Abstract

A time-resolved mid-infrared upconversion technique based on sum-frequency generation was applied to measure pulse propagation in λ~5.0 µm quantum cascade lasers operated in continuous wave at 30 K. The wavelength-dependent propagation delay of femtosecond mid-infrared pulses was measured to determine the total group-velocity dispersion. The material and waveguide dispersion were calculated and their contributions to the total group-velocity dispersion were found to be relatively small and constant. The small-signal gain dispersion was estimated from a measurement of the electroluminescence spectrum without a laser cavity, and was found to be the largest component of the total GVD. A negative group-velocity dispersion of β 2 (=d 2 β/ 2) approximately -4.6×10-6 ps2/µm was observed at the peak emission wavelength, and good agreement was found for the measured and calculated pulse-broadening.

© 2007 Optical Society of America

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    [Crossref]
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    [Crossref]
  5. 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]
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    [Crossref] [PubMed]
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    [Crossref]
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2007 (1)

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

2006 (2)

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

2004 (2)

R. Maulini, M. Beck, J. Faist, and E. Gini, “Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers,” Appl. Phys. Lett. 84, 1659–1661 (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]

2002 (2)

W. Lu, L. Yan, and C. R. Menyuk, “Dispersion Effects in an Actively Mode-Locked Inhomogeneously Broadened Laser,” IEEE J. Quantum Electron. QE-22, 1317–1324 (2002).
[Crossref]

C. Gmachl, A. Straub, R. Colombelli, D. L. Sivco, F. Capasso, and A. Y. Cho, “Minimal Group Refractive Index Dispersion and Gain Evolution in Ultra-Broad-Band Quantum Cascade Lasers,” IEEE Photon. Technol. Lett. 14, 1671–1673 (2002).
[Crossref]

2000 (2)

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Svico, 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. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

1999 (1)

D. Hofstetter and J. Faist, “Measurement of Semiconductor Laser Gain and Dispersion Curves Utilizing Fourier Transforms of the Emission Spectra,” IEEE Photon. Technol. Lett. 11, 1372–1374 (1999).
[Crossref]

1994 (1)

1992 (1)

M. P. Kesler and E. P. Ippen, “Femtosecond Time-Domain Measurements of Group Velocity Dispersion in Diode Lasers at 1.5µm,” IEEE J. Lightwave Technol. 10, 616–619 (1992).
[Crossref]

1991 (1)

G. P. Agrawal, “Effect of Gain Dispersion on Ultrashort Pulse Amplification,” IEEE J. Quantum Electron. 27, 1843–1849 (1991).
[Crossref]

1989 (1)

M. P. Kesler and E. P. Ippen, “Femtosecond Time-Domain Measurements of Group Velocity Dispersion in Al-GaAs Diode Lasers,” Electron. Lett. 25, 640–642 (1989).
[Crossref]

1988 (1)

J. Shah, “Ultrafast Luminescence Spectroscopy Using Sum Frequency Generation,” IEEE J. Quantum Electron. 24, 276–288 (1988).
[Crossref]

1986 (1)

H. A. Haus and Y. Silberberg, “Laser Mode Locking with Addition of Nonlinear Index,” IEEE J. Quantum Electron. QE-22, 1048–1060 (1986).

Agrawal, G. P.

G. P. Agrawal, “Effect of Gain Dispersion on Ultrashort Pulse Amplification,” IEEE J. Quantum Electron. 27, 1843–1849 (1991).
[Crossref]

Bailargeon, J. N.

R. Paiella, F. Capasso, C. Gmachl, D. L. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

Beck, M.

R. Maulini, M. Beck, J. Faist, and E. Gini, “Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers,” Appl. Phys. Lett. 84, 1659–1661 (2004).
[Crossref]

Belyanin, A.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

Bour, D.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

Capasso, F.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

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]

C. Gmachl, A. Straub, R. Colombelli, D. L. Sivco, F. Capasso, and A. Y. Cho, “Minimal Group Refractive Index Dispersion and Gain Evolution in Ultra-Broad-Band Quantum Cascade Lasers,” IEEE Photon. Technol. Lett. 14, 1671–1673 (2002).
[Crossref]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Svico, 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. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

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]

C. Gmachl, A. Straub, R. Colombelli, D. L. Sivco, F. Capasso, and A. Y. Cho, “Minimal Group Refractive Index Dispersion and Gain Evolution in Ultra-Broad-Band Quantum Cascade Lasers,” IEEE Photon. Technol. Lett. 14, 1671–1673 (2002).
[Crossref]

R. Paiella, F. Capasso, C. Gmachl, D. L. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Svico, 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]

Cleaver, J. R. A.

Colombelli, R.

C. Gmachl, A. Straub, R. Colombelli, D. L. Sivco, F. Capasso, and A. Y. Cho, “Minimal Group Refractive Index Dispersion and Gain Evolution in Ultra-Broad-Band Quantum Cascade Lasers,” IEEE Photon. Technol. Lett. 14, 1671–1673 (2002).
[Crossref]

Corzine, S.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

Diehl, L.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

Faist, J.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

R. Maulini, M. Beck, J. Faist, and E. Gini, “Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers,” Appl. Phys. Lett. 84, 1659–1661 (2004).
[Crossref]

D. Hofstetter and J. Faist, “Measurement of Semiconductor Laser Gain and Dispersion Curves Utilizing Fourier Transforms of the Emission Spectra,” IEEE Photon. Technol. Lett. 11, 1372–1374 (1999).
[Crossref]

Gini, E.

R. Maulini, M. Beck, J. Faist, and E. Gini, “Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers,” Appl. Phys. Lett. 84, 1659–1661 (2004).
[Crossref]

Gmachl, C.

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]

C. Gmachl, A. Straub, R. Colombelli, D. L. Sivco, F. Capasso, and A. Y. Cho, “Minimal Group Refractive Index Dispersion and Gain Evolution in Ultra-Broad-Band Quantum Cascade Lasers,” IEEE Photon. Technol. Lett. 14, 1671–1673 (2002).
[Crossref]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Svico, 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. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

Gordon, A.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

Gordon, R.

Haus, H. A.

H. A. Haus and Y. Silberberg, “Laser Mode Locking with Addition of Nonlinear Index,” IEEE J. Quantum Electron. QE-22, 1048–1060 (1986).

Heberle, A. P.

Hofler, G.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

Höfler, B. G.

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

Höfler, G.

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

Hofstetter, D.

D. Hofstetter and J. Faist, “Measurement of Semiconductor Laser Gain and Dispersion Curves Utilizing Fourier Transforms of the Emission Spectra,” IEEE Photon. Technol. Lett. 11, 1372–1374 (1999).
[Crossref]

Hutchinson, A. L.

R. Paiella, F. Capasso, C. Gmachl, D. L. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Svico, 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]

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. Svico, 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]

Ippen, E. P.

M. P. Kesler and E. P. Ippen, “Femtosecond Time-Domain Measurements of Group Velocity Dispersion in Diode Lasers at 1.5µm,” IEEE J. Lightwave Technol. 10, 616–619 (1992).
[Crossref]

M. P. Kesler and E. P. Ippen, “Femtosecond Time-Domain Measurements of Group Velocity Dispersion in Al-GaAs Diode Lasers,” Electron. Lett. 25, 640–642 (1989).
[Crossref]

Jirauschek, C.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[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]

Kärtner, F. X.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[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]

Kesler, M. P.

M. P. Kesler and E. P. Ippen, “Femtosecond Time-Domain Measurements of Group Velocity Dispersion in Diode Lasers at 1.5µm,” IEEE J. Lightwave Technol. 10, 616–619 (1992).
[Crossref]

M. P. Kesler and E. P. Ippen, “Femtosecond Time-Domain Measurements of Group Velocity Dispersion in Al-GaAs Diode Lasers,” Electron. Lett. 25, 640–642 (1989).
[Crossref]

Lee, G.

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

Liu, H. C.

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. Svico, 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]

Loncar, M.

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

Lu, W.

W. Lu, L. Yan, and C. R. Menyuk, “Dispersion Effects in an Actively Mode-Locked Inhomogeneously Broadened Laser,” IEEE J. Quantum Electron. QE-22, 1317–1324 (2002).
[Crossref]

Maulini, R.

R. Maulini, M. Beck, J. Faist, and E. Gini, “Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers,” Appl. Phys. Lett. 84, 1659–1661 (2004).
[Crossref]

Menyuk, C. R.

W. Lu, L. Yan, and C. R. Menyuk, “Dispersion Effects in an Actively Mode-Locked Inhomogeneously Broadened Laser,” IEEE J. Quantum Electron. QE-22, 1317–1324 (2002).
[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]

R. Paiella, F. Capasso, C. Gmachl, D. L. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Svico, 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]

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids, (Academic Press, New York, 1985).

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]

Sergent, A. M.

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]

Shah, J.

J. Shah, “Ultrafast Luminescence Spectroscopy Using Sum Frequency Generation,” IEEE J. Quantum Electron. 24, 276–288 (1988).
[Crossref]

Siegman, A.

A. Siegman, Lasers, (University Science Books, Sausalito, California, 1986).

Silberberg, Y.

H. A. Haus and Y. Silberberg, “Laser Mode Locking with Addition of Nonlinear Index,” IEEE J. Quantum Electron. QE-22, 1048–1060 (1986).

Sivco, D. 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]

C. Gmachl, A. Straub, R. Colombelli, D. L. Sivco, F. Capasso, and A. Y. Cho, “Minimal Group Refractive Index Dispersion and Gain Evolution in Ultra-Broad-Band Quantum Cascade Lasers,” IEEE Photon. Technol. Lett. 14, 1671–1673 (2002).
[Crossref]

Soibel, A.

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]

Straub, A.

C. Gmachl, A. Straub, R. Colombelli, D. L. Sivco, F. Capasso, and A. Y. Cho, “Minimal Group Refractive Index Dispersion and Gain Evolution in Ultra-Broad-Band Quantum Cascade Lasers,” IEEE Photon. Technol. Lett. 14, 1671–1673 (2002).
[Crossref]

Svico, D. L.

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Svico, 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. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

Troccoli, M.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

Wang, C. Y.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

Yan, L.

W. Lu, L. Yan, and C. R. Menyuk, “Dispersion Effects in an Actively Mode-Locked Inhomogeneously Broadened Laser,” IEEE J. Quantum Electron. QE-22, 1317–1324 (2002).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics, (WILEY, New York, 1989).

Zhu, J.

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

Appl. Phys. Lett. (4)

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Svico, 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]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Lee, B. G. Höfler, C. Y. Wang, M. Troccoli, and F. Capasso, “Pulsed- and Continuous-Mode Operation at High Temperature of Strained Quantum-Cascade Lasers Grown by Metalorganic Vapor Phase Epitaxy,” Appl. Phys. Lett. 88, 2011151–2011515 (2006).
[Crossref]

L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Lončar, M. Troccoli, and F. Capasso, “High-Power Quantum Cascade Lasers Grown by Low-Pressure Metal Organic Vapor-Phase Epitaxy Operating Continuous Wave Above 400 K,” Appl. Phys. Lett. 88, 0411021–0411023 (2006).

R. Maulini, M. Beck, J. Faist, and E. Gini, “Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers,” Appl. Phys. Lett. 84, 1659–1661 (2004).
[Crossref]

Electron. Lett. (1)

M. P. Kesler and E. P. Ippen, “Femtosecond Time-Domain Measurements of Group Velocity Dispersion in Al-GaAs Diode Lasers,” Electron. Lett. 25, 640–642 (1989).
[Crossref]

IEEE J. Lightwave Technol. (1)

M. P. Kesler and E. P. Ippen, “Femtosecond Time-Domain Measurements of Group Velocity Dispersion in Diode Lasers at 1.5µm,” IEEE J. Lightwave Technol. 10, 616–619 (1992).
[Crossref]

IEEE J. Quantum Electron. (5)

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]

G. P. Agrawal, “Effect of Gain Dispersion on Ultrashort Pulse Amplification,” IEEE J. Quantum Electron. 27, 1843–1849 (1991).
[Crossref]

H. A. Haus and Y. Silberberg, “Laser Mode Locking with Addition of Nonlinear Index,” IEEE J. Quantum Electron. QE-22, 1048–1060 (1986).

W. Lu, L. Yan, and C. R. Menyuk, “Dispersion Effects in an Actively Mode-Locked Inhomogeneously Broadened Laser,” IEEE J. Quantum Electron. QE-22, 1317–1324 (2002).
[Crossref]

J. Shah, “Ultrafast Luminescence Spectroscopy Using Sum Frequency Generation,” IEEE J. Quantum Electron. 24, 276–288 (1988).
[Crossref]

IEEE Photon. Technol. Lett. (2)

D. Hofstetter and J. Faist, “Measurement of Semiconductor Laser Gain and Dispersion Curves Utilizing Fourier Transforms of the Emission Spectra,” IEEE Photon. Technol. Lett. 11, 1372–1374 (1999).
[Crossref]

C. Gmachl, A. Straub, R. Colombelli, D. L. Sivco, F. Capasso, and A. Y. Cho, “Minimal Group Refractive Index Dispersion and Gain Evolution in Ultra-Broad-Band Quantum Cascade Lasers,” IEEE Photon. Technol. Lett. 14, 1671–1673 (2002).
[Crossref]

J. Opt. Soc. Am. B (1)

Phys. Rev. A (1)

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent Instabilities in a Semiconductor Laser with Fast Gain Recovery,” Phys. Rev. A 75, 031802-1–031802-4 (2007).
[Crossref]

Science (1)

R. Paiella, F. Capasso, C. Gmachl, D. L. Svico, J. N. Bailargeon, A. L. Hutchinson, and A. Y. Cho, “Self-Mode-locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science 290, 1739–1742 (2000).
[Crossref] [PubMed]

Other (3)

E. D. Palik, Handbook of optical constants of solids, (Academic Press, New York, 1985).

A. Yariv, Quantum Electronics, (WILEY, New York, 1989).

A. Siegman, Lasers, (University Science Books, Sausalito, California, 1986).

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Figures (10)

Fig. 1.
Fig. 1.

CW L-I-V characteristics of the D3281 QCL at 30 K. Inset: lasing spectrum (~5 µm) at the bias current of 0.14 A. Note that all the upconversion experiments for the GVD have been done below threshold (0.12 A at 30K) to prevent the device’s self-heating and also to minimize the optical feedback effect.

Fig. 2.
Fig. 2.

Experimental setup for the GVD measurements in a QCL. Transmitted mid-IR pulse is upconverted with 800-nm pulse to detect the sum frequency photon.

Fig. 3.
Fig. 3.

(a) Typical cross-correlation trace of mid-IR pulse at 5 µm, showing the intensity FWHM of ~220 fs. (b) Spectrally tunable mid-IR pulses are used to measure the mid-IR peak wavelength dependent pulse transit time.

Fig. 4.
Fig. 4.

(a) An example of a time-resolved upconversion trace is displayed for a QCL bias current of 0.12 A. (b) The upconversion signal at the reference time delay, i.e. time-zero delay, is shown for center wavelengths 4.92 µm (dashed) and 5.12 µm (solid). (c) Upconversion signals for two different center wavelengths are shown, illustrating the shift in pulse group delay with wavelength.

Fig. 5.
Fig. 5.

(a) The measured propagation delays (filled squares) are displayed as a function of the peak wavelength of the injected mid-IR pulse. A third-order polynomial fit (dashed line) to the measured delays is used to calculate GVD parameter β2 via Eqs. 2–3. (b) Assuming the mid-IR pulse as a Gaussian, the intensity FWHM of reference pulses (filled circles) and that of transmitted mid-IR pulses (filled upper triangles) are shown as a function of wavelength. The error bars from the chi-squared determined errors (~± 5 fs) are due to the long-term intensity fluctuation of our femtosecond laser sources.

Fig. 6.
Fig. 6.

(a) Effective refractive index vs. wavelength curve. The dashed line is a polynomial fit of the calculated discrete points. (b) The corresponding refractive index dispersion dn/ is shown as a function of wavelength.

Fig. 7.
Fig. 7.

Electroluminescence spectrum (D3281, solid line) without the laser cavity was measured at 30 K in order to determine the gain spectrum and thus the dispersion via the Kramers-Kronig relations. For simplicity, the spectrum was approximated by a Lorentzian line shape; the fit to the gain spectrum and the resulting dispersion are shown.

Fig. 8.
Fig. 8.

Calculated refractive index based on the Eq. 8 is displayed for three different values of the population inversion ΔN.

Fig. 9.
Fig. 9.

Calculated index dispersion dn/ and β 2 (using Eq. 45) only due to the small-signal gain are displayed in (a) and (b), respectively.

Fig. 10.
Fig. 10.

(a) Contributions to the total GVD are separately displayed. Filled squares are the total β2 (=d 2 β/d ω 2) from the upconversion measurements of Fig. 5(a). The material and waveguide dispersion (see Fig. 6) are shown as the dashed line, the gain dispersion (see Fig. 9) is as the dotted line, and total dispersion (sum of material, waveguide, and gain dispersion) is displayed as the solid line. (b) Corresponding pulse broadening, FWHM ratio τp /τp 0, is displayed. Filled squares are from the upconversion measurements and dashed line is from the total GVD calculations.

Equations (8)

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τ delay = L v g = L c n g
d n g d λ = c L d τ delay d λ
β 2 = d 2 β d ω 2 = d λ d ω d d λ ( 1 v g ) = λ 2 2 π c L d τ delay d λ
v g = c ( n λ d n d λ ) 1
β 2 = d 2 β d ω 2 = d λ d ω d d λ ( 1 v g ) = λ 3 2 π c 2 d 2 n d λ 2
χ " ( v ) = e 2 z if 2 Δ N 2 ε 0 h ̅ Δ v 2 π ( v v 0 ) 2 + ( Δ v 2 ) 2
χ ' ( v ) = e 2 z if 2 ( ω 0 ω ) T 2 Δ N 2 ε 0 h ̅ Δ v 2 π ( v v 0 ) 2 + ( Δ v 2 ) 2
n = Re ( ε b + ε 0 χ )

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