Abstract

Photonic modes in a two-dimensional square-lattice photonic crystal (PC) with anisotropic gain are analyzed for the first time. A plane-wave expansion method is improved to include the gain, which depends on not only the position but also the propagation direction of each plane wave. The anisotropic gain varies the photonic band structure, the near-field distributions, and the gain dispersion curves through variation in PC symmetry. Low-threshold operation of a PC laser with anisotropic-gain material such as nonpolar InGaN requires that the direction of higher gain in the material aligns along the ΓX direction of the PC.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
    [CrossRef]
  2. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002).
    [CrossRef]
  3. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
    [CrossRef] [PubMed]
  4. K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
    [CrossRef]
  5. G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
    [CrossRef]
  6. L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
    [CrossRef] [PubMed]
  7. O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
    [CrossRef]
  8. E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
    [CrossRef]
  9. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
    [CrossRef]
  10. S. Nojima, “Enhancement of optical gain in two-dimensional photonic crystals with active lattice points,” Jpn. J. Appl. Phys. 37(Part 2, No. 5B), L565–L567 (1998).
    [CrossRef]
  11. S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
    [CrossRef]
  12. M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
    [CrossRef] [PubMed]
  13. V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60(8), 5359–5365 (1999).
    [CrossRef]
  14. I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
    [CrossRef]
  15. S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007).
    [CrossRef]
  16. K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 46(5), 788–795 (2010).
    [CrossRef]
  17. K. Sakai, E. Miyai, and S. Noda, “Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization,” Opt. Express 15(7), 3981–3990 (2007).
    [CrossRef] [PubMed]
  18. K. Okamoto, J. Kashiwagi, T. Tanaka, and M. Kubota, “Nonpolar m-plane InGaN multiple quantum well laser diodes with a lasing wavelength of 499.8nm,” Appl. Phys. Lett. 94(7), 071105 (2009).
    [CrossRef]
  19. A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
    [CrossRef]
  20. Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
    [CrossRef]
  21. P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
    [CrossRef]
  22. T. Ohtoshi and T. Kuroda, “Dependence of optical gain on crystal orientation in wurtzite-GaN strained quantum-well lasers,” Appl. Phys. Lett. 82, 1518–1520 (1997).
  23. S.-H. Park, “Crystal orientation effects on many-body optical gain of wurtzite InGaN/GaN quantum well lasers,” Jpn. J. Appl. Phys. 42(Part 2, No. 2B), L170–L172 (2003).
    [CrossRef]
  24. W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009).
    [CrossRef]
  25. K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007).
    [CrossRef]
  26. T. Onuma, K. Okamoto, H. Ohta, and S. F. Chichibu, “Anisotropic optical gain in m-plane InxGa1-xN/GaN multiple quantum well laser diode wafers fabricated on the low defect density freestanding GaN substrate,” Appl. Phys. Lett. 93(9), 091112 (2008).
    [CrossRef]
  27. H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
    [CrossRef]
  28. M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
    [CrossRef] [PubMed]
  29. A. Yariv, Introduction to Optical Electronics (Holts, Rinehart and Winston. Inc, 1974).
  30. T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
    [CrossRef]
  31. M. J. Bergmann and H. C. Casey., “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys. 84(3), 1196–1203 (1998).
    [CrossRef]
  32. L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
    [CrossRef]
  33. K. Inoue and K. Ohtaka, Photonic Crystals (Springer-Verlag, 2004).
  34. R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation losses,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
    [CrossRef]

2010 (3)

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 46(5), 788–795 (2010).
[CrossRef]

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

2009 (4)

K. Okamoto, J. Kashiwagi, T. Tanaka, and M. Kubota, “Nonpolar m-plane InGaN multiple quantum well laser diodes with a lasing wavelength of 499.8nm,” Appl. Phys. Lett. 94(7), 071105 (2009).
[CrossRef]

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009).
[CrossRef]

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

2008 (6)

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef]

T. Onuma, K. Okamoto, H. Ohta, and S. F. Chichibu, “Anisotropic optical gain in m-plane InxGa1-xN/GaN multiple quantum well laser diode wafers fabricated on the low defect density freestanding GaN substrate,” Appl. Phys. Lett. 93(9), 091112 (2008).
[CrossRef]

H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
[CrossRef]

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

2007 (5)

S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007).
[CrossRef]

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007).
[CrossRef]

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

K. Sakai, E. Miyai, and S. Noda, “Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization,” Opt. Express 15(7), 3981–3990 (2007).
[CrossRef] [PubMed]

2005 (1)

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
[CrossRef]

2003 (2)

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

S.-H. Park, “Crystal orientation effects on many-body optical gain of wurtzite InGaN/GaN quantum well lasers,” Jpn. J. Appl. Phys. 42(Part 2, No. 2B), L170–L172 (2003).
[CrossRef]

2002 (1)

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002).
[CrossRef]

2001 (1)

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

2000 (1)

I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

1999 (1)

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60(8), 5359–5365 (1999).
[CrossRef]

1998 (2)

S. Nojima, “Enhancement of optical gain in two-dimensional photonic crystals with active lattice points,” Jpn. J. Appl. Phys. 37(Part 2, No. 5B), L565–L567 (1998).
[CrossRef]

M. J. Bergmann and H. C. Casey., “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys. 84(3), 1196–1203 (1998).
[CrossRef]

1997 (2)

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[CrossRef]

T. Ohtoshi and T. Kuroda, “Dependence of optical gain on crystal orientation in wurtzite-GaN strained quantum-well lasers,” Appl. Phys. Lett. 82, 1518–1520 (1997).

1994 (1)

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

1991 (1)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
[CrossRef] [PubMed]

1985 (1)

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation losses,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
[CrossRef]

Abram, R. A.

S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007).
[CrossRef]

Adachi, M.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Adachi, S.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[CrossRef]

Akita, K.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Amanti, M. I.

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Apostolopoulos, V.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Asano, T.

H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
[CrossRef]

Beere, H.

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Beere, H. E.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Bergmann, M. J.

M. J. Bergmann and H. C. Casey., “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys. 84(3), 1196–1203 (1998).
[CrossRef]

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Brand, S.

S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007).
[CrossRef]

Capasso, F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Casey, H. C.

M. J. Bergmann and H. C. Casey., “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys. 84(3), 1196–1203 (1998).
[CrossRef]

Chan, C. T.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Chen, X.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Chichibu, S. F.

T. Onuma, K. Okamoto, H. Ohta, and S. F. Chichibu, “Anisotropic optical gain in m-plane InxGa1-xN/GaN multiple quantum well laser diode wafers fabricated on the low defect density freestanding GaN substrate,” Appl. Phys. Lett. 93(9), 091112 (2008).
[CrossRef]

K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007).
[CrossRef]

Cho, A. Y.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Chutinan, A.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002).
[CrossRef]

Cohen, D. A.

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Colombelli, R.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

DenBaars, S. P.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Dunbar, L. A.

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Enya, Y.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Faist, J.

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Farrell, R. M.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

Fleury, B.

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

Freeman, J. R.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Fujita, M.

H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
[CrossRef]

Fujito, K.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Fuke, S.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[CrossRef]

Giovannini, M.

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Gmachl, C. F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Haeger, D. A.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

Hangleiter, A.

W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009).
[CrossRef]

Henry, C. H.

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation losses,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
[CrossRef]

Ho, K. H.

I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Ho, K. M.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Houdre, R.

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Houdré, R.

Hoyler, N.

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Hsu, P. S.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

Hu, E.

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

Ichihara, J.

K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007).
[CrossRef]

Ikegami, T.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Imada, M.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002).
[CrossRef]

Jiang, D. S.

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

Jiang, X.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Jianglin, Y.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef]

Kaliteevski, M. A.

S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007).
[CrossRef]

Kashiwagi, J.

K. Okamoto, J. Kashiwagi, T. Tanaka, and M. Kubota, “Nonpolar m-plane InGaN multiple quantum well laser diodes with a lasing wavelength of 499.8nm,” Appl. Phys. Lett. 94(7), 071105 (2009).
[CrossRef]

Katayama, K.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Kawashima, T.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[CrossRef]

Kazarinov, R. F.

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation losses,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
[CrossRef]

Kelchner, K. M.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

Kitagawa, H.

H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
[CrossRef]

Kubota, M.

K. Okamoto, J. Kashiwagi, T. Tanaka, and M. Kubota, “Nonpolar m-plane InGaN multiple quantum well laser diodes with a lasing wavelength of 499.8nm,” Appl. Phys. Lett. 94(7), 071105 (2009).
[CrossRef]

Kuroda, T.

T. Ohtoshi and T. Kuroda, “Dependence of optical gain on crystal orientation in wurtzite-GaN strained quantum-well lasers,” Appl. Phys. Lett. 82, 1518–1520 (1997).

Kyono, T.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Lin, Y.-D.

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Liu, Z. S.

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

Maradudin, A. A.

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
[CrossRef] [PubMed]

Marshall, O. P.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Matioli, E.

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

Matsubara, H.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef]

Melo, T.

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

Miyai, E.

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 46(5), 788–795 (2010).
[CrossRef]

K. Sakai, E. Miyai, and S. Noda, “Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization,” Opt. Express 15(7), 3981–3990 (2007).
[CrossRef] [PubMed]

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
[CrossRef]

Mochizuki, M.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002).
[CrossRef]

Modinos, A.

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60(8), 5359–5365 (1999).
[CrossRef]

Nakamura, S.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Nakamura, T.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Noda, S.

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 46(5), 788–795 (2010).
[CrossRef]

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef]

H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
[CrossRef]

K. Sakai, E. Miyai, and S. Noda, “Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization,” Opt. Express 15(7), 3981–3990 (2007).
[CrossRef] [PubMed]

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002).
[CrossRef]

Nojima, S.

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

S. Nojima, “Enhancement of optical gain in two-dimensional photonic crystals with active lattice points,” Jpn. J. Appl. Phys. 37(Part 2, No. 5B), L565–L567 (1998).
[CrossRef]

Ohnishi, D.

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
[CrossRef]

Ohta, H.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

T. Onuma, K. Okamoto, H. Ohta, and S. F. Chichibu, “Anisotropic optical gain in m-plane InxGa1-xN/GaN multiple quantum well laser diode wafers fabricated on the low defect density freestanding GaN substrate,” Appl. Phys. Lett. 93(9), 091112 (2008).
[CrossRef]

K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007).
[CrossRef]

Ohtoshi, T.

T. Ohtoshi and T. Kuroda, “Dependence of optical gain on crystal orientation in wurtzite-GaN strained quantum-well lasers,” Appl. Phys. Lett. 82, 1518–1520 (1997).

Ohtsuka, K.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[CrossRef]

Okamoto, K.

K. Okamoto, J. Kashiwagi, T. Tanaka, and M. Kubota, “Nonpolar m-plane InGaN multiple quantum well laser diodes with a lasing wavelength of 499.8nm,” Appl. Phys. Lett. 94(7), 071105 (2009).
[CrossRef]

T. Onuma, K. Okamoto, H. Ohta, and S. F. Chichibu, “Anisotropic optical gain in m-plane InxGa1-xN/GaN multiple quantum well laser diode wafers fabricated on the low defect density freestanding GaN substrate,” Appl. Phys. Lett. 93(9), 091112 (2008).
[CrossRef]

K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007).
[CrossRef]

Okano, T.

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
[CrossRef]

Onuma, T.

T. Onuma, K. Okamoto, H. Ohta, and S. F. Chichibu, “Anisotropic optical gain in m-plane InxGa1-xN/GaN multiple quantum well laser diode wafers fabricated on the low defect density freestanding GaN substrate,” Appl. Phys. Lett. 93(9), 091112 (2008).
[CrossRef]

Painter, O.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Park, S.-H.

S.-H. Park, “Crystal orientation effects on many-body optical gain of wurtzite InGaN/GaN quantum well lasers,” Jpn. J. Appl. Phys. 42(Part 2, No. 2B), L170–L172 (2003).
[CrossRef]

Plihal, M.

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
[CrossRef] [PubMed]

Rangel, E.

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

Ritchie, D.

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Ritchie, D. A.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Rungsawang, R.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Sadowski, M. L.

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Saito, H.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef]

Saito, M.

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Sakaguchi, T.

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
[CrossRef]

Sakai, K.

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 46(5), 788–795 (2010).
[CrossRef]

K. Sakai, E. Miyai, and S. Noda, “Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization,” Opt. Express 15(7), 3981–3990 (2007).
[CrossRef] [PubMed]

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
[CrossRef]

Scalari, G.

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Scheibenzuber, W.

W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009).
[CrossRef]

Schwarz, U.

W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009).
[CrossRef]

Sergent, A. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Sigalas, M. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Sirigu, L.

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Sivco, D. L.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Soukoulis, C. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Speck, J.

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

Speck, J. S.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Srinivasan, K.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Stefanou, N.

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60(8), 5359–5365 (1999).
[CrossRef]

Sumitomo, T.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Suto, T.

H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
[CrossRef]

Takasu, H.

K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007).
[CrossRef]

Tanaka, T.

K. Okamoto, J. Kashiwagi, T. Tanaka, and M. Kubota, “Nonpolar m-plane InGaN multiple quantum well laser diodes with a lasing wavelength of 499.8nm,” Appl. Phys. Lett. 94(7), 071105 (2009).
[CrossRef]

Tanaka, Y.

H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
[CrossRef]

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef]

Tennant, D. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Terazzi, R.

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Tokuyama, S.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Troccoli, M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Tyagi, A.

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Ueno, M.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Veprek, R.

W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009).
[CrossRef]

Walther, C.

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

Weisbuch, C.

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

Witzigmann, B.

W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009).
[CrossRef]

Yang, H.

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

Yannopapas, V.

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60(8), 5359–5365 (1999).
[CrossRef]

Yao, P.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Yoshikawa, H.

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[CrossRef]

Yoshimoto, S.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef]

Yoshizumi, Y.

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

Zhang, J.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Zhang, L. Q.

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

Zhang, S. M.

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

Zhao, D.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Zhao, D. G.

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

Zhu, J. J.

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

Appl. Phys. Express (5)

A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008).
[CrossRef]

Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009).
[CrossRef]

P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010).
[CrossRef]

H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008).
[CrossRef]

E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010).
[CrossRef]

Appl. Phys. Lett. (5)

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

T. Onuma, K. Okamoto, H. Ohta, and S. F. Chichibu, “Anisotropic optical gain in m-plane InxGa1-xN/GaN multiple quantum well laser diode wafers fabricated on the low defect density freestanding GaN substrate,” Appl. Phys. Lett. 93(9), 091112 (2008).
[CrossRef]

K. Okamoto, J. Kashiwagi, T. Tanaka, and M. Kubota, “Nonpolar m-plane InGaN multiple quantum well laser diodes with a lasing wavelength of 499.8nm,” Appl. Phys. Lett. 94(7), 071105 (2009).
[CrossRef]

T. Ohtoshi and T. Kuroda, “Dependence of optical gain on crystal orientation in wurtzite-GaN strained quantum-well lasers,” Appl. Phys. Lett. 82, 1518–1520 (1997).

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 46(5), 788–795 (2010).
[CrossRef]

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation losses,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
[CrossRef]

IEEE J. Sel. Areas Comm. (1)

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005).
[CrossRef]

J. Appl. Phys. (5)

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007).
[CrossRef]

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997).
[CrossRef]

M. J. Bergmann and H. C. Casey., “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys. 84(3), 1196–1203 (1998).
[CrossRef]

L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009).
[CrossRef]

Jpn. J. Appl. Phys. (3)

S. Nojima, “Enhancement of optical gain in two-dimensional photonic crystals with active lattice points,” Jpn. J. Appl. Phys. 37(Part 2, No. 5B), L565–L567 (1998).
[CrossRef]

S.-H. Park, “Crystal orientation effects on many-body optical gain of wurtzite InGaN/GaN quantum well lasers,” Jpn. J. Appl. Phys. 42(Part 2, No. 2B), L170–L172 (2003).
[CrossRef]

K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (5)

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60(8), 5359–5365 (1999).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002).
[CrossRef]

W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009).
[CrossRef]

Phys. Rev. B Condens. Matter (2)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991).
[CrossRef] [PubMed]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Science (2)

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef]

Other (2)

A. Yariv, Introduction to Optical Electronics (Holts, Rinehart and Winston. Inc, 1974).

K. Inoue and K. Ohtaka, Photonic Crystals (Springer-Verlag, 2004).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Schematic diagram of a PC layer (period: a; radius:r). Here α and β are the orthogonal gain directions of the PC material; k' is the wavevector for an expanded plane wave. The dashed line is parallel to a primitive transformation vector of PC. HL and BG represent the regions within or outside a circular cross-section.

Fig. 2
Fig. 2

Cross-section of calculated model. AROG denotes “air holes retained over growth,” whose layers provide the PC configuration. HL and BG correspond the regions within or outside a circular cross-section in Fig. 1.

Fig. 3
Fig. 3

Photonic band structure with four photonic modes, A, B, C, and D. Although calculation is undertaken for isotropic gain and anisotropic gain with θ = 0, 45, and 90 deg, no significant difference is observed in this axis range.

Fig. 4
Fig. 4

Normalized frequencies of photonic modes at the Γ2 point as a function of θ. Solid and dotted lines represent anisotropic and isotropic gains, respectively.

Fig. 5
Fig. 5

Near-field distribution of photonic modes at Γ2 point. Black circles represent the HL shape of the PC.

Fig. 6
Fig. 6

Gain dispersion of photonic modes for (a) isotropic gain and anisotropic gain with (b) θ = 0, (c) 45, and (d) 90 deg.

Fig. 7
Fig. 7

Gains of photonic modes at the Γ2 point as a function of θ. Solid and dotted lines are anisotropic and isotropic gains, respectively.

Fig. 8
Fig. 8

Near-field distribution of the anisotropic-gain photonic modes at Γ2 point. Δθ is defined as Δθ = 45 deg - θ. Black circles represent the HL shape of the PC.

Fig. 9
Fig. 9

Real and imaginary parts of B coefficients of expanded plane waves as a function of Δθ. (a), (b), (c), and (d) are A, B, C, and D modes, respectively. The parameters are reciprocal vectors, (G)1 to (G)4.

Fig. 10
Fig. 10

Gains of photonic modes at the Γ2 point as a function of θ with radiation loss. Solid and dotted lines are anisotropic and isotropic gains, respectively.

Equations (40)

Equations on this page are rendered with MathJax. Learn more.

H 3 ( x ¯ ) = G h 3 ( k , G , x ¯ ) exp ( i ω t ) ,
h 3 ( k , G , x ¯ ) = B ( k , G ) exp { i ( k + G ) x ¯ } ,
1 / ε ( k ' , x ¯ ) = G ' κ ¯ ( k ' , G ' ) exp ( i G ' x ¯ ) ,
κ ¯ ( k ' , G ' ) = { f / ε a ( k ' ) + ( 1 f ) / ε b ( k ' ) ( G ' = 0 ) , 2 f [ 1 / ε a ( k ' ) 1 / ε b ( k ' ) ] J 1 ( | G ' r | ) / | G ' r | ( G ' 0 ) ,
x 1 { 1 ε ( k + G , x ¯ ) x 1 h 3 ( k , G , x ¯ ) } + x 2 { 1 ε ( k + G , x ¯ ) x 2 h 3 ( k , G , x ¯ ) } = ω 2 c 2 h 3 ( k , G , x ¯ ) ,
x 1 G { 1 ε ( k + G , x ¯ ) x 1 h 3 ( k , G , x ¯ ) } + x 2 G { 1 ε ( k + G , x ¯ ) x 2 h 3 ( k , G , x ¯ ) } = ω 2 c 2 G h 3 ( k , G , x ¯ ) .
G G ' ( k + G ) ( k + G ' ) κ ¯ ( k + G ' , G G ' ) B ( k , G ' ) exp { i ( k + G ) x ¯ } = ω 2 c 2 G h 3 ( k , G , x ¯ ) .
G ' ( k + G ) ( k + G ' ) κ ¯ ( k + G ' , G G ' ) B ( k , G ' ) = ( ω 2 / c 2 ) B ( k , G )
1 / n γ 2 = cos 2 φ / n α 2 + sin 2 φ / n β 2 ,
1 / n γ 2 = 1 / ε ( k ' , x ¯ ) = G ' κ ¯ ( k ' , G ' ) exp ( i G ' x ¯ ) ,
1 / n α 2 = 1 / ε α ( x ¯ ) = G ' κ ¯ α ( G ' ) exp ( i G ' x ¯ ) ,
1 / n β 2 = 1 / ε β ( x ¯ ) = G ' κ ¯ β ( G ' ) exp ( i G ' x ¯ ) ,
κ ¯ ( k ' , G ' ) = κ ¯ α ( G ' ) cos 2 φ + κ ¯ β ( G ' ) sin 2 φ .
ω = ω r + i ω i .
H 3 ( x ¯ ) n = 1 4 B ( k , G n , ω ) exp i [ ( k + G n ) x ¯ ω t ] .
H 3 ( x ^ ) = n = 1 4 B x ¯ ( G n ) exp [ i ( k + G n ) x ¯ ] φ ( x 3 ) + Δ H ( x ^ ) ,
2 Δ H ( x ^ ) / x i x j = 2 B x ¯ ( G , ω ) / x i x j = 0 ,
2 φ ( x 3 ) / x 3 2 = ( ω / c ) 2 Δ ε ( x 3 ) φ ( x 3 ) ,
1 / ε ( x ^ ) = G κ ^ ( G , x 3 ) exp ( i G x ¯ ) ,
κ ^ ( G , x 3 ) = { κ ¯ p ( G ) ( g 1 x 3 g 2 ) , 1 / ε ( x 3 ) ( x 3 < g 1 , g 2 x 3 , G = 0 ) , 0 ( x 3 < g 1 , g 2 x 3 , G 0 ) ,
κ ¯ p ( G ) = { f / ε p a + ( 1 f ) / ε p b ( G = 0 ) , ( 1 / ε p a 1 / ε p b ) 2 f J 1 ( | G r | ) / | G r | ( G 0 ) .
x 1 [ 1 ε ( x ^ ) H 3 ( x ^ ) x 1 ] + x 2 [ 1 ε ( x ^ ) H 3 ( x ^ ) x 2 ] + 1 ε ( x ^ ) 2 H 3 ( x ^ ) x 3 2 = ω 2 c 2 H 3 ( x ^ ) .
G [ n = 1 4 κ ^ ( G G n , x 3 ) { i ( G + G n ) ¯ G G n + ( ω / c ) 2 Δ ε ( x 3 ) } B x ¯ ( G n ) φ ( x 3 ) + κ ^ ( G , x 3 ) ( i G ¯ + 2 / x 3 2 ) Δ H ( x ^ ) ] exp ( i G x ¯ ) + ( ω / c ) 2 [ n = 1 4 B x ¯ ( G n ) φ ( x 3 ) exp ( i G n x ¯ ) + Δ H ( x ^ ) ] = 0 ,
[ κ ^ ( 0 , x 3 ) 2 / x 3 2 + ( ω / c ) 2 ] Δ H ( x ^ ) = n = 1 4 κ ^ ( G n , x 3 ) [ i G n ¯ + ( ω / c ) 2 Δ ε ( x 3 ) ] B x ¯ ( G n ) φ ( x 3 ) .
Δ H ( x ^ ) = n = 1 4 [ κ ^ ( G n , t ) / κ ^ ( 0 , t ) ] [ i G n ¯ + ( ω / c ) 2 Δ ε ( t ) ] B x ¯ ( G n ) φ ( t ) G ˜ ( x 3 , t ) d t = n = 1 4 [ κ ¯ p ( G n ) / κ ¯ p ( 0 ) ] [ i G n ¯ + ( ω / c ) 2 Δ ε p ] B x ¯ ( G n ) g 1 g 2 φ ( t ) G ˜ ( x 3 , t ) d t ,
n = 1 4 κ ^ ( G m G n , x 3 ) { i ( G m + G n ) ¯ G m G n + ( ω / c ) 2 Δ ε ( x 3 ) } B x ¯ ( G n ) φ ( x 3 ) + κ ^ ( G m , x 3 ) ( i G m ¯ + 2 / x 3 2 ) Δ H ( x ^ ) + ( ω / c ) 2 B x ¯ ( G m ) φ ( x 3 ) = 0.
n = 1 4 [ i ( F ( G n , G m ) ¯ + A ( G n , G m ) ] B x ¯ ( G n ) + ( ω / c ) 2 B x ¯ ( G m ) = 0 ,
F ( G n , G m ) = κ ¯ p ( G m G n ) ( G m + G n ) [ κ ¯ p ( G m ) κ ¯ p ( G n ) / κ ¯ p ( 0 ) ] [ ς ( ω / c ) 2 Δ ε p G m + ξ G n ] ,
A ( G n , G m ) = κ ¯ p ( G m G n ) [ G m G n + ( ω / c ) 2 Δ ε p ] [ κ ¯ p ( G m ) κ ¯ p ( G n ) / κ ¯ p ( 0 ) ] ξ ( ω / c ) 2 Δ ε p ,
ς = ( 1 / Γ g ) g 1 g 2 g 1 g 2 φ ( x 3 ) φ ( t ) G ˜ ( x 3 , t ) d t d x 3 ,
ξ = ( 1 / Γ g ) g 1 g 2 φ ( x 3 ) [ 2 x 3 2 g 1 g 2 φ ( t ) G ˜ ( x 3 , t ) d t ] d x 3 .
Γ g = g 1 g 2 φ ( x 3 ) 2 d x 3 .
ς = [ i K 3 d g + 1 exp ( i K 3 d g ) ] / i K 3 3 d g ,
ξ = i [ 1 exp ( i K 3 d g ) ] / K 3 d g .
i [ B x 1 ( G 1 ) / x 1 ] = [ ( c m ± d m ) / ( a m ± b m ) ] B x 1 ( G 1 ) ,
i [ B x 1 ( G 2 ) / x 1 ] = [ ( c m ± d m ) / ( a m ± b m ) ] B x 1 ( G 2 ) ,
Q s = Im [ Γ g ( c m + d m ) / ( a m + b m ) ] = Im { Γ g | G m | 2 x 2 [ ( 1 + P 2 ) Δ ε + 1 / κ ¯ p ( 0 ) 2 ξ P 1 2 Δ ε ] ( 1 P 2 ) 1 ξ P 1 2 } ,
Q a = Im [ Γ g ( c m d m ) / ( a m b m ) ] = Im { Γ g | G m | 2 x 2 [ ( 1 P 2 ) Δ ε + 1 / κ ¯ p ( 0 ) ] ( 1 + P 2 ) 1 ς Δ ε ( x | G m | P 1 ) 2 } ,
Q A = Im { Γ g | G m | 2 x 2 [ ( 1 + P 2 + 2 P 3 ) Δ ε + 1 / κ ¯ p ( 0 ) 4 ξ P 1 2 Δ ε ] ( 1 P 2 ) 1 + P 3 ξ P 1 2 } ,
Q B = Im { Γ g | G m | 2 x 2 [ ( 1 + P 2 2 P 3 ) Δ ε 1 / κ ¯ p ( 0 ) ] ( 1 P 2 ) 1 + P 3 ξ P 1 2 } ,

Metrics