Abstract

Microscopic density matrix analysis on the linewidth enhancement factor (LEF) of both mid-infrared (mid-IR) and Terahertz (THz) quantum cascade lasers (QCLs) is reported, taking into account of the many body Coulomb interactions, coherence of resonant-tunneling transport and non-parabolicity. A non-zero LEF at the gain peak is obtained due to these combined microscopic effects. The results show that, for mid-IR QCLs, the many body Coulomb interaction and non-parabolicity contribute greatly to the non-zero LEF. In contrast, for THz QCLs, the many body Coulomb interactions and the resonant-tunneling effects greatly influence the LEF resulting in a non-zero value at the gain peak. This microscopic model not only partially explains the non-zero LEF of QCLs at the gain peak, which observed in the experiments for a while but cannot be explicitly explained, but also can be employed to improve the active region designs so as to reduce the LEF by optimizing the corresponding parameters.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]
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2013 (1)

T. Chattopadhyay and P. Bhattacharyya, “Role of linewidth enhancement factor on the frequency response of the synchronized quantum cascade laser,” Opt. Commun.309, 349–354 (2013).
[CrossRef]

2012 (2)

2010 (1)

E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density-matrix model applied to three-well terahertz quantum cascade lasers,” Phys. Rev. B81(20), 205311 (2010).
[CrossRef]

2009 (1)

S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B80(24), 245316 (2009).
[CrossRef]

2008 (2)

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

2007 (1)

S. Panda, B. K. Panda, and S. Fung, “Effect of conduction band nonparabolicity on the dark current in a quantum well infrared detector,” J. Appl. Phys.101(4), 043705 (2007).
[CrossRef]

2006 (2)

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

J. von Staden, T. Gensty, W. Elsässer, G. Giuliani, and C. Mann, “Measurements of the α factor of a distributed-feedback quantum cascade laser by an optical feedback self-mixing technique,” Opt. Lett.31(17), 2574–2576 (2006).
[CrossRef] [PubMed]

2004 (1)

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

2003 (1)

M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Linewidth enhancement factor of a type-I quantum-cascade laser,” J. Appl. Phys.94(8), 5426–5428 (2003).
[CrossRef]

2002 (1)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

2000 (1)

1998 (1)

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science264(5158), 553–556 (1994).
[CrossRef] [PubMed]

1989 (1)

U. Ekenberg, “Nonparabolicity effects in a quantum well: sublevel shift, parallel mass, and Landau levels,” Phys. Rev. B Condens. Matter40(11), 7714–7726 (1989).
[CrossRef] [PubMed]

1987 (1)

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor-lasers - an overview,” IEEE J. Quantum Electron.23(1), 9–29 (1987).
[CrossRef]

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor-lasers,” IEEE J. Quantum Electron.18(2), 259–264 (1982).
[CrossRef]

Aellen, T.

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

Akikusa, N.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

Baillargeon, J. N.

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “High-power, continuous-wave, current-tunable, single-mode quantum-cascade distributed-feedback lasers at lambda ~5.2 and lambda ~7.95 μm,” Opt. Lett.25(4), 230–232 (2000).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

Ban, D.

Beere, H. E.

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Beltram, F.

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Bhattacharyya, P.

T. Chattopadhyay and P. Bhattacharyya, “Role of linewidth enhancement factor on the frequency response of the synchronized quantum cascade laser,” Opt. Commun.309, 349–354 (2013).
[CrossRef]

Blaser, S.

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

Buus, J.

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor-lasers - an overview,” IEEE J. Quantum Electron.23(1), 9–29 (1987).
[CrossRef]

Capasso, F.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Linewidth enhancement factor of a type-I quantum-cascade laser,” J. Appl. Phys.94(8), 5426–5428 (2003).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “High-power, continuous-wave, current-tunable, single-mode quantum-cascade distributed-feedback lasers at lambda ~5.2 and lambda ~7.95 μm,” Opt. Lett.25(4), 230–232 (2000).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Chan, C. W. I.

Chattopadhyay, T.

T. Chattopadhyay and P. Bhattacharyya, “Role of linewidth enhancement factor on the frequency response of the synchronized quantum cascade laser,” Opt. Commun.309, 349–354 (2013).
[CrossRef]

Cho, A. Y.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Linewidth enhancement factor of a type-I quantum-cascade laser,” J. Appl. Phys.94(8), 5426–5428 (2003).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “High-power, continuous-wave, current-tunable, single-mode quantum-cascade distributed-feedback lasers at lambda ~5.2 and lambda ~7.95 μm,” Opt. Lett.25(4), 230–232 (2000).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Chu, S. N. G.

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

Chuang, S. L.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Linewidth enhancement factor of a type-I quantum-cascade laser,” J. Appl. Phys.94(8), 5426–5428 (2003).
[CrossRef]

Davies, A. G.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Dupont, E.

Edamura, T.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

Ekenberg, U.

U. Ekenberg, “Nonparabolicity effects in a quantum well: sublevel shift, parallel mass, and Landau levels,” Phys. Rev. B Condens. Matter40(11), 7714–7726 (1989).
[CrossRef] [PubMed]

Elsässer, W.

Faist, J.

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Fathololoumi, S.

Fung, S.

S. Panda, B. K. Panda, and S. Fung, “Effect of conduction band nonparabolicity on the dark current in a quantum well infrared detector,” J. Appl. Phys.101(4), 043705 (2007).
[CrossRef]

Gensty, T.

Giovannini, M.

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

Giuliani, G.

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

J. von Staden, T. Gensty, W. Elsässer, G. Giuliani, and C. Mann, “Measurements of the α factor of a distributed-feedback quantum cascade laser by an optical feedback self-mixing technique,” Opt. Lett.31(17), 2574–2576 (2006).
[CrossRef] [PubMed]

Gmachl, C.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Linewidth enhancement factor of a type-I quantum-cascade laser,” J. Appl. Phys.94(8), 5426–5428 (2003).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “High-power, continuous-wave, current-tunable, single-mode quantum-cascade distributed-feedback lasers at lambda ~5.2 and lambda ~7.95 μm,” Opt. Lett.25(4), 230–232 (2000).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

Green, R. P.

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

Henry, C. H.

C. H. Henry, “Theory of the linewidth of semiconductor-lasers,” IEEE J. Quantum Electron.18(2), 259–264 (1982).
[CrossRef]

Hoyler, N.

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

Hu, Q.

Hutchinson, A. L.

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “High-power, continuous-wave, current-tunable, single-mode quantum-cascade distributed-feedback lasers at lambda ~5.2 and lambda ~7.95 μm,” Opt. Lett.25(4), 230–232 (2000).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Hvozdara, L.

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

Iotti, R. C.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Ishihara, M.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

Jirauschek, C.

Kasahara, K.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

Kim, J.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

Köhler, R.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Kumar, S.

S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B80(24), 245316 (2009).
[CrossRef]

Kumazaki, N.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

Laframboise, S. R.

Lee, K. E.

T. Liu, K. E. Lee, and Q. J. Wang, “Microscopic density matrix model for optical gain of terahertz quantum cascade lasers: Many-body, nonparabolicity, and resonant tunneling effects,” Phys. Rev. B86(23), 235306 (2012).
[CrossRef]

Lerttamrab, M.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Linewidth enhancement factor of a type-I quantum-cascade laser,” J. Appl. Phys.94(8), 5426–5428 (2003).
[CrossRef]

Linfield, E. H.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Liu, H. C.

Liu, T.

T. Liu, K. E. Lee, and Q. J. Wang, “Microscopic density matrix model for optical gain of terahertz quantum cascade lasers: Many-body, nonparabolicity, and resonant tunneling effects,” Phys. Rev. B86(23), 235306 (2012).
[CrossRef]

Mahler, L.

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

Mann, C.

Mátyás, A.

Maulini, R.

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

Osinski, M.

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor-lasers - an overview,” IEEE J. Quantum Electron.23(1), 9–29 (1987).
[CrossRef]

Panda, B. K.

S. Panda, B. K. Panda, and S. Fung, “Effect of conduction band nonparabolicity on the dark current in a quantum well infrared detector,” J. Appl. Phys.101(4), 043705 (2007).
[CrossRef]

Panda, S.

S. Panda, B. K. Panda, and S. Fung, “Effect of conduction band nonparabolicity on the dark current in a quantum well infrared detector,” J. Appl. Phys.101(4), 043705 (2007).
[CrossRef]

Ritchie, D. A.

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Rossi, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Sivco, D. L.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Linewidth enhancement factor of a type-I quantum-cascade laser,” J. Appl. Phys.94(8), 5426–5428 (2003).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “High-power, continuous-wave, current-tunable, single-mode quantum-cascade distributed-feedback lasers at lambda ~5.2 and lambda ~7.95 μm,” Opt. Lett.25(4), 230–232 (2000).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Sugiyama, A.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

Takagi, Y.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

Terazzi, R.

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

Tredicucci, A.

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “High-power, continuous-wave, current-tunable, single-mode quantum-cascade distributed-feedback lasers at lambda ~5.2 and lambda ~7.95 μm,” Opt. Lett.25(4), 230–232 (2000).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

von Staden, J.

Wang, Q. J.

T. Liu, K. E. Lee, and Q. J. Wang, “Microscopic density matrix model for optical gain of terahertz quantum cascade lasers: Many-body, nonparabolicity, and resonant tunneling effects,” Phys. Rev. B86(23), 235306 (2012).
[CrossRef]

Wasilewski, Z. R.

Xu, J. H.

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

Appl. Phys. Lett. (4)

R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
[CrossRef]

T. Aellen, R. Maulini, R. Terazzi, N. Hoyler, M. Giovannini, J. Faist, S. Blaser, and L. Hvozdara, “Direct measurement of the linewidth enhancement factor by optical heterodyning of an amplitude-modulated quantum cascade laser,” Appl. Phys. Lett.89(9), 091121 (2006).
[CrossRef]

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett.92(12), 121104 (2008).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ≈8.5 μm,” Appl. Phys. Lett.72(12), 1430–1432 (1998).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor-lasers - an overview,” IEEE J. Quantum Electron.23(1), 9–29 (1987).
[CrossRef]

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers,” IEEE J. Quantum Electron.40(12), 1663–1674 (2004).
[CrossRef]

C. H. Henry, “Theory of the linewidth of semiconductor-lasers,” IEEE J. Quantum Electron.18(2), 259–264 (1982).
[CrossRef]

J. Appl. Phys. (2)

M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, “Linewidth enhancement factor of a type-I quantum-cascade laser,” J. Appl. Phys.94(8), 5426–5428 (2003).
[CrossRef]

S. Panda, B. K. Panda, and S. Fung, “Effect of conduction band nonparabolicity on the dark current in a quantum well infrared detector,” J. Appl. Phys.101(4), 043705 (2007).
[CrossRef]

Nature (1)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

T. Chattopadhyay and P. Bhattacharyya, “Role of linewidth enhancement factor on the frequency response of the synchronized quantum cascade laser,” Opt. Commun.309, 349–354 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (3)

T. Liu, K. E. Lee, and Q. J. Wang, “Microscopic density matrix model for optical gain of terahertz quantum cascade lasers: Many-body, nonparabolicity, and resonant tunneling effects,” Phys. Rev. B86(23), 235306 (2012).
[CrossRef]

E. Dupont, S. Fathololoumi, and H. C. Liu, “Simplified density-matrix model applied to three-well terahertz quantum cascade lasers,” Phys. Rev. B81(20), 205311 (2010).
[CrossRef]

S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B80(24), 245316 (2009).
[CrossRef]

Phys. Rev. B Condens. Matter (1)

U. Ekenberg, “Nonparabolicity effects in a quantum well: sublevel shift, parallel mass, and Landau levels,” Phys. Rev. B Condens. Matter40(11), 7714–7726 (1989).
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Science (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science264(5158), 553–556 (1994).
[CrossRef] [PubMed]

Other (1)

W. W. Chow, S. W. Koch, and M. S. I. I. I. Semiconductor-Laser Physics, (Springer-Verlag, Berlin, 1994).

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