Abstract

We calculate the loss and confinement factors of modes in terahertz quantum cascade laser structures at frequencies of 1–4 THz. The determination of the total loss splits naturally into the calculation of free-carrier losses in the active region and the waveguide losses. For both, we employ the Drude model. In the case of waveguide losses, we incorporate it into the formalism of the optical scattering matrix and trace the net threshold gain for laser operation in the waveguide for various frequencies as a function of thickness and doping of the buried contact layer. The results indicate that at lower frequencies and high doping, the preferred mode switches character from extended to tightly confined. This may have consequences for the creation of simplified longer-wavelength devices.

©2004 Optical Society of America

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  1. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
    [Crossref] [PubMed]
  2. C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
    [Crossref]
  3. R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
    [Crossref]
  4. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 416, 156–159 (2002).
    [Crossref]
  5. M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
    [Crossref]
  6. B. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. Reno, “Terahertz quantum-cascade laser at λ ≈ 100 μm using metal waveguide for mode confinement,” Applied Physics Letters 83, 2124–2126 (2003)
    [Crossref]
  7. D. Indjin, Z. Ikonic, P. Harrison, and R. W. Kelsall, “Surface plasmon waveguides with gradually doped or NiAl intermetallic compound buried contact for terahertz quantum cascade lasers,” Journal of Applied Physics 94, 3249–3252 (2003)
    [Crossref]
  8. Z. Ikonic, R. W. Kelsall, and P. Harrison, “Waveguide design for mid- and far-infrared p-Si/SiGe quantum cascade lasers,” Semiconductor Science and Technology 19, 76–81 (2004).
    [Crossref]
  9. D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Physical Review B 38, 9945–9951 (1988)
    [Crossref]
  10. D. Ko and J. R. Sambles, “Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals Journal of the Optical Society of America A  5, 1863–1866 (1988).
  11. C. D. Ager and H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Physical Review B 44, 13452–13465 (1991).
    [Crossref]
  12. J. Chilwell and I. Hodgkinson, “Thin-films Field Transfer Matrix Theory of Planar Multilayer Waveguides and Reflection from Prism-loaded Waveguides,” Journal of the Optical Society of America A 1, 742–753 (1984).
    [Crossref]
  13. J. Szczyrbowski, “A new simple method of determining the effective mass of an electron or the thickness of thin metal films,” Journal of Physics D: Applied Physics 191257–1263 (1986).
    [Crossref]
  14. M. Lovejoy, M. Melloch, and M. S. Lundstrom, “Temperature dependence of minority and majority carrier mobilities in degenerately doped GaAs,” Applied Physics Letters 67, 1101–1103 (1995)
    [Crossref]
  15. G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
    [Crossref] [PubMed]
  16. D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
    [Crossref] [PubMed]
  17. H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
    [Crossref]
  18. M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Applied Physics Letters 56, 1694–1696 (1990).
    [Crossref]

2004 (2)

Z. Ikonic, R. W. Kelsall, and P. Harrison, “Waveguide design for mid- and far-infrared p-Si/SiGe quantum cascade lasers,” Semiconductor Science and Technology 19, 76–81 (2004).
[Crossref]

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

2003 (2)

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

D. Indjin, Z. Ikonic, P. Harrison, and R. W. Kelsall, “Surface plasmon waveguides with gradually doped or NiAl intermetallic compound buried contact for terahertz quantum cascade lasers,” Journal of Applied Physics 94, 3249–3252 (2003)
[Crossref]

2002 (2)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 416, 156–159 (2002).
[Crossref]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[Crossref]

2001 (1)

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

1998 (1)

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

1997 (1)

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

1995 (1)

M. Lovejoy, M. Melloch, and M. S. Lundstrom, “Temperature dependence of minority and majority carrier mobilities in degenerately doped GaAs,” Applied Physics Letters 67, 1101–1103 (1995)
[Crossref]

1994 (1)

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

1991 (1)

C. D. Ager and H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Physical Review B 44, 13452–13465 (1991).
[Crossref]

1990 (2)

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Applied Physics Letters 56, 1694–1696 (1990).
[Crossref]

1988 (2)

D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Physical Review B 38, 9945–9951 (1988)
[Crossref]

D. Ko and J. R. Sambles, “Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals Journal of the Optical Society of America A  5, 1863–1866 (1988).

1986 (1)

J. Szczyrbowski, “A new simple method of determining the effective mass of an electron or the thickness of thin metal films,” Journal of Physics D: Applied Physics 191257–1263 (1986).
[Crossref]

1984 (1)

J. Chilwell and I. Hodgkinson, “Thin-films Field Transfer Matrix Theory of Planar Multilayer Waveguides and Reflection from Prism-loaded Waveguides,” Journal of the Optical Society of America A 1, 742–753 (1984).
[Crossref]

Ager, C. D.

C. D. Ager and H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Physical Review B 44, 13452–13465 (1991).
[Crossref]

Ajili, L.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[Crossref]

Allen, S. J.

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

Beere, H.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[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,” Nature 416, 156–159 (2002).
[Crossref]

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,” Nature 416, 156–159 (2002).
[Crossref]

Bhat, R.

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

Brozak, G.

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

Callebaut, H.

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

Capasso, F.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

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

Chilwell, J.

J. Chilwell and I. Hodgkinson, “Thin-films Field Transfer Matrix Theory of Planar Multilayer Waveguides and Reflection from Prism-loaded Waveguides,” Journal of the Optical Society of America A 1, 742–753 (1984).
[Crossref]

Cho, A. Y.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

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

Chung, S.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Colombelli, R.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

Davies, A. G.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 416, 156–159 (2002).
[Crossref]

Davies, G.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[Crossref]

DeRosa, F.

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

Faist, J.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[Crossref]

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

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

Gmachl, C.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

Grischkowsky, D.

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Applied Physics Letters 56, 1694–1696 (1990).
[Crossref]

Harrison, P.

Z. Ikonic, R. W. Kelsall, and P. Harrison, “Waveguide design for mid- and far-infrared p-Si/SiGe quantum cascade lasers,” Semiconductor Science and Technology 19, 76–81 (2004).
[Crossref]

D. Indjin, Z. Ikonic, P. Harrison, and R. W. Kelsall, “Surface plasmon waveguides with gradually doped or NiAl intermetallic compound buried contact for terahertz quantum cascade lasers,” Journal of Applied Physics 94, 3249–3252 (2003)
[Crossref]

Heiliger, H.-M.

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

Heinrich, W.

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

Helm, M.

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

Hey, R.

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

Hodgkinson, I.

J. Chilwell and I. Hodgkinson, “Thin-films Field Transfer Matrix Theory of Planar Multilayer Waveguides and Reflection from Prism-loaded Waveguides,” Journal of the Optical Society of America A 1, 742–753 (1984).
[Crossref]

Hu, Q.

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

Hughes, H. P.

C. D. Ager and H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Physical Review B 44, 13452–13465 (1991).
[Crossref]

Hutchinson, A. L.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

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

Ikonic, Z.

Z. Ikonic, R. W. Kelsall, and P. Harrison, “Waveguide design for mid- and far-infrared p-Si/SiGe quantum cascade lasers,” Semiconductor Science and Technology 19, 76–81 (2004).
[Crossref]

D. Indjin, Z. Ikonic, P. Harrison, and R. W. Kelsall, “Surface plasmon waveguides with gradually doped or NiAl intermetallic compound buried contact for terahertz quantum cascade lasers,” Journal of Applied Physics 94, 3249–3252 (2003)
[Crossref]

Indjin, D.

D. Indjin, Z. Ikonic, P. Harrison, and R. W. Kelsall, “Surface plasmon waveguides with gradually doped or NiAl intermetallic compound buried contact for terahertz quantum cascade lasers,” Journal of Applied Physics 94, 3249–3252 (2003)
[Crossref]

Inkson, J. C.

D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Physical Review B 38, 9945–9951 (1988)
[Crossref]

Inoue, M.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Iotti, R. C.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 416, 156–159 (2002).
[Crossref]

Kelsall, R. W.

Z. Ikonic, R. W. Kelsall, and P. Harrison, “Waveguide design for mid- and far-infrared p-Si/SiGe quantum cascade lasers,” Semiconductor Science and Technology 19, 76–81 (2004).
[Crossref]

D. Indjin, Z. Ikonic, P. Harrison, and R. W. Kelsall, “Surface plasmon waveguides with gradually doped or NiAl intermetallic compound buried contact for terahertz quantum cascade lasers,” Journal of Applied Physics 94, 3249–3252 (2003)
[Crossref]

Khodaparast, G. A.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Ko, D.

D. Ko and J. R. Sambles, “Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals Journal of the Optical Society of America A  5, 1863–1866 (1988).

Ko, D. Y. K.

D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Physical Review B 38, 9945–9951 (1988)
[Crossref]

Köhler, R.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 416, 156–159 (2002).
[Crossref]

Kono, J.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Koza, M.

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

Kumar, S.

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

Kurz, H.

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

Larrabee, D. C.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Linfield, E.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[Crossref]

Linfield, E. H.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 416, 156–159 (2002).
[Crossref]

Lovejoy, M.

M. Lovejoy, M. Melloch, and M. S. Lundstrom, “Temperature dependence of minority and majority carrier mobilities in degenerately doped GaAs,” Applied Physics Letters 67, 1101–1103 (1995)
[Crossref]

Lundstrom, M. S.

M. Lovejoy, M. Melloch, and M. S. Lundstrom, “Temperature dependence of minority and majority carrier mobilities in degenerately doped GaAs,” Applied Physics Letters 67, 1101–1103 (1995)
[Crossref]

Melloch, M.

M. Lovejoy, M. Melloch, and M. S. Lundstrom, “Temperature dependence of minority and majority carrier mobilities in degenerately doped GaAs,” Applied Physics Letters 67, 1101–1103 (1995)
[Crossref]

Nagel, M.

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

Nakai, M.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Nakajima, Y.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Perry, C. H.

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

Ploog, K.

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

Reno, J.

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

Ritchie, D.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[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,” Nature 416, 156–159 (2002).
[Crossref]

Rochat, M.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[Crossref]

Roskos, H. G.

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

Rossi, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 416, 156–159 (2002).
[Crossref]

Sambles, J. R.

D. Ko and J. R. Sambles, “Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals Journal of the Optical Society of America A  5, 1863–1866 (1988).

Santos, M.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Sasa, S.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Scalari, G.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Schnieder, F.

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

Sergent, A. M.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

Sirtori, C.

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

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

Sivco, D.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

Sivco, D. L.

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

Szczyrbowski, J.

J. Szczyrbowski, “A new simple method of determining the effective mass of an electron or the thickness of thin metal films,” Journal of Physics D: Applied Physics 191257–1263 (1986).
[Crossref]

Tittel, F. K.

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

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,” Nature 416, 156–159 (2002).
[Crossref]

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

van Exter, M.

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Applied Physics Letters 56, 1694–1696 (1990).
[Crossref]

Wanke, M. C.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

Willenberg, H.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[Crossref]

Williams, B.

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

Applied Physics Letters (6)

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Applied Physics Letters 78, 2620–2622 (2001).
[Crossref]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers ,“ Applied Physics Letters 81, 1381–1383 (2002).
[Crossref]

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

M. Lovejoy, M. Melloch, and M. S. Lundstrom, “Temperature dependence of minority and majority carrier mobilities in degenerately doped GaAs,” Applied Physics Letters 67, 1101–1103 (1995)
[Crossref]

H.-M. Heiliger, M. Nagel, H. G. Roskos, H. Kurz, F. Schnieder, W. Heinrich, R. Hey, and K. Ploog, “Low-dispersion thin-film microstrip lines with cyclotene (benzocyclobutene) as dielectric medium”, Applied Physics Letters 70, 2233–2235 (1997).
[Crossref]

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Applied Physics Letters 56, 1694–1696 (1990).
[Crossref]

Journal of Applied Physics (1)

D. Indjin, Z. Ikonic, P. Harrison, and R. W. Kelsall, “Surface plasmon waveguides with gradually doped or NiAl intermetallic compound buried contact for terahertz quantum cascade lasers,” Journal of Applied Physics 94, 3249–3252 (2003)
[Crossref]

Journal of Physics D: Applied Physics (1)

J. Szczyrbowski, “A new simple method of determining the effective mass of an electron or the thickness of thin metal films,” Journal of Physics D: Applied Physics 191257–1263 (1986).
[Crossref]

Journal of the Optical Society of America A (1)

J. Chilwell and I. Hodgkinson, “Thin-films Field Transfer Matrix Theory of Planar Multilayer Waveguides and Reflection from Prism-loaded Waveguides,” Journal of the Optical Society of America A 1, 742–753 (1984).
[Crossref]

Nature (1)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 416, 156–159 (2002).
[Crossref]

Optics Letters (2)

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ ≈ 8-11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Optics Letters 23, 1366–1368 (1998).
[Crossref]

D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Optics Letters 29, 122–124 (2004).
[Crossref] [PubMed]

Physical Review B (2)

C. D. Ager and H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Physical Review B 44, 13452–13465 (1991).
[Crossref]

D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Physical Review B 38, 9945–9951 (1988)
[Crossref]

Physical Review Letters (1)

G. Brozak, M. Helm, F. DeRosa, C. H. Perry, M. Koza, R. Bhat, and S. J. Allen, “Thermal Saturation of Band Transport in a Superlattice,” Physical Review Letters 64, 3163–3166 (1990) .
[Crossref] [PubMed]

Science (1)

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

Semiconductor Science and Technology (1)

Z. Ikonic, R. W. Kelsall, and P. Harrison, “Waveguide design for mid- and far-infrared p-Si/SiGe quantum cascade lasers,” Semiconductor Science and Technology 19, 76–81 (2004).
[Crossref]

Other (1)

D. Ko and J. R. Sambles, “Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals Journal of the Optical Society of America A  5, 1863–1866 (1988).

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Figures (3)

Fig. 1.
Fig. 1. Schematic of the laser structure and the radiation modes. Electric current and gain exist in the active region between the top metal layer and the buried contact layer. The quantities varied in our calculations were the thickness of the active layer and that of the contact layer, as well as the contact layer doping, and the photon energy of the laser radiation.
Fig. 2.
Fig. 2. Plot of G w,th = l w /Γ vs. thickness of active layer for a contact layer thickness of 1 μm. Solid (dashed) curves refer to Mode 1 (Mode 0). Note that G w,th is the component of the material threshold gain due to the waveguide losses. The total material threshold gain is obtained by adding L fc , the bulk value of free-carrier attenuation in the active region.
Fig. 3.
Fig. 3. Surface plot of logarithmic threshold gain (log G w,th) vs thickness d of contact layer and doping n of contact layer. The parameters used in Ref. [4] are indicated.

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