Abstract

We investigated the effects of non-lasing bands on the beam patterns in photonic-crystal lasers by evaluating the omnidirectional band structure both experimentally and theoretically. We found that a new, weak dual-streak pattern is occasionally generated around the main lobe of the output beam because of scattering of the lasing beam in the non-lasing bands despite a wavenumber mismatch. This result indicates that we can design the high-quality devices without such a noise pattern. In addition, this evaluation method is expected to be useful for developing various high-functionality PC lasers.

© 2012 OSA

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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(3), 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(1), 7–9 (1999).
    [CrossRef]
  3. 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,” Science293(5532), 1123–1125 (2001).
    [CrossRef] [PubMed]
  4. 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(10), 1325–1327 (2001).
    [CrossRef]
  5. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65(19), 195306 (2002).
    [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(19), 3476–3478 (2002).
    [CrossRef]
  7. M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron.39(9), 1074–1080 (2003).
    [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(6), 689–700 (2003).
    [CrossRef]
  9. 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. Express12(8), 1562–1568 (2004).
    [CrossRef] [PubMed]
  10. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
    [CrossRef] [PubMed]
  11. H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science319(5862), 445–447 (2008), doi:.
    [CrossRef] [PubMed]
  12. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (2008).
    [CrossRef]
  13. Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal lasers by shape of air holes,” Opt. Express16(22), 18485–18494 (2008).
    [CrossRef] [PubMed]
  14. Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
    [CrossRef]
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    [CrossRef]
  16. S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express19(13), 11963–11968 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  19. Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
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2011 (1)

2010 (2)

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
[CrossRef]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Air-hole design in a vertical direction for high-power two-dimensional photonic-crystal surface-emitting lasers,” J. Opt. Soc. Am. B27(6), 1204–1207 (2010).
[CrossRef]

2009 (1)

Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
[CrossRef]

2008 (3)

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science319(5862), 445–447 (2008), doi:.
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (2008).
[CrossRef]

Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal lasers by shape of air holes,” Opt. Express16(22), 18485–18494 (2008).
[CrossRef] [PubMed]

2006 (1)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[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]

2004 (1)

2003 (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(9), 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(6), 689–700 (2003).
[CrossRef]

2002 (2)

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65(19), 195306 (2002).
[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(19), 3476–3478 (2002).
[CrossRef]

2001 (2)

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,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

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(10), 1325–1327 (2001).
[CrossRef]

1999 (2)

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(3), 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(1), 7–9 (1999).
[CrossRef]

Chutinan, A.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65(19), 195306 (2002).
[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,” Science293(5532), 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(3), 316–318 (1999).
[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(1), 7–9 (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. Express12(8), 1562–1568 (2004).
[CrossRef] [PubMed]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65(19), 195306 (2002).
[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,” Science293(5532), 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(3), 316–318 (1999).
[CrossRef]

Iwahashi, S.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express19(13), 11963–11968 (2011).
[CrossRef] [PubMed]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Air-hole design in a vertical direction for high-power two-dimensional photonic-crystal surface-emitting lasers,” J. Opt. Soc. Am. B27(6), 1204–1207 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
[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,” Science319(5862), 445–447 (2008), doi:.
[CrossRef] [PubMed]

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(1), 7–9 (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(19), 3476–3478 (2002).
[CrossRef]

Kitamura, K.

Kunishi, W.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (2008).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[CrossRef] [PubMed]

Kurosaka, Y.

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(19), 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(19), 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(19), 3476–3478 (2002).
[CrossRef]

Liang, Y.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (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,” Science319(5862), 445–447 (2008), doi:.
[CrossRef] [PubMed]

Meier, M.

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(1), 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(1), 7–9 (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(6), 689–700 (2003).
[CrossRef]

Miyai, E.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
[CrossRef]

Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal lasers by shape of air holes,” Opt. Express16(22), 18485–18494 (2008).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (2008).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[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. B65(19), 195306 (2002).
[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,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

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(3), 316–318 (1999).
[CrossRef]

Nalamasu, O.

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(1), 7–9 (1999).
[CrossRef]

Noda, S.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express19(13), 11963–11968 (2011).
[CrossRef] [PubMed]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Air-hole design in a vertical direction for high-power two-dimensional photonic-crystal surface-emitting lasers,” J. Opt. Soc. Am. B27(6), 1204–1207 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
[CrossRef]

Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal lasers by shape of air holes,” Opt. Express16(22), 18485–18494 (2008).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (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,” Science319(5862), 445–447 (2008), doi:.
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[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]

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. Express12(8), 1562–1568 (2004).
[CrossRef] [PubMed]

M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron.39(9), 1074–1080 (2003).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65(19), 195306 (2002).
[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,” Science293(5532), 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(3), 316–318 (1999).
[CrossRef]

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(10), 1325–1327 (2001).
[CrossRef]

Ohnishi, D.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (2008).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[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]

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. Express12(8), 1562–1568 (2004).
[CrossRef] [PubMed]

Okano, T.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (2008).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[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]

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. Express12(8), 1562–1568 (2004).
[CrossRef] [PubMed]

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(19), 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,” Science319(5862), 445–447 (2008), doi:.
[CrossRef] [PubMed]

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.

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express19(13), 11963–11968 (2011).
[CrossRef] [PubMed]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Air-hole design in a vertical direction for high-power two-dimensional photonic-crystal surface-emitting lasers,” J. Opt. Soc. Am. B27(6), 1204–1207 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
[CrossRef]

Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal lasers by shape of air holes,” Opt. Express16(22), 18485–18494 (2008).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (2008).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[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]

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(3), 316–318 (1999).
[CrossRef]

Slusher, R. E.

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(1), 7–9 (1999).
[CrossRef]

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(10), 1325–1327 (2001).
[CrossRef]

Takayama, N.

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(10), 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,” Science319(5862), 445–447 (2008), doi:.
[CrossRef] [PubMed]

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(1), 7–9 (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(3), 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(6), 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(9), 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,” Science293(5532), 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,” Science319(5862), 445–447 (2008), doi:.
[CrossRef] [PubMed]

Appl. Phys. Express (1)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Linearly polarized single-lobed beam in a surface-emitting photonic-crystal laser,” Appl. Phys. Express1, 062002 (2008).
[CrossRef]

Appl. Phys. Lett. (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(3), 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(1), 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(10), 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(19), 3476–3478 (2002).
[CrossRef]

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(9), 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(6), 689–700 (2003).
[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]

IEICE Electron. Express (1)

Y. Kurosaka, S. Iwahashi, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “Band structure observation of 2D photonic crystal with various V-shaped air-hole arrangements,” IEICE Electron. Express6(13), 966–971 (2009).
[CrossRef]

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

Nat. Photonics (1)

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics4(7), 447–450 (2010).
[CrossRef]

Nature (1)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[CrossRef] [PubMed]

Opt. Express (3)

Phys. Rev. B (1)

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65(19), 195306 (2002).
[CrossRef]

Science (2)

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,” Science293(5532), 1123–1125 (2001).
[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,” Science319(5862), 445–447 (2008), doi:.
[CrossRef] [PubMed]

Other (2)

S. Iwahashi, T. Nobuoka, Y. Kurosaka, and S. Noda, “Comprehensive investigation of composite photonic-crystal cavities emitting arbitrary-angled laser beams,” in Proceedings of IPC2011 (IEEE, 2011), paper WP1.

K. Sakoda, “Eigenmodes of photonic crystals,” in Optical Properties of Photonic Crystals, K. Sakoda, ed. (Springer-Verlag, Heidelberg, 2005).

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Figures (11)

Fig. 1
Fig. 1

Device structure. (a) Layout of the 2D PC laser. (b) Scanning electron microscope image of the fabricated PC layer before burial. The Γ-J and the Γ-X directions are defined as indicated by the black arrows.

Fig. 2
Fig. 2

Schematic diagram of measurement apparatus for omnidirectional band structure.

Fig. 3
Fig. 3

(a) Real space of the triangular PC. (b) Reciprocal lattice space of the triangular PC.

Fig. 4
Fig. 4

Lasing beam patterns under CW operation (100 mA). (a) With ND filter (OD = 8); (b) with ND filter (OD = 5).

Fig. 5
Fig. 5

Measured omnidirectional band structure under CW operation (93 mA).

Fig. 6
Fig. 6

(a) Vertical cross section of measured omnidirectional band structure. (b) Lasing spectrum.

Fig. 7
Fig. 7

Horizontal cross section of measured omnidirectional band structure at lasing frequency (0.3433 c/a) under CW operation (93 mA).

Fig. 8
Fig. 8

Calculated omnidirectional band structures. (a) Band A, (b) band B, (c) band C, (d) band D, (e) band E, (f) band F.

Fig. 9
Fig. 9

Horizontal cross section of calculated omnidirectional band structure at frequency corresponding to the edge of band A. Bands A, B, and C are plotted with blue, green, and red dots, respectively.

Fig. 10
Fig. 10

Conceptual drawing of calculation procedure.

Fig. 11
Fig. 11

(a) Rectangle, (b) shifted rectangle, (c) right-angled triangle.

Equations (13)

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

k x = a λ sinθcosϕ,
k y = a λ sinθsinϕ,
f= a λ .
G' κ( GG' )( k+G )( k+G' ) H z,k ( G' )= ω 2 c 2 H z,k ( G ) ,
1 ε( r ) = G κ( G ) e iGr ,
a 1 =( a,0 ), a 2 =( acos60°,asin60° ),
b 1 = 2π asin60° ( sin60°,cos60° ), b 2 = 2π asin60° (0,1).
G=m b 1 +n b 2 ,
κ( G )= 1 a 2 sin60° Shape 1 Δε exp( iGr ) dxdy,
κ 1 ( G )= 4hl a 2 sin60°Δε :m=n=0, 2l nπaΔε sin( 2πnh asin60° ):m=0,n0, 2h mπasin60°Δε sin( 2πml a ):m0,m=2n, 1 m π 2 (nmcos60°)Δε sin( 2πml a )sin( 2π( nmcos60° )h asin60° ):m0,m2n.
κ 2 ( G )= κ 1 ( G )exp( i 2mπl a ).
κ 3 ( G )= 2 h 2 a 2 sin60°tanφΔε :m=n=0, i 1 2nπatanφΔε { asin60° nπ sin( 2nπh asin60° )+2hexp( i 2nπh asin60° ) }:m=0,n0, i 1 2mπasin60°Δε { atanφ mπ exp( i 2mπh atanφ )sin( 2mπh atanφ )+2h }:m0,m=2n, i 1 2mπasin60°Δε { 2hexp( i 2mπh atanφ ) asin60° π( nmcos60° ) sin( 2πh(nmcos60°) asin60° ) }:m0,m=n, i 1 2m π 2 Δε [ exp( i 2mπh atanφ ) nmcos60°m sin60° tanφ sin{ 2πh asin60° ( nmcos60°m sin60° tanφ ) } 1 nmcos60° sin{ 2πh asin60° ( nmcos60° ) } ]:m0,n0,m2n.
κ 4 ( G )= κ 2 ( G )+ κ 3 ( G ).

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