Abstract

We consider the impact of saturable nonlinearity and group velocity dispersion on self-induced transparency (SIT) modelocking of quantum cascade lasers (QCLs). We find that self-induced transparency modelocking in QCLs can be obtained in the presence of saturable nonlinearity if the saturable loss or gain is below a critical limit. The limit for the saturable loss is significantly more stringent than the limit for the saturable gain. Stable modelocked pulses are also obtained in the presence of both normal and anomalous group velocity dispersion when its magnitude is below a critical value. The stability limit for the saturable loss becomes less stringent when group velocity dispersion is simultaneously present. However, the stability limit for the saturable gain is not significantly affected. All these limits depend on the ratio of the SIT-induced gain and absorption to the linear loss. Realistic values for both the saturable nonlinearity and chromatic dispersion are within the range in which SIT modelocking is predicted to be stable.

© 2010 Optical Society of America

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  1. J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
    [CrossRef] [PubMed]
  2. C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
    [CrossRef] [PubMed]
  3. C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
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  5. H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
    [CrossRef] [PubMed]
  6. H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
    [CrossRef]
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    [CrossRef]
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  9. T. Uchida and A. Ueki, "Self locking of gas lasers," IEEE J. Quantum Electron. 3, 17?30 (1967).
    [CrossRef]
  10. H. A. Haus, "Theory of mode locking with a fast saturable absorber," J. Appl. Phys. 46, 3049?3058 (1975).
    [CrossRef]
  11. S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908?912 (1967).
    [CrossRef]
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    [CrossRef] [PubMed]
  19. A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
    [CrossRef]
  20. H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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2009 (5)

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

C. R. Menyuk and M. A. Talukder, "Self-induced transparency modelocking of quantum cascade lasers," Phys. Rev. Lett. 102, 023903 (2009).
[CrossRef] [PubMed]

M. A. Talukder and C. R. Menyuk, "Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers," Phys. Rev. A 79, 063841 (2009).
[CrossRef]

M. A. Talukder and C. R. Menyuk, "Effects of backward propagating waves and lumped mirror losses on selfinduced transparency modelocking in quantum cascade lasers," Appl. Phys. Lett. 95, 071109 (2009).
[CrossRef]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
[CrossRef] [PubMed]

2008 (2)

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

2007 (2)

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

2000 (2)

H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Quantum. Electron. 6, 1173?1185 (2000).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

1999 (1)

V. V. Kozlov, "Self-induced transparency soliton laser," JETP Lett. 69, 906?911 (1999) [Pis’ma Zh. Eksp. Teor. Fiz. 69, 856 (1999)].
[CrossRef]

1997 (1)

V. V. Kozlov, "Self-induced transparency soliton laser via coherent mode locking," Phys. Rev. A 56, 1607?1612 (1997).
[CrossRef]

1994 (1)

J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
[CrossRef] [PubMed]

1975 (1)

H. A. Haus, "Theory of mode locking with a fast saturable absorber," J. Appl. Phys. 46, 3049?3058 (1975).
[CrossRef]

1969 (1)

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457?489 (1969).
[CrossRef]

1968 (1)

H. Risken and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662?4672 (1968);R. Graham and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420?450 (1968).
[CrossRef]

H. Risken and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662?4672 (1968);R. Graham and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420?450 (1968).
[CrossRef]

1967 (3)

P. W. Smith, "The self-pulsing laser oscillator," IEEE J. Quantum Electron. 3, 627?635 (1967).
[CrossRef]

T. Uchida and A. Ueki, "Self locking of gas lasers," IEEE J. Quantum Electron. 3, 17?30 (1967).
[CrossRef]

S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908?912 (1967).
[CrossRef]

Baillargeon, J. N.

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

Belkin, M. A.

Belyanin, A.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Bour, D.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Capasso, F.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
[CrossRef] [PubMed]

Cho, A.

J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
[CrossRef] [PubMed]

Cho, A. Y.

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

Choi, H.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

Corzine, S.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Diehl, L.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Faist, J.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
[CrossRef] [PubMed]

Giovannini, M.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

Gkortsas, V. M.

Gmachl, C.

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

Gordon, A.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Graham, R.

H. Risken and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662?4672 (1968);R. Graham and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420?450 (1968).
[CrossRef]

Grant, P.

Haffouz, S.

Hahn, E. L.

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457?489 (1969).
[CrossRef]

S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908?912 (1967).
[CrossRef]

Haken, H.

H. Risken and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662?4672 (1968);R. Graham and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420?450 (1968).
[CrossRef]

Ham, D.

Haus, H. A.

H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Quantum. Electron. 6, 1173?1185 (2000).
[CrossRef]

H. A. Haus, "Theory of mode locking with a fast saturable absorber," J. Appl. Phys. 46, 3049?3058 (1975).
[CrossRef]

Hofler, G.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Hutchinson, A.

J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
[CrossRef] [PubMed]

Hutchinson, A. L.

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

Jirauschek, C.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Kartner, F. X.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Kozlov, V. V.

V. V. Kozlov, "Self-induced transparency soliton laser," JETP Lett. 69, 906?911 (1999) [Pis’ma Zh. Eksp. Teor. Fiz. 69, 856 (1999)].
[CrossRef]

V. V. Kozlov, "Self-induced transparency soliton laser via coherent mode locking," Phys. Rev. A 56, 1607?1612 (1997).
[CrossRef]

Kuznetsova, L.

Li, X.

Liu, H. C.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

Maier, T.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

McCall, S. L.

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457?489 (1969).
[CrossRef]

S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908?912 (1967).
[CrossRef]

Menyuk, C. R.

C. R. Menyuk and M. A. Talukder, "Self-induced transparency modelocking of quantum cascade lasers," Phys. Rev. Lett. 102, 023903 (2009).
[CrossRef] [PubMed]

M. A. Talukder and C. R. Menyuk, "Effects of backward propagating waves and lumped mirror losses on selfinduced transparency modelocking in quantum cascade lasers," Appl. Phys. Lett. 95, 071109 (2009).
[CrossRef]

M. A. Talukder and C. R. Menyuk, "Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers," Phys. Rev. A 79, 063841 (2009).
[CrossRef]

Norris, T. B.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

Nummedal, K.

H. Risken and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662?4672 (1968);R. Graham and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420?450 (1968).
[CrossRef]

Paiella, R.

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

Risken, H.

H. Risken and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662?4672 (1968);R. Graham and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420?450 (1968).
[CrossRef]

Schneider, H.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Sirtori, C.

J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
[CrossRef] [PubMed]

Sivco, D.

J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
[CrossRef] [PubMed]

Sivco, D. L.

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

Smith, P. W.

P. W. Smith, "The self-pulsing laser oscillator," IEEE J. Quantum Electron. 3, 627?635 (1967).
[CrossRef]

Song, C. Y.

Talukder, M. A.

C. R. Menyuk and M. A. Talukder, "Self-induced transparency modelocking of quantum cascade lasers," Phys. Rev. Lett. 102, 023903 (2009).
[CrossRef] [PubMed]

M. A. Talukder and C. R. Menyuk, "Effects of backward propagating waves and lumped mirror losses on selfinduced transparency modelocking in quantum cascade lasers," Appl. Phys. Lett. 95, 071109 (2009).
[CrossRef]

M. A. Talukder and C. R. Menyuk, "Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers," Phys. Rev. A 79, 063841 (2009).
[CrossRef]

Troccoli, M.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Uchida, T.

T. Uchida and A. Ueki, "Self locking of gas lasers," IEEE J. Quantum Electron. 3, 17?30 (1967).
[CrossRef]

Ueki, A.

T. Uchida and A. Ueki, "Self locking of gas lasers," IEEE J. Quantum Electron. 3, 17?30 (1967).
[CrossRef]

Wang, C. Y.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Wasilewski, Z. R.

Wu, Z.-K.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

Zhu, J.

Appl. Phys. Lett. (1)

M. A. Talukder and C. R. Menyuk, "Effects of backward propagating waves and lumped mirror losses on selfinduced transparency modelocking in quantum cascade lasers," Appl. Phys. Lett. 95, 071109 (2009).
[CrossRef]

IEEE J. Quantum Electron. (3)

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009).
[CrossRef]

P. W. Smith, "The self-pulsing laser oscillator," IEEE J. Quantum Electron. 3, 627?635 (1967).
[CrossRef]

T. Uchida and A. Ueki, "Self locking of gas lasers," IEEE J. Quantum Electron. 3, 17?30 (1967).
[CrossRef]

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

H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Quantum. Electron. 6, 1173?1185 (2000).
[CrossRef]

J. Appl. Phys. (2)

H. A. Haus, "Theory of mode locking with a fast saturable absorber," J. Appl. Phys. 46, 3049?3058 (1975).
[CrossRef]

H. Risken and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662?4672 (1968);R. Graham and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420?450 (1968).
[CrossRef]

JETP Lett. (1)

V. V. Kozlov, "Self-induced transparency soliton laser," JETP Lett. 69, 906?911 (1999) [Pis’ma Zh. Eksp. Teor. Fiz. 69, 856 (1999)].
[CrossRef]

Opt. Express (2)

Phys. Rev. (1)

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457?489 (1969).
[CrossRef]

Phys. Rev. A (4)

V. V. Kozlov, "Self-induced transparency soliton laser via coherent mode locking," Phys. Rev. A 56, 1607?1612 (1997).
[CrossRef]

M. A. Talukder and C. R. Menyuk, "Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers," Phys. Rev. A 79, 063841 (2009).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007).
[CrossRef]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908?912 (1967).
[CrossRef]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008).
[CrossRef] [PubMed]

C. R. Menyuk and M. A. Talukder, "Self-induced transparency modelocking of quantum cascade lasers," Phys. Rev. Lett. 102, 023903 (2009).
[CrossRef] [PubMed]

Science (2)

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994).
[CrossRef] [PubMed]

Other (3)

L. Allen and J. H. Eberley, Optical Resonance and Two Level Atoms (Dover, New York, 1987).

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, London, 2003).

C. Sirtori and R. Teissier, "Quantum Cascade Lasers: Overview of Basic Principles of Operation and State of the Art," in Intersubband Transitions in Quantum Structures, R. Paiella, ed., (McGraw-Hill, New York, 2006).

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Figures (17)

Fig. 1.
Fig. 1.

Refractive index profile and resulting intensity distribution of the fundamental waveguide mode along the lateral direction of a conventional QCL waveguide in case of (a) saturable loss and (b) saturable gain. The intensity profile changes due to the strong index nonlinearity of the active region. (a) If the intensity increases, the index near the center of the waveguide increases and the mode is more tightly confined. (b) If the intensity decreases, the index near the center of the waveguide decreases and the mode is more weakly confined.

Fig. 2.
Fig. 2.

Modelocked pulse evolution in presence of saturable loss. The saturable nonlinearity coefficient γ=10-12 m/V2. We set = 4 and = 5. The dispersion coefficient (β 2) is set to zero.

Fig. 3.
Fig. 3.

Equilibrium modelocked pulse shapes vs. the saturable nonlinearity coefficient (γ). In each case, the pulse is shown after it has propagated a distance of 1000Lc. We set = 4 and = 5. The dispersion coefficient (β2) is set to zero.

Fig. 4.
Fig. 4.

The normalized maximum intensity and pulse duration (FWHM/1.763) of the stable modelocked pulse vs. the saturable nonlinearity coefficient (γ). We set = 4 and = 5. The dispersion coefficient (β2) is set to zero.

Fig. 5.
Fig. 5.

The critical values of the saturable nonlinearity coefficient (γc ) vs. the normalized absorption coefficient () for two values of the normalized gain coefficient (). The dispersion coefficient (β2) is set to zero.

Fig. 6.
Fig. 6.

Modelocked pulse evolution in the presence of saturable gain. The saturable non-linearity coefficient γ = -10 × 10-12 m/V2. We set = 4 and = 5. The dispersion coefficient (β2) is set to zero.

Fig. 7.
Fig. 7.

Equilibrium modelocked pulse shapes vs. the saturable nonlinearity coefficient (γ). In each case, the pulse is shown after it has propagated a distance of 1000Lc. We set = 4 and = 5. The dispersion coefficient (β2) is set to zero.

Fig. 8.
Fig. 8.

The normalized equilibrium maximum intensity and pulse duration (FWHM/1.763) of the stable modelocked pulse vs. the saturable nonlinearity coefficient (γ). We set = 4 and = 5. The dispersion coefficient (β2) is set to zero.

Fig. 9.
Fig. 9.

Critical values of the saturable nonlinearity coefficient (γc ) vs. the normalized absorption coefficient () for two values of the normalized gain coefficient (). The dispersion coefficient (β2) is set to zero.

Fig. 10.
Fig. 10.

Modelocked pulse evolution in presence of group velocity dispersion. The dispersion coefficient |β2| = 5 ps2/m. We set = 4 and = 5. The saturable nonlinearity coefficient (γ) is set to zero.

Fig. 11.
Fig. 11.

Equilibrium modelocked pulse shapes vs. group velocity dispersion coefficient (|β2|). In each case, the pulse is shown at a propagation length of 1000Lc. We set = 4 and = 5. The saturable nonlinearity coefficient (γ) is set to zero.

Fig. 12.
Fig. 12.

The normalized maximum intensity and pulse duration (FWHM/1.763) at equilibrium vs. the dispersion coefficient (β2). We set = 4, = 5. The saturable nonlinearity coefficient (γ) is set to zero.

Fig. 13.
Fig. 13.

The critical values of the dispersion coefficient (|β2c|) vs. the normalized absorption coefficient () for two values of the normalized gain coefficient (). The saturable nonlinearity coefficient (γ) is set to zero.

Fig. 14.
Fig. 14.

Contour plot of the normalized maximum intensity vs. the saturable nonlinearity coefficient (γ > 0) and group velocity dispersion coefficient (β2). The maximum intensity has been calculated after the pulse has propagated a distance of 1000Lc. We set = 4 and = 5.

Fig. 15.
Fig. 15.

Contour plot of the duration vs. the saturable nonlinearity coefficient (γ > 0) and group velocity dispersion coefficient (β2). The duration has been calculated after the pulse has propagated a distance of 1000Lc. We set = 4 and = 5.

Fig. 16.
Fig. 16.

Contour plot of the normalized maximum intensity vs. the saturable nonlinearity coefficient (γ < 0) and group velocity dispersion coefficient (β2). The maximum intensity has been calculated after the pulse has propagated a distance of 1000Lc. We set = 4 and = 5.

Fig. 17.
Fig. 17.

Contour plot of the duration vs. the saturable nonlinearity coefficient (γ < 0) and group velocity dispersion (β2). The duration has been calculated after the pulse has propagated a distance of 1000Lc. We set = 4 and = 5.

Equations (7)

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

n c E t = E z i k N g Γ g μ g 2 ε 0 n 2 η g i k N a Γ a μ a 2 ε 0 n 2 η a 1 2 l ( E 2 ) E i 1 2 β 2 2 E t 2 ,
η g t = i μ g 2 ħ Δ g E η g T 2 g ,
Δ g t = i μ g ħ η g E * i μ g ħ η g * E + Δ g 0 Δ g T 1 g ,
η a t = i μ a 2 ħ Δ a E η a T 2 a ,
Δ a t = i μ a ħ η a E * i μ a ħ η a * E + Δ a 0 Δ a T 1 a ,
l ( E 2 ) = l 0 γ E 2 ,
g = k N g Γ g μ g 2 T 2 g 2 ε 0 n 2 ħ , a = k N a Γ a μ a 2 T 2 a 2 ε 0 n 2 ħ .

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