Abstract

Based on a coupled simulation of carrier transport and optical cavity field, the intrinsic linewidth in resonant phonon terahertz quantum cascade lasers is self-consistently analyzed. For high power structures, values on the order of Hz are obtained. Thermal photons are found to play a considerable role at elevated temperatures. A linewidth enhancement factor of 0.5 is calculated for the investigated designs.

© 2010 OSA

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  1. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 89–90 (2006).
    [CrossRef]
  2. A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “High-power and high-temperature THz quantum-cascade lasers based on lens-coupled metal-metal waveguides,” Opt. Lett. 32, 2840–2842 (2007).
    [CrossRef]
  3. M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum-cascade lasers: Hidden reason for the narrow linewidth and line-broadening by thermal photons,” IEEE J. Quantum Electron. 44, 12–29 (2008).
    [CrossRef]
  4. S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
    [CrossRef]
  5. A. Barkan, F. K. Tittel, D. M. Mittleman, R. Dengler, P. H. Siegel, G. Scalari, L. Ajili, J. Faist, H. E. Beere, E. H. Linfield, A. G. Davies, and D. A. Ritchie, “Linewidth and tuning characteristics of terahertz quantum cascade lasers,” Opt. Lett. 29, 575–577 (2004).
    [CrossRef] [PubMed]
  6. H. Hübers, S. G. Pavlov, A. D. Semenov, R. Köhler, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and E. H. Linfield, “Terahertz quantum cascade laser as local oscillator in a heterodyne receiver,” Opt. Express 13, 5890–5896 (2005).
    [CrossRef] [PubMed]
  7. A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
    [CrossRef]
  8. A. A. Danylov, T. M. Goyette, J. Waldman, M. J. Coulombe, A. J. Gatesman, R. H. Giles, W. D. Goodhue, X. Qian, and W. E. Nixon, “Frequency stabilization of a single mode terahertz quantum cascade laser to the kilohertz level,” Opt. Express 17, 7525–7532 (2009).
    [CrossRef] [PubMed]
  9. D. Rabanus, U. U. Graf, M. Philipp, O. Ricken, J. Stutzki, B. Vowinkel, M. C. Wiedner, C. Walther, M. Fischer, and J. Faist, “Phase locking of a 15 Terahertz quantum cascade laser and use as a local oscillator in a heterodyne HEB receiver,” Opt. Express 17, 1159–1168 (2009).
    [CrossRef] [PubMed]
  10. S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
    [CrossRef]
  11. C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. 96, 011 103 (2010).
    [CrossRef]
  12. C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron. 45, 1059–1067 (2009).
    [CrossRef]
  13. C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. 105, 123 102 (2009).
    [CrossRef]
  14. C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys. 107, 013 104 (2010).
    [CrossRef]
  15. G. Grau and W. Freude, Optische Nachrichtentechnik - Eine Einführung (Springer, 1991).
  16. H. Haug and H. Haken, “Theory of noise in semiconductor laser emission,” Z. Phys. 204, 262–275 (1967).
    [CrossRef]
  17. 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. Express 13, 3331–3339 (2005).
    [CrossRef] [PubMed]
  18. S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053 106 (2005).
    [CrossRef]
  19. C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
    [CrossRef]
  20. R. P. Green, J. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071 106 (2008).
    [CrossRef]

2010 (4)

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. 96, 011 103 (2010).
[CrossRef]

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys. 107, 013 104 (2010).
[CrossRef]

2009 (4)

2008 (2)

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum-cascade lasers: Hidden reason for the narrow linewidth and line-broadening by thermal photons,” IEEE J. Quantum Electron. 44, 12–29 (2008).
[CrossRef]

R. P. Green, J. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071 106 (2008).
[CrossRef]

2007 (1)

2006 (2)

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 89–90 (2006).
[CrossRef]

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

2005 (3)

2004 (1)

1982 (1)

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

1967 (1)

H. Haug and H. Haken, “Theory of noise in semiconductor laser emission,” Z. Phys. 204, 262–275 (1967).
[CrossRef]

Adam, A. J. L.

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

Ajili, L.

Akikusa, N.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum-cascade lasers: Hidden reason for the narrow linewidth and line-broadening by thermal photons,” IEEE J. Quantum Electron. 44, 12–29 (2008).
[CrossRef]

Barbieri, S.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Barkan, A.

Bartalini, S.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Baryshev, A.

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

Beere, H.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Beere, H. E.

Beltram, F.

R. P. Green, J. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071 106 (2008).
[CrossRef]

Borri, S.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Cancio, P.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Castrillo, A.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Colombelli, R.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Coulombe, M. J.

Danylov, A. A.

Davies, A. G.

de Natale, P.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Dengler, R.

Ding, L.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Edamura, T.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum-cascade lasers: Hidden reason for the narrow linewidth and line-broadening by thermal photons,” IEEE J. Quantum Electron. 44, 12–29 (2008).
[CrossRef]

Faist, J.

Fischer, M.

Freude, W.

G. Grau and W. Freude, Optische Nachrichtentechnik - Eine Einführung (Springer, 1991).

Fujita, K.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum-cascade lasers: Hidden reason for the narrow linewidth and line-broadening by thermal photons,” IEEE J. Quantum Electron. 44, 12–29 (2008).
[CrossRef]

Galli, I.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Gao, J. R.

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

Gatesman, A. J.

Gellie, P.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Gianfrani, L.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Giles, R. H.

Giuliani, G.

R. P. Green, J. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071 106 (2008).
[CrossRef]

Giusfredi, G.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Goodhue, W. D.

Goyette, T. M.

Graf, U. U.

Grau, G.

G. Grau and W. Freude, Optische Nachrichtentechnik - Eine Einführung (Springer, 1991).

Green, R. P.

R. P. Green, J. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071 106 (2008).
[CrossRef]

Haken, H.

H. Haug and H. Haken, “Theory of noise in semiconductor laser emission,” Z. Phys. 204, 262–275 (1967).
[CrossRef]

Haug, H.

H. Haug and H. Haken, “Theory of noise in semiconductor laser emission,” Z. Phys. 204, 262–275 (1967).
[CrossRef]

Henry, C.

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

Hovenier, J. N.

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

Hu, Q.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “High-power and high-temperature THz quantum-cascade lasers based on lens-coupled metal-metal waveguides,” Opt. Lett. 32, 2840–2842 (2007).
[CrossRef]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 89–90 (2006).
[CrossRef]

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053 106 (2005).
[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. Express 13, 3331–3339 (2005).
[CrossRef] [PubMed]

Hübers, H.

Jirauschek, C.

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys. 107, 013 104 (2010).
[CrossRef]

C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. 96, 011 103 (2010).
[CrossRef]

C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron. 45, 1059–1067 (2009).
[CrossRef]

C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. 105, 123 102 (2009).
[CrossRef]

Kan, H.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum-cascade lasers: Hidden reason for the narrow linewidth and line-broadening by thermal photons,” IEEE J. Quantum Electron. 44, 12–29 (2008).
[CrossRef]

Kašalynas, I.

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

Klaassen, T. O.

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

Kohen, S.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053 106 (2005).
[CrossRef]

Köhler, R.

Kumar, S.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “High-power and high-temperature THz quantum-cascade lasers based on lens-coupled metal-metal waveguides,” Opt. Lett. 32, 2840–2842 (2007).
[CrossRef]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 89–90 (2006).
[CrossRef]

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[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. Express 13, 3331–3339 (2005).
[CrossRef] [PubMed]

Lee, A. W. M.

Linfield, E. H.

Lugli, P.

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys. 107, 013 104 (2010).
[CrossRef]

C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys. 105, 123 102 (2009).
[CrossRef]

Mahler, L.

R. P. Green, J. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071 106 (2008).
[CrossRef]

H. Hübers, S. G. Pavlov, A. D. Semenov, R. Köhler, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and E. H. Linfield, “Terahertz quantum cascade laser as local oscillator in a heterodyne receiver,” Opt. Express 13, 5890–5896 (2005).
[CrossRef] [PubMed]

Maineult, W.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Matyas, A.

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys. 107, 013 104 (2010).
[CrossRef]

Mazzotti, D.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. de Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: Beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083 904 (2010).
[CrossRef]

Mittleman, D. M.

Nixon, W. E.

Pavlov, S. G.

Philipp, M.

Qian, X.

Qin, Q.

Rabanus, D.

Reno, J. L.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “High-power and high-temperature THz quantum-cascade lasers based on lens-coupled metal-metal waveguides,” Opt. Lett. 32, 2840–2842 (2007).
[CrossRef]

A. Baryshev, J. N. Hovenier, A. J. L. Adam, I. Kašalynas, J. R. Gao, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Phase locking and spectral linewidth of a two-mode terahertz quantum cascade laser,” Appl. Phys. Lett. 89, 031 115 (2006).
[CrossRef]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42, 89–90 (2006).
[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. Express 13, 3331–3339 (2005).
[CrossRef] [PubMed]

Ricken, O.

Ritchie, D.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Ritchie, D. A.

Santarelli, G.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Scalari, G.

Semenov, A. D.

Siegel, P. H.

Sirtori, C.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[CrossRef]

Stutzki, J.

Tittel, F. K.

Tredicucci, A.

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Figures (1)

Fig. 1
Fig. 1

(a) Susceptibility χ vs frequency f = ω/(2π) for internal powers of 145, 160 and 175mW, corresponding to N = 1.01 × 109, 1.11 × 109, and 1.21 × 109, respectively. (b) Intrinsic linewidth as a function of temperature without and with thermal photons included.

Equations (10)

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( n 0 / c ) t N = ( Γ g a ) N + Γ g n sp + a n th ,
g ± ( ω ) = π Z 0 ω V n 0 ħ n , j ± E i n j > 0 ( 1 f j k n ) | d i n j | 2 i n j ( ω ) .
i n j ( ω ) = { 1 π 1 ω | ω i n j | + i γ i n j } = 1 π γ i n j γ i n j 2 + ( ω | ω i n j | ) 2
I N ( ω ) = ( Γ N / V g ) ħ ω c / n 0 .
r i j sp = π Z 0 n 0 ħ 2 | d i j | 2 ( 1 f j k ) m I N = 1 ( ω m ) i j ( ω m )
δ f = ( 4 π ) 1 K ( 1 + α 2 ) t N | sp N 1 = ( 4 π ) 1 K ( 1 + α 2 ) γ n sp N 1 ,
δ f = ( 4 π ) 1 ( 1 + α 2 ) γ ( n sp + n th ) N 1 .
δ f = ( 4 π ) 1 ( 1 + α 2 ) γ [ n sp + ( 1 + n sp ) n th ] N 1 .
K H = [ ( R 1 + R 2 ) ( 1 R 1 R 2 ) R 1 R 2 ln ( R 1 R 2 ) ] 2 ,
α = N { χ ( ω L ) } N { χ ( ω L ) } = N { g c ( ω L ) } N { g c ( ω L ) } .

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