Abstract

Photonic-crystal lasers operating on Γ-point band-edge states of a photonic structure naturally exploit the so-called “nonradiative” modes. As the surface output coupling efficiency of these modes is low, they have relatively high Q factors, which favor lasing. We propose a new 2D photonic-crystal design that is capable of reversing this mode competition and achieving lasing on the radiative modes instead. Previously, this has only been shown in 1D structures, where the central idea is to introduce anisotropy into the system, both at unit-cell and resonator scales. By applying this concept to 2D photonic-crystal patterned terahertz frequency quantum cascade lasers, surface-emitting devices with diffraction-limited beams are demonstrated, with 17 mW peak output power.

© 2014 Optical Society of America

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References

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).
  2. Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
    [CrossRef]
  3. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef]
  4. M. Narimatsu, S. Kita, H. Abe, and T. Baba, Appl. Phys. Lett. 100, 121117 (2012).
    [CrossRef]
  5. C. Sirtori, S. Barbieri, and R. Colombelli, Nat. Photonics 7, 691 (2013).
    [CrossRef]
  6. X. Checoury, R. Colombelli, and J. M. Lourtioz, in Compact Semiconductor Lasers, ed. (Wiley, 2014), pp. 91–149.
  7. M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 3, 586 (2009).
    [CrossRef]
  8. T. Y. Kao, Q. Hu, and J. L. Reno, Opt. Lett. 37, 2070 (2012).
    [CrossRef]
  9. 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]
  10. G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
    [CrossRef]
  11. J. A. Fan, M. A. Belkin, and F. Capasso, Opt. Express 14, 11672 (2006).
    [CrossRef]
  12. S. Kumar, B. S. Williams, Q. Qin, A. M. Lee, Q. Hu, and J. L. Reno, Opt. Express 15, 113 (2007).
    [CrossRef]
  13. G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
    [CrossRef]
  14. G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
    [CrossRef]
  15. E. Istrate and E. H. Sargent, Rev. Mod. Phys. 78, 455 (2006).
    [CrossRef]
  16. All modeling studies were carried out with 2D FDTD modeling using Lumerical Software ( www.lumerical.com ).
  17. J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
    [CrossRef]
  18. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
    [CrossRef]

2013 (2)

C. Sirtori, S. Barbieri, and R. Colombelli, Nat. Photonics 7, 691 (2013).
[CrossRef]

G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
[CrossRef]

2012 (3)

M. Narimatsu, S. Kita, H. Abe, and T. Baba, Appl. Phys. Lett. 100, 121117 (2012).
[CrossRef]

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

T. Y. Kao, Q. Hu, and J. L. Reno, Opt. Lett. 37, 2070 (2012).
[CrossRef]

2010 (2)

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

2009 (2)

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 3, 586 (2009).
[CrossRef]

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

2007 (1)

2006 (2)

J. A. Fan, M. A. Belkin, and F. Capasso, Opt. Express 14, 11672 (2006).
[CrossRef]

E. Istrate and E. H. Sargent, Rev. Mod. Phys. 78, 455 (2006).
[CrossRef]

2003 (1)

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

2002 (1)

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Abe, H.

M. Narimatsu, S. Kita, H. Abe, and T. Baba, Appl. Phys. Lett. 100, 121117 (2012).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Amanti, M. I.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 3, 586 (2009).
[CrossRef]

Asano, T.

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Baba, T.

M. Narimatsu, S. Kita, H. Abe, and T. Baba, Appl. Phys. Lett. 100, 121117 (2012).
[CrossRef]

Barbieri, S.

C. Sirtori, S. Barbieri, and R. Colombelli, Nat. Photonics 7, 691 (2013).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

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

Beck, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 3, 586 (2009).
[CrossRef]

Beere, H.

G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
[CrossRef]

Beere, H. E.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

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

Belarouci, A.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

Belkin, M. A.

Capasso, F.

Chassagneux, Y.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

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

Checoury, X.

X. Checoury, R. Colombelli, and J. M. Lourtioz, in Compact Semiconductor Lasers, ed. (Wiley, 2014), pp. 91–149.

Colombelli, R.

C. Sirtori, S. Barbieri, and R. Colombelli, Nat. Photonics 7, 691 (2013).
[CrossRef]

G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
[CrossRef]

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

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

X. Checoury, R. Colombelli, and J. M. Lourtioz, in Compact Semiconductor Lasers, ed. (Wiley, 2014), pp. 91–149.

Davies, A. G.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

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

Faist, J.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 3, 586 (2009).
[CrossRef]

Fan, J. A.

Fischer, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 3, 586 (2009).
[CrossRef]

Fowler, D.

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

Halioua, Y.

G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
[CrossRef]

Hu, Q.

Istrate, E.

E. Istrate and E. H. Sargent, Rev. Mod. Phys. 78, 455 (2006).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Julien, F. H.

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

Kao, T. Y.

Khanna, S. P.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

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

Kita, S.

M. Narimatsu, S. Kita, H. Abe, and T. Baba, Appl. Phys. Lett. 100, 121117 (2012).
[CrossRef]

Kumar, S.

Lee, A. M.

Letartre, X.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

Li, L.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

Linfield, E. H.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

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

Loncar, M.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Lourtioz, J. M.

X. Checoury, R. Colombelli, and J. M. Lourtioz, in Compact Semiconductor Lasers, ed. (Wiley, 2014), pp. 91–149.

Mabuchi, H.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Maineult, W.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

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

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Moumdji, S.

G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
[CrossRef]

Narimatsu, M.

M. Narimatsu, S. Kita, H. Abe, and T. Baba, Appl. Phys. Lett. 100, 121117 (2012).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Qin, Q.

Reno, J. L.

Ritchie, D.

G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
[CrossRef]

Ritchie, D. A.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

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

Sargent, E. H.

E. Istrate and E. H. Sargent, Rev. Mod. Phys. 78, 455 (2006).
[CrossRef]

Scalari, G.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 3, 586 (2009).
[CrossRef]

Scherer, A.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Sevin, G.

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Sirtori, C.

C. Sirtori, S. Barbieri, and R. Colombelli, Nat. Photonics 7, 691 (2013).
[CrossRef]

Song, B.

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Vuckovic, J.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Williams, B. S.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Xu, G.

G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
[CrossRef]

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Appl. Phys. Lett. (3)

M. Narimatsu, S. Kita, H. Abe, and T. Baba, Appl. Phys. Lett. 100, 121117 (2012).
[CrossRef]

G. Xu, Y. Halioua, S. Moumdji, R. Colombelli, H. Beere, and D. Ritchie, Appl. Phys. Lett. 102, 231105 (2013).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, Appl. Phys. Lett. 96, 031104 (2010).
[CrossRef]

Electron. Lett. (1)

G. Sevin, D. Fowler, G. Xu, F. H. Julien, R. Colombelli, H. E. Beere, and D. A. Ritchie, Electron. Lett. 46, 1513 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Nat. Commun. (1)

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, Nat. Commun. 3, 952 (2012).
[CrossRef]

Nat. Photonics (2)

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, Nat. Photonics 3, 586 (2009).
[CrossRef]

C. Sirtori, S. Barbieri, and R. Colombelli, Nat. Photonics 7, 691 (2013).
[CrossRef]

Nature (2)

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[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, Nature 457, 174 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Rev. Mod. Phys. (1)

E. Istrate and E. H. Sargent, Rev. Mod. Phys. 78, 455 (2006).
[CrossRef]

Other (3)

All modeling studies were carried out with 2D FDTD modeling using Lumerical Software ( www.lumerical.com ).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

X. Checoury, R. Colombelli, and J. M. Lourtioz, in Compact Semiconductor Lasers, ed. (Wiley, 2014), pp. 91–149.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Typical bandstructure of a 2nd order metal/semiconductor DFB grating of period a. The upper band (at k=0) is identified with the radiative mode, the lower band with the non-radiative mode. (b) Schematic representation of the grading effect in a GPH (ai+1=a1·α, abs(α)<1) from center to the edges. A “photonic well” ensures confinement of the radiative modes (red and black dashed lines) while the non-radiative modes are displaced, from the band center to the edges. (c) Dispersion curve of a 2D square metal/semiconductor PhC. Inset: Brillouin zone of a square lattice (d) Band structure of a PhC with anisotropic lattice (lattice=28×36μm2, hole radius=8μm). The two upper branches are identified (from top to bottom) with the non-radiative (monopolar) and radiative modes (dipolar), respectively, according to their lattice field profiles. Their dispersion, in a portion of the Brillouin zone around the Γ-point, is similar to a 2nd order DFB. Bottom left inset: Ez and Hy components of the dipolar mode. The unit-cell anisotropy (bottom right inset) splits the degeneracy along orthogonal directions of the lattice, hence the ΓX direction is introduced. However, this region of the reciprocal space is not relevant in this context since the modes of interest oscillate along ΓX.

Fig. 2.
Fig. 2.

(a) Image of the sample. The gray surrounding zone is an absorbing region. The scale bar (top right) is 100 μm long. Green and red arrows define the scanning angles used in beam profiling measurements. (b) Typical current density-voltage and current density-output power curves. The output peak power is typically 1517mW. The inset shows the frequency of the laser emission for various scaling parameters S of the PhC: 0.95, 1, 1.016 and 1.032, respectively. The PhC lasers typically exhibit single mode operation.

Fig. 3.
Fig. 3.

(a) The measured far-field pattern for a typical PhC laser operating on the radiative mode. The far-field emission is naturally single-lobed, and the divergence angles (7°×10°) are close to the diffraction limit expected from the size of the device. (b) Numerical simulation—obtained by FDTD analysis—of the emission far-field of the analyzed device. (c) Current-voltage and current-output power curves for various sizes of PhCs. As the lateral size of the resonator is increased from 414 μm (blue curve) to 533 μm (green curve) and 651 μm (red curve), the peak power increases from 6 mW to 9.5 mW and 13 mW, respectively, at 8 K.

Fig. 4.
Fig. 4.

In plane Q factor as a function of the lattice anisotropy, defined as the ratio of ay/ax (ax being the grading axis) and grading parameter α, the rule ai+1=ai·α being applied to the outermost four lateral holes. The color map shows an optimum operation point in a region corresponding to 1.075 anisotropy and grading α=1.015. The white circle locates the operating point of the reference PhC used in the article.

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