Abstract

We use the finite-difference time domain method to calculate the vertical optical confinement, which corresponds to the quality factor in the vertical direction, of two-dimensional photonic-crystal (PC) lasers as a function of the asymmetry of the shape of the air holes that form the PC. The vertical optical confinement for triangular air holes, which give the highest output power measured thus far, is decreased by two thirds when V-shaped air holes are used. In contrast, the vertical optical confinement becomes infinite for rhomboid air holes. The vertical optical confinement decreases when the air holes are deformed such that areas of opposing electric fields exist in regions of the PC with different dielectric constants. In this way, the vertical optical confinement can be controlled by changing the shape of the air holes.

© 2008 Optical Society of America

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  1. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
    [CrossRef]
  2. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
    [CrossRef]
  3. K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys. 38, L157-L159 (1999).
    [CrossRef]
  4. M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
    [CrossRef]
  5. M. Notomi, H. Suzuki, and T. Tamamura, "Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps," Appl. Phys. Lett. 78, 1325-1327 (2001).
    [CrossRef]
  6. H. -Y. Ryu, S. -H. Kwon, Y. - J. Lee, Y. -H. Lee, and J. - S. Kim, "Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs," Appl. Phys. Lett. 80, 3476-3478 (2002).
    [CrossRef]
  7. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 1-8 (2002).
    [CrossRef]
  8. I. Vurgaftman and J. R. Meyer, "Design Optimization for High-Brightness Surface-Emitting Photonic-Crystal Distributed-Feedback Lasers," IEEE J. Quantum Electron. 39, 689-700 (2003).
    [CrossRef]
  9. K. Sakai, E. Miyai, and S. Noda, "Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode," Appl. Phys. Lett. 89, 021101 1-3 (2006).
    [CrossRef]
  10. K. Sakai, E. Miyai, and S. Noda, "Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization," Opt. Express 15, 3981-3990 (2007).
    [CrossRef] [PubMed]
  11. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design," Science 293, 1123-1125 (2001).
    [CrossRef] [PubMed]
  12. M. Yokoyama and S. Noda, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser Having a Square Lattice Structure," IEEE J. Quantum Electron. 39, 1074-1080 (2003).
    [CrossRef]
  13. E. Miyai and S. Noda, "Phase-shift effect on a two-dimensional surface-emitting photonic-crystal laser," Appl. Phys. Lett. 86, 111113 1-3 (2005).
    [CrossRef]
  14. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, "Lasers producing tailored beams," Nature 441, 946 (2006).
    [CrossRef] [PubMed]
  15. 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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
    [CrossRef]
  16. D. Ohnishi, T. Okano, M. Imada, and S. Noda, "Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser," Opt. Express 12, 1562-1568 (2004).
    [CrossRef] [PubMed]
  17. W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, "High-Power Single-Lobed Surface-Emitting Photonic-Crystal Laser," in Proceedings of the Conference on Lasers and Electro-optics, Paper CMKK1 (2006).
  18. E. Miyai, K. Sakai, W. Kunishi, D. Ohnishi, and S. Noda "Linearly-polarized single-lobed beams by photonic-crystal lasers with triangular lattice points," to be submitted.
  19. Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).

2008 (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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
[CrossRef]

2007 (1)

2006 (1)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, "Lasers producing tailored beams," Nature 441, 946 (2006).
[CrossRef] [PubMed]

2004 (1)

2003 (3)

M. Yokoyama and S. Noda, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser Having a Square Lattice Structure," IEEE J. Quantum Electron. 39, 1074-1080 (2003).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).

I. Vurgaftman and J. R. Meyer, "Design Optimization for High-Brightness Surface-Emitting Photonic-Crystal Distributed-Feedback Lasers," IEEE J. Quantum Electron. 39, 689-700 (2003).
[CrossRef]

2002 (1)

H. -Y. Ryu, S. -H. Kwon, Y. - J. Lee, Y. -H. Lee, and J. - S. Kim, "Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs," Appl. Phys. Lett. 80, 3476-3478 (2002).
[CrossRef]

2001 (2)

M. Notomi, H. Suzuki, and T. Tamamura, "Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps," Appl. Phys. Lett. 78, 1325-1327 (2001).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

1999 (4)

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys. 38, L157-L159 (1999).
[CrossRef]

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

Akahane, Y.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).

Asano, T.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).

Chutinan, A.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 1-8 (2002).
[CrossRef]

Dodabalapur, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

Haus, J. W.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys. 38, L157-L159 (1999).
[CrossRef]

Imada, M.

D. Ohnishi, T. Okano, M. Imada, and S. Noda, "Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser," Opt. Express 12, 1562-1568 (2004).
[CrossRef] [PubMed]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 1-8 (2002).
[CrossRef]

Inoue, K.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys. 38, L157-L159 (1999).
[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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
[CrossRef]

Joannopoulos, J. D.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

Kawamata, J.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys. 38, L157-L159 (1999).
[CrossRef]

Kim, J. - S.

H. -Y. Ryu, S. -H. Kwon, Y. - J. Lee, Y. -H. Lee, and J. - S. Kim, "Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs," Appl. Phys. Lett. 80, 3476-3478 (2002).
[CrossRef]

Kunishi, W.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, "Lasers producing tailored beams," Nature 441, 946 (2006).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, W. Kunishi, D. Ohnishi, and S. Noda "Linearly-polarized single-lobed beams by photonic-crystal lasers with triangular lattice points," to be submitted.

Kwon, S. -H.

H. -Y. Ryu, S. -H. Kwon, Y. - J. Lee, Y. -H. Lee, and J. - S. Kim, "Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs," Appl. Phys. Lett. 80, 3476-3478 (2002).
[CrossRef]

Lee, Y. - J.

H. -Y. Ryu, S. -H. Kwon, Y. - J. Lee, Y. -H. Lee, and J. - S. Kim, "Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs," Appl. Phys. Lett. 80, 3476-3478 (2002).
[CrossRef]

Lee, Y. -H.

H. -Y. Ryu, S. -H. Kwon, Y. - J. Lee, Y. -H. Lee, and J. - S. Kim, "Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs," Appl. Phys. Lett. 80, 3476-3478 (2002).
[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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
[CrossRef]

Meier, M.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

Mekis, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

Meyer, J. R.

I. Vurgaftman and J. R. Meyer, "Design Optimization for High-Brightness Surface-Emitting Photonic-Crystal Distributed-Feedback Lasers," IEEE J. Quantum Electron. 39, 689-700 (2003).
[CrossRef]

Miyai, E.

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

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, "Lasers producing tailored beams," Nature 441, 946 (2006).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, W. Kunishi, D. Ohnishi, and S. Noda "Linearly-polarized single-lobed beams by photonic-crystal lasers with triangular lattice points," to be submitted.

K. Sakai, E. Miyai, and S. Noda, "Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode," Appl. Phys. Lett. 89, 021101 1-3 (2006).
[CrossRef]

E. Miyai and S. Noda, "Phase-shift effect on a two-dimensional surface-emitting photonic-crystal laser," Appl. Phys. Lett. 86, 111113 1-3 (2005).
[CrossRef]

Mochizuki, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 1-8 (2002).
[CrossRef]

Murata, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

Murray, C. A.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

Nalamasu, O.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

Noda, 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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
[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, 3981-3990 (2007).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, "Lasers producing tailored beams," Nature 441, 946 (2006).
[CrossRef] [PubMed]

D. Ohnishi, T. Okano, M. Imada, and S. Noda, "Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser," Opt. Express 12, 1562-1568 (2004).
[CrossRef] [PubMed]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).

M. Yokoyama and S. Noda, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser Having a Square Lattice Structure," IEEE J. Quantum Electron. 39, 1074-1080 (2003).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

E. Miyai and S. Noda, "Phase-shift effect on a two-dimensional surface-emitting photonic-crystal laser," Appl. Phys. Lett. 86, 111113 1-3 (2005).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 1-8 (2002).
[CrossRef]

K. Sakai, E. Miyai, and S. Noda, "Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode," Appl. Phys. Lett. 89, 021101 1-3 (2006).
[CrossRef]

E. Miyai, K. Sakai, W. Kunishi, D. Ohnishi, and S. Noda "Linearly-polarized single-lobed beams by photonic-crystal lasers with triangular lattice points," to be submitted.

Notomi, M.

M. Notomi, H. Suzuki, and T. Tamamura, "Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps," Appl. Phys. Lett. 78, 1325-1327 (2001).
[CrossRef]

Ohnishi, D.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, "Lasers producing tailored beams," Nature 441, 946 (2006).
[CrossRef] [PubMed]

D. Ohnishi, T. Okano, M. Imada, and S. Noda, "Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser," Opt. Express 12, 1562-1568 (2004).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, W. Kunishi, D. Ohnishi, and S. Noda "Linearly-polarized single-lobed beams by photonic-crystal lasers with triangular lattice points," to be submitted.

Okano, T.

Rogers, J. A.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

Ruel, R.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

Ryu, H. -Y.

H. -Y. Ryu, S. -H. Kwon, Y. - J. Lee, Y. -H. Lee, and J. - S. Kim, "Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs," Appl. Phys. Lett. 80, 3476-3478 (2002).
[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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
[CrossRef]

Sakai, K.

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

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, "Lasers producing tailored beams," Nature 441, 946 (2006).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, W. Kunishi, D. Ohnishi, and S. Noda "Linearly-polarized single-lobed beams by photonic-crystal lasers with triangular lattice points," to be submitted.

K. Sakai, E. Miyai, and S. Noda, "Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode," Appl. Phys. Lett. 89, 021101 1-3 (2006).
[CrossRef]

Sakoda, K.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys. 38, L157-L159 (1999).
[CrossRef]

Sasada, M.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys. 38, L157-L159 (1999).
[CrossRef]

Sasaki, G.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

Slusher, R. E.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

Song, B. S.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).

Suzuki, H.

M. Notomi, H. Suzuki, and T. Tamamura, "Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps," Appl. Phys. Lett. 78, 1325-1327 (2001).
[CrossRef]

Tamamura, T.

M. Notomi, H. Suzuki, and T. Tamamura, "Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps," Appl. Phys. Lett. 78, 1325-1327 (2001).
[CrossRef]

Tanaka, 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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).

Timko, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

Tokuda, T.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

Vurgaftman, I.

I. Vurgaftman and J. R. Meyer, "Design Optimization for High-Brightness Surface-Emitting Photonic-Crystal Distributed-Feedback Lasers," IEEE J. Quantum Electron. 39, 689-700 (2003).
[CrossRef]

Yokoyama, M.

M. Yokoyama and S. Noda, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser Having a Square Lattice Structure," IEEE J. Quantum Electron. 39, 1074-1080 (2003).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
[CrossRef]

Appl. Phys. Lett. (5)

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999).
[CrossRef]

M. Notomi, H. Suzuki, and T. Tamamura, "Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps," Appl. Phys. Lett. 78, 1325-1327 (2001).
[CrossRef]

H. -Y. Ryu, S. -H. Kwon, Y. - J. Lee, Y. -H. Lee, and J. - S. Kim, "Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs," Appl. Phys. Lett. 80, 3476-3478 (2002).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).

IEEE J. Quantum Electron. (2)

M. Yokoyama and S. Noda, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser Having a Square Lattice Structure," IEEE J. Quantum Electron. 39, 1074-1080 (2003).
[CrossRef]

I. Vurgaftman and J. R. Meyer, "Design Optimization for High-Brightness Surface-Emitting Photonic-Crystal Distributed-Feedback Lasers," IEEE J. Quantum Electron. 39, 689-700 (2003).
[CrossRef]

J. Appl. Phys. (1)

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, "Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding," J. Appl. Phys. 86, 3502-3507 (1999).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys. 38, L157-L159 (1999).
[CrossRef]

Nature (1)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, "Lasers producing tailored beams," Nature 441, 946 (2006).
[CrossRef] [PubMed]

Opt. Express (2)

Science (2)

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, 445-447 (2008); published online 20 December 2007 (10.1126/science.1150413).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

Other (5)

K. Sakai, E. Miyai, and S. Noda, "Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode," Appl. Phys. Lett. 89, 021101 1-3 (2006).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 1-8 (2002).
[CrossRef]

W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, "High-Power Single-Lobed Surface-Emitting Photonic-Crystal Laser," in Proceedings of the Conference on Lasers and Electro-optics, Paper CMKK1 (2006).

E. Miyai, K. Sakai, W. Kunishi, D. Ohnishi, and S. Noda "Linearly-polarized single-lobed beams by photonic-crystal lasers with triangular lattice points," to be submitted.

E. Miyai and S. Noda, "Phase-shift effect on a two-dimensional surface-emitting photonic-crystal laser," Appl. Phys. Lett. 86, 111113 1-3 (2005).
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

Schematic picture of model used in FDTD calculations. (a) Top view. A Bloch boundary was employed around the unit cell in the horizontal direction. (b) Side view. Perfectly matched layers were employed for the vertical boundaries.

Fig. 2.
Fig. 2.

Photonic band structure of a square-lattice photonic-crystal with circular air holes, calculated using the plane-wave expansion method.

Fig. 3.
Fig. 3.

(a) Detailed view of band structure around the gamma point. (b)–(e) Calculated in-plane electric field distributions for band-edges A, B, C and D.

Fig. 4.
Fig. 4.

(a) Air hole shapes investigated in this paper. (b) Detailed representation of air holes H1 to H5. (c) Detailed representation of air holes H6 and H7.

Fig. 5.
Fig. 5.

Calculated values of Q v using the FDTD method for air hole shapes H1 to H7.

Fig. 6.
Fig. 6.

In-plane electric field distribution calculated using the FDTD method for air hole H5 and band edge A. Arrows represent the electric field and solid and dotted lines are explained in the main text.

Fig. 7.
Fig. 7.

In-plane electric field distributions calculated using the FDTD method for air holes H1 to H7 and band-edge A. The vertical dashed lines indicate the y-axis, which runs through the node of the in-plane electric field distribution.

Fig. 8.
Fig. 8.

In-plane electric field distributions calculated using the FDTD method for air holes H1 to H7 and band-edge B. The vertical dashed lines indicate the y-axis, which runs through the node of the in-plane electric field distribution.

Fig. A1
Fig. A1

Fig. A1(a) Air hole shapes discussed in the appendix. (b) Detailed representation of air holes P1 to P5. (c) Detailed representation of air hole P6.

Fig. A2
Fig. A2

Fig. A2(a) In-plane electric field distributions calculated using the FDTD method for air holes P1 to P6 and band-edge A. (b) In-plane electric field distributions calculated using the FDTD method for air holes P1 to P6 and band-edge B.

Fig. A3
Fig. A3

Fig. A3 Calculated values of Q v using the FDTD method for air hole shapes P1 to P6.

Equations (1)

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Q v = ω × W d W d t ,

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