Abstract

Compared to near infra-red photonic crystal (PhC) band-edge lasers, achieving vertical emission with quantum cascade (QC) material operating in the THz range needs dedicated engineering because the TM polarized emission of QCLs favors in-plane emitting schemes and the currently used double plasmon waveguide, prevents vertical light extraction. We present an approach with independent refractive index and extraction losses modulation. The extraction losses are obtained with small extracting holes located at appropriate positions. The modal operation of the PhC is shown to critically depend on the external losses introduced. Very high surface emission power for optimum loss extractor design is achieved.

© 2011 OSA

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  1. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
    [CrossRef] [PubMed]
  2. O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
    [CrossRef]
  3. L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
    [CrossRef] [PubMed]
  4. 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 457(7226), 174–178 (2009).
    [CrossRef] [PubMed]
  5. J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser - a new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
    [CrossRef]
  6. H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
    [CrossRef]
  7. E. Kapon, A. Hardy, and A. Katzir, “The effect of complex coupling-coefficients on distributed feedback lasers,” IEEE J. Quantum Electron. 18(1), 66–71 (1982).
    [CrossRef]
  8. S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
    [CrossRef]
  9. O. Demichel, L. Mahler, T. Losco, C. Mauro, R. Green, A. Tredicucci, J. Xu, F. Beltram, H. E. Beere, D. A. Ritchie, and V. Tamosinuas, “Surface plasmon photonic structures in terahertz quantum cascade lasers,” Opt. Express 14(12), 5335–5345 (2006).
    [CrossRef] [PubMed]
  10. J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
    [CrossRef] [PubMed]
  11. S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15(1), 113–128 (2007).
    [CrossRef] [PubMed]
  12. H. Zhang, L. A. Dunbar, G. Scalari, R. Houdré, and J. Faist, “Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15(25), 16818–16827 (2007).
    [CrossRef] [PubMed]
  13. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
    [CrossRef] [PubMed]
  14. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
    [CrossRef] [PubMed]
  15. B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
    [CrossRef]
  16. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83(11), 2124–2126 (2003).
    [CrossRef]
  17. H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
    [CrossRef]
  18. H. Zhang, G. Scalari, R. Houdré, and J. Faist, “In-plane and surface emitting high performance THz pillar type photonic crystal lasers with complete photonic bandgaps” in Proceedings of the IEEE Lasers and Electro-Optics 2009 and European Quantum Electronics Conference (CLEO Europe - EQEC2009), DOI 10.1109/CLEOE-EQEC.2009.5192585.
  19. COMSOL-Multiphysics, http://www.comsol.com .
  20. M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
    [CrossRef]
  21. K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A two-dimensional photonic crystal laser,” Jpn. J. Appl. Phys. 38(Part 2, No. 2B), L157–L159 (1999).
    [CrossRef]
  22. M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
    [CrossRef]

2010 (1)

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
[CrossRef]

2009 (3)

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

2008 (2)

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (2)

2003 (2)

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83(11), 2124–2126 (2003).
[CrossRef]

2002 (1)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

2001 (1)

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

1999 (1)

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A two-dimensional photonic crystal laser,” Jpn. J. Appl. Phys. 38(Part 2, No. 2B), L157–L159 (1999).
[CrossRef]

1994 (2)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser - a new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

1982 (1)

E. Kapon, A. Hardy, and A. Katzir, “The effect of complex coupling-coefficients on distributed feedback lasers,” IEEE J. Quantum Electron. 18(1), 66–71 (1982).
[CrossRef]

1972 (1)

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

Amanti, M. I.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

Apostolopoulos, V.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[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, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

Beck, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (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 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

O. Demichel, L. Mahler, T. Losco, C. Mauro, R. Green, A. Tredicucci, J. Xu, F. Beltram, H. E. Beere, D. A. Ritchie, and V. Tamosinuas, “Surface plasmon photonic structures in terahertz quantum cascade lasers,” Opt. Express 14(12), 5335–5345 (2006).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Belkin, M. A.

Beltram, F.

O. Demichel, L. Mahler, T. Losco, C. Mauro, R. Green, A. Tredicucci, J. Xu, F. Beltram, H. E. Beere, D. A. Ritchie, and V. Tamosinuas, “Surface plasmon photonic structures in terahertz quantum cascade lasers,” Opt. Express 14(12), 5335–5345 (2006).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser - a new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser - a new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

Callebaut, H.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83(11), 2124–2126 (2003).
[CrossRef]

Capasso, F.

J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
[CrossRef] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

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 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

Cho, A. Y.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

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 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

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 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Demichel, O.

Dowling, J. P.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser - a new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

Dunbar, L. A.

Faist, J.

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
[CrossRef]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

H. Zhang, L. A. Dunbar, G. Scalari, R. Houdré, and J. Faist, “Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15(25), 16818–16827 (2007).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Fan, J. A.

Fischer, M.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

Freeman, J. R.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Gallo, P.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

Giovannini, M.

Gmachl, C. F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Green, R.

Hardy, A.

E. Kapon, A. Hardy, and A. Katzir, “The effect of complex coupling-coefficients on distributed feedback lasers,” IEEE J. Quantum Electron. 18(1), 66–71 (1982).
[CrossRef]

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(Part 2, No. 2B), L157–L159 (1999).
[CrossRef]

Houdré, R.

Hu, Q.

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15(1), 113–128 (2007).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83(11), 2124–2126 (2003).
[CrossRef]

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

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(Part 2, No. 2B), L157–L159 (1999).
[CrossRef]

Iotti, R. C.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Kapon, E.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

E. Kapon, A. Hardy, and A. Katzir, “The effect of complex coupling-coefficients on distributed feedback lasers,” IEEE J. Quantum Electron. 18(1), 66–71 (1982).
[CrossRef]

Katzir, A.

E. Kapon, A. Hardy, and A. Katzir, “The effect of complex coupling-coefficients on distributed feedback lasers,” IEEE J. Quantum Electron. 18(1), 66–71 (1982).
[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(Part 2, No. 2B), L157–L159 (1999).
[CrossRef]

Khanna, S.

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, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

Kogelnik, H.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

Köhler, R.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Kumar, S.

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15(1), 113–128 (2007).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83(11), 2124–2126 (2003).
[CrossRef]

Lachab, M.

Lee, A. W. M.

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 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Losco, T.

Mahler, L.

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 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

Marshall, O. P.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Mauro, C.

Nojima, S.

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

Painter, O.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Qin, Q.

Reno, J. L.

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15(1), 113–128 (2007).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83(11), 2124–2126 (2003).
[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, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

O. Demichel, L. Mahler, T. Losco, C. Mauro, R. Green, A. Tredicucci, J. Xu, F. Beltram, H. E. Beere, D. A. Ritchie, and V. Tamosinuas, “Surface plasmon photonic structures in terahertz quantum cascade lasers,” Opt. Express 14(12), 5335–5345 (2006).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Rossi, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Rudra, A.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

Rungsawang, R.

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

Sakoda, K.

K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “A two-dimensional photonic crystal laser,” Jpn. J. Appl. Phys. 38(Part 2, No. 2B), L157–L159 (1999).
[CrossRef]

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(Part 2, No. 2B), L157–L159 (1999).
[CrossRef]

Scalari, G.

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
[CrossRef]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

H. Zhang, L. A. Dunbar, G. Scalari, R. Houdré, and J. Faist, “Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15(25), 16818–16827 (2007).
[CrossRef] [PubMed]

Scalora, M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser - a new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

Sergent, A. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Shank, C. V.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

Sirigu, L.

Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Sivco, D. L.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Srinivasan, K.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Tamosinuas, V.

Tennant, D. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Terazzi, R.

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008).
[CrossRef] [PubMed]

Tredicucci, A.

O. Demichel, L. Mahler, T. Losco, C. Mauro, R. Green, A. Tredicucci, J. Xu, F. Beltram, H. E. Beere, D. A. Ritchie, and V. Tamosinuas, “Surface plasmon photonic structures in terahertz quantum cascade lasers,” Opt. Express 14(12), 5335–5345 (2006).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Troccoli, M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Williams, B. S.

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[CrossRef]

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15(1), 113–128 (2007).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83(11), 2124–2126 (2003).
[CrossRef]

Xu, J.

Zhang, H.

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
[CrossRef]

H. Zhang, L. A. Dunbar, G. Scalari, R. Houdré, and J. Faist, “Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15(25), 16818–16827 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83(11), 2124–2126 (2003).
[CrossRef]

O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. Kapon, A. Hardy, and A. Katzir, “The effect of complex coupling-coefficients on distributed feedback lasers,” IEEE J. Quantum Electron. 18(1), 66–71 (1982).
[CrossRef]

J. Appl. Phys. (4)

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser - a new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
[CrossRef]

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(Part 2, No. 2B), L157–L159 (1999).
[CrossRef]

N. J. Phys. (1)

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” N. J. Phys. 11(12), 125022 (2009).
[CrossRef]

Nat. Photonics (2)

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[CrossRef]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

Nature (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 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Opt. Express (5)

Science (2)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. 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(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Other (2)

H. Zhang, G. Scalari, R. Houdré, and J. Faist, “In-plane and surface emitting high performance THz pillar type photonic crystal lasers with complete photonic bandgaps” in Proceedings of the IEEE Lasers and Electro-Optics 2009 and European Quantum Electronics Conference (CLEO Europe - EQEC2009), DOI 10.1109/CLEOE-EQEC.2009.5192585.

COMSOL-Multiphysics, http://www.comsol.com .

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Figures (4)

Fig. 1
Fig. 1

(a), Photonic crystal dispersion curves calculated by 2D Plane wave expansion, several complete bandgaps are observed (semi-transparent gray shadows, e.g. PBG1 and PBG2). Blue dashed lines indicate the light light. Red dashed circle locates the two slow light band-edge states of interest (Γ2, Γ3). The pillar filling factor (ff) is 40%. (b), Sketch of the surface emitting lasing scheme at the band-edges (Γ2, Γ3). The pillar height is about 15 µm and the lattice constant range is between 32 and 40 µm. (c), Left: Side view SEM image of PhC pillar after dry etching. Top right: Top view SEM image of holes-on-pillars (HOP) device. Bottom right: Top view SEM image of holes-on-BCB (HOB) device. (d), Top panel, extraction modal Q on the Γ3 state as a function of the extractor size. Bottom panel, eigenfrequency on the Γ3 state as a function of the extractor size. The holes-on-pillars (HOP) scheme always has a larger impact on the band structure than the holes-on-BCB (HOB) scheme.

Fig. 2
Fig. 2

Elliptical pillar photonic crystal degeneracy lifting. (a) Left, PhC dispersion of circular pillar around PBG2 calculated along k-vector direction of K-Γ-M. Ez field maps of each band-edges (Γ2 and Γ3) are shown as inserts. A schematic drawing of the lattice is inserted with circular pillar configuration. Right, lasing spectra of such circular pillar-PhC laser at a = 40 μm, the zoom region show the multimode behavior at the quasi-degenerated band-edge. (b) Left, PhC dispersion of elliptical pillars calculated along k-vector direction of K-Γ-M. Elliptical pillars are designed with x/y ratio of 0.8, and rotated with 30° angle respective to the horizontal direction. A schematic drawing of the lattice is inserted with elliptical pillar configuration. The degeneracy of the Γ2 and Γ3 band-edge states is lifted. The splitting is about Δu = 0.0224 in reduced energy, which corresponds to a broad frequency bandwidth of 168 GHz at lattice constant a = 40 μm. Right, lasing spectra of such elliptical pillar PhC lasers at a = 36 μm and a = 38 μm. For a = 36 μm, two sharp peaks were observed whose splitting energy is in good agreement with the calculated value Δu = 0.0224 between Γ2 and Γ 3 states. The multimode behavior is due to the gain bandwidth wide enough to overlap with both states. For a = 38 μm, single mode was observed as the gain bandwidth overlaps with only one of the two states (Γ3). The elliptical pillar structure has 6-fold degenerated M points, they split in two groups: a 2-fold of M points, and 4-fold of M* points.

Fig. 3
Fig. 3

Light–current–voltage (LIV) a circular pillar type photonic-crystal laser with lattice constant a = 40 μm, with extractor scheme of Holes-on-BCB. The maximum power collected from the top of the device exceeds 31 mW.

Fig. 4
Fig. 4

Light–current–voltage (LIV) and spectral characterizations of elliptical pillar type photonic crystal quantum cascade lasers. (a) and (b), Light–current–voltage (LIV) characteristics as a function of temperature for the two type of extractors. The maximum power collected from the top of the devices are 18.2 mW and 13.4 mW, for holes on pillars and holes on BCB extraction schemes, respectively. The maximum operating temperature for both devices is 120 K, which is the same as the standard FP ridge lasers (embedded with BCB) fabricated on the same batch with the same material. (c) and (d), Dispersion curves and lasing spectra of elliptical pillar-type photonic-crystal lasers at lattice constant a = 32 µm, with holes on pillars and holes on BCB configurations, as shown insert SEM images for (c) and (d), respectively. The intense line at u = 0.35 correspond to lasing at a M3* point.

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