Abstract

By altering the lattice geometry of the photonic crystal (PhC) surface-emitting lasers (PCSELs), we tune the regular lasing band edges of quadratic dispersions to form a single accidental Dirac point of linear dispersion at the Brillouin zone center. This not only increases the mode spacing by orders of magnitude but also eliminates the distributed in-plane feedback to enable single-mode PCSELs of substantially larger area and thus substantially higher output power. The advantages of using accidental Dirac cones are systematically evaluated through two-dimensional in-plane calculations and confirmed by three-dimensional simulations of PhC slab devices.

© 2014 Optical Society of America

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  1. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, Phys. Rev. B 65, 195306 (2002).
    [CrossRef]
  2. X. K. Sun and A. Yariv, Opt. Express 16, 9155 (2008).
    [CrossRef]
  3. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, Nature 457, 174 (2009).
    [CrossRef]
  4. W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, in Conference on Lasers and Electro-Optics (Optical Society of America, 2006), paper CMKK1.
  5. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
    [CrossRef]
  6. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
    [CrossRef]
  7. Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
    [CrossRef]
  8. C. H. Henry, R. F. Kazarinov, R. A. Logan, and R. Yen, IEEE J. Quantum Electron. 21, 151 (1985).
    [CrossRef]
  9. T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125107 (2001).
    [CrossRef]
  10. S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  11. S.-L. Chua, Y. D. Chong, A. D. Stone, M. Soljačić, and J. Bravo-Abad, Opt. Express 19, 1539 (2011).
    [CrossRef]
  12. X. Huang, Y. Lai, Z. Hang, H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
    [CrossRef]
  13. K. Sakoda, J. Opt. Soc. Am. B 29, 2770 (2012).
    [CrossRef]
  14. Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, Phys. Rev. B 84, 195119 (2011).
    [CrossRef]
  15. M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565 (1991).
    [CrossRef]
  16. Y. D. Chong, X.-G. Wen, and M. Soljačić, Phys. Rev. B 77, 235125 (2008).
    [CrossRef]
  17. Y. A. Urzhumov and G. Shvets, Phys. Rev. E 72, 026608 (2005).
    [CrossRef]
  18. S. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef]
  19. J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, Proc. Natl. Acad. Sci. USA. 109, 9761 (2012).
    [CrossRef]
  20. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
    [CrossRef]

2012

K. Sakoda, J. Opt. Soc. Am. B 29, 2770 (2012).
[CrossRef]

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, Proc. Natl. Acad. Sci. USA. 109, 9761 (2012).
[CrossRef]

2011

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, Phys. Rev. B 84, 195119 (2011).
[CrossRef]

S.-L. Chua, Y. D. Chong, A. D. Stone, M. Soljačić, and J. Bravo-Abad, Opt. Express 19, 1539 (2011).
[CrossRef]

X. Huang, Y. Lai, Z. Hang, H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

2010

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

2009

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, Nature 457, 174 (2009).
[CrossRef]

2008

X. K. Sun and A. Yariv, Opt. Express 16, 9155 (2008).
[CrossRef]

Y. D. Chong, X.-G. Wen, and M. Soljačić, Phys. Rev. B 77, 235125 (2008).
[CrossRef]

2006

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef]

2005

Y. A. Urzhumov and G. Shvets, Phys. Rev. E 72, 026608 (2005).
[CrossRef]

2002

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, Phys. Rev. B 65, 195306 (2002).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

2001

T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125107 (2001).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef]

S. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef]

1991

M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565 (1991).
[CrossRef]

1985

C. H. Henry, R. F. Kazarinov, R. A. Logan, and R. Yen, IEEE J. Quantum Electron. 21, 151 (1985).
[CrossRef]

Barbieri, S.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, Nature 457, 174 (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, Nature 457, 174 (2009).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Bravo-Abad, J.

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, Proc. Natl. Acad. Sci. USA. 109, 9761 (2012).
[CrossRef]

S.-L. Chua, Y. D. Chong, A. D. Stone, M. Soljačić, and J. Bravo-Abad, Opt. Express 19, 1539 (2011).
[CrossRef]

Chan, C. T.

X. Huang, Y. Lai, Z. Hang, H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[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, Nature 457, 174 (2009).
[CrossRef]

Chong, Y. D.

Chua, S.-L.

Chutinan, A.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, Phys. Rev. B 65, 195306 (2002).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef]

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, Nature 457, 174 (2009).
[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, Nature 457, 174 (2009).
[CrossRef]

Fan, S.

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Hang, Z.

X. Huang, Y. Lai, Z. Hang, H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Henry, C. H.

C. H. Henry, R. F. Kazarinov, R. A. Logan, and R. Yen, IEEE J. Quantum Electron. 21, 151 (1985).
[CrossRef]

Huang, X.

X. Huang, Y. Lai, Z. Hang, H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Imada, M.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, Phys. Rev. B 65, 195306 (2002).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef]

Iwahashi, S.

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, Phys. Rev. B 84, 195119 (2011).
[CrossRef]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

Joannopoulos, J. D.

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, Proc. Natl. Acad. Sci. USA. 109, 9761 (2012).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

S. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef]

Johnson, S.

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Kazarinov, R. F.

C. H. Henry, R. F. Kazarinov, R. A. Logan, and R. Yen, IEEE J. Quantum Electron. 21, 151 (1985).
[CrossRef]

Khanna, S. P.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, Nature 457, 174 (2009).
[CrossRef]

Kunishi, W.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef]

W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, in Conference on Lasers and Electro-Optics (Optical Society of America, 2006), paper CMKK1.

Kurosaka, Y.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

Lai, Y.

X. Huang, Y. Lai, Z. Hang, H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Liang, Y.

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, Phys. Rev. B 84, 195119 (2011).
[CrossRef]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[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, Nature 457, 174 (2009).
[CrossRef]

Logan, R. A.

C. H. Henry, R. F. Kazarinov, R. A. Logan, and R. Yen, IEEE J. Quantum Electron. 21, 151 (1985).
[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, Nature 457, 174 (2009).
[CrossRef]

Maradudin, A. A.

M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565 (1991).
[CrossRef]

Miyai, E.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef]

W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, in Conference on Lasers and Electro-Optics (Optical Society of America, 2006), paper CMKK1.

Mochizuki, M.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, Phys. Rev. B 65, 195306 (2002).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef]

Noda, S.

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, Phys. Rev. B 84, 195119 (2011).
[CrossRef]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, Phys. Rev. B 65, 195306 (2002).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef]

W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, in Conference on Lasers and Electro-Optics (Optical Society of America, 2006), paper CMKK1.

Ochiai, T.

T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Ohnishi, D.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef]

W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, in Conference on Lasers and Electro-Optics (Optical Society of America, 2006), paper CMKK1.

Okano, T.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Peng, C.

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, Phys. Rev. B 84, 195119 (2011).
[CrossRef]

Plihal, M.

M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565 (1991).
[CrossRef]

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, Nature 457, 174 (2009).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Sakai, K.

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, Phys. Rev. B 84, 195119 (2011).
[CrossRef]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef]

W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, in Conference on Lasers and Electro-Optics (Optical Society of America, 2006), paper CMKK1.

Sakoda, K.

K. Sakoda, J. Opt. Soc. Am. B 29, 2770 (2012).
[CrossRef]

T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Shvets, G.

Y. A. Urzhumov and G. Shvets, Phys. Rev. E 72, 026608 (2005).
[CrossRef]

Soljacic, M.

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, Proc. Natl. Acad. Sci. USA. 109, 9761 (2012).
[CrossRef]

S.-L. Chua, Y. D. Chong, A. D. Stone, M. Soljačić, and J. Bravo-Abad, Opt. Express 19, 1539 (2011).
[CrossRef]

Y. D. Chong, X.-G. Wen, and M. Soljačić, Phys. Rev. B 77, 235125 (2008).
[CrossRef]

Stone, A. D.

Sun, X. K.

Urzhumov, Y. A.

Y. A. Urzhumov and G. Shvets, Phys. Rev. E 72, 026608 (2005).
[CrossRef]

Wen, X.-G.

Y. D. Chong, X.-G. Wen, and M. Soljačić, Phys. Rev. B 77, 235125 (2008).
[CrossRef]

Yariv, A.

Yen, R.

C. H. Henry, R. F. Kazarinov, R. A. Logan, and R. Yen, IEEE J. Quantum Electron. 21, 151 (1985).
[CrossRef]

Yokoyama, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef]

Zheng, H.

X. Huang, Y. Lai, Z. Hang, H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Comput. Phys. Commun.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

IEEE J. Quantum Electron.

C. H. Henry, R. F. Kazarinov, R. A. Logan, and R. Yen, IEEE J. Quantum Electron. 21, 151 (1985).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Mater.

X. Huang, Y. Lai, Z. Hang, H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Nat. Photonics

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, Nat. Photonics 4, 447 (2010).
[CrossRef]

Nature

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, Nature 457, 174 (2009).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, Nature 441, 946 (2006).
[CrossRef]

Opt. Express

Phys. Rev. B

Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, Phys. Rev. B 84, 195119 (2011).
[CrossRef]

M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565 (1991).
[CrossRef]

Y. D. Chong, X.-G. Wen, and M. Soljačić, Phys. Rev. B 77, 235125 (2008).
[CrossRef]

T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125107 (2001).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, Phys. Rev. B 65, 195306 (2002).
[CrossRef]

Phys. Rev. E

Y. A. Urzhumov and G. Shvets, Phys. Rev. E 72, 026608 (2005).
[CrossRef]

Proc. Natl. Acad. Sci. USA.

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, Proc. Natl. Acad. Sci. USA. 109, 9761 (2012).
[CrossRef]

Science

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef]

Other

W. Kunishi, D. Ohnishi, E. Miyai, K. Sakai, and S. Noda, in Conference on Lasers and Electro-Optics (Optical Society of America, 2006), paper CMKK1.

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Figures (3)

Fig. 1.
Fig. 1.

TM photonic band structure and DOS of a 2D triangular array of dielectric rods ϵrod=12.5 in air background ϵbg=1. (a) The rod radius r is tuned so that the doubly degenerate modes (with E1 symmetry in the C6v point group) are accidentally degenerate with a singly degenerate A1 mode (red band) at Γ. The modal profiles of the three accidentally degenerate modes at Γ are depicted with electric field pointing into the page and having positive (negative) values in red (blue). (b) The usual case where r is detuned from accidental degeneracy and the band edges are of quadratic dispersions.

Fig. 2.
Fig. 2.

(a) Finite-sized 2D PhC cavity consisting of a triangular array of dielectric rods ϵrod=12.5 embedded in air with dimension L=40a. (b) The high Q band dispersions of three PhCs with different rod radii. At Γ, the red band has a linear dispersion while the green and blue bands have quadratic dispersions. (c) Band edge modes of two finite-sized PhC cavities of L=300a with linear dispersion (top plot) and of L=40a with quadratic dispersion (lower plot). Insets show the mode profiles with electric field pointing into the page and having positive (negative) values in red (blue). (d) The upper plot illustrates the band edge mode spacing (Δω/ω0 where ω0 is the band edge frequency) as a function of the cavity area. The lower plot illustrates Q of the band edge mode as a function of the cavity area. The filled circles and squares correspond to the results shown in (c).

Fig. 3.
Fig. 3.

(a) 2×2 unit-cells of a GaAs-based 2D PhC slab on AlAs (n=3) substrate. A square array of air-holes with radius 0.285a is patterned in the top 0.47a-thick GaInP (n=3.22) layer. Sandwiched between GaInP and the substrate is a homogeneous 1a-thick GaAs (n=3.52) layer. a is the lattice constant. (b) Band structure (TE-like modes near Γ) of the considered PhC slab. The hole radius is tuned so that the pair of doubly degenerate modes (blue bands) is accidentally degenerate with a singly degenerate mode (red) at Γ. Bottom inset shows the corresponding Q-plot of the three bands in a small region near Γ, where Q diverges only for the red band.

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