Abstract

We propose and study the feasibility of a THz GaN/AlGaN quantum cascade laser (QCL) consisting of only five periods with confinement provided by a spoof surface plasmon (SSP) waveguide for room temperature operation. The QCL design takes advantages of the large optical phonon energy and the ultrafast phonon scattering in GaN that allow for engineering favorable laser state lifetimes. Our analysis has shown that the waveguide loss is sufficiently low for the QCL to reach its threshold at the injection current density around 6 kA/cm2 at room temperature.

© 2013 Optical Society of America

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  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,” Nature417(6885), 156–159 (2002).
    [CrossRef] [PubMed]
  2. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express13(9), 3331–3339 (2005).
    [CrossRef] [PubMed]
  3. M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express16(5), 3242–3248 (2008).
    [CrossRef] [PubMed]
  4. M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
    [CrossRef]
  5. S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-THz quantum cascade laser operating significantly above the temperature of ω/kB,” Nat. Phys.7(2), 166–171 (2011).
    [CrossRef]
  6. S. Fathololoumi, E. Dupont, C. W. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. C. Liu, “Terahertz quantum cascade lasers operating up to ~200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express20(4), 3866–3876 (2012).
    [CrossRef] [PubMed]
  7. G. Sun, R. A. Soref, and J. B. Khurgin, “Active region design of a terahertz GaN/ Al0.15Ga0.85N quantum cascade laser,” Superlattices Microstruct.37(2), 107–113 (2005).
    [CrossRef]
  8. N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
    [CrossRef]
  9. J. D. Heber, C. Gmachl, H. M. Ng, and A. Y. Cho, “Comparative study of ultrafast intersubband electron scattering times at ~1.55 μm wavelength in GaN/ALGaN heterostructures,” Appl. Phys. Lett.81(7), 1237–1239 (2002).
    [CrossRef]
  10. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
    [CrossRef] [PubMed]
  11. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
    [CrossRef]
  12. W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater.19(22), 3771–3782 (2007).
    [CrossRef]
  13. C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
    [CrossRef]
  14. T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
    [CrossRef]
  15. V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett.80(7), 1204–1206 (2002).
    [CrossRef]
  16. H. Ünlü and A. Asenov, “Band offsets in III-nitride heterostructures,” J. Phys. D Appl. Phys.35(7), 591–594 (2002).
    [CrossRef]
  17. H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, “Terahertz quantum-cascade lasers based on a three-well active module,” Appl. Phys. Lett.90(4), 041112 (2007).
    [CrossRef]
  18. G. Sun and J. B. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron.29(4), 1104–1111 (1993).
    [CrossRef]
  19. W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, “Electronic properties of zinc-blende GaN, AlN, and their alloys Ga1-xAlxN,” J. Appl. Phys.79(1), 188–194 (1996).
    [CrossRef]
  20. J. B. Khurgin and Y. Dikmelik, “Transport and gain in a quantum cascade laser: model and equivalent circuit,” Opt. Eng.49(11), 111110 (2010).
    [CrossRef]
  21. A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” J. Appl. Phys. A100(2), 375–378 (2010).
    [CrossRef]
  22. S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
    [CrossRef] [PubMed]
  23. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
    [CrossRef]
  24. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser operating up to 137 K,” Appl. Phys. Lett.83(25), 5142–5144 (2003).
    [CrossRef]
  25. M. Brandstetter, C. Deutsch, A. Benz, G. D. Cole, H. Detz, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “THz quantum cascade lasers with wafer bonded active regions,” Opt. Express20(21), 23832–23837 (2012).
    [CrossRef] [PubMed]

2012

2011

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-THz quantum cascade laser operating significantly above the temperature of ω/kB,” Nat. Phys.7(2), 166–171 (2011).
[CrossRef]

2010

J. B. Khurgin and Y. Dikmelik, “Transport and gain in a quantum cascade laser: model and equivalent circuit,” Opt. Eng.49(11), 111110 (2010).
[CrossRef]

A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” J. Appl. Phys. A100(2), 375–378 (2010).
[CrossRef]

2009

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

2008

2007

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater.19(22), 3771–3782 (2007).
[CrossRef]

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, “Terahertz quantum-cascade lasers based on a three-well active module,” Appl. Phys. Lett.90(4), 041112 (2007).
[CrossRef]

2006

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

2005

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express13(9), 3331–3339 (2005).
[CrossRef] [PubMed]

G. Sun, R. A. Soref, and J. B. Khurgin, “Active region design of a terahertz GaN/ Al0.15Ga0.85N quantum cascade laser,” Superlattices Microstruct.37(2), 107–113 (2005).
[CrossRef]

2004

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

2003

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser operating up to 137 K,” Appl. Phys. Lett.83(25), 5142–5144 (2003).
[CrossRef]

2002

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett.80(7), 1204–1206 (2002).
[CrossRef]

H. Ünlü and A. Asenov, “Band offsets in III-nitride heterostructures,” J. Phys. D Appl. Phys.35(7), 591–594 (2002).
[CrossRef]

J. D. Heber, C. Gmachl, H. M. Ng, and A. Y. Cho, “Comparative study of ultrafast intersubband electron scattering times at ~1.55 μm wavelength in GaN/ALGaN heterostructures,” Appl. Phys. Lett.81(7), 1237–1239 (2002).
[CrossRef]

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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

2000

N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

1996

W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, “Electronic properties of zinc-blende GaN, AlN, and their alloys Ga1-xAlxN,” J. Appl. Phys.79(1), 188–194 (1996).
[CrossRef]

1993

G. Sun and J. B. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron.29(4), 1104–1111 (1993).
[CrossRef]

1991

T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Aers, G. C.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, “Terahertz quantum-cascade lasers based on a three-well active module,” Appl. Phys. Lett.90(4), 041112 (2007).
[CrossRef]

Ambacher, O.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett.80(7), 1204–1206 (2002).
[CrossRef]

Andrews, A. M.

Andrews, S. R.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

Asano, T.

N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
[CrossRef]

Asenov, A.

H. Ünlü and A. Asenov, “Band offsets in III-nitride heterostructures,” J. Phys. D Appl. Phys.35(7), 591–594 (2002).
[CrossRef]

Ban, D.

Barnes, W. L.

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater.19(22), 3771–3782 (2007).
[CrossRef]

Beere, H. E.

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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Belkin, M. A.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express16(5), 3242–3248 (2008).
[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, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Belyanin, A.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

Benz, A.

Bernardini, F.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett.80(7), 1204–1206 (2002).
[CrossRef]

Brandstetter, M.

Callebaut, H.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser operating up to 137 K,” Appl. Phys. Lett.83(25), 5142–5144 (2003).
[CrossRef]

Cao, J. C.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, “Terahertz quantum-cascade lasers based on a three-well active module,” Appl. Phys. Lett.90(4), 041112 (2007).
[CrossRef]

Capasso, F.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express16(5), 3242–3248 (2008).
[CrossRef] [PubMed]

Chan, C. W.

Chan, C. W. I.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-THz quantum cascade laser operating significantly above the temperature of ω/kB,” Nat. Phys.7(2), 166–171 (2011).
[CrossRef]

Cho, A. Y.

J. D. Heber, C. Gmachl, H. M. Ng, and A. Y. Cho, “Comparative study of ultrafast intersubband electron scattering times at ~1.55 μm wavelength in GaN/ALGaN heterostructures,” Appl. Phys. Lett.81(7), 1237–1239 (2002).
[CrossRef]

Chong, T. C.

W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, “Electronic properties of zinc-blende GaN, AlN, and their alloys Ga1-xAlxN,” J. Appl. Phys.79(1), 188–194 (1996).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Cole, G. D.

Davies, A. G.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express16(5), 3242–3248 (2008).
[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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Detz, H.

Deutsch, C.

Dikmelik, Y.

J. B. Khurgin and Y. Dikmelik, “Transport and gain in a quantum cascade laser: model and equivalent circuit,” Opt. Eng.49(11), 111110 (2010).
[CrossRef]

Dupont, E.

Durach, M.

A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” J. Appl. Phys. A100(2), 375–378 (2010).
[CrossRef]

Duscher, G.

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Fan, J. A.

Fan, W. J.

W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, “Electronic properties of zinc-blende GaN, AlN, and their alloys Ga1-xAlxN,” J. Appl. Phys.79(1), 188–194 (1996).
[CrossRef]

Fanciulli, M.

T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
[CrossRef]

Fathololoumi, S.

Fiorentini, V.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett.80(7), 1204–1206 (2002).
[CrossRef]

Franzen, S.

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

García-Vidal, F. J.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Gmachl, C.

J. D. Heber, C. Gmachl, H. M. Ng, and A. Y. Cho, “Comparative study of ultrafast intersubband electron scattering times at ~1.55 μm wavelength in GaN/ALGaN heterostructures,” Appl. Phys. Lett.81(7), 1237–1239 (2002).
[CrossRef]

Graham, R. J.

T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
[CrossRef]

Heber, J. D.

J. D. Heber, C. Gmachl, H. M. Ng, and A. Y. Cho, “Comparative study of ultrafast intersubband electron scattering times at ~1.55 μm wavelength in GaN/ALGaN heterostructures,” Appl. Phys. Lett.81(7), 1237–1239 (2002).
[CrossRef]

Hormoz, S.

Hu, Q.

Iizuka, N.

N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
[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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Jirauschek, C.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Kaneko, K.

N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
[CrossRef]

Khanna, S. P.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express16(5), 3242–3248 (2008).
[CrossRef] [PubMed]

Khurgin, J. B.

J. B. Khurgin and Y. Dikmelik, “Transport and gain in a quantum cascade laser: model and equivalent circuit,” Opt. Eng.49(11), 111110 (2010).
[CrossRef]

G. Sun, R. A. Soref, and J. B. Khurgin, “Active region design of a terahertz GaN/ Al0.15Ga0.85N quantum cascade laser,” Superlattices Microstruct.37(2), 107–113 (2005).
[CrossRef]

G. Sun and J. B. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron.29(4), 1104–1111 (1993).
[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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Kumar, S.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-THz quantum cascade laser operating significantly above the temperature of ω/kB,” Nat. Phys.7(2), 166–171 (2011).
[CrossRef]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express13(9), 3331–3339 (2005).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser operating up to 137 K,” Appl. Phys. Lett.83(25), 5142–5144 (2003).
[CrossRef]

Lachab, M.

Laframboise, S. R.

Laughlin, B.

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

Lei, T.

T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
[CrossRef]

Leonard, D. N.

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Li, M. F.

W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, “Electronic properties of zinc-blende GaN, AlN, and their alloys Ga1-xAlxN,” J. Appl. Phys.79(1), 188–194 (1996).
[CrossRef]

Linfield, E. H.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express16(5), 3242–3248 (2008).
[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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Liu, H. C.

Losego, M.

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

Luo, H.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, “Terahertz quantum-cascade lasers based on a three-well active module,” Appl. Phys. Lett.90(4), 041112 (2007).
[CrossRef]

Maier, S. A.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

Maria, J. P.

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

Martín-Moreno, L.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Mátyás, A.

Molnar, R. J.

T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
[CrossRef]

Moustakas, T. D.

T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
[CrossRef]

Murray, W. A.

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater.19(22), 3771–3782 (2007).
[CrossRef]

Ng, H. M.

J. D. Heber, C. Gmachl, H. M. Ng, and A. Y. Cho, “Comparative study of ultrafast intersubband electron scattering times at ~1.55 μm wavelength in GaN/ALGaN heterostructures,” Appl. Phys. Lett.81(7), 1237–1239 (2002).
[CrossRef]

Noda, S.

N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
[CrossRef]

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Pflugl, C.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

Reno, J. L.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-THz quantum cascade laser operating significantly above the temperature of ω/kB,” Nat. Phys.7(2), 166–171 (2011).
[CrossRef]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express13(9), 3331–3339 (2005).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser operating up to 137 K,” Appl. Phys. Lett.83(25), 5142–5144 (2003).
[CrossRef]

Rhodes, C.

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

Ritchie, D. A.

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,” Nature417(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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Rusina, A.

A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” J. Appl. Phys. A100(2), 375–378 (2010).
[CrossRef]

Scanlon, J.

T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
[CrossRef]

Schrenk, W.

Soref, R. A.

G. Sun, R. A. Soref, and J. B. Khurgin, “Active region design of a terahertz GaN/ Al0.15Ga0.85N quantum cascade laser,” Superlattices Microstruct.37(2), 107–113 (2005).
[CrossRef]

Stockman, M. I.

A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” J. Appl. Phys. A100(2), 375–378 (2010).
[CrossRef]

Strasser, G.

Sun, G.

G. Sun, R. A. Soref, and J. B. Khurgin, “Active region design of a terahertz GaN/ Al0.15Ga0.85N quantum cascade laser,” Superlattices Microstruct.37(2), 107–113 (2005).
[CrossRef]

G. Sun and J. B. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron.29(4), 1104–1111 (1993).
[CrossRef]

Suzuki, N.

N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Tredicucci, A.

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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Ünlü, H.

H. Ünlü and A. Asenov, “Band offsets in III-nitride heterostructures,” J. Phys. D Appl. Phys.35(7), 591–594 (2002).
[CrossRef]

Unterrainer, K.

Wada, O.

N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
[CrossRef]

Wang, Q. J.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

Wasilewski, Z. R.

Weibel, S.

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

Williams, B. S.

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express13(9), 3331–3339 (2005).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser operating up to 137 K,” Appl. Phys. Lett.83(25), 5142–5144 (2003).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Xia, J. B.

W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, “Electronic properties of zinc-blende GaN, AlN, and their alloys Ga1-xAlxN,” J. Appl. Phys.79(1), 188–194 (1996).
[CrossRef]

Adv. Mater.

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater.19(22), 3771–3782 (2007).
[CrossRef]

Appl. Phys. Lett.

T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, “Epitaxial growth of zinc blende and wurtzitic gallium nitride thin films on (001) silicon,” Appl. Phys. Lett.59(8), 944–946 (1991).
[CrossRef]

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett.80(7), 1204–1206 (2002).
[CrossRef]

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, “Terahertz quantum-cascade lasers based on a three-well active module,” Appl. Phys. Lett.90(4), 041112 (2007).
[CrossRef]

N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, “Ultrafast intersubband relaxation (150 fs) in AlGaN/GaN multiple quantum wells,” Appl. Phys. Lett.77(5), 648–650 (2000).
[CrossRef]

J. D. Heber, C. Gmachl, H. M. Ng, and A. Y. Cho, “Comparative study of ultrafast intersubband electron scattering times at ~1.55 μm wavelength in GaN/ALGaN heterostructures,” Appl. Phys. Lett.81(7), 1237–1239 (2002).
[CrossRef]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser operating up to 137 K,” Appl. Phys. Lett.83(25), 5142–5144 (2003).
[CrossRef]

IEEE J. Quantum Electron.

G. Sun and J. B. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron.29(4), 1104–1111 (1993).
[CrossRef]

IEEE Sel. Top. Quantum Electron.

M. A. Belkin, Q. J. Wang, C. Pflugl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfield, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE Sel. Top. Quantum Electron.15(3), 952–967 (2009).
[CrossRef]

J. Appl. Phys.

W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, “Electronic properties of zinc-blende GaN, AlN, and their alloys Ga1-xAlxN,” J. Appl. Phys.79(1), 188–194 (1996).
[CrossRef]

C. Rhodes, S. Franzen, J. P. Maria, M. Losego, D. N. Leonard, B. Laughlin, G. Duscher, and S. Weibel, “Surface plasmon resonance in conducting metal oxides,” J. Appl. Phys.100(5), 054905 (2006).
[CrossRef]

J. Appl. Phys. A

A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” J. Appl. Phys. A100(2), 375–378 (2010).
[CrossRef]

J. Phys. D Appl. Phys.

H. Ünlü and A. Asenov, “Band offsets in III-nitride heterostructures,” J. Phys. D Appl. Phys.35(7), 591–594 (2002).
[CrossRef]

Nat. Phys.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-THz quantum cascade laser operating significantly above the temperature of ω/kB,” Nat. Phys.7(2), 166–171 (2011).
[CrossRef]

Nature

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,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Opt. Eng.

J. B. Khurgin and Y. Dikmelik, “Transport and gain in a quantum cascade laser: model and equivalent circuit,” Opt. Eng.49(11), 111110 (2010).
[CrossRef]

Opt. Express

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

Science

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Superlattices Microstruct.

G. Sun, R. A. Soref, and J. B. Khurgin, “Active region design of a terahertz GaN/ Al0.15Ga0.85N quantum cascade laser,” Superlattices Microstruct.37(2), 107–113 (2005).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Illustration of the SSP waveguide confined THz GaN/Al0.2Ga0.8N QCL and (b) band structure and envelope wavefunctions of the active region of the proposed THzzTT showing two periods with each period consisting of 3 GaN QWs and 3 Al0.2Ga0.8N barriers with layer thicknesses (Å) starting from the tunneling barrier: 50/45/25/25/55/30 (wells in bold and barrier in plain) under an electric bias of 45 kV/cm.

Fig. 2
Fig. 2

Temperature dependence of lifetimes of upper ( τ 3 ) and lower laser states ( τ 2 ), as well as the scattering between them ( τ 32 ).

Fig. 3
Fig. 3

Dispersions of (a) the Au/GaN SSP waveguide of a=1.0µm, t=2.0µm, h=0.5µm d=0.2µm, and (b) the SPP propagating at the Au/GaN interface.

Fig. 4
Fig. 4

(a) Loss comparison between Au/GaN SSP (a=1.0µm, t=2.0µm, h=0.5µm) and SP waveguides for λ 0 90 µm vs. the waveguide thickness d, and (b) temperature dependence of the threshold current density for 5 periods of the THz GaN/Al0.2Ga0.8N QCL in the SSP waveguide of a=1.0µm, t=2.0µm, h=0.5µm d=0.2µm with its mode profile | E(x,y) | 2 shown as inset in (b).

Equations (5)

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

d N 3 dt = J e + N 1 τ 13 + N 2 τ 23 N 3 τ 3 = J e N 3 N 1 e Δ 31 / k B T τ 31 N 3 N 2 e Δ 32 / k B T τ 32 d N 2 dt = N 1 τ 12 N 2 τ 2 + N 3 τ 32 = N 3 N 2 e Δ 32 / k B T τ 32 N 2 N 1 e Δ 21 / k B T τ 21 N= N 1 + N 2 + N 3 .
g= 2 e 2 | z 23 | 2 n ε o ( Γ 23 ) 2π λ o N 3 N 2 L
ε x = ε y = (ta) ε m +a ε d t , ε z = t (ta)/ ε m +a/ ε d .
Ε=A e j( k s zωt) { k s cos[ k h ( | x |hd/2 ) ] ε x cos( k h h ) e ^ x j x | x | k h sin[ k h ( | x |hd/2 ) ] ε z cos( k h h ) e ^ z , d 2 <| x |<h+ d 2 k s ε d cosh( k d x) cosh( k d d/2) e ^ x +j k d ε d sinh( k d x) cosh( k d d/2) e ^ z , |x|< d 2
k s 2 = ε d k 0 2 + 8 ε d k h tan( k h h ) 4 ε z ε d k h dtan( k h h ) 1 d .

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