but including the sapphire substrate) for both TE and TM polarizations.

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