Abstract

The impact of upper state lifetime and spatial hole burning on pulse shape and stability in actively mode locked QCLs is investigated by numerical simulations. It is shown that an extended upper state lifetime is necessary to achieve stable isolated pulse formation per roundtrip. Spatial hole burning helps to reduce the pulse duration by supporting broadband multimode lasing, but introduces pulse instabilities which eventually lead to strongly structured pulse shapes that further degrade with increased pumping. At high pumping levels gain saturation and recovery between pulses leads to suppression of mode locking. In the absence of spatial hole burning the laser approaches single-mode lasing, while in the presence of spatial hole burning the mode locking becomes unstable and the laser dynamics does not reach a steady state anymore.

© 2010 OSA

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2009 (2)

2008 (3)

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 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(16), 167401 (2008).
[CrossRef] [PubMed]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92(12), 122114–122117 (2008).
[CrossRef]

2007 (1)

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

2005 (1)

T. Maier, H. Schneider, H. C. Liu, M. Walther, and P. Koidl, “Two-photon QWIPs for quadratic detection of weak mid-infrared laser pulses,” Infrared Phys. Technol. 47(1-2), 182–187 (2005).
[CrossRef]

2004 (3)

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
[CrossRef]

R. Torre, P. Bartolini, and R. Righini, “Structural relaxation in supercooled water by time-resolved spectroscopy,” Nature 428(6980), 296–299 (2004).
[CrossRef] [PubMed]

2003 (1)

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
[CrossRef] [PubMed]

2002 (3)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

H. C. Liu and E. Dupont, “Nonlinear quantum well infrared photodetector,” J. Nonlinear Opt. Phys. Mater. 11(4), 433–443 (2002).
[CrossRef]

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and tow-phonon resonance quantum cascade lasers for high duty cycle, high temperature operation,” IEEE J. Quantum Electron. 38(6), 533–546 (2002).
[CrossRef]

2001 (1)

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[CrossRef] [PubMed]

2000 (2)

R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

1993 (1)

J. J. Macklin, J. D. Kmetec, and C. L. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70(6), 766–769 (1993).
[CrossRef] [PubMed]

Abstreiter, G.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[CrossRef] [PubMed]

Aellen, T.

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and tow-phonon resonance quantum cascade lasers for high duty cycle, high temperature operation,” IEEE J. Quantum Electron. 38(6), 533–546 (2002).
[CrossRef]

Aquila, A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
[CrossRef] [PubMed]

Attwood, D. T.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
[CrossRef] [PubMed]

Backus, S.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
[CrossRef] [PubMed]

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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

Bartolini, P.

R. Torre, P. Bartolini, and R. Righini, “Structural relaxation in supercooled water by time-resolved spectroscopy,” Nature 428(6980), 296–299 (2004).
[CrossRef] [PubMed]

Beck, M.

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and tow-phonon resonance quantum cascade lasers for high duty cycle, high temperature operation,” IEEE J. Quantum Electron. 38(6), 533–546 (2002).
[CrossRef]

Belkin, M. A.

Belyanin, A.

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. Express 17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

Bichler, M.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[CrossRef] [PubMed]

Blaser, S.

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and tow-phonon resonance quantum cascade lasers for high duty cycle, high temperature operation,” IEEE J. Quantum Electron. 38(6), 533–546 (2002).
[CrossRef]

Bour, D.

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

Brodschelm, A.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[CrossRef] [PubMed]

Capasso, F.

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. Express 17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92(12), 122114–122117 (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(16), 167401 (2008).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Cho, A. Y.

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Choi, H.

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(16), 167401 (2008).
[CrossRef] [PubMed]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92(12), 122114–122117 (2008).
[CrossRef]

Christov, I. P.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
[CrossRef] [PubMed]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Corzine, S.

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

Diehl, L.

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. Express 17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92(12), 122114–122117 (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(16), 167401 (2008).
[CrossRef] [PubMed]

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

Dudley, J. M.

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A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
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E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
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E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
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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(16), 167401 (2008).
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H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92(12), 122114–122117 (2008).
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A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
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C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
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J. J. Macklin, J. D. Kmetec, and C. L. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70(6), 766–769 (1993).
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Gresch, T.

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92(12), 122114–122117 (2008).
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E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
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A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
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C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
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J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and tow-phonon resonance quantum cascade lasers for high duty cycle, high temperature operation,” IEEE J. Quantum Electron. 38(6), 533–546 (2002).
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R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
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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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
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J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
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C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
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A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
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E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
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C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
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J. J. Macklin, J. D. Kmetec, and C. L. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70(6), 766–769 (1993).
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T. Maier, H. Schneider, H. C. Liu, M. Walther, and P. Koidl, “Two-photon QWIPs for quadratic detection of weak mid-infrared laser pulses,” Infrared Phys. Technol. 47(1-2), 182–187 (2005).
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Leitenstorfer, A.

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Liu, H. C.

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. Express 17(15), 12929–12943 (2009).
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A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
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T. Maier, H. Schneider, H. C. Liu, M. Walther, and P. Koidl, “Two-photon QWIPs for quadratic detection of weak mid-infrared laser pulses,” Infrared Phys. Technol. 47(1-2), 182–187 (2005).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
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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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
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J. J. Macklin, J. D. Kmetec, and C. L. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70(6), 766–769 (1993).
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A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
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T. Maier, H. Schneider, H. C. Liu, M. Walther, and P. Koidl, “Two-photon QWIPs for quadratic detection of weak mid-infrared laser pulses,” Infrared Phys. Technol. 47(1-2), 182–187 (2005).
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C. R. Menyuk and M. A. Talukder, “Self-induced transparency modelocking of quantum cascade lasers,” Phys. Rev. Lett. 102(2), 023903 (2009).
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E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
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H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92(12), 122114–122117 (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(16), 167401 (2008).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
[CrossRef]

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E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
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J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and tow-phonon resonance quantum cascade lasers for high duty cycle, high temperature operation,” IEEE J. Quantum Electron. 38(6), 533–546 (2002).
[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. Express 17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

T. Maier, H. Schneider, H. C. Liu, M. Walther, and P. Koidl, “Two-photon QWIPs for quadratic detection of weak mid-infrared laser pulses,” Infrared Phys. Technol. 47(1-2), 182–187 (2005).
[CrossRef]

Sergent, A. M.

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
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Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Sivco, D.

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
[CrossRef]

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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
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J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
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A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
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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(2), 023903 (2009).
[CrossRef] [PubMed]

Tauser, F.

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[CrossRef] [PubMed]

Tobey, R.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
[CrossRef] [PubMed]

Torre, R.

R. Torre, P. Bartolini, and R. Righini, “Structural relaxation in supercooled water by time-resolved spectroscopy,” Nature 428(6980), 296–299 (2004).
[CrossRef] [PubMed]

Troccoli, M.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

Trocolli, M.

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

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T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

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E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
[CrossRef] [PubMed]

Walther, M.

T. Maier, H. Schneider, H. C. Liu, M. Walther, and P. Koidl, “Two-photon QWIPs for quadratic detection of weak mid-infrared laser pulses,” Infrared Phys. Technol. 47(1-2), 182–187 (2005).
[CrossRef]

Wang, C.

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

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. Express 17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 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, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

R. Paiella, F. Capasso, C. Gmachl, H. Hwang, D. Sivco, A. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
[CrossRef]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92(12), 122114–122117 (2008).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, D. Sivco, A. Y. Cho, H. C. Liu, 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(3), 197–204 (2004).
[CrossRef]

A. Soibel, F. Capasso, C. Gmachl, M. Peabody, A. M. Sergent, R. Paiella, H. Hwang, D. Sivco, A. Y. Cho, H. C. Liu, C. Jirauschek, and F. X. Kartner, “Active Mode locking of Broadband quantum Cascade Lasers,” IEEE J. Quantum Electron. 40(7), 844–851 (2004).
[CrossRef]

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and tow-phonon resonance quantum cascade lasers for high duty cycle, high temperature operation,” IEEE J. Quantum Electron. 38(6), 533–546 (2002).
[CrossRef]

Infrared Phys. Technol. (1)

T. Maier, H. Schneider, H. C. Liu, M. Walther, and P. Koidl, “Two-photon QWIPs for quadratic detection of weak mid-infrared laser pulses,” Infrared Phys. Technol. 47(1-2), 182–187 (2005).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

H. C. Liu and E. Dupont, “Nonlinear quantum well infrared photodetector,” J. Nonlinear Opt. Phys. Mater. 11(4), 433–443 (2002).
[CrossRef]

Nature (3)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, “How many-particle interactions develop after ultrafast excitation of an electron-hole plasma,” Nature 414(6861), 286–289 (2001).
[CrossRef] [PubMed]

R. Torre, P. Bartolini, and R. Righini, “Structural relaxation in supercooled water by time-resolved spectroscopy,” Nature 428(6980), 296–299 (2004).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. A (2)

A. Gordon, C. Wang, L. Diehl, F. Kaertner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, H. C. Liu, H. Schneider, T. Maier, M. Trocolli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hoefler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

C. R. Menyuk and M. A. Talukder, “Self-induced transparency modelocking of quantum cascade lasers,” Phys. Rev. Lett. 102(2), 023903 (2009).
[CrossRef] [PubMed]

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(16), 167401 (2008).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Science (3)

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994).
[CrossRef] [PubMed]

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 nonlinearities,” Science 290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

Other (1)

C. Wang, L. Kuznetsova, L. Diehl, F. Kaertner, M. Belkin, H. Schneider, H. C. Liu, and F. Capasso, “Stable Mode-locked pulses from Mid-Infrared Quantum Cascade Lasers,” Postdeadline paper, Conference of Lasers and Electro optics, San Jose, CA, USA, 2008.

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Figures (17)

Fig. 1
Fig. 1

Intensity (black line) and inversion (red line) for (a) fast gain recovery time and (b) slow gain recovery time

Fig. 2
Fig. 2

a) Device used in the experiment, b) Modulation scheme for the actively mode locked QCL. The cavity is in total 2.6 mm long and the short modulator section at the beginning of the cavity is 240 μm long.

Fig. 3
Fig. 3

a) Three-level system which describes QCL dynamics, b) Open two-level model that we use in the simulations

Fig. 4
Fig. 4

Steady state intensity (blue line) and inversion (green line) in the cavity without SHB and without modulation for DC pumping p = 1.1 after 1785 roundtrips.

Fig. 5
Fig. 5

Pumping, inversion and intensity for a point inside the modulation section for p = 1.1 and m = 5 without SHB.

Fig. 6
Fig. 6

Intensity profile of output pulse train for modulation with AC-amplitude m = 5 for different DC pumping levels without SHB. a) p = 1.1 b) p = 1.45, and c) p = 1.61

Fig. 7
Fig. 7

Spectral intensities for modulation with AC-amplitude m = 5 for different DC pumping levels without SHB a) p = 1.1 b) p = 1.45, and c) p = 1.61

Fig. 8
Fig. 8

Interferometric autocorrelation traces (IACs) for modulation with AC amplitude m = 5 for different DC pumping levels without SHB a) p = 1.1 b) p = 1.45, and c) p = 1.61

Fig. 9
Fig. 9

Measured interferometric autocorrelation traces (IACs) for modulation with AC amplitude m = 5 (35 dBm applied RF-power) for different DC pumping levels. a) p = 1.1 (340 mA) b) p = 1.45 (450 mA), and c) p = 1.61 (500 mA) [12].

Fig. 10
Fig. 10

Average inversion Δ0 (blue line) and total inversion along the cavity length including the inversion grating (red line) for DC pumping p = 1.1 and no modulation after a) 5357 roundtrips, b) 10714 roundtrips c) 17857 roundtrips.

Fig. 11
Fig. 11

Average inversion Δ0 (blue line) and total inversion along the cavity length including the inversion grating (red line) for DC pumping p = 2 and no modulation after a) 5357 roundtrips, b) 10714 roundtrips c) 17857 roundtrips.

Fig. 12
Fig. 12

Intensity profile (blue line) and total inversion (red line) along the cavity for DC pumping p = 1.1 and AC amplitude m = 5 a) when the pulse is reflected off the left facet and propagates to the right b) when the pulse is in the middle of the cavity and propagates to the right c) when the pulse is reflected off the right facet and propagates to the left.

Fig. 13
Fig. 13

Intensity profile (blue line) and total inversion (red line) along the cavity for DC pumping p = 2 and AC amplitude m = 5 a) when the pulse is reflected off the left facet and propagates to the right b) when the pulse is in the middle of the cavity and propagates to the right c) when the pulse is reflected off the right facet and propagates to the left.

Fig. 14
Fig. 14

Spectral intensities for modulation with AC amplitude m = 5 for different DC pumping levels including SHB a) p = 1.1 b) p = 1.45, and c) p = 1.61

Fig. 15
Fig. 15

Intensity profile of output pulse train for modulation with AC amplitude m = 5 for different DC pumping levels including SHB a) p = 1.1 b) p = 1.45, and c) p = 1.61

Fig. 16
Fig. 16

Interferometric autocorrelation traces (IACs) for modulation with AC amplitude m = 5 for different DC pumping levels including SHB. a) p = 1.1 b) p = 1.45, and c) p = 1.61

Fig. 17
Fig. 17

Interferometric autocorrelation traces (IACs) for modulation with AC amplitude m = 5, and DC pumping level p = 1.1 a) for T1 = 50 ps and Tg = 10 ps b) for T1 = 5 ps and Tg = 2.5 ps. Comparing the two figures with Fig. 13a we see that the structure is more pronounced in these figures due to the stronger SHB.

Tables (1)

Tables Icon

Table 1 Parameters used in simulations if not otherwise noted

Equations (26)

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d N 2 d t = J σ I p h ( N 2 N 1 ) 1 T 21 N 2
d N 1 d t = σ I p h ( N 2 N 1 ) + 1 T 21 N 2 1 T 10 N 1
d N 0 d t = J + 1 T 10 N 1
d N 2 d t = J σ I p h N 2 1 T 21 N 2
N 1 = 0
t ρ a b = i ω ρ a b + i d E Δ ρ a b T 2
t Δ = λ 2 i d E ( ρ a b * ρ a b ) Δ T 1 + D 2 Δ z 2
z 2 E n 2 c 2 t 2 E = N d ε 0 c 2 t 2 ( ρ a b + ρ a b * )
E ( z , t ) = 1 2 [ E + * ( z , t ) e i ( ω t k z ) + E + ( z , t ) e i ( ω t k z ) ] + 1 2 [ E * ( z , t ) e i ( ω t + k z ) + E ( z , t ) e i ( ω t + k z ) ]
ρ a b ( z , t ) = η + ( z , t ) e i ( ω t k z ) + η ( z , t ) e i ( ω t + k z )
Δ ( z , t ) = Δ 0 ( z , t ) + Δ 2 ( z , t ) e 2 i k z + Δ 2 * ( z , t ) e 2 i k z
n c t E ± = z E ± i N d k ε 0 n 2 η ± E ±
t η ± = i d 2 ( Δ 0 E ± + Δ 2 E ) η ± T 2
t Δ 0 = λ + i d ( E + * η + + E * η c . c . ) Δ 0 T 1
t Δ 2 ± = ± i d ( E + * η η + * E ) ( 1 T 1 + 4 k 2 D ) Δ 2 ±
E ˜ E d
η ˜ N d 2 k ε 0 n 2 η
Δ ˜ 0 N d 2 k ε 0 n 2 Δ 0
Δ ˜ 2 N d 2 k ε 0 n 2 Δ 2
λ ˜ N d 2 k ε 0 n 2 λ
n c t E ˜ ± = z E ˜ ± i η ˜ ± E ˜ ±
t η ˜ ± = i 2 ( Δ ˜ 0 E ˜ ± + Δ ˜ 2 E ˜ ) η ˜ ± T 2
t Δ ˜ 0 = λ ˜ + i ( E ˜ + * η ˜ + + E ˜ * η ˜ c . c . ) Δ ˜ 0 T 1
t Δ ˜ 2 ± = ± i ( E ˜ + * η ˜ η ˜ + * E ˜ ) ( 1 T 1 + 4 k 2 D ) Δ ˜ 2 ±
η ˜ ¯ = i T 2 2 ( Δ ˜ ¯ 0 + Δ ˜ ¯ 2 ) E ˜ ¯
( z + n c t ) E ˜ ¯ = T 2 2 ( Δ ˜ ¯ 0 + Δ ˜ ¯ 2 ) E ˜ ¯ E ˜ ¯

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