Abstract

In high-contrast (HC) photonic crystals (PC) slabs, the high-order coupling is so intense that it is indispensable for analyzing the guided mode resonance (GMR) effect. In this paper, a semi-analytical approach is proposed for analyzing GMR in HC PC slabs with TE-like polarization. The intense high-order coupling is included by using a convergent recursive procedure. The reflection of radiative waves at high-index-contrast interfaces is also considered by adopting a strict Green’s function for multi-layer structures. Modal properties of interest like band structure, radiation constant, field profile are calculated, agreeing well with numerical finite-difference time-domain simulations. This analysis is promising for the design and optimization of various HC PC devices.

© 2013 Optical Society of America

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2013 (2)

2012 (3)

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

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [PubMed]

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

2011 (2)

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]

2010 (2)

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

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun.181, 687–702 (2010).
[CrossRef]

2009 (2)

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. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[CrossRef]

2008 (6)

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

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

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers,” Appl. Phys. Lett.92, 171108 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high-contrast grating,” IEEE Photon. Technol. Lett.20, 434–436 (2008).
[CrossRef]

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasersbased on two-dimensional photoniccrystal resonators,” Opt. Express16, 5206–5217 (2008).
[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]

2007 (2)

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics1, 119–122 (2007).
[CrossRef]

2006 (3)

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, “Photonics: 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]

2005 (1)

2003 (1)

H. Ryu, M. Notomi, and Y. 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]

2002 (1)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65, 235112 (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,” Science293, 1123–1125 (2001).
[CrossRef] [PubMed]

2000 (3)

P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B61, 2090–2101 (2000).
[CrossRef]

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B62, 4204–4207 (2000).
[CrossRef]

A. Mekis, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Two-dimensional photonic crystal couplers for unidirectional light output,” Opt. Lett.25, 942–944 (2000).
[CrossRef]

1999 (3)

M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and purcell enhancement from thin-film 2-d photonic crystals,” J. Lightwave Technol.17, 2096–2112 (1999).
[CrossRef]

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

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60, 5751–5758 (1999).
[CrossRef]

1998 (1)

M. J. Bergmann and H. C. Casey, “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys.84, 1196–1203 (1998).
[CrossRef]

1997 (2)

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

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

1996 (1)

1995 (1)

1976 (1)

W. Streifer, D. R. Scifres, and R. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides - I,” IEEE J. Quantum Electron.12, 422–428 (1976).
[CrossRef]

Amanti, M. I.

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 (London)457, 174–178 (2009).
[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 (London)457, 174–178 (2009).
[CrossRef]

Bergmann, M. J.

M. J. Bergmann and H. C. Casey, “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys.84, 1196–1203 (1998).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun.181, 687–702 (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).
[CrossRef]

Bhat, R.

Boroditsky, M.

Burnham, R.

W. Streifer, D. R. Scifres, and R. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides - I,” IEEE J. Quantum Electron.12, 422–428 (1976).
[CrossRef]

Busch, A.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[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).
[CrossRef]

Casey, H. C.

M. J. Bergmann and H. C. Casey, “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys.84, 1196–1203 (1998).
[CrossRef]

Chang-Hasnain, C.

Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high-contrast grating,” IEEE Photon. Technol. Lett.20, 434–436 (2008).
[CrossRef]

Chang-Hasnain, C. J.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers,” Appl. Phys. Lett.92, 171108 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics1, 119–122 (2007).
[CrossRef]

Chase, C.

Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[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 (London)457, 174–178 (2009).
[CrossRef]

Chen, S.

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

Chow, E.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

Chua, S. L.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature (London)499, 188–191 (2013).
[CrossRef]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [PubMed]

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
[CrossRef] [PubMed]

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

Coccioli, R.

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 (London)457, 174–178 (2009).
[CrossRef]

Cowan, A. R.

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B62, 4204–4207 (2000).
[CrossRef]

Cunningham, B. T.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

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 (London)457, 174–178 (2009).
[CrossRef]

Dodabalapur, A.

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Giovannini, M.

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C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature (London)499, 188–191 (2013).
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Y. Zhou, M. C. Y. Huang, and C. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high-contrast grating,” IEEE Photon. Technol. Lett.20, 434–436 (2008).
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Imada, 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,” Science293, 1123–1125 (2001).
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Ishizaki, K.

Iwahashi, S.

Y. Liang, C. Peng, K. Ishizaki, S. Iwahashi, K. Sakai, Y. Tanaka, K. Kitamura, and S. Noda, “Three-dimensional coupled-wave analysis for triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization,” Opt. Express21, 565–580 (2013).
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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).
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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).
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A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun.181, 687–702 (2010).
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Joannopoulos, J. D.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature (London)499, 188–191 (2013).
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J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [PubMed]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65, 235112 (2002).
[CrossRef]

A. Mekis, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Two-dimensional photonic crystal couplers for unidirectional light output,” Opt. Lett.25, 942–944 (2000).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60, 5751–5758 (1999).
[CrossRef]

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
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Johnson, S.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

Johnson, S. G.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature (London)499, 188–191 (2013).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun.181, 687–702 (2010).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60, 5751–5758 (1999).
[CrossRef]

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
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Johnson, S. R.

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B62, 4204–4207 (2000).
[CrossRef]

Kanskar, M.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

Kao, C.

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

Karagodsky, V.

Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[CrossRef]

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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).
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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]

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).
[CrossRef]

Kitamura, K.

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60, 5751–5758 (1999).
[CrossRef]

Krauss, T. F.

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, “Photonics: Lasers producing tailored beams,” Nature (London)441, 946 (2006).
[CrossRef]

Kuo, H.

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

Kurosaka, 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]

Lee, J.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature (London)499, 188–191 (2013).
[CrossRef]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [PubMed]

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
[CrossRef] [PubMed]

Lee, Y.

H. Ryu, M. Notomi, and Y. 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]

Liang, X.

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
[CrossRef] [PubMed]

Liang, Y.

Y. Liang, C. Peng, K. Ishizaki, S. Iwahashi, K. Sakai, Y. Tanaka, K. Kitamura, and S. Noda, “Three-dimensional coupled-wave analysis for triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization,” Opt. Express21, 565–580 (2013).
[CrossRef] [PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting 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 a centered-rectangular lattice photonic crystal laser with a 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 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,” Nature Photon.4, 447–450 (2010).
[CrossRef]

Lin, L.

T. Lu, S. Chen, L. Lin, T. Kao, C. Kao, P. Yu, H. Kuo, S. Wang, and S. Fan, “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).
[CrossRef]

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 (London)457, 174–178 (2009).
[CrossRef]

Lu, T.

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

MacKenzie, J.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

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 (London)457, 174–178 (2009).
[CrossRef]

Malyarchuk, V.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

Mandeville, W. J.

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B62, 4204–4207 (2000).
[CrossRef]

Mathias, P. C.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

Matsubara, H.

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

Meier, M.

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

Mekis, A.

A. Mekis, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Two-dimensional photonic crystal couplers for unidirectional light output,” Opt. Lett.25, 942–944 (2000).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. 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.

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]

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]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: 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]

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

Moewe, M.

Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[CrossRef]

Moharam, M. G.

Morin, R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

Morris, G. M.

Nalamasu, O.

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

Noda, S.

Y. Liang, C. Peng, K. Ishizaki, S. Iwahashi, K. Sakai, Y. Tanaka, K. Kitamura, and S. Noda, “Three-dimensional coupled-wave analysis for triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization,” Opt. Express21, 565–580 (2013).
[CrossRef] [PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting 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 a centered-rectangular lattice photonic crystal laser with a transverse-electric-like mode,” Phys. Rev. B86, 035108 (2012).
[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. 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]

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]

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]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: 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]

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]

Notomi, M.

H. Ryu, M. Notomi, and Y. 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]

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, “Photonics: Lasers producing tailored beams,” Nature (London)441, 946 (2006).
[CrossRef]

Okano, T.

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

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun.181, 687–702 (2010).
[CrossRef]

Pacradouni, V.

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B62, 4204–4207 (2000).
[CrossRef]

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

Paddon, P.

P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B61, 2090–2101 (2000).
[CrossRef]

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B62, 4204–4207 (2000).
[CrossRef]

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

Peng, C.

Peng, S.

Pesala, B.

Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[CrossRef]

Pommet, D. A.

Qiu, W.

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [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 (London)457, 174–178 (2009).
[CrossRef]

Rodriguez, A. W.

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
[CrossRef] [PubMed]

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. Friesem, “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. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun.181, 687–702 (2010).
[CrossRef]

Ryu, H.

H. Ryu, M. Notomi, and Y. 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]

Saito, H.

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

Sakai, K.

Y. Liang, C. Peng, K. Ishizaki, S. Iwahashi, K. Sakai, Y. Tanaka, K. Kitamura, and S. Noda, “Three-dimensional coupled-wave analysis for triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization,” Opt. Express21, 565–580 (2013).
[CrossRef] [PubMed]

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting 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 a centered-rectangular lattice photonic crystal laser with a 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 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,” Nature Photon.4, 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]

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, “Photonics: Lasers producing tailored beams,” Nature (London)441, 946 (2006).
[CrossRef]

Scifres, D. R.

W. Streifer, D. R. Scifres, and R. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides - I,” IEEE J. Quantum Electron.12, 422–428 (1976).
[CrossRef]

Sedgwick, F.

Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[CrossRef]

Shapira, O.

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [PubMed]

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
[CrossRef] [PubMed]

Sharon, A.

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

Sirigu, L.

Slusher, R.

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

Slusher, R. E.

Smith, A. D.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

Soares, J. a. N. T.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

Soljacic, M.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature (London)499, 188–191 (2013).
[CrossRef]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [PubMed]

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
[CrossRef] [PubMed]

Streifer, W.

W. Streifer, D. R. Scifres, and R. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides - I,” IEEE J. Quantum Electron.12, 422–428 (1976).
[CrossRef]

Tanaka, Y.

Terazzi, R.

Tiedje, T.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

Timko, A.

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

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60, 5751–5758 (1999).
[CrossRef]

Vrijen, R.

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).
[CrossRef]

Wang, S.

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

Yablonovitch, E.

Yokoyama, M.

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]

Yoshimoto, S.

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

Young, J.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

Young, J. F.

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B62, 4204–4207 (2000).
[CrossRef]

P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B61, 2090–2101 (2000).
[CrossRef]

Yu, P.

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

Yue, J.

Zhang, W.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

Zhen, B.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature (London)499, 188–191 (2013).
[CrossRef]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [PubMed]

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
[CrossRef] [PubMed]

Zhou, Y.

Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers,” Appl. Phys. Lett.92, 171108 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high-contrast grating,” IEEE Photon. Technol. Lett.20, 434–436 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics1, 119–122 (2007).
[CrossRef]

Appl. Phys. Lett. (6)

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. Young, S. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70, 1438–1440 (1997).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett.74, 7–9 (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]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers,” Appl. Phys. Lett.92, 171108 (2008).
[CrossRef]

T. Lu, S. Chen, L. Lin, T. Kao, C. Kao, P. Yu, H. Kuo, S. Wang, and S. Fan, “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]

Comp. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun.181, 687–702 (2010).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

W. Streifer, D. R. Scifres, and R. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides - I,” IEEE J. Quantum Electron.12, 422–428 (1976).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron.15, 1485–1499 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Zhou, M. C. Y. Huang, and C. Chang-Hasnain, “Large fabrication tolerance for VCSELs using high-contrast grating,” IEEE Photon. Technol. Lett.20, 434–436 (2008).
[CrossRef]

J. Appl. Phys. (1)

M. J. Bergmann and H. C. Casey, “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys.84, 1196–1203 (1998).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

Nat. Photonics (1)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics1, 119–122 (2007).
[CrossRef]

Nature (London) (3)

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature (London)499, 188–191 (2013).
[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, “Photonics: Lasers producing tailored beams,” Nature (London)441, 946 (2006).
[CrossRef]

Nature Nano. (1)

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. a. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nano.2, 515–520 (2007).
[CrossRef]

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]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. B (7)

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 a centered-rectangular lattice photonic crystal laser with a transverse-electric-like mode,” Phys. Rev. B86, 035108 (2012).
[CrossRef]

H. Ryu, M. Notomi, and Y. 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]

P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B61, 2090–2101 (2000).
[CrossRef]

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B62, 4204–4207 (2000).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60, 5751–5758 (1999).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65, 235112 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett.109, 067401 (2012).
[CrossRef] [PubMed]

Science (2)

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” 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]

Other (1)

B. Zhen, S. L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special fano resonances of macroscopic photonic crystals,” Proc. Natl. Acad. Sci. USA (2013). In press.
[CrossRef] [PubMed]

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Figures (12)

Fig. 1
Fig. 1

Schematic cross-sectional view of (a) a low-index-contrast (LC) photonic crystal (PC) multi-layer structure and (b) a high-index-contrast (HC) PC slab. Green curves indicate the profiles of basic Bloch waves. (c) Schematic view of an HC PC slab with circular air holes; (d) Examples of air-hole designs: (i) circular (CC) and (ii) equilateral triangular (ET); (e) Blochwave states represented by wave vectors (arrows) in reciprocal space. Basic waves (blue arrows, denoted by Rx, Sx, Ry, Sy) and high-order waves (green arrows and black arrows) are considered. A simplified model considers eight wave vectors (blue and green arrows) [34]. A large number of high-order waves are included in [29,31]. In HC PC slabs, wave coupling among high-order waves (dashed red arrows) should be depicted to ensure accuracy.

Fig. 2
Fig. 2

Flowchart of the iteration procedure in high-index-contrast coupled wave theory.

Fig. 3
Fig. 3

In-plane E-field vector distribution (arrows) and Hz patterns (in color) of the four band-edge modes (A–D). The thick black circles indicate the shapes and locations of the air holes.

Fig. 4
Fig. 4

Vertical field profile comparison of wave vectors with different in-plane wave index: (a) basic, (m,n)=(1,0) (b) radiative, (m,n)=(0,0) and high-order waves with (c) (m,n) = (2,1) and (d) (m,n) = (4,3). The colored regions indicate the PC layer. The vertical field profile of basic waves is the same as that of the fundamental waveguide mode. The FDTD profiles are obtained by solving (Ex, Ey, Hz) in whole space considering the vertical multilayer structure and the horizontal permittivity modulation. The vertical field profiles of radiative and high-order waves are plotted for mode B (similar features are observed for other modes) and are calculated based on Eqs. (1) and (2) (only Ey field is plotted and field outside the PC layer is calculated by imposing continuity conditions on E field at the layer interfaces).

Fig. 5
Fig. 5

Mode Frequency vs. Filling factor with circular air holes.

Fig. 6
Fig. 6

Radiation constant vs. Filling factor with circular air holes.

Fig. 7
Fig. 7

Mode Frequency vs. Filling factor with equilateral triangular air holes.

Fig. 8
Fig. 8

Radiation constant vs. Filling factor with equilateral triangular air holes.

Fig. 9
Fig. 9

Mode frequencies of the HC PC slabs with circular air holes.

Fig. 10
Fig. 10

Radiation constants of the HC PC slabs with circular air holes.

Fig. 11
Fig. 11

Mode frequencies of the HC PC slabs with equilateral triangular air holes.

Fig. 12
Fig. 12

Radiation constants of the HC PC slabs with equilateral triangular air holes.

Equations (5)

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

[ 2 z 2 + n 0 2 k 0 2 ( m x 2 + n y 2 ) β 0 2 ] ( n y E x , m n m x E y , m n ) = k 0 2 ξ m m , n n ( n y E x , m n m x E y , m n )
n 0 2 ( m x E x , m n + n y E y , m n ) = ξ m m , n n ( m x E x , m n + n y E y , m n )
G ( z , z ) = i 2 k P C κ 1 κ e i k P C | z z | i 2 k P C 1 1 κ e i k P C | z z | .
κ = k P C k air k P C + k air e 2 i k P C h P C , k i = ε i k 0 2 Δ 2 β 0 2 , i = air , P C
k V = C V ,

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