Abstract

We present an experimental investigation of the multimode dynamics and the coherence of terahertz quantum cascade lasers emitting over a spectral bandwidth of ~1THz. The devices are studied in free-running and under direct RF modulation. Depending on the pump current we observe different regimes of operation, where RF spectra displaying single and multiple narrow beat-note signals alternate with spectra showing a single beat-note characterized by an intense phase-noise, extending over a bandwidth up to a few GHz. We investigate the relation between this phase-noise and the dynamics of the THz modes through the electro-optic sampling of the laser emission. We find that when the phase-noise is large, the laser operates in an unstable regime where the lasing modes are incoherent. Under RF modulation of the laser current such instability can be suppressed and the modes coherence recovered, while, simultaneously, generating a strong broadening of the THz emission spectrum.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  26. M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
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  28. W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
    [Crossref]
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    [Crossref] [PubMed]
  30. S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
    [Crossref]
  31. Water absorption dips are probably due to the fact that a small fraction (~5%) of the optical path, from the QCL to the cryostat window, was not evacuated but only purged with dried air.
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    [Crossref]
  35. We exclude the fact that multiple RF beatnotes are due to the presence of higher order lateral modes inside the waveguide. Indeed, using a finite element code, we found that for the present ridge waveguide higher order modes present much larger propagation losses compared to the fundamental one. We also measured the laser far field and found no clear evidence of the presence of higher order modes.
  36. S. Bennet, C. M. Snowden, and S. Iezekiel, “Non-linear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum, Electron 33(11), 2076–2083 (1997).
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  38. D. M. Kane and K. A. Shore, Unlocking dynamical diversity: optical feedback effects on semiconductor lasers, (John Wiley & Sons, Chichester, West Sussex, England, 2005).
  39. In support of this hypothesis we note that for sidebands located symmetrically on different sides of the RF modulation we recorded the same broadening using the Max Hold function of the spectrum Analyzer (data not shown). This is expected since the phase noise of the RF modulation is negligible.
  40. We found that when the EO crystal was perpendicular to the beam axis, changing the distance between the crystal and the QCL produced a shift of the THz modes, hence of the beat-notes in the DCE spectra. This was not the case when the crystal was tilted at 45deg, indicating a considerable reduction of the feedback.
  41. J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
    [Crossref] [PubMed]

2015 (2)

2014 (8)

L. L. Columbo and M. Brambilla, “Multimode regimes in quantum cascade lasers with optical feedback,” Opt. Express 22(9), 10105–10118 (2014).
[Crossref] [PubMed]

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

M. Wienold, B. Röben, L. Schrottke, and H. T. Grahn, “Evidence for frequency comb emission from a Fabry-Pérot terahertz quantum-cascade laser,” Opt. Express 22(25), 30410–30424 (2014).
[Crossref] [PubMed]

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett. 104(8), 081118 (2014).
[Crossref]

2013 (2)

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

C. Sirtori, S. Barbieri, and R. Colombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7(9), 691–701 (2013).
[Crossref]

2012 (4)

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
[Crossref] [PubMed]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

2011 (3)

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011).
[Crossref] [PubMed]

D. Turčinková, G. Scalari, F. Castellano, M. Amanti, M. Beck, and J. Faist, “Ultra-broadband heterogeneous quantum cascade laser emitting from 2.2 to 3.2THz,” Appl. Phys. Lett. 99(19), 191104 (2011).
[Crossref]

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

2010 (3)

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

2009 (2)

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

2008 (2)

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

2007 (3)

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

A. Wei Min Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “High-power and high-temperature THz quantum-cascade lasers based on lens-coupled metal-metal waveguides,” Opt. Lett. 32(19), 2840–2842 (2007).
[Crossref] [PubMed]

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

2004 (1)

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
[Crossref]

1997 (1)

S. Bennet, C. M. Snowden, and S. Iezekiel, “Non-linear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum, Electron 33(11), 2076–2083 (1997).

1991 (1)

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order optical non-linearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59(23), 2932 (1991).
[Crossref]

Akalin, T.

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

Alton, J.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
[Crossref]

Amanti, M.

D. Turčinková, G. Scalari, F. Castellano, M. Amanti, M. Beck, and J. Faist, “Ultra-broadband heterogeneous quantum cascade laser emitting from 2.2 to 3.2THz,” Appl. Phys. Lett. 99(19), 191104 (2011).
[Crossref]

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Andronico, A.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

Auyang, S. Y.

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order optical non-linearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59(23), 2932 (1991).
[Crossref]

Bachmann, D.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

Barbieri, S.

C. Sirtori, S. Barbieri, and R. Colombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7(9), 691–701 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
[Crossref] [PubMed]

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

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
[Crossref]

Bartalini, S.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Bartolini, P.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Beck, M.

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

D. Turčinková, G. Scalari, F. Castellano, M. Amanti, M. Beck, and J. Faist, “Ultra-broadband heterogeneous quantum cascade laser emitting from 2.2 to 3.2THz,” Appl. Phys. Lett. 99(19), 191104 (2011).
[Crossref]

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Beere, H.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

Beere, H. E.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
[Crossref]

Belyanin, 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 instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Bennet, S.

S. Bennet, C. M. Snowden, and S. Iezekiel, “Non-linear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum, Electron 33(11), 2076–2083 (1997).

Bigourd, D.

Blaser, S.

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

Bocquet, R.

Bour, D.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Brambilla, M.

Burghoff, D.

D. Burghoff, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs,” Opt. Express 23(2), 1190–1202 (2015).
[Crossref] [PubMed]

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Cai, X.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Calligaro, M.

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

Cancio, P.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Capasso, F.

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 instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Castellano, F.

D. Turčinková, G. Scalari, F. Castellano, M. Amanti, M. Beck, and J. Faist, “Ultra-broadband heterogeneous quantum cascade laser emitting from 2.2 to 3.2THz,” Appl. Phys. Lett. 99(19), 191104 (2011).
[Crossref]

Cavalie, P.

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

Chan, C. W. I.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Colombelli, R.

C. Sirtori, S. Barbieri, and R. Colombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7(9), 691–701 (2013).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Columbo, L. L.

Consolino, L.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Corzine, S.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Cuisset, A.

Darmo, J.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

Davies, A. G.

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

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

De Natale, P.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

De Pas, M.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Del’Haye, P.

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011).
[Crossref] [PubMed]

Deutsch, C.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

Dhillon, S.

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

Dhillon, S. S.

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

Diehl, L.

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 instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Dikmelik, Y.

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett. 104(8), 081118 (2014).
[Crossref]

Ding, L.

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Faist, J.

G. Villares and J. Faist, “Quantum cascade laser combs: effects of modulation and dispersion,” Opt. Express 23(2), 1651–1669 (2015).
[Crossref] [PubMed]

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett. 104(8), 081118 (2014).
[Crossref]

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

D. Turčinková, G. Scalari, F. Castellano, M. Amanti, M. Beck, and J. Faist, “Ultra-broadband heterogeneous quantum cascade laser emitting from 2.2 to 3.2THz,” Appl. Phys. Lett. 99(19), 191104 (2011).
[Crossref]

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Fertein, E.

Filloux, P.

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

Fischer, M.

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Fowler, J.

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
[Crossref]

Freeman, J. R.

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

Friedli, P.

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

Gallo, P.

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Gao, J.-R.

D. Burghoff, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs,” Opt. Express 23(2), 1190–1202 (2015).
[Crossref] [PubMed]

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Gavartin, E.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011).
[Crossref] [PubMed]

Gellie, P.

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

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

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 instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Gorodetsky, M.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

Gorodetsky, M. L.

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011).
[Crossref] [PubMed]

Grahn, H. T.

Green, R. P.

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

Han, N.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Hartinger, K.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

Hayton, D. J.

D. Burghoff, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs,” Opt. Express 23(2), 1190–1202 (2015).
[Crossref] [PubMed]

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Herr, T.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011).
[Crossref] [PubMed]

Hindle, F.

Hinkov, B.

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

Höfler, G.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Holzwarth, R.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011).
[Crossref] [PubMed]

Hu, Q.

Hugi, A.

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett. 104(8), 081118 (2014).
[Crossref]

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

Iezekiel, S.

S. Bennet, C. M. Snowden, and S. Iezekiel, “Non-linear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum, Electron 33(11), 2076–2083 (1997).

Jagtap, V.

Jukam, N.

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

Kao, T.-Y.

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Kapon, E.

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Kärtner, F. X.

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 instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Khanna, S. P.

Khurgin, J. B.

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett. 104(8), 081118 (2014).
[Crossref]

Kippenberg, T. J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011).
[Crossref] [PubMed]

Krall, M.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

Kröll, J.

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

Kumar, S.

Lampin, J.-F.

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

Leo, G.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

Linfield, E. H.

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
[Crossref] [PubMed]

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

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
[Crossref]

Liu, H. C.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[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 instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (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 instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Maineult, W.

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

Mangeney, J.

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

Manquest, C.

Marcadet, X.

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

Matton, S.

Maussang, K.

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

Maysonnave, J.

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

Mouret, G.

Murdin, B.

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

Peytavit, E.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

Pidgeon, C.

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

Qin, Q.

Ravaro, M.

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
[Crossref] [PubMed]

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

Reno, J.

Reno, J. L.

Riedi, S.

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

Riemensberger, J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

Ritchie, D.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

Ritchie, D. A.

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
[Crossref]

Röben, B.

Rösch, M.

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

Rudra, A.

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Sagnes, I.

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

Santarelli, G.

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
[Crossref] [PubMed]

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

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Scalari, G.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

D. Turčinková, G. Scalari, F. Castellano, M. Amanti, M. Beck, and J. Faist, “Ultra-broadband heterogeneous quantum cascade laser emitting from 2.2 to 3.2THz,” Appl. Phys. Lett. 99(19), 191104 (2011).
[Crossref]

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Schneider, H.

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 instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Schrottke, L.

Sigg, H.

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

Sirtori, C.

C. Sirtori, S. Barbieri, and R. Colombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7(9), 691–701 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
[Crossref] [PubMed]

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

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

Snowden, C. M.

S. Bennet, C. M. Snowden, and S. Iezekiel, “Non-linear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum, Electron 33(11), 2076–2083 (1997).

Sugimoto, M.

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order optical non-linearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59(23), 2932 (1991).
[Crossref]

Taschin, A.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Terazzi, R.

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Tignon, J.

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

Torre, R.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Tredicucci, A.

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

Troccoli, M.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Turcinková, D.

D. Turčinková, G. Scalari, F. Castellano, M. Amanti, M. Beck, and J. Faist, “Ultra-broadband heterogeneous quantum cascade laser emitting from 2.2 to 3.2THz,” Appl. Phys. Lett. 99(19), 191104 (2011).
[Crossref]

Unterrainer, K.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

Villares, G.

G. Villares and J. Faist, “Quantum cascade laser combs: effects of modulation and dispersion,” Opt. Express 23(2), 1651–1669 (2015).
[Crossref] [PubMed]

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

Vinh, N. Q.

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

Vitiello, M. S.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Walrod, D.

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order optical non-linearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59(23), 2932 (1991).
[Crossref]

Wang, C. Y.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Wei Min Lee, A.

Wienold, M.

Williams, B.

Williams, B. S.

Wolff, P. A.

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order optical non-linearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59(23), 2932 (1991).
[Crossref]

Yang, Y.

D. Burghoff, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs,” Opt. Express 23(2), 1190–1202 (2015).
[Crossref] [PubMed]

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Appl. Phys. Lett. (9)

P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck, and J. Faist, “Four-wavemixing in a quantum cascade laser amplifier,” Appl. Phys. Lett. 102(22), 222104 (2013).
[Crossref]

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett. 104(8), 081118 (2014).
[Crossref]

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, T. Akalin, J.-F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of terahertz quantum cascade lasers: a transmission-line approach,” Appl. Phys. Lett. 96(2), 021108 (2010).
[Crossref]

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. Beere, D. Ritchie, J. Mangeney, S. Dhillon, and J. Tignon, “Direct intensity sampling of a mode-locked Terahertz quantum cascade laser,” Appl. Phys. Lett. 101(18), 181115 (2012).
[Crossref]

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105(18), 181118 (2014).
[Crossref]

D. Turčinková, G. Scalari, F. Castellano, M. Amanti, M. Beck, and J. Faist, “Ultra-broadband heterogeneous quantum cascade laser emitting from 2.2 to 3.2THz,” Appl. Phys. Lett. 99(19), 191104 (2011).
[Crossref]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85(10), 1674–1676 (2004).
[Crossref]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, J. Alton, H. Beere, and D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93, 183508 (2008).
[Crossref]

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order optical non-linearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59(23), 2932 (1991).
[Crossref]

IEEE J. Quantum, Electron (1)

S. Bennet, C. M. Snowden, and S. Iezekiel, “Non-linear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum, Electron 33(11), 2076–2083 (1997).

Nat. Commun. (1)

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

Nat. Photonics (7)

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

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

C. Sirtori, S. Barbieri, and R. Colombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7(9), 691–701 (2013).
[Crossref]

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in micro resonators,” Nat. Photonics 6(7), 480–487 (2012).
[Crossref]

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

D. Burghoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Nature (2)

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449(7163), 698–701 (2007).
[Crossref] [PubMed]

New J. Phys. (1)

M. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

Opt. Express (7)

B. Williams, S. Kumar, Q. Hu, and J. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express 13(9), 3331–3339 (2005).
[Crossref] [PubMed]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
[Crossref] [PubMed]

M. Wienold, B. Röben, L. Schrottke, and H. T. Grahn, “Evidence for frequency comb emission from a Fabry-Pérot terahertz quantum-cascade laser,” Opt. Express 22(25), 30410–30424 (2014).
[Crossref] [PubMed]

D. Burghoff, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs,” Opt. Express 23(2), 1190–1202 (2015).
[Crossref] [PubMed]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18(20), 20799–20816 (2010).
[Crossref] [PubMed]

G. Villares and J. Faist, “Quantum cascade laser combs: effects of modulation and dispersion,” Opt. Express 23(2), 1651–1669 (2015).
[Crossref] [PubMed]

L. L. Columbo and M. Brambilla, “Multimode regimes in quantum cascade lasers with optical feedback,” Opt. Express 22(9), 10105–10118 (2014).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (1)

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilitiesto spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Phys. Rev. B (1)

R. P. Green, A. Tredicucci, N. Q. Vinh, B. Murdin, C. Pidgeon, H. E. Beere, and D. A. Ritchie, “Gain recovery dynamics of a terahertz quantum cascade laser,” Phys. Rev. B 80(7), 075303 (2009).
[Crossref]

Phys. Rev. Lett. (1)

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011).
[Crossref] [PubMed]

Phys. Rev. X (1)

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy,” Phys. Rev. X 4(2), 021006 (2014).
[Crossref]

Other (7)

We exclude the fact that multiple RF beatnotes are due to the presence of higher order lateral modes inside the waveguide. Indeed, using a finite element code, we found that for the present ridge waveguide higher order modes present much larger propagation losses compared to the fundamental one. We also measured the laser far field and found no clear evidence of the presence of higher order modes.

Water absorption dips are probably due to the fact that a small fraction (~5%) of the optical path, from the QCL to the cryostat window, was not evacuated but only purged with dried air.

R. W. Boyd, Non-linear optics 2nd Ed., Chapter 8, 297 (Academic, San Diego, 2003).

A. E. Siegman, Lasers, Chapter 6, 316 (University Science Books, Sausalito, 1986).

D. M. Kane and K. A. Shore, Unlocking dynamical diversity: optical feedback effects on semiconductor lasers, (John Wiley & Sons, Chichester, West Sussex, England, 2005).

In support of this hypothesis we note that for sidebands located symmetrically on different sides of the RF modulation we recorded the same broadening using the Max Hold function of the spectrum Analyzer (data not shown). This is expected since the phase noise of the RF modulation is negligible.

We found that when the EO crystal was perpendicular to the beam axis, changing the distance between the crystal and the QCL produced a shift of the THz modes, hence of the beat-notes in the DCE spectra. This was not the case when the crystal was tilted at 45deg, indicating a considerable reduction of the feedback.

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Figures (17)
Fig. 1
Fig. 1 Schematic representation of the three experimental setups used in this work. (a) Fourier Transform Infrared Spectrometer (FTIR). (b) Measurement setup for the RF modulation of the QCL and the simultaneous detection of the RF beatnote spectrum (see text). The black and red arrows represent respectively the modulation from the RF generator and the RF beat-note signal generated by the THz QCL. (c) Electro-optic detection of the QCL field amplitude (see text).

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Fig. 2
Fig. 2 (a) Schematic of the mounting adopted to guide the RF modulation to the QCL (see text). The thin black lines represent the wire-bondings. (b) Photograph of the QCL, Indium-bonded to the copper holder. The microstrip-line is also visible behind the laser. The QCL image results from specular reflection on the back plane of the hyper-hemispherical Silicon lens. (c) Front view of the hyper-hemispherical Silicon lens embedded inside a copper mount. The latter allows fixing the lens in front of the QCL output facet. This is achieved thanks to a circular metal spring.

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Fig. 3
Fig. 3 (a) Voltage vs Current (black) and Collected power vs Current (red) characteristics of the device studied (3mm-long, 50μm-wide ridge waveguide). The laser was driven in CW at constant voltage (T = 30K). For clarity, points beyond the onset of negative differential resistance are in blue. (b,c,d) Emission spectra at difference currents, indicated by the black arrows in panel (a). Spectra were recorded with an FTIR spectrometer with a resolution of 7.5GHz. To eliminate water absorption the FTIR was operated under vacuum.

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Fig. 4
Fig. 4 (a) THz emission (in normalized arbitrary units) vs drive current in intensity color scale. (b) Corresponding RF beat-note spectra (in dBm). The QCL was driven in CW (T = 30K) and operated in free running. The vertical dashed lines identify six current intervals corresponding to different operating regimes (see text).

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Fig. 5
Fig. 5 QCL driven in free running at T = 30K. THz emission (left) and corresponding RF beat-note spectra (right) at different drive currents. The curves are extracted from Fig. 4(a), and 4(b). The red trace is the detection noise-floor. The red numbers on the left panels indicate the current regions of Fig. 4 to which each spectrum belongs.

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Fig. 6
Fig. 6 Schematic of resonant non-degenerate four-wave mixing (see text). (a) Initial mode frequencies, ν1 and ν2, separated by δ. (b) Schematic of the resonant non-linear mixing. The wavy red and black lines represent photons at ν1 and ν2. The gray line shows schematically the electronic potential profile that confines the upper and lower laser levels, represented by the horizontal black lines. As shown in the equation the population inversion Δn(t) is modulated at δ through gain saturation. E1 and E2 are the electric field amplitudes of the two modes, and ΔI(t) is the resulting current modulation. (c) Final frequencies resulting from four-wave mixing, with the two sidebands at ν1 - δ and ν2 + δ shown in green.

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Fig. 7
Fig. 7 (a) Emission spectra in linear scale for currents corresponding to regions 1 (dashed line) and 2 (solid lines) in Fig. 4. Black and red vertical arrows indicate two sets of modes with a mode spacing of 26.3GHz (see text). Blue vertical arrows indicate two modes spaced by 2 x 26.3GHz (see text). (b) Zoom of the spectral region of panel (a) delimited by the dashed rectangle. δ1 = 12.7+/−0.3GHz and δ2 = 13.6+/−0.3GHz are the average mode intervals derived from panel (c). (c) Intervals between the modes of panel (b) for the currents belonging to region 2 in Fig. 4. Dash-dotted and dashed lines correspond to the values of δ1 and δ2 derived from Fig. 5(b), while the solid line corresponds to 13.15GHz = 26.3/2GHz.

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Fig. 8
Fig. 8 Schematic of the generation of the lowest frequency beat-note in the spectrum of Fig. 5(b). By exploiting the intrinsic non-linearity of the laser Current-Voltage characteristic a first beating (black cross labeled “1” in the Fig.) is produced at Δ = δ1 - δ2. This frequency is finally mixed (black cross labeled “2” in the Fig.) with δ1 to produce a third line at δ3 = δ1 - Δ.

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Fig. 9
Fig. 9 (a) Low frequency part of the spectrum of panel (b). The spectrum was obtained by subtracting the background in order to remove spurious RF lines. (b) Same RF-beat-note spectrum of Fig. 5(b). (c) Spectra of the beat-notes oscillating at δ1, δ2 and δ3 in panel (b) obtained by operating the Spectrum Analyzer in the Max. Hold mode during 3 minutes. The frequency offsets were removed. (d) Result of a two-tone modulation of the QCL current at 11.8GHz and 13.4GHz (see text).

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Fig. 10
Fig. 10 (a)T Hz emission (in normalized arbitrary units) vs drive current in intensity color scale. (b) Corresponding RF beat-note spectra (in dBm). The QCL was driven in CW (T = 30K) and modulated at 13.22GHz with a synthesizer power level of + 23dBm. The vertical dashed lines identify three current intervals corresponding to different operating regimes (see text).

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Fig. 11
Fig. 11 QCL modulated at 13.22GHz with a power from the synthesizer of + 23dBm (T = 30K). THz emission (left) and corresponding RF beat-note spectra (right) at different drive currents. The curves are extracted from Fig. 10(a), and 10(b). In the RF spectra the peak of the 13.22GHz line is at −25dBm, and corresponds to the intensity of the RF modulation signal reflected by the device (Fig. 1(b)). The intensity scale was deliberately reduced in order to magnify the effect of the phase noise. The red trace corresponds to the detection noise-floor. The red numbers on the left panels indentify the current regions of Fig. 10 to which each spectrum belongs.

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Fig. 12
Fig. 12 (a) Schematic representation of the down-conversion process produced by the EO sampling of three arbitrarily spaced modes of frequencies ν1, ν2 and ν3. The THz frequencies are coherently transformed into the corresponding frequencies f1, f2 and f3 in the MHz range (see text for the explanation).(c) Schematic of the down-conversion of a THz QCL comb with a mode spacing f rep QCL (see text).

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Fig. 13
Fig. 13 Examples of DCE spectra (left column) and their corresponding THz emission spectra (right column) at different currents. The DCE spectra were collected with a resolution bandwidth of 1MHz. The spectral resolution of the emission spectra is 7.5GHz. The red dashed lines in the right column represent the minimum THz intensity detectable with the EOS system as deduced from the spectra in the left column. In panels (a), (b), (c), and (d) the QCL was operated in free running. In panels (e) and (f) it was RF modulated at 13.2GHz with + 24dBm from the synthesizer.

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Fig. 14
Fig. 14 (a) RF beat-note spectra and (b) corresponding DCE spectra vs RF modulation power in intensity color scale. The QCL was driven in CW at a current of 450mA (T = 30K). The vertical dashed lines identify three regions corresponding to different operating regimes (see text) (c) RF beat-note spectrum without RF modulation. (d) Corresponding DCE spectrum. (e),(g), and (i): RF beat-note spectra extracted from panel (a). The red numbers indentify the regions of panels (a) and (b) to which each spectrum belongs. (f),(h), and (l): corresponding DCE spectra extracted from panel (b). The red curves represent the noise floor. Note that the spectrum in panel (h) is the same to that of Fig. 13(e).

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Fig. 15
Fig. 15 DCE spectrum of the QCL driven in CW at a current of 450mA. The resolution bandwidth is 1MHz and the Spectrum Analyser is operated in Max. Hold mode. The laser is RF modulated at 14GHz, with a power of + 24dBm from the synthesizer. The lowest frequency line (blue arrow) is phase locked to the fs-laser repetition rate (see text). The red arrows indicate the lines that are not drift-broadened.

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Fig. 16
Fig. 16 (a),(b),(c)Schematic of the RF beat-note generation by two groups of independent sub-combs with different frequency offsets and sharing the same inter-mode spacing, δ. Δ is the frequency difference between the offsets. The black cross indicates the mixing process inherent to a process of quadratic (power) detection. (d),(e) Example of experimental RF multi-line beat-note spectrum that could be interpreted as the signature of the presence of sub-combs.(f),(g) Example of broad RF beat-note spectrum. The low frequency spectraof panels (d) and (f) were obtained by subtracting the background in order to remove spurious RF lines.

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Fig. 17
Fig. 17 Schematic of the setup used to phase-lock the 44MHz line (blue arrow) of Fig. 15 to a harmonic of the repetition rate of the fs-laser (see text).

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