Abstract

Using the three-dimensional (3D) finite-difference time-domain (FDTD) method, we have investigated in detail the optical properties of a two-dimensional (2D) photonic crystal (PC) surface-emitting laser having a square-lattice structure. In this study we perform the 3D-FDTD calculation for the structure of an actual fabricated device. The device is based on band-edge resonance, and four band edges are present at the corresponding band edge point. For these band edges, we calculate the quality (Q) factor. The results show that the Q factor of a resonant mode labeled A1 is larger than that of other resonant modes; that is, lasing occurs easily in mode A1. The device can thus achieve single-mode lasing oscillation. To increase the Q factor, we also consider the optimization of device parameters. The results provide important guidelines for device fabrication.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  2. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
    [CrossRef] [PubMed]
  3. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
    [CrossRef] [PubMed]
  4. S. Noda, M. Imada, and A. Chutinan, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
    [CrossRef] [PubMed]
  5. B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
    [CrossRef] [PubMed]
  6. S. Noda and T. Baba, Eds., Roadmap on Photonic Crystals, (Kluwer Academic, New York, 2003).
  7. 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]
  8. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65, 195306 (2002).
    [CrossRef]
  9. 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]
  10. M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron. 39, 1074–1080 (2003).
    [CrossRef]
  11. M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser having a Square-Lattice Slab Structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).
  12. 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]
  13. K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A Two-Dimensional Photonic Crystal Laser,” Jpn. J. Appl. Phys. 38, L157–L159 (1999).
    [CrossRef]
  14. M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
    [CrossRef]
  15. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
    [CrossRef] [PubMed]
  16. K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
    [CrossRef]
  17. K. S. Yee, “Numerical Solution of Initial Boundary Value Problem Involving Maxwell’s Equations in Isotropic Media,” in Proceedings of IEEE Conference on Antennas and Propagat. AP-14 (Institute of Electrical and Electronics Engineers, New York, 1966), pp. 302–307.
  18. M. Okano and S. Noda, “Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains,” Phys. Rev. B 70, 125105 (2004).
    [CrossRef]
  19. M. Plihal, A. Shambrook, and A. A. Maradudin, “Two-dimensional photonic band structures,” Opt. Comm. 80, 199–204 (1991).
    [CrossRef]
  20. K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982–7986 (1995).
    [CrossRef]
  21. K. Sakoda, Optical Properties of Photonic Crystals, (Springer Verlag, Berlin, 2001).
  22. G. Mur, “Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations,” in Proceedings of IEEE Conference on Electromagn. Compat. EMC-23 (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 377–382.
  23. O. J. Painter, J. Vuckovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
    [CrossRef]
  24. D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser,” Opt. Express 12, 1562–1568 (2004).
    [CrossRef] [PubMed]
  25. T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
    [CrossRef]
  26. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  27. M. Imada, S. Noda, H. Kobayashi, and G. Sasaki, “Characterization of a Distributed Feedback Laser with Air/Semiconductor Gratings Embedded by the Wafer Fusion Technique,” IEEE J. Quantum Electron. 35, 1277–1283 (1999).
    [CrossRef]

2004 (4)

M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser having a Square-Lattice Slab Structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

M. Okano and S. Noda, “Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains,” Phys. Rev. B 70, 125105 (2004).
[CrossRef]

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

2003 (3)

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

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef] [PubMed]

2002 (2)

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

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

2001 (2)

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[CrossRef] [PubMed]

2000 (2)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

S. Noda, M. Imada, and A. Chutinan, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

1999 (7)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[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. 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]

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A Two-Dimensional Photonic Crystal Laser,” Jpn. J. Appl. Phys. 38, L157–L159 (1999).
[CrossRef]

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
[CrossRef]

M. Imada, S. Noda, H. Kobayashi, and G. Sasaki, “Characterization of a Distributed Feedback Laser with Air/Semiconductor Gratings Embedded by the Wafer Fusion Technique,” IEEE J. Quantum Electron. 35, 1277–1283 (1999).
[CrossRef]

O. J. Painter, J. Vuckovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

1995 (1)

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982–7986 (1995).
[CrossRef]

1991 (1)

M. Plihal, A. Shambrook, and A. A. Maradudin, “Two-dimensional photonic band structures,” Opt. Comm. 80, 199–204 (1991).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Asano, T.

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef] [PubMed]

Baba, T.

S. Noda and T. Baba, Eds., Roadmap on Photonic Crystals, (Kluwer Academic, New York, 2003).

Capasso, F.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Cho, A. Y.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Cho, A.Y.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

Chutinan, A.

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

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[CrossRef] [PubMed]

S. Noda, M. Imada, and A. Chutinan, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[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]

Colombelli, R.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[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]

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
[CrossRef]

Fan, S.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Gmachl, C.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Haus, J. W.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A Two-Dimensional Photonic Crystal Laser,” Jpn. J. Appl. Phys. 38, L157–L159 (1999).
[CrossRef]

Imada, M.

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

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

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[CrossRef] [PubMed]

S. Noda, M. Imada, and A. Chutinan, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[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, S. Noda, H. Kobayashi, and G. Sasaki, “Characterization of a Distributed Feedback Laser with Air/Semiconductor Gratings Embedded by the Wafer Fusion Technique,” IEEE J. Quantum Electron. 35, 1277–1283 (1999).
[CrossRef]

Inoue, K.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A Two-Dimensional Photonic Crystal Laser,” Jpn. J. Appl. Phys. 38, L157–L159 (1999).
[CrossRef]

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[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]

Kawamata, J.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A Two-Dimensional Photonic Crystal Laser,” Jpn. J. Appl. Phys. 38, L157–L159 (1999).
[CrossRef]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Kobayashi, H.

M. Imada, S. Noda, H. Kobayashi, and G. Sasaki, “Characterization of a Distributed Feedback Laser with Air/Semiconductor Gratings Embedded by the Wafer Fusion Technique,” IEEE J. Quantum Electron. 35, 1277–1283 (1999).
[CrossRef]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Maradudin, A. A.

M. Plihal, A. Shambrook, and A. A. Maradudin, “Two-dimensional photonic band structures,” Opt. Comm. 80, 199–204 (1991).
[CrossRef]

Meier, M.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (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]

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]

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
[CrossRef]

Mochizuki, M.

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

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[CrossRef] [PubMed]

Mur, G.

G. Mur, “Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations,” in Proceedings of IEEE Conference on Electromagn. Compat. EMC-23 (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 377–382.

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]

Murray, C. A.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
[CrossRef]

Nalamasu, O.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (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]

Noda, S.

M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser having a Square-Lattice Slab Structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).

M. Okano and S. Noda, “Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains,” Phys. Rev. B 70, 125105 (2004).
[CrossRef]

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

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef] [PubMed]

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

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

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[CrossRef] [PubMed]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

S. Noda, M. Imada, and A. Chutinan, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[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, S. Noda, H. Kobayashi, and G. Sasaki, “Characterization of a Distributed Feedback Laser with Air/Semiconductor Gratings Embedded by the Wafer Fusion Technique,” IEEE J. Quantum Electron. 35, 1277–1283 (1999).
[CrossRef]

S. Noda and T. Baba, Eds., Roadmap on Photonic Crystals, (Kluwer Academic, New York, 2003).

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Ochiai, T.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Ohnishi, D.

Okano, M.

M. Okano and S. Noda, “Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains,” Phys. Rev. B 70, 125105 (2004).
[CrossRef]

Okano, T.

Painter, O.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Painter, O. J.

Plihal, M.

M. Plihal, A. Shambrook, and A. A. Maradudin, “Two-dimensional photonic band structures,” Opt. Comm. 80, 199–204 (1991).
[CrossRef]

Rogers, J. A.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
[CrossRef]

Ruel, R.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
[CrossRef]

Sakoda, K.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A Two-Dimensional Photonic Crystal Laser,” Jpn. J. Appl. Phys. 38, L157–L159 (1999).
[CrossRef]

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982–7986 (1995).
[CrossRef]

K. Sakoda, Optical Properties of Photonic Crystals, (Springer Verlag, Berlin, 2001).

Sasada, M.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A Two-Dimensional Photonic Crystal Laser,” Jpn. J. Appl. Phys. 38, L157–L159 (1999).
[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]

M. Imada, S. Noda, H. Kobayashi, and G. Sasaki, “Characterization of a Distributed Feedback Laser with Air/Semiconductor Gratings Embedded by the Wafer Fusion Technique,” IEEE J. Quantum Electron. 35, 1277–1283 (1999).
[CrossRef]

Scherer, A.

O. J. Painter, J. Vuckovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Sergent, A. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Sergent, A.M.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

Shambrook, A.

M. Plihal, A. Shambrook, and A. A. Maradudin, “Two-dimensional photonic band structures,” Opt. Comm. 80, 199–204 (1991).
[CrossRef]

Sivco, D. L.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Sivco, D.L.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

Slusher, R. E.

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

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
[CrossRef]

Song, B. S.

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef] [PubMed]

Srinivasan, K.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Tennant, D. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Tennant, D.M.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

Timko, A.

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (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]

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]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

Troccoli, M.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Vuckovic, J.

Yablonovitch, E.

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Yee, K. S.

K. S. Yee, “Numerical Solution of Initial Boundary Value Problem Involving Maxwell’s Equations in Isotropic Media,” in Proceedings of IEEE Conference on Antennas and Propagat. AP-14 (Institute of Electrical and Electronics Engineers, New York, 1966), pp. 302–307.

Yokoyama, M.

M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser having a Square-Lattice Slab Structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).

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

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[CrossRef] [PubMed]

App. Phys. Lett. (1)

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D.M. Tennant, A.M. Sergent, D.L. Sivco, A.Y. Cho, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” App. Phys. Lett. 84, 4164–4166 (2004).
[CrossRef]

Appl. Phys. Lett. (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]

IEEE J. Quantum Electron. (2)

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

M. Imada, S. Noda, H. Kobayashi, and G. Sasaki, “Characterization of a Distributed Feedback Laser with Air/Semiconductor Gratings Embedded by the Wafer Fusion Technique,” IEEE J. Quantum Electron. 35, 1277–1283 (1999).
[CrossRef]

IEICE Trans. Electron. (1)

M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser having a Square-Lattice Slab Structure,” IEICE Trans. Electron. E87-C, 386–392 (2004).

J. Appl. Phys. (1)

M. Meier, A. Dodabalapur, J. A. Rogers, R. E. Slusher, A. Mekis, A. Timko, C. A. Murray, R. Ruel, and O. Nalamasu, “Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding,” J. Appl. Phys. 86, 3502–3507 (1999).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A Two-Dimensional Photonic Crystal Laser,” Jpn. J. Appl. Phys. 38, L157–L159 (1999).
[CrossRef]

Nature (1)

S. Noda, M. Imada, and A. Chutinan, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Opt. Comm. (1)

M. Plihal, A. Shambrook, and A. A. Maradudin, “Two-dimensional photonic band structures,” Opt. Comm. 80, 199–204 (1991).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (5)

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

M. Okano and S. Noda, “Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains,” Phys. Rev. B 70, 125105 (2004).
[CrossRef]

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982–7986 (1995).
[CrossRef]

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

Phys. Rev. Lett. (1)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Science (5)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[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]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[CrossRef] [PubMed]

Other (4)

K. Sakoda, Optical Properties of Photonic Crystals, (Springer Verlag, Berlin, 2001).

G. Mur, “Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations,” in Proceedings of IEEE Conference on Electromagn. Compat. EMC-23 (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 377–382.

S. Noda and T. Baba, Eds., Roadmap on Photonic Crystals, (Kluwer Academic, New York, 2003).

K. S. Yee, “Numerical Solution of Initial Boundary Value Problem Involving Maxwell’s Equations in Isotropic Media,” in Proceedings of IEEE Conference on Antennas and Propagat. AP-14 (Institute of Electrical and Electronics Engineers, New York, 1966), pp. 302–307.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

(a), (b), (c), (d) Magnetic field distributions at band edges A1, B1, E, and E, respectively. The amplitudes of the magnetic fields in the direction perpendicular to the plane are indicated by white and black areas, which denote positive and negative regions, respectively. The thick black circles indicate the shapes and locations of lattice points.

Fig. 2.
Fig. 2.

Coordinates and symmetry of the square lattice structure having a circular unit cell structure

Fig. 3.
Fig. 3.

Schematic of 3D-FDTD calculations. The device is composed of an n-cladding layer, a p-cladding layer, and an active layer. The 2D PC is embedded at the cladding layer close to the active layer.

Fig. 4.
Fig. 4.

(a) Magnetic field distributions of A1 mode normal to the photonic crystal plane at the center of the active layer. The PC size is 100×100. (b) Wave number space (k-space) patterns of (a). The figure is obtained by Fourier transformation of the magnetic field of the photonic crystal area in Fig 4(a). The white dotted square represents the first Brillouin zone.

Fig. 5.
Fig. 5.

The resonant frequency of each resonant mode versus air filling factor. We can classify air filling factor into three regions depending on the by the relative height the resonant frequency. The horizontal line at a frequency of 0.3116 is the cladding light line, above which light leaks to the cladding layer.

Fig. 6.
Fig. 6.

(a) (b) (c) Typical band structures of regions A, B, and C around the Γ2 point, respectively. These band structures are calculated by the 2D PW expansion method. The dielectric constants inside the unit cell are 9.26, 9.86, and 10.01, respectively. The dielectric constants outside the unit cell are 10.60, 10.47, and 10.38 respectively. The air filling factors are 8.50%, 30.0%, and 50.0%, respectively.

Fig. 7.
Fig. 7.

(a)(b) The wave number space (k-space) patterns of the electric field (E x ) of the A1 mode, when the air filling factors are 10% and 60%, respectively. The circles indicated by a solid line, a broken line, and a dotted line are the light cones determined by the refractive index of the active layer, the cladding layer, and air, respectively.

Fig. 8.
Fig. 8.

Q factors as functions of air filling factor for A1, B1, and E modes. Size of the PC is 100×100. The Q factor of the A1 mode is larger than those of the other resonant modes. This result indicates that, among the resonant modes, the A1 mode allows relatively easy lasing.

Fig. 9.
Fig. 9.

(a)(b) Horizontal Q factor (Q) and vertical Q factor (Q ) as functions of the air filling factor for A1, B1, and E modes. Q and Q represent losses of guided mode and out-of-plane radiation, respectively, in the direction normal to the photonic crystal plane.

Fig. 10.
Fig. 10.

Frequency differences between maximum and minimum resonant frequencies for each of the A1, B1, and E resonant modes. The solid line is obtained by the 3D-FDTD calculation and the dotted line is obtained by the 2D PW expansion method using the effective refractive index. The characteristic trend is similar to that for Q.

Metrics