Abstract

The coupled-wave theory (CWT) is extended to a photonic crystal structure with arbitrary sidewalls, and a simple, fast, and effective model for the quantitatively analysis of the radiative characteristics of two-dimensional (2D) photonic-crystal surface-emitting lasers (PC-SELs) has been developed. For illustrating complicated coupling effects accurately, sufficient numbers of waves are included in the formulation, by considering their vertical field profiles. The radiation of band-edge modes is analyzed for two in-plane air-hole geometries, in the case of two types of sidewalls: i.e. “tapered case” and “tilted case.” The results of CWT analysis agree well with the results of finite-difference time-domain (FDTD) numerical simulation. From the analytical solutions of the CWT, the symmetry properties of the band-edge modes are investigated. In-plane asymmetry of the air holes is crucial for achieving high output power because it causes partial constructive interference. Asymmetric air holes and tilted sidewalls help in inducing in-plane asymmetries. By breaking the symmetries with respect to the two orthogonal symmetric axes of the band-edge modes, the two factors can be tuned independently, so that the radiation power is enhanced while preserving the mode selectivity performance. Finally, top-down reactive ion etching (RIE) approach is suggested for the fabrication of such a structure.

© 2011 OSA

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    [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,” Science 293, 1123–1125 (2001).
    [CrossRef] [PubMed]
  4. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B. 65, 195306 (2002).
  5. G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Operating characteristics of a semiconducting polymer laser pumped by a microchip laser,” Appl. Phys. Lett. 82, 313–315 (2003).
    [CrossRef]
  6. 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]
  7. D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser,” Optics Express. 12, 1562–1568 (2004).
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  8. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Lasers producing tailored beams,” Nature,  441, 946 (2006).
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  10. L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, and J. Faist, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Optics Express. 16, 5206–5217 (2008).
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  11. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
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  12. 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).
    [CrossRef]
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  19. 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, 144–150 (1985).
    [CrossRef]
  20. M. Toda, “Proposed cross grating single-mode DFB laser,” IEEE J. Quantum Electron. 28, 1653–1662, (1992).
    [CrossRef]
  21. 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 (2006).
    [CrossRef]
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    [CrossRef]
  25. H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B. 68, 045209 (2003).
    [CrossRef]
  26. M. J. Bergmann and H. C. Casey, “Optical-field cacualtions for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys. 84, 1196 (1998).
    [CrossRef]
  27. Y. Ding and R. Magnusson, “Band gaps and leaky-wave effects in resonant photonic-crystal waveguides,” Optics Express 15, 680–694 (2007).
    [CrossRef] [PubMed]
  28. D. Rosenblatt, A. Sharon, and A. A. Friesen, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
    [CrossRef]
  29. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
    [CrossRef]
  30. Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for square-lattice photonic-crystal lasers with TE polarizaiton — finite-size effects,” Optics Express. (in preparation).
    [PubMed]
  31. S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
    [CrossRef] [PubMed]

2010 (5)

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nature Photon. 4, 447–450 (2010).
[CrossRef]

M. Kamp, “Photonic crystal lasers: On-chip beam steering,” Nature Photonics, News and Views,  4, 412–413 (2010).

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 45, 788–795 (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,” JOSA B.  27, 1204–1207 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
[CrossRef]

2009 (2)

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

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

2007 (1)

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

2006 (2)

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 (2006).
[CrossRef]

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

2005 (1)

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Optics Express. 13, 2869–2880 (2005).
[CrossRef] [PubMed]

2004 (1)

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

2003 (3)

G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Operating characteristics of a semiconducting polymer laser pumped by a microchip laser,” Appl. Phys. Lett. 82, 313–315 (2003).
[CrossRef]

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]

H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B. 68, 045209 (2003).
[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 (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, 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]

1998 (1)

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

1997 (1)

D. Rosenblatt, A. Sharon, and A. A. Friesen, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

1992 (1)

M. Toda, “Proposed cross grating single-mode DFB laser,” IEEE J. Quantum Electron. 28, 1653–1662, (1992).
[CrossRef]

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, 144–150 (1985).
[CrossRef]

1977 (1)

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupled wave analysis of DFB and DBR lasers” IEEE J. Quantum Electron. 13, 134–141 (1977).
[CrossRef]

1972 (1)

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Amanti, M. I.

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

Andrew, P.

G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Operating characteristics of a semiconducting polymer laser pumped by a microchip laser,” Appl. Phys. Lett. 82, 313–315 (2003).
[CrossRef]

Barbieri, S.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

Barnes, W. L.

G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Operating characteristics of a semiconducting polymer laser pumped by a microchip laser,” Appl. Phys. Lett. 82, 313–315 (2003).
[CrossRef]

Beere, H. E.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

Bergmann, M. J.

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

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
[CrossRef]

Bewley, W. W.

M. Kim, C. S. Kim, W. W. Bewley, J. 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).

Burnham, R. D.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupled wave analysis of DFB and DBR lasers” IEEE J. Quantum Electron. 13, 134–141 (1977).
[CrossRef]

Canedy, C. L.

M. Kim, C. S. Kim, W. W. Bewley, J. 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).

Casey, H. C.

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

Chassagneux, Y.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

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.

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 (2002).

Colombelli, R.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

Davies, A. G.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

Ding, Y.

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

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]

Faist, J.

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

Friesen, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesen, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Giovannini, M.

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

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, 144–150 (1985).
[CrossRef]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
[CrossRef]

Imada, M.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[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,” Optics 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 (2002).

Ishizaki, K.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[CrossRef] [PubMed]

Iwahashi, S.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nature Photon. 4, 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,” JOSA B.  27, 1204–1207 (2010).
[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for square-lattice photonic-crystal lasers with TE polarizaiton — finite-size effects,” Optics Express. (in preparation).
[PubMed]

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).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
[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]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
[CrossRef]

Kamp, M.

M. Kamp, “Photonic crystal lasers: On-chip beam steering,” Nature Photonics, News and Views,  4, 412–413 (2010).

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]

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, 144–150 (1985).
[CrossRef]

Khanna, S. P.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

Kim, C. S.

M. Kim, C. S. Kim, W. W. Bewley, J. 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).

Kim, M.

M. Kim, C. S. Kim, W. W. Bewley, J. 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).

Kogelnik, H.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

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,” Nature Photon. 4, 447–450 (2010).
[CrossRef]

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.

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,” JOSA B.  27, 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,” Nature Photon. 4, 447–450 (2010).
[CrossRef]

Lee, Y. H.

H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B. 68, 045209 (2003).
[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,” Nature Photon. 4, 447–450 (2010).
[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for square-lattice photonic-crystal lasers with TE polarizaiton — finite-size effects,” Optics Express. (in preparation).
[PubMed]

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, J. R.

M. Kim, C. S. Kim, W. W. Bewley, J. 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).

Linfield, E.H.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

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]

Magnusson, R.

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

Maineult, W.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

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).
[CrossRef]

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, 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]

Meyer, J. R.

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]

M. Kim, C. S. Kim, W. W. Bewley, J. 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).

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,” Nature Photon. 4, 447–450 (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. 45, 788–795 (2010).
[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, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89, 021101 (2006).
[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 (2002).

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]

Nakamori, T.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[CrossRef] [PubMed]

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, 7–9 (1999).
[CrossRef]

Noda, S.

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,” JOSA B.  27, 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,” Nature Photon. 4, 447–450 (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. 45, 788–795 (2010).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[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, 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, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89, 021101 (2006).
[CrossRef]

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Optics Express. 13, 2869–2880 (2005).
[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,” Optics 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 (2002).

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for square-lattice photonic-crystal lasers with TE polarizaiton — finite-size effects,” Optics Express. (in preparation).
[PubMed]

Notomi, M.

H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B. 68, 045209 (2003).
[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,” Nature Photon. 4, 447–450 (2010).
[CrossRef]

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,” Optics Express. 12, 1562–1568 (2004).
[CrossRef] [PubMed]

Okano, M.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[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]

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

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
[CrossRef]

Ota, Y.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[CrossRef] [PubMed]

Peng, C.

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for square-lattice photonic-crystal lasers with TE polarizaiton — finite-size effects,” Optics Express. (in preparation).
[PubMed]

Ritchie, D. A.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. A. Friesen, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
[CrossRef]

Ryu, H. Y.

H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B. 68, 045209 (2003).
[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).
[CrossRef]

Sakai, K.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nature Photon. 4, 447–450 (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. 45, 788–795 (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,” JOSA B.  27, 1204–1207 (2010).
[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 (2006).
[CrossRef]

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

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for square-lattice photonic-crystal lasers with TE polarizaiton — finite-size effects,” Optics Express. (in preparation).
[PubMed]

Samuel, I. D. W.

G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Operating characteristics of a semiconducting polymer laser pumped by a microchip laser,” Appl. Phys. Lett. 82, 313–315 (2003).
[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]

Scifres, D. R.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupled wave analysis of DFB and DBR lasers” IEEE J. Quantum Electron. 13, 134–141 (1977).
[CrossRef]

Shank, C. V.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

Sharon, A.

D. Rosenblatt, A. Sharon, and A. A. Friesen, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Sirigu, L.

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

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, 7–9 (1999).
[CrossRef]

Streifer, W.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupled wave analysis of DFB and DBR lasers” IEEE J. Quantum Electron. 13, 134–141 (1977).
[CrossRef]

Suzuki, K.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[CrossRef] [PubMed]

Takahashi, S.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[CrossRef] [PubMed]

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).
[CrossRef]

Terazzi, R.

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, and J. Faist, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Optics Express. 16, 5206–5217 (2008).
[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, 7–9 (1999).
[CrossRef]

Toda, M.

M. Toda, “Proposed cross grating single-mode DFB laser,” IEEE J. Quantum Electron. 28, 1653–1662, (1992).
[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]

Turnbull, G. A.

G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Operating characteristics of a semiconducting polymer laser pumped by a microchip laser,” Appl. Phys. Lett. 82, 313–315 (2003).
[CrossRef]

Vurgaftman,

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]

Vurgaftman, I.

M. Kim, C. S. Kim, W. W. Bewley, J. 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).

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]

Yokoyama, M.

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Optics Express. 13, 2869–2880 (2005).
[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]

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).
[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. (6)

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]

G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Operating characteristics of a semiconducting polymer laser pumped by a microchip laser,” Appl. Phys. Lett. 82, 313–315 (2003).
[CrossRef]

M. Kim, C. S. Kim, W. W. Bewley, J. 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).

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]

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 (2006).
[CrossRef]

Computer Physics Communications (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications 181, 687C702 (2010)
[CrossRef]

IEEE J. Quantum Electron. (6)

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 45, 788–795 (2010).
[CrossRef]

D. Rosenblatt, A. Sharon, and A. A. Friesen, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupled wave analysis of DFB and DBR lasers” IEEE J. Quantum Electron. 13, 134–141 (1977).
[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, 144–150 (1985).
[CrossRef]

M. Toda, “Proposed cross grating single-mode DFB laser,” IEEE J. Quantum Electron. 28, 1653–1662, (1992).
[CrossRef]

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. (2)

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[CrossRef]

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

JOSA B (1)

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,” JOSA B.  27, 1204–1207 (2010).
[CrossRef]

Nature (2)

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

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature,  457, 174–178 (2009).
[CrossRef] [PubMed]

Nature Materials (1)

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials 8, 721–725 (2009).
[CrossRef] [PubMed]

Nature Photon. (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,” Nature Photon. 4, 447–450 (2010).
[CrossRef]

Nature Photonics, News and Views (1)

M. Kamp, “Photonic crystal lasers: On-chip beam steering,” Nature Photonics, News and Views,  4, 412–413 (2010).

Optics Express (1)

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

Optics Express. (3)

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Optics Express. 13, 2869–2880 (2005).
[CrossRef] [PubMed]

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, and J. Faist, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Optics Express. 16, 5206–5217 (2008).
[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,” Optics Express. 12, 1562–1568 (2004).
[CrossRef] [PubMed]

Phys. Rev. B. (2)

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

H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B. 68, 045209 (2003).
[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 wavelengths,” Science,  319, 445–447 (2008).
[CrossRef]

Other (2)

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with TE polarization — a general approach,” Phy. Rev. B. (submitted), http://arxiv.org/abs/1107.1772 .

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for square-lattice photonic-crystal lasers with TE polarizaiton — finite-size effects,” Optics Express. (in preparation).
[PubMed]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic structure of the surface-emitting PC laser with circular (CC) and right-angled isosceles triangular (RIT) air holes; (b) band structure of RIT PC laser near the Γ-point (using the PWE method)

Fig. 2
Fig. 2

Schematic of two types of air-hole sidewalls for two in-plane shapes. (a),(c): CC air holes; (b),(d): RIT air holes. Figs. (a)(b) show the “tapered case” for tilt angle θ. Figs. (c)(d) show the “tilted case” for tilt angle θ and direction ϕ.

Fig. 4
Fig. 4

Radiation constant vs. tilt angle θ for modes A and B in the “tapered case” shown in Figs. 2(a–b): (a) CC air holes; (b) RIT air holes. The inset solid and dashed shapes show the up and down facets of the air holes, respectively; both CWT and FDTD results are plotted.

Fig. 5
Fig. 5

Radiation constant vs. tilt angle θ for modes A and B in the “tilt case” with the CC air holes shown in Fig. 2(c) in tilt directions indicated by red arrows: (a) ϕ = 0°; (b) ϕ = 135°. The inset solid and dashed shapes show the up and down facets of the air holes, respectively; both CWT and FDTD results are plotted.

Fig. 6
Fig. 6

Radiation constant vs. tilt angle θ for modes A and B in the “tilt case” with the RIT air holes shown in Fig. 2(d) in tilt directions indicated by red arrows indicated: (a) ϕ = 0°; (b) ϕ = 135°. The inset solid and dashed shapes show the up and down facets of the air holes, respectively; both CWT and FDTD results are plotted.

Fig. 3
Fig. 3

Field distribution and eigenvectors of modes A and B, for the: (a) CC air holes, and (b) RIT air holes. The color pattern in the field distribution shows the magnetic field distribution, and the black arrows show the electric field distribution. The eigenvectors of modes A and B are illustrated in coordinate space, with the dashed arrows showing the propagating directions of four basic waves; the red and blue arrows show the amplitudes and polarizations of their electric fields, and the gray arrows show the amplitudes and polarizations of the radiative waves determined by Eq 14.

Tables (1)

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Table 1 Parameters for the vertical structure

Equations (36)

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× × E ( r ) = ɛ ( r ) k 0 2 E ( r )
ɛ ( z ) = ɛ 0 ( z ) + m , n 0 ξ m n ( z ) e im β 0 x in β 0 y
[ 2 z 2 + ɛ 0 ( z ) k 0 2 n 2 β 0 2 ] E x , mn + k 0 2 m m , n n ξ m m , n n ( z ) E x , m n + mn β 0 2 E y , mn = 0
[ 2 z 2 + ɛ 0 ( z ) 2 k 0 2 n 2 β 0 2 ] E y , mn + k 0 2 m m , n n ξ m m , n n ( z ) E y , m n + mn β 0 2 E x , mn = 0
E x , 10 = 0 E y , 10 = R x Θ 0 ( z )
E x , 10 = 0 E y , 10 = S x Θ 0 ( z )
E x , 01 = R y Θ 0 ( z ) E y , 01 = 0
E x , 0 1 = S y Θ 0 ( z ) E y , 0 1 = 0
[ 2 Θ 0 z 2 + ( ɛ 0 ( z ) k 0 2 β 0 2 ) Θ 0 ] R x = k 0 2 m m , n n ξ 1 m , n ( z ) ɛ 0 ( z ) E y , m n ( z )
2 Θ 0 z 2 + [ ɛ 0 ( z ) k 2 β 0 2 ] Θ 0 = 0
ɛ 0 ( z ) ( k 0 2 k 2 ) Θ 0 ( z ) R x = k 0 2 ξ 20 ( z ) S x Θ 0 ( z ) k 0 2 ξ 10 ( z ) Δ E y ( z ) k 0 2 | m 2 + n 2 | > 1 ξ 1 m n ( z ) E y , m n ( z )
h δ k R x = k 0 2 S x PC ξ 20 ( z ) | Θ 0 ( z ) | 2 d z k 0 2 PC ξ 10 ( z ) Δ E y ( z ) Θ 0 * ( z ) d z k 0 2 | m 2 + n 2 | > 1 PC ξ 1 m n ( z ) E y , m n ( z ) Θ 0 * ( z ) d z
[ 2 z 2 + ɛ 0 ( z ) k 0 2 ] Δ E y ( z ) = k 0 2 m , n 0 ξ m n ( z ) E y , m n ( z )
Δ E y ( z ) k 0 2 R x PC ξ 1 , 0 ( z ) G ( z , z ) Θ 0 ( z ) d z k 0 2 S x PC ξ 1 , 0 ( z ) G ( z , z ) Θ 0 ( z ) d z
[ 2 z 2 + ɛ 0 ( z ) k 0 2 ( m 2 + n 2 ) β 0 2 ] ( n E x , mn m E y , m n ) = k 0 2 ξ m m n n ( z ) ( n E x , m n m E y , m n )
[ 2 z 2 + ɛ 0 ( z ) k 0 2 ] ( m E x , mn + n E y , mn ) = k 0 2 ξ m m , n n ( z ) ( m E x , m n + n E y , m n )
PC ( n E x , mn m E y , mn ) Θ 0 * ( z ) dz m μ m , n 1 , 0 R x m μ m , n 1 , 0 S x + n μ m , n 0 , 1 R y + n μ m , n 0 , 1 S y E
PC ( m E x , mn + n E y , mn ) Θ 0 * ( z ) dz n ν m , n 1 , 0 R x + n ν m , n 1 , 0 S x + m ν m , n 0 , 1 R y + m ν m , n 0 , 1 S y E +
P C E x , mn ( z ) Θ 0 * ( z ) dz = m E + + n E m 2 + n 2 , PC E y , mn ( z ) Θ 0 * ( z ) d z = n E + m E m 2 + n 2
δ k V = C V
α r = β 0 Q = 2 π / a Q
[ 2 z 2 + ( ɛ 0 ( z ) k 0 2 β mn 2 ) ] G ( z , z ) = δ ( z z )
G = A i e i k i , z ( z h i ) + B i e i k i , z ( z h i )
G = A i + 1 e i k i + 1 , z ( z h i + 1 ) + B i + 1 e i k i + 1 , z ( z h i + 1 )
( A i B i ) = [ 1 2 ( 1 + k i + 1 , z k i , z ) e i k i , z ( h i + 1 h i ) 1 2 ( 1 k i + 1 , z k i , z ) e i k i , z ( h i + 1 h i ) 1 2 ( 1 k i + 1 , z k i , z ) e i k i , z ( h i + 1 h i ) 1 2 ( 1 + k i + 1 , z k i , z ) e i k i , z ( h i + 1 h i ) ] ( A i + 1 B i + 1 ) = T i + 1 ( A i + 1 B i + 1 )
( A 0 B 0 ) = T 1 ( A 1 B 1 ) = = T 1 T 2 T N ( A N B N ) = T ( A N B N )
B 0 = T 21 T 11 A 0 = κ p 1 A 0
G = C i e i k i , z ( z h i ) + D i e i k i , z ( z h i )
G = C i + 1 e i k i + 1 , z ( z h i + 1 ) + D i + 1 e i k i + 1 , z ( z h i + 1 )
( C 0 D 0 ) = T 0 1 ( C 1 D 1 ) = = T 0 1 T 1 1 T N + 1 1 ( C N D N ) = T * ( C N D N )
C 0 = T 12 * T 22 * D 0 = κ p 2 D 0
A 0 + B 0 = C 0 + D 0
A 0 B 0 C 0 + D 0 = i / k 0 , z
A 0 = i 2 k 0 , Z 1 + κ p 2 1 κ p 1 κ p 2 B 0 = i 2 k 0 , Z κ p 1 ( 1 + κ p 2 ) 1 κ p 1 κ p 2
C 0 = i 2 k 0 , z κ p 2 ( 1 + κ p 1 ) 1 κ p 1 κ p 2 D 0 = i 2 k 0 , z 1 + κ p 1 1 κ p 1 κ p 2
G ( z , z ) = { A 0 e i k 0 , z ( z z ) + B 0 e i k 0 , z ( z z ) z > z C 0 e i k 0 , z ( z z ) + D 0 e i k 0 , z ( z z ) z < z

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