Abstract

We theoretically show that quantum coherent saturable absorption can be used to obtain ultra-short pulses from mid-infrared quantum cascade lasers (QCLs). In this proposal, quantum cascade structures are processed as two electrically isolated sections. The two sections will be biased with two different voltages so that one of the sections produces gain as is done in typical QCLs, while the other produces quantum coherent resonant absorption for the propagating waves. The quantum coherent absorbing section is saturable and favors the generation of ultra-short pulses. We find that stable ultra-short pulses on the order of ∼100 ps are created from a two-section QCL when the pumping in the gain and absorbing sections remains within critical limits. The intensity and the duration of the stable pulses can be significantly varied when the pumping in the gain and absorbing sections and the length of the gain and absorbing sections are varied.

© 2014 Optical Society of America

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  1. 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,” Science290, 1739–1742 (2000).
    [CrossRef] [PubMed]
  2. R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (2000).
    [CrossRef]
  3. A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
    [CrossRef]
  4. A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
    [CrossRef]
  5. C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, 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. Express17, 12929–12943 (2009).
    [CrossRef] [PubMed]
  6. A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
    [CrossRef]
  7. S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
    [CrossRef]
  8. A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared fequency comb based on a quantum cascade laser,” Nature492, 229–233 (2012).
    [CrossRef] [PubMed]
  9. Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on Fabry-Perot quantum cascade laser,” Appl. Phys. Lett.104, 031114 (2014).
    [CrossRef]
  10. J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett.104, 081118 (2014).
    [CrossRef]
  11. D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
    [CrossRef]
  12. V. M. Gkortsas, C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner, “Dynamics of actively mode-locked quantum cascade lasers,” Opt. Express18, 13616–13630 (2010).
    [CrossRef] [PubMed]
  13. A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
    [CrossRef]
  14. C. R. Menyuk and M. A. Talukder, “Self-induced transparency modelocking of quantum cascade lasers,” Phys. Rev. Lett.102, 023903 (2009).
    [CrossRef] [PubMed]
  15. M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A79, 063841 (2009).
    [CrossRef]
  16. S. S. Shimu, A. Docherty, M. A. Talukder, and C. R. Menyuk, “Suppression of spatial hole burning and pulse stabilization for actively modelocked quantum cascade lasers using quantum coherent absorption,” J. Appl. Phys.113, 053106 (2013).
    [CrossRef]
  17. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003).
  18. R. Terazzi and J. Faist, “A density matrix model of transport and radiation in quantum cascade lasers,” New J. Phys.12, 033045 (2010).
    [CrossRef]
  19. M. A. Talukder and C. R. Menyuk, “Temperature-dependent coherent carrier transport in quantum cascade lasers,” New J. Phys.13, 083027 (2011).
    [CrossRef]
  20. M. A. Talukder, “Modeling of gain recovery of quantum cascade lasers,” J. Appl. Phys.109, 033104 (2011).
    [CrossRef]
  21. M. A. Talukder and C. R. Menyuk, “Calculation of the microscopic parameters of a self-induced transparency modelocked quantum cascade laser,” Opt. Comm.295, 115–118 (2013).
    [CrossRef]
  22. S. L. McCall and E. L. Hahn, “Self-induced transparency,” Phys. Rev.183, 457–489 (1969).
    [CrossRef]
  23. I. M. Asher, “Experimental investigation of self-induced transparency and and pulse delay in Ruby,” Phys. Rev. A5, 349–355 (1972).
    [CrossRef]
  24. M. A. Talukder and C. R. Menyuk, “Self-induced transparency modelocking of quantum cascade lasers in the presence of saturable nonlinearity and group velocity dispersion,” Opt. Express18, 5639–5653 (2010).
    [CrossRef] [PubMed]

2014 (3)

Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on Fabry-Perot quantum cascade laser,” Appl. Phys. Lett.104, 031114 (2014).
[CrossRef]

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett.104, 081118 (2014).
[CrossRef]

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

2013 (3)

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
[CrossRef]

S. S. Shimu, A. Docherty, M. A. Talukder, and C. R. Menyuk, “Suppression of spatial hole burning and pulse stabilization for actively modelocked quantum cascade lasers using quantum coherent absorption,” J. Appl. Phys.113, 053106 (2013).
[CrossRef]

M. A. Talukder and C. R. Menyuk, “Calculation of the microscopic parameters of a self-induced transparency modelocked quantum cascade laser,” Opt. Comm.295, 115–118 (2013).
[CrossRef]

2012 (1)

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared fequency comb based on a quantum cascade laser,” Nature492, 229–233 (2012).
[CrossRef] [PubMed]

2011 (3)

M. A. Talukder and C. R. Menyuk, “Temperature-dependent coherent carrier transport in quantum cascade lasers,” New J. Phys.13, 083027 (2011).
[CrossRef]

M. A. Talukder, “Modeling of gain recovery of quantum cascade lasers,” J. Appl. Phys.109, 033104 (2011).
[CrossRef]

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

2010 (3)

2009 (3)

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, 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. Express17, 12929–12943 (2009).
[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]

M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A79, 063841 (2009).
[CrossRef]

2008 (1)

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

2004 (2)

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

2000 (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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (2000).
[CrossRef]

1972 (1)

I. M. Asher, “Experimental investigation of self-induced transparency and and pulse delay in Ruby,” Phys. Rev. A5, 349–355 (1972).
[CrossRef]

1969 (1)

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

Asher, I. M.

I. M. Asher, “Experimental investigation of self-induced transparency and and pulse delay in Ruby,” Phys. Rev. A5, 349–355 (1972).
[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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

Barbieri, S.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Belkin, M. A.

Belyanin, A.

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
[CrossRef]

V. M. Gkortsas, C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner, “Dynamics of actively mode-locked quantum cascade lasers,” Opt. Express18, 13616–13630 (2010).
[CrossRef] [PubMed]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, 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. Express17, 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Blanchard, R.

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
[CrossRef]

Blaser, S.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared fequency comb based on a quantum cascade laser,” Nature492, 229–233 (2012).
[CrossRef] [PubMed]

Bour, D.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Boyd, R. W.

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

Burghoff, D.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Cai, X.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Capasso, F.

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
[CrossRef]

V. M. Gkortsas, C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner, “Dynamics of actively mode-locked quantum cascade lasers,” Opt. Express18, 13616–13630 (2010).
[CrossRef] [PubMed]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, 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. Express17, 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

Chan, C. W. I.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Cho, A. Y.

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (2000).
[CrossRef]

Corzine, S.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Diehl, L.

Dikmelik, Y.

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett.104, 081118 (2014).
[CrossRef]

Docherty, A.

S. S. Shimu, A. Docherty, M. A. Talukder, and C. R. Menyuk, “Suppression of spatial hole burning and pulse stabilization for actively modelocked quantum cascade lasers using quantum coherent absorption,” J. Appl. Phys.113, 053106 (2013).
[CrossRef]

Faist, J.

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett.104, 081118 (2014).
[CrossRef]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared fequency comb based on a quantum cascade laser,” Nature492, 229–233 (2012).
[CrossRef] [PubMed]

R. Terazzi and J. Faist, “A density matrix model of transport and radiation in quantum cascade lasers,” New J. Phys.12, 033045 (2010).
[CrossRef]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Gao, J.-R.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Gellie, P.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Giles Davies, A.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Gkortsas, V. M.

Gmachl, C.

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

Gordon, A.

V. M. Gkortsas, C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner, “Dynamics of actively mode-locked quantum cascade lasers,” Opt. Express18, 13616–13630 (2010).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[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]

Ham, D.

Han, N.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Hayton, D. J.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Höfler, G.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Hu, Q.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Hugi, A.

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett.104, 081118 (2014).
[CrossRef]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared fequency comb based on a quantum cascade laser,” Nature492, 229–233 (2012).
[CrossRef] [PubMed]

Hutchinson, A. L.

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

Hwang, H. Y.

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (2000).
[CrossRef]

Jirauschek, C.

V. M. Gkortsas, C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner, “Dynamics of actively mode-locked quantum cascade lasers,” Opt. Express18, 13616–13630 (2010).
[CrossRef] [PubMed]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

Kao, T.-Y.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Kärtner, F. X.

V. M. Gkortsas, C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner, “Dynamics of actively mode-locked quantum cascade lasers,” Opt. Express18, 13616–13630 (2010).
[CrossRef] [PubMed]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, 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. Express17, 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

Khanna, S. P.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Khurgin, J. B.

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett.104, 081118 (2014).
[CrossRef]

Kuznetsova, L.

Li, X.

Linfield, E. H.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Liu, H. C.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared fequency comb based on a quantum cascade laser,” Nature492, 229–233 (2012).
[CrossRef] [PubMed]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, 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. Express17, 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

Maier, T.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Malara, P.

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
[CrossRef]

Manquest, C.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Mansuripur, T. S.

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
[CrossRef]

McCall, S. L.

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

Menyuk, C. R.

M. A. Talukder and C. R. Menyuk, “Calculation of the microscopic parameters of a self-induced transparency modelocked quantum cascade laser,” Opt. Comm.295, 115–118 (2013).
[CrossRef]

S. S. Shimu, A. Docherty, M. A. Talukder, and C. R. Menyuk, “Suppression of spatial hole burning and pulse stabilization for actively modelocked quantum cascade lasers using quantum coherent absorption,” J. Appl. Phys.113, 053106 (2013).
[CrossRef]

M. A. Talukder and C. R. Menyuk, “Temperature-dependent coherent carrier transport in quantum cascade lasers,” New J. Phys.13, 083027 (2011).
[CrossRef]

M. A. Talukder and C. R. Menyuk, “Self-induced transparency modelocking of quantum cascade lasers in the presence of saturable nonlinearity and group velocity dispersion,” Opt. Express18, 5639–5653 (2010).
[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]

M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A79, 063841 (2009).
[CrossRef]

Paiella, R.

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (2000).
[CrossRef]

Peabody, M. L.

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

Ravora, M.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Reno, J. L.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Santarelli, G.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Schneider, H.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, 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. Express17, 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Sergent, A. M.

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

Shimu, S. S.

S. S. Shimu, A. Docherty, M. A. Talukder, and C. R. Menyuk, “Suppression of spatial hole burning and pulse stabilization for actively modelocked quantum cascade lasers using quantum coherent absorption,” J. Appl. Phys.113, 053106 (2013).
[CrossRef]

Sirtori, C.

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

Sivco, D. L.

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

Soibel, A.

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

Song, C. Y.

Soskind, M. G.

Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on Fabry-Perot quantum cascade laser,” Appl. Phys. Lett.104, 031114 (2014).
[CrossRef]

Talukder, M. A.

S. S. Shimu, A. Docherty, M. A. Talukder, and C. R. Menyuk, “Suppression of spatial hole burning and pulse stabilization for actively modelocked quantum cascade lasers using quantum coherent absorption,” J. Appl. Phys.113, 053106 (2013).
[CrossRef]

M. A. Talukder and C. R. Menyuk, “Calculation of the microscopic parameters of a self-induced transparency modelocked quantum cascade laser,” Opt. Comm.295, 115–118 (2013).
[CrossRef]

M. A. Talukder and C. R. Menyuk, “Temperature-dependent coherent carrier transport in quantum cascade lasers,” New J. Phys.13, 083027 (2011).
[CrossRef]

M. A. Talukder, “Modeling of gain recovery of quantum cascade lasers,” J. Appl. Phys.109, 033104 (2011).
[CrossRef]

M. A. Talukder and C. R. Menyuk, “Self-induced transparency modelocking of quantum cascade lasers in the presence of saturable nonlinearity and group velocity dispersion,” Opt. Express18, 5639–5653 (2010).
[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]

M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A79, 063841 (2009).
[CrossRef]

Terazzi, R.

R. Terazzi and J. Faist, “A density matrix model of transport and radiation in quantum cascade lasers,” New J. Phys.12, 033045 (2010).
[CrossRef]

Troccoli, M.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Villares, G.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared fequency comb based on a quantum cascade laser,” Nature492, 229–233 (2012).
[CrossRef] [PubMed]

Wang, C.

Wang, C. Y.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, 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. Express17, 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Wang, W.

Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on Fabry-Perot quantum cascade laser,” Appl. Phys. Lett.104, 031114 (2014).
[CrossRef]

Wang, Y.

Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on Fabry-Perot quantum cascade laser,” Appl. Phys. Lett.104, 031114 (2014).
[CrossRef]

Wasilewski, Z. R.

Wójcik, A. K.

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
[CrossRef]

Wysocki, G.

Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on Fabry-Perot quantum cascade laser,” Appl. Phys. Lett.104, 031114 (2014).
[CrossRef]

Yang, Y.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Appl. Phys. Lett. (4)

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett.77, 169–171 (2000).
[CrossRef]

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett.103, 231102 (2013).
[CrossRef]

Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on Fabry-Perot quantum cascade laser,” Appl. Phys. Lett.104, 031114 (2014).
[CrossRef]

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett.104, 081118 (2014).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, D. L. Sivco, A. Y. Cho, and H. C. Liu, “Stability of pulse emission and enhancement of intracavity second-harmonic generation in self-mode-locked quantum cascade lasers,” IEEE J. Quantum Electron.40, 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. L. Peabody, A. M. Sergent, R. Paiella, H. Y. Hwang, D. L. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kärtner, “Active mode locking of broadband quantum cascade lasers,” IEEE J. Quantum Electron.40, 844–851 (2004).
[CrossRef]

J. Appl. Phys. (2)

S. S. Shimu, A. Docherty, M. A. Talukder, and C. R. Menyuk, “Suppression of spatial hole burning and pulse stabilization for actively modelocked quantum cascade lasers using quantum coherent absorption,” J. Appl. Phys.113, 053106 (2013).
[CrossRef]

M. A. Talukder, “Modeling of gain recovery of quantum cascade lasers,” J. Appl. Phys.109, 033104 (2011).
[CrossRef]

Nat. Photonics (2)

S. Barbieri, M. Ravora, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. Giles Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency syntesis,” Nat. Photonics5, 306–313 (2011).
[CrossRef]

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics8, 462–467 (2014).
[CrossRef]

Nature (1)

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared fequency comb based on a quantum cascade laser,” Nature492, 229–233 (2012).
[CrossRef] [PubMed]

New J. Phys. (2)

R. Terazzi and J. Faist, “A density matrix model of transport and radiation in quantum cascade lasers,” New J. Phys.12, 033045 (2010).
[CrossRef]

M. A. Talukder and C. R. Menyuk, “Temperature-dependent coherent carrier transport in quantum cascade lasers,” New J. Phys.13, 083027 (2011).
[CrossRef]

Opt. Comm. (1)

M. A. Talukder and C. R. Menyuk, “Calculation of the microscopic parameters of a self-induced transparency modelocked quantum cascade laser,” Opt. Comm.295, 115–118 (2013).
[CrossRef]

Opt. Express (3)

Phys. Rev. (1)

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

Phys. Rev. A (3)

I. M. Asher, “Experimental investigation of self-induced transparency and and pulse delay in Ruby,” Phys. Rev. A5, 349–355 (1972).
[CrossRef]

M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A79, 063841 (2009).
[CrossRef]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, 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. A77, 053804 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (1)

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,” Science290, 1739–1742 (2000).
[CrossRef] [PubMed]

Other (1)

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

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Figures (6)

Fig. 1
Fig. 1

Schematic of a two-section QCL with gain and saturable absorbing sections.

Fig. 2
Fig. 2

Intensity and population inversion in the cavity after 100 round trips for (a) λg = 2.5λg,min and λa = 0.3λa,max, and (b) λg = 2.5λg,min and λa = 0.7λa,max.

Fig. 3
Fig. 3

Intensity output with λg = 2.5λg,min and (a) λa = 0.3λa,max, (b) λa = 0.6λa,max, (c) λa = 0.9λa,max, and (d) λa = λa,max.

Fig. 4
Fig. 4

Full width at half maximum (FWHM) duration of stable pulses with different pumping levels in the gain and absorbing sections.

Fig. 5
Fig. 5

Full width at half maximum (FWHM) duration of stable pulses with different recovery time in the absorbing section. The recovery time in the gain section is kept fixed at 50 ps.

Fig. 6
Fig. 6

Intensity output with λg = 2.5λg,min and λa = 0.7λa,max when (a) Lg = 2.0 mm, La = 0.6 mm, (b) Lg = 2.3 mm, La = 0.3 mm, and (c) Lg = 2.5 mm, La = 0.1 mm.

Tables (1)

Tables Icon

Table 1 Key parameter values

Equations (34)

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n c E ± t = E ± z i N g Γ g d g k ε 0 n 2 n g ± l E ± ,
η g ± t = i d g 2 h ¯ ( Δ 0 g E ± + Δ 2 g E ) η g ± T 2 g ,
Δ 0 g t = λ g + i d g h ¯ ( E + * η g + + E * η g c . c . ) Δ 0 g T 1 g ,
Δ 2 g ± t = i d g h ¯ ( E ± * η g E η g ± * ) ( 1 T 1 g + 4 k 2 D ) Δ 2 g ± ,
n c E ± t = E ± z i N a Γ a d a k ε 0 n 2 η a ± l E ± ,
η a ± t = i d a 2 h ¯ ( Δ 0 a E ± + Δ 2 a E ) η a ± T 2 a ,
Δ 0 a t = λ a + i d a h ¯ ( E + * η a + + E * η a c . c . ) Δ 0 a T 1 a ,
Δ 2 a ± t = i d a h ¯ ( E ± * η a E η a ± * ) ( 1 T 1 a + 4 k 2 D ) Δ 2 a ± ,
E ˜ ± = d g h ¯ E ± ,
η ˜ g , a ± = k N g , a Γ g , a d g , a 2 h ¯ ε 0 n 2 η g , a ± ,
Δ ˜ 0 g a = k N g , a Γ g , a d g , a 2 h ¯ ε 0 n 2 Δ 0 g , a ,
Δ ˜ 2 g , a = k N g , a Γ g , a d g , a 2 h ¯ ε 0 n 2 Δ 2 g , a ,
λ ˜ g , a = k N g , a Γ g , a d g , a 2 h ¯ ε 0 n 2 λ g , a .
n c E ˜ ± t = E ˜ ± z i η ˜ g ± l E ˜ ± ,
η ˜ g ± t = i 2 ( Δ ˜ 0 g E ˜ ± + Δ ˜ 2 g E ˜ ) η ˜ g ± T 2 g ,
Δ ˜ 0 g t = λ ˜ g + i ( E ˜ + * η ˜ g + + E ˜ * η ˜ g c . c . ) Δ ˜ 0 g T 1 g ,
Δ ˜ 2 g ± t = i ( E ˜ ± * η ˜ g E ˜ η ˜ g ± * ) ( 1 T 1 g + 4 k 2 D ) Δ ˜ 2 g ± ,
n c E ˜ ± t = E ˜ ± z i d g d a η ˜ a ± l E ˜ ± ,
η ˜ a ± t = i 2 d a d g ( Δ ˜ 0 a E ˜ ± + Δ ˜ 2 a E ˜ ) η ˜ a ± T 2 a ,
Δ ˜ 0 a t = λ ˜ a + i d a d g ( E ˜ + * η ˜ a + + E ˜ * η ˜ a c . c . ) Δ ˜ 0 a T 1 a ,
Δ ˜ 2 a + t = i d a d g ( E ˜ ± * η ˜ a E ˜ η ˜ a ± * ) ( 1 T 1 a + 4 k 2 D ) Δ ˜ 2 a ± .
E ˜ + = E ˜ = E ¯ ,
η ˜ g , a = η ˜ g , a = η ¯ g , a ,
Δ ˜ 0 g , a = Δ ¯ 0 g , a ,
Δ ˜ 2 g , a + = Δ ˜ 2 g , a = Δ ¯ 2 g , a .
η ¯ g = i T 2 g 2 ( Δ ¯ 0 g E ¯ + Δ ¯ 2 g E ¯ ) .
( z + n c t ) E ¯ = T 2 g 2 ( Δ ¯ 0 g + Δ ¯ 2 g ) E l E ¯ .
E + = E = 0 ,
Δ ˜ 2 g + = Δ ˜ 2 g = 0 .
g L g a L a [ l L c + 1 2 ln ( 1 r 1 ) + 1 2 ln ( 1 r 2 ) ] = 0 ,
g min L g [ l L c + 1 2 ln ( 1 r 1 ) + 1 2 ln ( 1 r 2 ) ] = 0 .
λ g , min = 2 T 1 g T 2 g L g [ l L c + 1 2 ln ( 1 r 1 ) + 1 2 ln ( 1 r 2 ) ] .
a max L a = g L g [ l L c + 1 2 ln ( 1 r 1 ) + 1 2 ln ( 1 r 2 ) ] .
λ a , max = λ g T 1 g T 2 g L g T 1 a T 2 a L a 2 T 1 a T 2 a L a [ l L c + 1 2 ln ( 1 r 1 ) + 1 2 ln ( 1 r 2 ) ] .

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