Abstract

We investigate the air-hole shape of photonic-crystal lasers in the vertical direction to increase the radiation constant for the surface emission. Numerical analysis indicates a maximum radiation constant when the air-hole depth is half the wavelength and a minimum when it is about the same as the wavelength, due to the interference of light waves diffracted in the vertical direction. We propose an air-hole design using two photonic-crystal layers offset by a half-period; the design more than doubles the radiation constant over that of a conventional design, leading to higher-power operation.

© 2010 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. 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]
  3. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65, 195306 (2002).
    [CrossRef]
  4. 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]
  5. 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]
  6. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Lasers producing tailored beams,” Nature 441, 946 (2006).
    [CrossRef] [PubMed]
  7. G. Vecchi, F. Raineri, I. Sagnes, A. Yacomotti, P. Monnier, T. J. Karle, K.-H. Lee, R. Braive, L. Le Gratiet, S. Guilet, G. Beaudoin, A. Talneau, S. Bouchoule, A. Levenson, and R. Raj, “Continuous-wave operation of photonic band-edge laser near 1.55 μm on silicon wafer,” Opt. Express 15, 7551–7556 (2007).
    [CrossRef] [PubMed]
  8. M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
    [CrossRef]
  9. L. Sirigu, R. Terazzi, M. Amanti, M. Giovannini, and J. Faist, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16, 5206–5217 (2008).
    [CrossRef] [PubMed]
  10. H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelength,” Science 319, 445–447 (2008).
    [CrossRef]
  11. T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
    [CrossRef]
  12. Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal laser by shape of air holes,” Opt. Express 16, 18485–18494 (2008).
    [CrossRef] [PubMed]
  13. M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser having a square-lattice slab structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).
  14. 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 Commun. 23, 1335–1340 (2005).
    [CrossRef]

2008 (4)

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

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

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

Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal laser by shape of air holes,” Opt. Express 16, 18485–18494 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (2)

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

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[CrossRef]

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 Commun. 23, 1335–1340 (2005).
[CrossRef]

2004 (2)

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]

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser having a square-lattice slab structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).

2003 (1)

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)

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

2001 (1)

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 (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]

Amanti, M.

Beaudoin, G.

Bewley, W. W.

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[CrossRef]

Bouchoule, S.

Braive, R.

Canedy, C. L.

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[CrossRef]

Chen, S. W.

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

Chutinan, A.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65, 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,” 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]

Faist, J.

Giovannini, M.

Guilet, S.

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]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65, 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,” 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]

Jianglin, Y.

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

Kao, C. C.

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

Kao, T. T.

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

Karle, T. J.

Kim, C. S.

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[CrossRef]

Kim, M.

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[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]

Kuo, H. C.

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

Kurosaka, Y.

Le Gratiet, L.

Lee, K. -H.

Levenson, A.

Lin, L. F.

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

Lindle, C. R.

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[CrossRef]

Lindle, J. R.

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[CrossRef]

Lu, T. C.

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[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 wavelength,” Science 319, 445–447 (2008).
[CrossRef]

Meyer, J. R.

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[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]

Miyai, E.

Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal laser by shape of air holes,” Opt. Express 16, 18485–18494 (2008).
[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]

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 Commun. 23, 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, 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,” Science 293, 1123–1125 (2001).
[CrossRef] [PubMed]

Monnier, P.

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]

Noda, S.

Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal laser by shape of air holes,” Opt. Express 16, 18485–18494 (2008).
[CrossRef] [PubMed]

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

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Lasers producing tailored beams,” Nature 441, 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 Commun. 23, 1335–1340 (2005).
[CrossRef]

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser having a square-lattice slab structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).

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]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65, 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,” 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]

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]

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 Commun. 23, 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. Express 12, 1562–1568 (2004).
[CrossRef] [PubMed]

Okano, T.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Lasers producing tailored beams,” Nature 441, 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 Commun. 23, 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. Express 12, 1562–1568 (2004).
[CrossRef] [PubMed]

Raineri, F.

Raj, R.

Sagnes, I.

Saito, H.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelength,” Science 319, 445–447 (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 Commun. 23, 1335–1340 (2005).
[CrossRef]

Sakai, K.

Y. Kurosaka, K. Sakai, E. Miyai, and S. Noda, “Controlling vertical optical confinement in two-dimensional surface-emitting photonic-crystal laser by shape of air holes,” Opt. Express 16, 18485–18494 (2008).
[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]

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 Commun. 23, 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, 316–318 (1999).
[CrossRef]

Sirigu, L.

Talneau, A.

Tanaka, Y.

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

Terazzi, R.

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]

Vecchi, G.

Vurgaftman, I.

M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[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]

Wang, S. C.

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

Yacomotti, A.

Yokoyama, M.

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser having a square-lattice slab structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).

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 wavelength,” Science 319, 445–447 (2008).
[CrossRef]

Yu, P.

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

Appl. Phys. Lett. (3)

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. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006).
[CrossRef]

T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett. 92, 011129 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

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]

IEEE J. Sel. Areas Commun. (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 Commun. 23, 1335–1340 (2005).
[CrossRef]

IEICE Trans. Electron. (1)

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser having a square-lattice slab structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).

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 (4)

Phys. Rev. B (1)

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65, 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,” Science 293, 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 wavelength,” Science 319, 445–447 (2008).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Structure of a 2D PC laser. (b) Schematic model used in FDTD calculations.

Fig. 2
Fig. 2

(a) L shaped square lattice PC used in this paper. The dimensions of L are 0.4 a on each side and 0.2 a wide. (b) Corresponding band structure around the Γ point. The first- and second-lowest frequency modes, indicated by dots, are expected to be lased.

Fig. 3
Fig. 3

Radiation constants versus PC depth ( d ) calculated with the FDTD method. They change periodically by increasing d.

Fig. 4
Fig. 4

Diffraction model when the PC depth equals (a) λ v / 2 and (b) λ v . The phase difference between radiation waves from the upper and lower parts within the air hole is π / 2 for (a), so the destructive interference is imperfect. A pair of perfectly opposite phase waves exists for (b). These opposite phases weaken the radiation through destructive interference.

Fig. 5
Fig. 5

(a) Conventional structure and (b) two-tiered structure, where we add a second PC layer on top of a conventional λ v / 2 deep PC layer by a half-period ( a / 2 ) to both x and y directions as shown in (c).

Fig. 6
Fig. 6

Radiation constants versus PC depth ( d ) for a conventional structure (solid curve—same as Fig. 3) and a two-tiered structure (dotted curve).

Fig. 7
Fig. 7

Diffraction model for the two-tiered structure. Diffracted waves from the upper and lower parts of air hole have identical phases and constructively interfere in the vertical direction.

Fig. 8
Fig. 8

Air-hole shape in unit cell and corresponding magnetic field in z direction at center of active layer for (a) a conventional structure ( d = 0.5 a ) and (b) the two-tiered structure ( d = 1.0 a ) .

Equations (2)

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α v = 2 π a 1 Q v ,
α t h = α v + α + α i n .

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