Abstract

We report on micropillar-based terahertz lasers with active pillars that are much smaller than the emission wavelength. These micropillar array lasers correspond to scaled-down band-edge photonic crystal lasers forming an active photonic metamaterial. In contrast to photonic crystal lasers which use significantly larger pillar structures, lasing emission is not observed close to high-symmetry points in the photonic band diagram, but in the effective medium regime. We measure stimulated emission at 4 THz for micropillar array lasers with pillar diameters of 5 µm. Our results not only demonstrate the integration of active subwavelength optics in a terahertz laser, but are also an important step towards the realization of nanowire-based terahertz lasers.

© 2014 Optical Society of America

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  1. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
    [CrossRef] [PubMed]
  2. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
    [CrossRef] [PubMed]
  3. M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, O. Painter, “Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap,” Opt. Express 15(10), 5948–5965 (2007).
    [CrossRef] [PubMed]
  4. L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdré, L. Sirigu, G. Scalari, M. Giovannini, N. Hoyler, J. Faist, “Design, fabrication and optical characterization of quantum cascade lasers at terahertz frequencies using photonic crystal reflectors,” Opt. Express 13(22), 8960–8968 (2005).
    [CrossRef] [PubMed]
  5. A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
    [CrossRef] [PubMed]
  6. M. Notomi, H. Suzuki, T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
    [CrossRef]
  7. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
    [CrossRef]
  8. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
    [CrossRef]
  9. H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
    [CrossRef] [PubMed]
  10. H. Zhang, L. A. Dunbar, G. Scalari, R. Houdré, J. Faist, “Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15(25), 16818–16827 (2007).
    [CrossRef] [PubMed]
  11. A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
    [CrossRef] [PubMed]
  12. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
    [CrossRef] [PubMed]
  13. H. Zhang, G. Scalari, M. Beck, J. Faist, R. Houdré, “Complex-coupled photonic crystal THz lasers with independent loss and refractive index modulation,” Opt. Express 19(11), 10707–10713 (2011).
    [CrossRef] [PubMed]
  14. S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
    [CrossRef]
  15. H. Yasuda, I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
    [CrossRef]
  16. E. Perret, N. Zerounian, S. David, F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
    [CrossRef]
  17. S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
    [CrossRef] [PubMed]
  18. P. Lalanne, “Effective medium theory applied to photonic crystals composed of cubic or square cylinders,” Appl. Opt. 35(27), 5369–5380 (1996).
    [CrossRef] [PubMed]
  19. P. Halevi, A. A. Krokhin, J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
    [CrossRef]
  20. D. J. Bergman, D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
    [CrossRef]
  21. S. Johnson, J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
    [CrossRef] [PubMed]
  22. B. Vasić, G. Isić, R. Gajić, K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
    [CrossRef] [PubMed]
  23. K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
    [CrossRef]
  24. H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, 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]
  25. M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
    [CrossRef]
  26. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
    [CrossRef] [PubMed]
  27. S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, H. C. Liu, “Terahertz quantum cascade lasers operating up to ~ 200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express 20(4), 3866–3876 (2012).
    [CrossRef] [PubMed]
  28. N. S. Wingreen, C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
    [CrossRef]
  29. C.-F. Hsu, J. -S. O, P. Zory, D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).
  30. E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
    [CrossRef] [PubMed]
  31. S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
    [CrossRef]
  32. T. Grange, “Nanowire terahertz quantum cascade lasers,” arXiv:1301.1258 [cond–mat.mes–hall] (2013).
  33. M. I. Amanti, A. Bismuto, M. Beck, L. Isa, K. Kumar, E. Reimhult, J. Faist, “Electrically driven nanopillars for THz quantum cascade lasers,” Opt. Express 21(9), 10917–10923 (2013).
    [CrossRef] [PubMed]
  34. S. Kumar, Q. Hu, J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
    [CrossRef]
  35. C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
    [CrossRef]
  36. M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
    [CrossRef]

2013 (4)

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

M. I. Amanti, A. Bismuto, M. Beck, L. Isa, K. Kumar, E. Reimhult, J. Faist, “Electrically driven nanopillars for THz quantum cascade lasers,” Opt. Express 21(9), 10917–10923 (2013).
[CrossRef] [PubMed]

2012 (1)

2011 (1)

2010 (2)

B. Vasić, G. Isić, R. Gajić, K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[CrossRef] [PubMed]

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, 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 (5)

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[CrossRef]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[CrossRef] [PubMed]

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

S. Kumar, Q. Hu, J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[CrossRef]

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

2008 (3)

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef] [PubMed]

H. Yasuda, I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
[CrossRef]

E. Perret, N. Zerounian, S. David, F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[CrossRef]

2007 (3)

2005 (1)

2003 (1)

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

2002 (2)

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

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

2001 (3)

M. Notomi, H. Suzuki, T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[CrossRef]

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

S. Johnson, J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

2000 (1)

C.-F. Hsu, J. -S. O, P. Zory, D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

1999 (4)

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

P. Halevi, A. A. Krokhin, J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[CrossRef]

1997 (1)

N. S. Wingreen, C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
[CrossRef]

1996 (1)

1993 (1)

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

1992 (1)

D. J. Bergman, D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[CrossRef]

Amanti, M. I.

Andrews, A. M.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[CrossRef] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[CrossRef] [PubMed]

Aniel, F.

E. Perret, N. Zerounian, S. David, F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[CrossRef]

Arriaga, J.

P. Halevi, A. A. Krokhin, J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[CrossRef]

Bahriz, M.

Ban, D.

Barbieri, S.

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

Bastard, G.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Beck, M.

Beere, H. E.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, 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, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Beltram, F.

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

Benz, A.

Bergman, D. J.

D. J. Bergman, D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[CrossRef]

Bismuto, A.

Botez, D.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[CrossRef]

C.-F. Hsu, J. -S. O, P. Zory, D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

Brandstetter, M.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

Capasso, F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

Carpenter, B. A.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Chan, C. T.

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

Chan, C. W. I.

Chassagneux, Y.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, 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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

Chutinan, A.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[CrossRef]

Colombelli, R.

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

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, O. Painter, “Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap,” Opt. Express 15(10), 5948–5965 (2007).
[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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

Crisafulli, O.

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Datta, S.

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

David, S.

E. Perret, N. Zerounian, S. David, F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[CrossRef]

Davies, A. G.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, 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, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

de Vaulchier, L.-A.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

Detz, H.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

Deutsch, C.

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

Deutsch, Ch.

Dodabalapur, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Dunbar, L. A.

Dupont, E.

Faist, J.

Fasching, G.

Fathololoumi, S.

Ferreira, R.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Ferrini, R.

Gajic, R.

Giovannini, M.

Gmachl, C.

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Grange, T.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Guldner, Y.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

Halevi, P.

P. Halevi, A. A. Krokhin, J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[CrossRef]

Helm, M.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Hingerl, K.

Ho, K. M.

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

Hosako, I.

H. Yasuda, I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
[CrossRef]

Houdré, R.

Hoyler, N.

Hsu, C.-F.

C.-F. Hsu, J. -S. O, P. Zory, D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

Hu, Q.

Hwang, H. Y.

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

Imada, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (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, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Isa, L.

Isic, G.

Jianglin, Y.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef] [PubMed]

Jirauschek, C.

Joannopoulos, J.

Joannopoulos, J. D.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Johnson, S.

Khandekar, A. A.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[CrossRef]

Khanna, S. P.

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

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Klang, P.

Köhler, R.

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

Krall, M.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

Krokhin, A. A.

P. Halevi, A. A. Krokhin, J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[CrossRef]

Kuech, T. F.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[CrossRef]

Kumar, K.

Kumar, S.

S. Kumar, Q. Hu, J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[CrossRef]

Laframboise, S. R.

Lalanne, P.

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Linfield, E. H.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, 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, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Liu, H. C.

Liu, H. Y.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Maëro, S.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

Maineult, W.

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

Matsubara, H.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef] [PubMed]

Mátyás, A.

Meier, M.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Mekis, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Moreau, V.

Murata, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[CrossRef]

Nalamasu, O.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Noda, S.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[CrossRef]

Nojima, S.

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

Notomi, M.

M. Notomi, H. Suzuki, T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[CrossRef]

O, J. -S.

C.-F. Hsu, J. -S. O, P. Zory, D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Painter, O.

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, O. Painter, “Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap,” Opt. Express 15(10), 5948–5965 (2007).
[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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Perret, E.

E. Perret, N. Zerounian, S. David, F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[CrossRef]

Porter, N. E.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Rathi, M. K.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[CrossRef]

Reimhult, E.

Reno, J. L.

S. Kumar, Q. Hu, J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[CrossRef]

Ritchie, D. A.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, 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, 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, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Saito, H.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef] [PubMed]

Sasaki, G.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[CrossRef]

Scalari, G.

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Schrenk, W.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[CrossRef] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[CrossRef] [PubMed]

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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

Shin, J. C.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[CrossRef]

Sirigu, L.

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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

Skolnick, M. S.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Slusher, R. E.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Soukoulis, C. M.

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Stafford, C. A.

N. S. Wingreen, C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
[CrossRef]

Stehr, D.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Strasser, G.

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[CrossRef] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[CrossRef] [PubMed]

Stroud, D.

D. J. Bergman, D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[CrossRef]

Suzuki, H.

M. Notomi, H. Suzuki, T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[CrossRef]

Tamamura, T.

M. Notomi, H. Suzuki, T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[CrossRef]

Tanaka, Y.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef] [PubMed]

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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Timko, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

Tokuda, T.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[CrossRef]

Tredicucci, A.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, 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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Tsvid, G.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[CrossRef]

Unterrainer, K.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[CrossRef] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[CrossRef] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

Vasic, B.

Wasilewski, Z. R.

Wilson, L. R.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Wingreen, N. S.

N. S. Wingreen, C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
[CrossRef]

Winnerl, S.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Yasuda, H.

H. Yasuda, I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
[CrossRef]

Yoshimoto, S.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef] [PubMed]

Zederbauer, T.

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

Zerounian, N.

E. Perret, N. Zerounian, S. David, F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[CrossRef]

Zhang, H.

Zibik, E. A.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Zory, P.

C.-F. Hsu, J. -S. O, P. Zory, D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

Appl. Opt. (1)

Appl. Phys. Lett. (7)

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[CrossRef]

S. Kumar, Q. Hu, J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[CrossRef]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[CrossRef]

M. Notomi, H. Suzuki, T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[CrossRef]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

N. S. Wingreen, C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
[CrossRef]

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

C.-F. Hsu, J. -S. O, P. Zory, D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

J. Appl. Phys. (2)

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, 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]

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

J. Electron. Mater. (1)

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Yasuda, I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
[CrossRef]

Microelectron. Eng. (1)

E. Perret, N. Zerounian, S. David, F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[CrossRef]

Nat. Mater. (1)

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[CrossRef] [PubMed]

Nature (2)

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

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

Opt. Express (10)

S. Johnson, J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdré, L. Sirigu, G. Scalari, M. Giovannini, N. Hoyler, J. Faist, “Design, fabrication and optical characterization of quantum cascade lasers at terahertz frequencies using photonic crystal reflectors,” Opt. Express 13(22), 8960–8968 (2005).
[CrossRef] [PubMed]

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, O. Painter, “Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap,” Opt. Express 15(10), 5948–5965 (2007).
[CrossRef] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[CrossRef] [PubMed]

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

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[CrossRef] [PubMed]

B. Vasić, G. Isić, R. Gajić, K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[CrossRef] [PubMed]

H. Zhang, G. Scalari, M. Beck, J. Faist, R. Houdré, “Complex-coupled photonic crystal THz lasers with independent loss and refractive index modulation,” Opt. Express 19(11), 10707–10713 (2011).
[CrossRef] [PubMed]

S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, H. C. Liu, “Terahertz quantum cascade lasers operating up to ~ 200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express 20(4), 3866–3876 (2012).
[CrossRef] [PubMed]

M. I. Amanti, A. Bismuto, M. Beck, L. Isa, K. Kumar, E. Reimhult, J. Faist, “Electrically driven nanopillars for THz quantum cascade lasers,” Opt. Express 21(9), 10917–10923 (2013).
[CrossRef] [PubMed]

Phys. Rev. B Condens. Matter (1)

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

P. Halevi, A. A. Krokhin, J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[CrossRef]

Proc. SPIE (1)

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[CrossRef]

Science (3)

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[CrossRef] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[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, F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[CrossRef] [PubMed]

Solid State Phys. (1)

D. J. Bergman, D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[CrossRef]

Other (1)

T. Grange, “Nanowire terahertz quantum cascade lasers,” arXiv:1301.1258 [cond–mat.mes–hall] (2013).

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Figures (4)

Fig. 1
Fig. 1

Scaling of a pillar array from a photonic crystal to the effective medium regime. (a) Photonic band diagram of TM-modes calculated for infinitely long pillars in a hexagonal array with r/a = 0.45, ε1 = 13.32 (GaAs) [15], and ε2 = 2.45 (BCB) [16]. Reducing the size of the pillars, while keeping r/a constant, moves down the gain spectrum of the active material towards the effective medium regime. (b) Magnitude of the electric field at several points in the lowest band plotted on a linear scale. In contrast to a large confinement of the electric field in the pillars at the high symmetry points (M, K), practically no confinement is observed in the effective medium regime (A). The effective filling factor calculated using Eq. (2) decreases from 0.89 at the K-point to 0.75 at point ‘A’.

Fig. 2
Fig. 2

(a) Schematic illustration of the micropillar array terahertz laser. The densely packed pillar array is sandwiched between two metal layers and forms a ridge-waveguide. The space between the pillars is filled with a low-loss polymer. (b) Scanning electron microscope images of fabricated micropillar array lasers with pillar diameters of 5 µm. Inset: Facet of the laser ridge (top), and closer view of a micropillar before planarization (bottom).

Fig. 3
Fig. 3

(a) Comparison of the current-voltage (IV) characteristic of a bulk structure and micropillar arrays with various pillar diameters. The current density in the micropillar arrays is calculated using the physical dimensions of the pillars. Surface states are causing a partial carrier depletion in the micropillars, which significantly reduces the current density for small pillar diameters. The inset shows the effective diameters available for charge transport depending on the physical diameters of the micropillars, including a linear fit to the data. A surface depletion width of approximately 170 nm can be extracted from the decreasing current density. (b) Low-temperature light-current-voltage (LIV) characteristics of a 120 x 1000 x 10 µm micropillar array laser with a pillar size of 5 µm and a filling factor of 0.75 (r/a = 0.45). The current density is given as the density in the micropillars calculated from the measured current and the filling factor of the array.

Fig. 4
Fig. 4

Laser output spectra of a 120 x 1000 x 10 µm micropillar array laser with a pillar size of 5 µm and a filling factor of 0.75 (r/a = 0.45). The measurements are performed at a heat sink temperature of 5 K. (a) Overlay of the emission spectrum with the photonic band diagram. In contrast to photonic crystal lasers, high-symmetry points of the photonic lattice are far outside the gain region and no lasing is observed at these points. The emission frequency of approximately 4 THz corresponds to a normalized frequency (fa/c) of about 0.07. (b) The two dominant emission modes with slightly varying frequency close to the operation points of the two output maxima in the LI-curve of Fig. 3. The spectra are vertically shifted for clarity.

Equations (2)

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

ε eff = ε 1 η+ ε 2 (1η),
η eff = ε= ε 1 dr| E( r ) | dr| E( r ) | .

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