S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Centered-rectangular lattice photonic-crystal surface-emitting lasers,” Phys. Rev. B85, 035304 (2012).

[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic-crystal lasers with transverse electric polarization: Finite-size effects,” Opt. Express20, 15945–15961 (2012).

[CrossRef]
[PubMed]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave theory analysis of centered-rectangular lattice photonic crystal with transverse-electric-like mode,” Phys. Rev. B86, 035108 (2012).

[CrossRef]

M. Koba and P. Szczepanski, “The threshold mode structure analysis of the two-dimensional photonic crystal lasers,” Prog. Electromagn. Res.125, 365–389 (2012).

[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with transverse electric polarization: A general approach,” Phys. Rev. B84, 195119 (2011).

[CrossRef]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express19, 24672–24686 (2011).

[CrossRef]
[PubMed]

L. Mahler and A. Tredicucci, “Photonic engineering of surface-emitting terahertz quantum cascade lasers,” Laser Photonics Rev.5, 647–658 (2011).

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

[CrossRef]
[PubMed]

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, 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.46, 788–795 (2010).

[CrossRef]

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 (London)457, 174–178 (2009).

[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, 445–447 (2008).

[CrossRef]

K. Sakai, J. Yue, and S. Noda, “Coupled-wave model for triangular-lattice photonic crystal with transverse electric polarization,” Opt. Express16, 6033–6040 (2008).

[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]

K. Forberich, M. Diem, J. Crewett, U. Lemmer, A. Gombert, and K. Busch, “Lasing action in two-dimensional organic photonic crystal lasers with hexagonal symmetry,” Appl. Phys. B82, 539–541 (2006).

[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).

[CrossRef]

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

[CrossRef]

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express13, 2869–2880 (2005).

[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]

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]

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. B68, 045209 (2003).

[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65, 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, 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]

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B52, 7982 (1995).

[CrossRef]

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[CrossRef]

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

[CrossRef]

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 (London)457, 174–178 (2009).

[CrossRef]

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 (London)457, 174–178 (2009).

[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).

[CrossRef]

K. Forberich, M. Diem, J. Crewett, U. Lemmer, A. Gombert, and K. Busch, “Lasing action in two-dimensional organic photonic crystal lasers with hexagonal symmetry,” Appl. Phys. B82, 539–541 (2006).

[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).

[CrossRef]

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 (London)457, 174–178 (2009).

[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65, 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, 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]

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 (London)457, 174–178 (2009).

[CrossRef]

K. Forberich, M. Diem, J. Crewett, U. Lemmer, A. Gombert, and K. Busch, “Lasing action in two-dimensional organic photonic crystal lasers with hexagonal symmetry,” Appl. Phys. B82, 539–541 (2006).

[CrossRef]

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 (London)457, 174–178 (2009).

[CrossRef]

K. Forberich, M. Diem, J. Crewett, U. Lemmer, A. Gombert, and K. Busch, “Lasing action in two-dimensional organic photonic crystal lasers with hexagonal symmetry,” Appl. Phys. B82, 539–541 (2006).

[CrossRef]

K. Forberich, M. Diem, J. Crewett, U. Lemmer, A. Gombert, and K. Busch, “Lasing action in two-dimensional organic photonic crystal lasers with hexagonal symmetry,” Appl. Phys. B82, 539–541 (2006).

[CrossRef]

K. Forberich, M. Diem, J. Crewett, U. Lemmer, A. Gombert, and K. Busch, “Lasing action in two-dimensional organic photonic crystal lasers with hexagonal symmetry,” Appl. Phys. B82, 539–541 (2006).

[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Norwood, 2005).

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, 1562–1568 (2004).

[CrossRef]
[PubMed]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65, 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, 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]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave theory analysis of centered-rectangular lattice photonic crystal with transverse-electric-like mode,” Phys. Rev. B86, 035108 (2012).

[CrossRef]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Centered-rectangular lattice photonic-crystal surface-emitting lasers,” Phys. Rev. B85, 035304 (2012).

[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic-crystal lasers with transverse electric polarization: Finite-size effects,” Opt. Express20, 15945–15961 (2012).

[CrossRef]
[PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with transverse electric polarization: A general approach,” Phys. Rev. B84, 195119 (2011).

[CrossRef]

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

[CrossRef]
[PubMed]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express19, 24672–24686 (2011).

[CrossRef]
[PubMed]

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, 447–450 (2010).

[CrossRef]

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

[CrossRef]

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 (London)457, 174–178 (2009).

[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).

[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).

[CrossRef]

M. Koba and P. Szczepanski, “The threshold mode structure analysis of the two-dimensional photonic crystal lasers,” Prog. Electromagn. Res.125, 365–389 (2012).

[CrossRef]

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

[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, 447–450 (2010).

[CrossRef]

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

[CrossRef]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Centered-rectangular lattice photonic-crystal surface-emitting lasers,” Phys. Rev. B85, 035304 (2012).

[CrossRef]

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

[CrossRef]
[PubMed]

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, 447–450 (2010).

[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. B68, 045209 (2003).

[CrossRef]

K. Forberich, M. Diem, J. Crewett, U. Lemmer, A. Gombert, and K. Busch, “Lasing action in two-dimensional organic photonic crystal lasers with hexagonal symmetry,” Appl. Phys. B82, 539–541 (2006).

[CrossRef]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave theory analysis of centered-rectangular lattice photonic crystal with transverse-electric-like mode,” Phys. Rev. B86, 035108 (2012).

[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic-crystal lasers with transverse electric polarization: Finite-size effects,” Opt. Express20, 15945–15961 (2012).

[CrossRef]
[PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with transverse electric polarization: A general approach,” Phys. Rev. B84, 195119 (2011).

[CrossRef]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express19, 24672–24686 (2011).

[CrossRef]
[PubMed]

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, 447–450 (2010).

[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).

[CrossRef]

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 (London)457, 174–178 (2009).

[CrossRef]

L. Mahler and A. Tredicucci, “Photonic engineering of surface-emitting terahertz quantum cascade lasers,” Laser Photonics Rev.5, 647–658 (2011).

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 (London)457, 174–178 (2009).

[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, 445–447 (2008).

[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).

[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]

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, 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.46, 788–795 (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 (London)441, 946 (2006).

[CrossRef]

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. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65, 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, 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]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave theory analysis of centered-rectangular lattice photonic crystal with transverse-electric-like mode,” Phys. Rev. B86, 035108 (2012).

[CrossRef]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Centered-rectangular lattice photonic-crystal surface-emitting lasers,” Phys. Rev. B85, 035304 (2012).

[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic-crystal lasers with transverse electric polarization: Finite-size effects,” Opt. Express20, 15945–15961 (2012).

[CrossRef]
[PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with transverse electric polarization: A general approach,” Phys. Rev. B84, 195119 (2011).

[CrossRef]

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

[CrossRef]
[PubMed]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express19, 24672–24686 (2011).

[CrossRef]
[PubMed]

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron.46, 788–795 (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, 447–450 (2010).

[CrossRef]

K. Sakai, J. Yue, and S. Noda, “Coupled-wave model for triangular-lattice photonic crystal with transverse electric polarization,” Opt. Express16, 6033–6040 (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 wavelengths,” Science319, 445–447 (2008).

[CrossRef]

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

[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]

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express13, 2869–2880 (2005).

[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. Express12, 1562–1568 (2004).

[CrossRef]
[PubMed]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B65, 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, 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]

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. B68, 045209 (2003).

[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, 447–450 (2010).

[CrossRef]

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

[CrossRef]

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. Express12, 1562–1568 (2004).

[CrossRef]
[PubMed]

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

[CrossRef]

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. Express12, 1562–1568 (2004).

[CrossRef]
[PubMed]

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[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic-crystal lasers with transverse electric polarization: Finite-size effects,” Opt. Express20, 15945–15961 (2012).

[CrossRef]
[PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with transverse electric polarization: A general approach,” Phys. Rev. B84, 195119 (2011).

[CrossRef]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express19, 24672–24686 (2011).

[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 (London)457, 174–178 (2009).

[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. B68, 045209 (2003).

[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, 445–447 (2008).

[CrossRef]

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]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave theory analysis of centered-rectangular lattice photonic crystal with transverse-electric-like mode,” Phys. Rev. B86, 035108 (2012).

[CrossRef]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Centered-rectangular lattice photonic-crystal surface-emitting lasers,” Phys. Rev. B85, 035304 (2012).

[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic-crystal lasers with transverse electric polarization: Finite-size effects,” Opt. Express20, 15945–15961 (2012).

[CrossRef]
[PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with transverse electric polarization: A general approach,” Phys. Rev. B84, 195119 (2011).

[CrossRef]

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

[CrossRef]
[PubMed]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express19, 24672–24686 (2011).

[CrossRef]
[PubMed]

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron.46, 788–795 (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, 447–450 (2010).

[CrossRef]

K. Sakai, J. Yue, and S. Noda, “Coupled-wave model for triangular-lattice photonic crystal with transverse electric polarization,” Opt. Express16, 6033–6040 (2008).

[CrossRef]
[PubMed]

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

[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]

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]

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B52, 7982 (1995).

[CrossRef]

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]

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

[CrossRef]

M. Koba and P. Szczepanski, “The threshold mode structure analysis of the two-dimensional photonic crystal lasers,” Prog. Electromagn. Res.125, 365–389 (2012).

[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Norwood, 2005).

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

[CrossRef]

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

[CrossRef]

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]

L. Mahler and A. Tredicucci, “Photonic engineering of surface-emitting terahertz quantum cascade lasers,” Laser Photonics Rev.5, 647–658 (2011).

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).

[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]

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express13, 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,” Science293, 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, 445–447 (2008).

[CrossRef]

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[CrossRef]

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. 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]

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]

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

[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]

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

[CrossRef]

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]

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

[CrossRef]

L. Mahler and A. Tredicucci, “Photonic engineering of surface-emitting terahertz quantum cascade lasers,” Laser Photonics Rev.5, 647–658 (2011).

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, 447–450 (2010).

[CrossRef]

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 (London)457, 174–178 (2009).

[CrossRef]

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

[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, 1562–1568 (2004).

[CrossRef]
[PubMed]

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express13, 2869–2880 (2005).

[CrossRef]
[PubMed]

K. Sakai, J. Yue, and S. Noda, “Coupled-wave model for triangular-lattice photonic crystal with transverse electric polarization,” Opt. Express16, 6033–6040 (2008).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express19, 24672–24686 (2011).

[CrossRef]
[PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic-crystal lasers with transverse electric polarization: Finite-size effects,” Opt. Express20, 15945–15961 (2012).

[CrossRef]
[PubMed]

S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Centered-rectangular lattice photonic-crystal surface-emitting lasers,” Phys. Rev. B85, 035304 (2012).

[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. B68, 045209 (2003).

[CrossRef]

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

[CrossRef]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with transverse electric polarization: A general approach,” Phys. Rev. B84, 195119 (2011).

[CrossRef]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave theory analysis of centered-rectangular lattice photonic crystal with transverse-electric-like mode,” Phys. Rev. B86, 035108 (2012).

[CrossRef]

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B52, 7982 (1995).

[CrossRef]

M. Koba and P. Szczepanski, “The threshold mode structure analysis of the two-dimensional photonic crystal lasers,” Prog. Electromagn. Res.125, 365–389 (2012).

[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, 445–447 (2008).

[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, 1123–1125 (2001).

[CrossRef]
[PubMed]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Norwood, 2005).