Abstract

We study the time dependence of the optical power emitted by terahertz and mid-IR quantum cascade lasers in presence of optical reinjection and demonstrate unprecedented continuous wave (CW) emission stability for strong feedback. We show that the absence of coherence collapse or other CW instabilities typical of diode lasers is inherently associated with the high value of the photon to carrier lifetime ratio and the negligible linewidth enhancement factor of quantum cascade lasers.

© 2013 OSA

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  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]
  2. 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]
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    [CrossRef]
  4. M. S. Vitiello and A. Tredicucci, “Tunable emission in a THz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol.1(1), 76–84 (2011).
    [CrossRef]
  5. M. Tonouchi, “Cutting edge terahertz technology,” Nat. Photonics1(2), 97–105 (2007).
    [CrossRef]
  6. R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
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  8. R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
    [CrossRef]
  9. S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
    [CrossRef]
  10. C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express17(15), 12929–12943 (2009).
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  11. N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
    [CrossRef] [PubMed]
  12. A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
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  13. 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,” Science290(5497), 1739–1742 (2000).
    [CrossRef] [PubMed]
  14. L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
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  15. J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
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  18. Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
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  20. F. P. Mezzapesa, V. Spagnolo, A. Antonio, and G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett.101(17), 171107 (2012).
    [CrossRef]
  21. J. Helms and K. Petermann, “A simple analytic expression for the stable operation range of laser diodes with optical feedback,” IEEE J. Quantum Electron.26(5), 833–836 (1990).
    [CrossRef]
  22. 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]
  23. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16(3), 347–355 (1980).
    [CrossRef]
  24. R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol.4(11), 1655–1661 (1986).
    [CrossRef]
  25. B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability Analysis for a Semiconductor Laser in an External Cavity,” IEEE J. Quantum Electron.20(9), 1023–1032 (1984).
    [CrossRef]
  26. M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
    [CrossRef]
  27. M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
    [CrossRef]
  28. D. Weidmann, K. Smith, and B. Ellison, “Experimental investigation of high-frequency noise and optical feedback effects using a 9.7 microm continuous-wave distributed-feedback quantum-cascade laser,” Appl. Opt.46(6), 947–953 (2007).
    [CrossRef] [PubMed]

2012

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

M. C. Phillips and M. S. Taubman, “Intracavity sensing via compliance voltage in an external cavity quantum cascade laser,” Opt. Lett.37(13), 2664–2666 (2012).
[CrossRef] [PubMed]

F. P. Mezzapesa, V. Spagnolo, A. Antonio, and G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett.101(17), 171107 (2012).
[CrossRef]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[CrossRef]

2011

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

M. S. Vitiello and A. Tredicucci, “Tunable emission in a THz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol.1(1), 76–84 (2011).
[CrossRef]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

2010

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

2009

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

2008

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
[CrossRef]

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]

2007

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics1(9), 517–525 (2007).
[CrossRef]

D. Weidmann, K. Smith, and B. Ellison, “Experimental investigation of high-frequency noise and optical feedback effects using a 9.7 microm continuous-wave distributed-feedback quantum-cascade laser,” Appl. Opt.46(6), 947–953 (2007).
[CrossRef] [PubMed]

M. Tonouchi, “Cutting edge terahertz technology,” Nat. Photonics1(2), 97–105 (2007).
[CrossRef]

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
[CrossRef]

2002

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]

2001

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[CrossRef]

2000

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,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

1994

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]

1990

J. Helms and K. Petermann, “A simple analytic expression for the stable operation range of laser diodes with optical feedback,” IEEE J. Quantum Electron.26(5), 833–836 (1990).
[CrossRef]

1986

R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol.4(11), 1655–1661 (1986).
[CrossRef]

1984

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability Analysis for a Semiconductor Laser in an External Cavity,” IEEE J. Quantum Electron.20(9), 1023–1032 (1984).
[CrossRef]

1980

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16(3), 347–355 (1980).
[CrossRef]

Akikusa, N.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
[CrossRef]

Antonio, A.

F. P. Mezzapesa, V. Spagnolo, A. Antonio, and G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett.101(17), 171107 (2012).
[CrossRef]

Baillargeon, J. N.

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[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,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

Barbieri, S.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

Bartalini, S.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[CrossRef]

Bartolini, P.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

Beere, H. E.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

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]

Belkin, M. A.

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]

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. Express17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Bour, D.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Calligaro, M.

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
[CrossRef]

Cancio, P.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

Capasso, F.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[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,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

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]

Cho, A. Y.

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[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,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

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]

Chraplyvy, A. R.

R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol.4(11), 1655–1661 (1986).
[CrossRef]

Consolino, L.

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[CrossRef]

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

Corzine, S.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Crozier, K. B.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

Cubukcu, E.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

Curl, R. F.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Darmo, J.

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
[CrossRef]

Davies, A. G.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[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]

De Natale, P.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[CrossRef]

Dean, P.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Dhillon, S.

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (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. Express17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Edamura, T.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
[CrossRef]

Ellison, B.

Faist, J.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[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]

Fujita, K.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
[CrossRef]

Gellie, P.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[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]

Gkortsas, V. M.

Gmachl, C.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[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,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

Gordon, A.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Grant, P.

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]

Haffouz, S.

Ham, D.

Harrison, P.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Helms, J.

J. Helms and K. Petermann, “A simple analytic expression for the stable operation range of laser diodes with optical feedback,” IEEE J. Quantum Electron.26(5), 833–836 (1990).
[CrossRef]

Höfler, G.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Hutchinson, A. L.

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Self-Mode-Locking of Quantum Cascade Lasers with Giant Ultrafast Optical Nonlinearities,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

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]

Hwang, H. Y.

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[CrossRef]

Ikonic, Z.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Indjin, D.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Inguscio, M.

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[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]

Kan, H.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
[CrossRef]

Kärtner, F. X.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Khanna, S. P.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

Kliese, R.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16(3), 347–355 (1980).
[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]

Kosterev, A. A.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Kroll, J.

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
[CrossRef]

Kuznetsova, L.

Lachab, M.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16(3), 347–355 (1980).
[CrossRef]

Lewicki, R.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Li, X.

Lim, Y. L.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Linfield, E.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Linfield, E. H.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

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]

Linfield, H.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

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. Express17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[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,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

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]

Maier, T.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Manquest, C.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

Marcadet, X.

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
[CrossRef]

Martini, R.

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[CrossRef]

Mc Manus, B.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Mezzapesa, F. P.

F. P. Mezzapesa, V. Spagnolo, A. Antonio, and G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett.101(17), 171107 (2012).
[CrossRef]

Nikolic, M.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Olesen, H.

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability Analysis for a Semiconductor Laser in an External Cavity,” IEEE J. Quantum Electron.20(9), 1023–1032 (1984).
[CrossRef]

Osmundsen, J. H.

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability Analysis for a Semiconductor Laser in an External Cavity,” IEEE J. Quantum Electron.20(9), 1023–1032 (1984).
[CrossRef]

Paiella, R.

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[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,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

Petermann, K.

J. Helms and K. Petermann, “A simple analytic expression for the stable operation range of laser diodes with optical feedback,” IEEE J. Quantum Electron.26(5), 833–836 (1990).
[CrossRef]

Phillips, M. C.

Pusharsky, M.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Rakic, A. D.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Ravaro, M.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

Ritchie, D. A.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

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]

Santarelli, G.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

Scamarcio, G.

F. P. Mezzapesa, V. Spagnolo, A. Antonio, and G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett.101(17), 171107 (2012).
[CrossRef]

Schneider, H.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Sirtori, C.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
[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]

Sivco, D. L.

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[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,” Science290(5497), 1739–1742 (2000).
[CrossRef] [PubMed]

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]

Smith, K.

Song, C. Y.

Spagnolo, V.

F. P. Mezzapesa, V. Spagnolo, A. Antonio, and G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett.101(17), 171107 (2012).
[CrossRef]

Taschin, A.

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[CrossRef]

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

Taubman, M. S.

Tittel, F. K.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Tkach, R. W.

R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol.4(11), 1655–1661 (1986).
[CrossRef]

Tonouchi, M.

M. Tonouchi, “Cutting edge terahertz technology,” Nat. Photonics1(2), 97–105 (2007).
[CrossRef]

Torre, R.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

Tredicucci, A.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[CrossRef]

M. S. Vitiello and A. Tredicucci, “Tunable emission in a THz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol.1(1), 76–84 (2011).
[CrossRef]

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]

Troccoli, M.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Tromborg, B.

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability Analysis for a Semiconductor Laser in an External Cavity,” IEEE J. Quantum Electron.20(9), 1023–1032 (1984).
[CrossRef]

Unterrainer, K.

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
[CrossRef]

Valavanis, A.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett.36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Vitiello, M. S.

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[CrossRef]

M. S. Vitiello and A. Tredicucci, “Tunable emission in a THz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol.1(1), 76–84 (2011).
[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. Express17(15), 12929–12943 (2009).
[CrossRef] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A77(5), 053804 (2008).
[CrossRef]

Wasilewski, Z. R.

Weidmann, D.

Whittaker, E. A.

R. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[CrossRef]

Williams, B. S.

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics1(9), 517–525 (2007).
[CrossRef]

Wilson, S. J.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

Wojcik, A. K.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

Wysocki, G.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

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]

Yamanishi, M.

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
[CrossRef]

Yu, N.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett.99(8), 081108 (2011).
[CrossRef]

F. P. Mezzapesa, V. Spagnolo, A. Antonio, and G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett.101(17), 171107 (2012).
[CrossRef]

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. Paiella, R. Martini, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, E. A. Whittaker, and H. C. Liu, “High-frequency modulation without the relaxation oscillation resonance in quantum cascade lasers,” Appl. Phys. Lett.79(16), 2526–2528 (2001).
[CrossRef]

J. Kroll, J. Darmo, K. Unterrainer, S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, “Longitudinal spatial hole burning in terahertz quantum cascade lasers,” Appl. Phys. Lett.91(16), 161108 (2007).
[CrossRef]

Chem. Phys. Lett.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. Mc Manus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
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IEEE J. Quantum Electron.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16(3), 347–355 (1980).
[CrossRef]

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability Analysis for a Semiconductor Laser in an External Cavity,” IEEE J. Quantum Electron.20(9), 1023–1032 (1984).
[CrossRef]

M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
[CrossRef]

J. Helms and K. Petermann, “A simple analytic expression for the stable operation range of laser diodes with optical feedback,” IEEE J. Quantum Electron.26(5), 833–836 (1990).
[CrossRef]

IEEE Trans. Terahertz Sci. Technol.

M. S. Vitiello and A. Tredicucci, “Tunable emission in a THz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol.1(1), 76–84 (2011).
[CrossRef]

J. Lightwave Technol.

R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol.4(11), 1655–1661 (1986).
[CrossRef]

Nat Commun

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat Commun3, 1040 (2012).
[CrossRef] [PubMed]

Nat. Photonics

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics1(9), 517–525 (2007).
[CrossRef]

M. Tonouchi, “Cutting edge terahertz technology,” Nat. Photonics1(2), 97–105 (2007).
[CrossRef]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
[CrossRef]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics6(8), 525–528 (2012).
[CrossRef]

Nature

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).
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Opt. Lett.

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Phys. Rev. Lett.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, and F. Capasso, “Coherent Coupling of Multiple Transverse Modes in Quantum Cascade Lasers,” Phys. Rev. Lett.102(1), 013901 (2009).
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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,” Science290(5497), 1739–1742 (2000).
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Figures (4)

Fig. 1
Fig. 1

Schematic layout of the experimental configuration. The THz QCL radiation is focused on the external target (a metallic mirror) and re-injected into the laser cavity. The inset shows the equivalent configuration with a mid-IR QCL or a conventional laser diode (LD). ND: neutral density filter. TPX foils are used as attenuator with QCLs.

Fig. 2
Fig. 2

Normalized FFT (Blackman window weighting approximation) of representative oscilloscope traces showing the time dependence of the SM signals detected by: (a) voltage modulation at the THz QCL terminals; (b) voltage modulation at the mid-IR QCL terminals; (c)-(d) LD integrated photodiode. Figure 2(a): stable CW emission of THz QCL subject to the maximum feedback strength, i.e. for k = 7.5 × 10−2. Figure 2(b): stable CW operation of the mid-IR QCL at the maximum feedback strength, i.e. for k = 6.8 × 10−2. Figures 2(c) and 2(d): coherence collapse (k = 1.1 × 10−3) and stable CW emission (k = 0.8 × 10−3) in a diode laser, respectively.

Fig. 3
Fig. 3

Results of LSA from the numerical solution of Eq. (5), coinciding with the Eq. (7) for γ >> 1. In Fig. 3(a) we plot the critical kC vs γ obtained for typical laser diode parameters (i.e. α = 5; τc = 3.8 ps; τp = 3.3 ps; λLD = 832 nm; L = 14 mm). For γ < 1, the critical feedback level monotonically increases; these instabilities are associated to undamped relaxation oscillations, as representatively shown in Fig. 3(b) for γ = 0.01 and Ip = 2.5 (note that the pump threshold is (Ip)th = 1): the undamped relaxation frequency is ωr ≈35 GHz. For γ > 1, the critical feedback level saturates at kC = 0.045, beyond which the unstable regime is due to external cavity mode competition, as representatively shown in Figs. 3(c) and 3(d) for γ = 10 and Ip = 1.5: the beating frequencies are at multiples of ω1 ≈60 GHz (panel c) and ω2 ≈6 GHz (panel d) for an external cavity length of 14 and 140 mm, respectively. In the latter case, i.e. for ω2 ≈6 GHz, ten external modes are present in the frequency range covering one free spectral range of the former case, as expected.

Fig. 4
Fig. 4

THz QCL ultra stability under optical re-injection: results of numerical simulations. Figure 4(a): minimum feedback strength for the onset of CW instability vs α for realistic parameters of a THz QCL. The critical feedback level increases with decreasing α up to kmax = τc/2τp = 0.58, corresponding to a critical linewidth enhancement factor (αC). Ultra stable dynamics under optical re-injection are predicted for α < αC. Figure 4(b): plot of αC vs the external cavity round trip time (τ = 2L/c). The other parameters are: γ = 10; τc = 37.4 ps; τp = 32.4 ps; λTHz-QCL = 76 μm; L = 140 mm.

Equations (13)

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dE(t) dt = 1 2 (1+iα)(N(t)1)E(t)+ k τ p τ c E(tτ) e i ω 0 τ
dN(t) dt =γ[ I p N(t)(1+ | E(t) | 2 )]
N S =12k τ p τ c cos( ω F τ); | E S | 2 = I p N S 1; ω F = ω 0 (k τ p τ c )[αcos( ω F τ)+sin( ω F τ)]
( I p I ps ) th =(2k τ p τ c )cos( ω F τ)
λ 3 + a 2 (λ) λ 2 + a 1 (λ)λ+ a 0 (λ)=0
a 2 =γ I p N S +2 k τ p τ c (1 e λτ )cos( ω F τ)
a 1 =γ[ 2 I p k τ p N S τ c (1 e λτ )cos( ω F τ)+ E S 2 N S ]+ [ k τ p τ c (1 e λτ ) ] 2
a 0 =γ{ [ E S 2 N S k τ p τ c (1 e λτ )[cos( ω F τ)αsin( ω F τ)]+ I p N S [ k τ p τ c (1 e λτ ) ] 2 }
λ 2 + b 1 (λ)λ+ b 0 (λ)=0
b 1 =2 k τ p τ c (1 e λτ )cos( ω F τ)+ E S 2 N S 2 I p
b 0 = E S 2 N S 2 k τ p I p τ c (1 e λτ )[cos( ω F τ)αsin( ω F τ)]+ [ k τ p τ c (1 e λτ ) ] 2
k=ε R ext R (1R)
P P = 2πf(f f 2 (D/2) 2 ) 2π f 2 =0.21P

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