Abstract

We consider here a time domain model representing the dynamics of quantum cascade lasers (QCLs) generating frequency combs (FCs) in both THz and long wave infrared (LWIR λ = 8-12µm) spectral ranges. Using common specifications for these QCLs we confirm that the free running laser enters a regime of operation yielding a pseudo-randomly frequency modulated (FM) radiation in the time domain corresponding to FCs with stable phase relations in the frequency domain. We provide an explanation for this unusual behavior as a consequence of competition for the most efficient regime of operation. Expanding the model previously developed in [Opt. Eng. 57(1), 011009 (2017)] we analyze the performance of realistic THz and LWIR QCLs and show, despite the vastly different scale of many parameters, that both types of lasers offer very similar characteristics, namely FM operation with an FM period commensurate with the gain recovery time and an FM amplitude comparable with the gain bandwidth. We also identify the true culprit behind pseudo-random dynamics of the FM comb to be spatial hole burning, rather than the more pervasive spectral hole burning.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

2017 (1)

N. Henry, D. Burghoff, Y. Yang, Q. Hu, and J. B. Khurgin, “Pseudorandom dynamics of frequency combs in free-running quantum cascade lasers,” Opt. Eng. 57(1), 011009 (2017).
[Crossref]

2016 (3)

2015 (3)

2014 (3)

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. 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. 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]

2012 (3)

D. Burghoff, C. Wang Ivan Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(26), 261111 (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]

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

2011 (2)

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]

D. Burghoff, T.-Y. Kao, D. Ban, A. W. M. Lee, Q. Hu, and J. Reno, “A terahertz pulse emitter monolithically integrated with a quantum cascade laser,” Appl. Phys. Lett. 98(6), 061112 (2011).
[Crossref]

2010 (1)

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

2009 (3)

J. B. Khurgin, Y. Dikmelik, P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, and C. F. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009).
[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. Express 17(15), 12929–12943 (2009).
[Crossref] [PubMed]

S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[Crossref]

2008 (1)

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
[Crossref] [PubMed]

2006 (1)

T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. In Al As–In Ga As/ In P midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006).
[Crossref]

2005 (1)

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).
[Crossref]

2003 (1)

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

2002 (2)

1998 (1)

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

1996 (1)

B. Gelmont, V. Gorfinkel, and S. Luryi, “Theory of the spectral line shape and gain in quantum wells with intersubband transitions,” Appl. Phys. Lett. 68(16), 2171–2173 (1996).
[Crossref]

1994 (1)

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

1991 (1)

Aellen, T.

T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. In Al As–In Ga As/ In P midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006).
[Crossref]

Akikusa, N.

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

Baillargeon, J. N.

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

Ban, D.

D. Burghoff, T.-Y. Kao, D. Ban, A. W. M. Lee, Q. Hu, and J. Reno, “A terahertz pulse emitter monolithically integrated with a quantum cascade laser,” Appl. Phys. Lett. 98(6), 061112 (2011).
[Crossref]

Barbieri, S.

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]

Baumann, E.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

Beck, M.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5(2), 272–291 (2016).
[Crossref]

T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. In Al As–In Ga As/ In P midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006).
[Crossref]

Belkin, M. A.

Belyanin, A.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared Quantum Cascade Lasers,” Opt. Express 17(15), 12929–12943 (2009).
[Crossref] [PubMed]

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

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]

Bonzon, C.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5(2), 272–291 (2016).
[Crossref]

Burghoff, D.

N. Henry, D. Burghoff, Y. Yang, Q. Hu, and J. B. Khurgin, “Pseudorandom dynamics of frequency combs in free-running quantum cascade lasers,” Opt. Eng. 57(1), 011009 (2017).
[Crossref]

Y. Yang, D. Burghoff, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz multiheterodyne spectroscopy using laser frequency combs,” Optica 3(5), 499–502 (2016).
[Crossref]

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]

D. Burghoff, C. Wang Ivan Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(26), 261111 (2012).
[Crossref]

D. Burghoff, T.-Y. Kao, D. Ban, A. W. M. Lee, Q. Hu, and J. Reno, “A terahertz pulse emitter monolithically integrated with a quantum cascade laser,” Appl. Phys. Lett. 98(6), 061112 (2011).
[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]

Capasso, F.

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared Quantum Cascade Lasers,” Opt. Express 17(15), 12929–12943 (2009).
[Crossref] [PubMed]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
[Crossref] [PubMed]

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

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

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

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]

Cho, A. Y.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

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

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

Choi, H.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
[Crossref] [PubMed]

Chu, S. G.

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

Coddington, I.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

Colombelli, R.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[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]

De Natale, P.

Diddams, S.

S. Diddams, “Optical frequency combs: Introduction, sources and applications,” in Proceedings of IEEE International Frequency Control Symposium (IEEE, 2009)
[Crossref]

Diddams, S. A.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

Diehl, L.

Dikmelik, Y.

J. 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]

J. B. Khurgin, Y. Dikmelik, P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, and C. F. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009).
[Crossref]

Edamura, T.

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

Escarra, M. D.

J. B. Khurgin, Y. Dikmelik, P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, and C. F. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009).
[Crossref]

Faist, J.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5(2), 272–291 (2016).
[Crossref]

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

J. 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]

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]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
[Crossref] [PubMed]

T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. In Al As–In Ga As/ In P midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006).
[Crossref]

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

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

Franz, K. J.

J. B. Khurgin, Y. Dikmelik, P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, and C. F. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009).
[Crossref]

Fujita, K.

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

Furuta, S.

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

Gaeta, A. L.

Gao, J.-R.

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]

Gelmont, B.

B. Gelmont, V. Gorfinkel, and S. Luryi, “Theory of the spectral line shape and gain in quantum wells with intersubband transitions,” Appl. Phys. Lett. 68(16), 2171–2173 (1996).
[Crossref]

Gini, E.

T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. In Al As–In Ga As/ In P midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006).
[Crossref]

Giorgetta, F. R.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

Giovannini, M.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
[Crossref] [PubMed]

T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. In Al As–In Ga As/ In P midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006).
[Crossref]

Gkortsas, V. M.

Gmachl, C.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

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

Gmachl, C. F.

J. B. Khurgin, Y. Dikmelik, P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, and C. F. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009).
[Crossref]

Gorfinkel, V.

B. Gelmont, V. Gorfinkel, and S. Luryi, “Theory of the spectral line shape and gain in quantum wells with intersubband transitions,” Appl. Phys. Lett. 68(16), 2171–2173 (1996).
[Crossref]

Grant, P.

Griffith, A. G.

Haffouz, S.

Ham, D.

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]

Hänsch, T. W.

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

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

Hayton, D. J.

Henry, N.

N. Henry, D. Burghoff, Y. Yang, Q. Hu, and J. B. Khurgin, “Pseudorandom dynamics of frequency combs in free-running quantum cascade lasers,” Opt. Eng. 57(1), 011009 (2017).
[Crossref]

Herman, D.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

Hoffman, A. J.

J. B. Khurgin, Y. Dikmelik, P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, and C. F. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009).
[Crossref]

Holzwarth, R.

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

Hoyler, N.

T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. In Al As–In Ga As/ In P midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006).
[Crossref]

Hu, Q.

N. Henry, D. Burghoff, Y. Yang, Q. Hu, and J. B. Khurgin, “Pseudorandom dynamics of frequency combs in free-running quantum cascade lasers,” Opt. Eng. 57(1), 011009 (2017).
[Crossref]

Y. Yang, D. Burghoff, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz multiheterodyne spectroscopy using laser frequency combs,” Optica 3(5), 499–502 (2016).
[Crossref]

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]

D. Burghoff, C. Wang Ivan Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(26), 261111 (2012).
[Crossref]

D. Burghoff, T.-Y. Kao, D. Ban, A. W. M. Lee, Q. Hu, and J. Reno, “A terahertz pulse emitter monolithically integrated with a quantum cascade laser,” Appl. Phys. Lett. 98(6), 061112 (2011).
[Crossref]

S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[Crossref]

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).
[Crossref]

Hugi, A.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5(2), 272–291 (2016).
[Crossref]

J. 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]

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]

Hutchinson, A. L.

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

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

Ikonic, Z.

Kan, H.

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[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]

D. Burghoff, T.-Y. Kao, D. Ban, A. W. M. Lee, Q. Hu, and J. Reno, “A terahertz pulse emitter monolithically integrated with a quantum cascade laser,” Appl. Phys. Lett. 98(6), 061112 (2011).
[Crossref]

Kärtner, F. X.

Kean, P. N.

Khanna, S. 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]

Khurgin, J.

J. 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]

Khurgin, J. B.

N. Henry, D. Burghoff, Y. Yang, Q. Hu, and J. B. Khurgin, “Pseudorandom dynamics of frequency combs in free-running quantum cascade lasers,” Opt. Eng. 57(1), 011009 (2017).
[Crossref]

J. B. Khurgin, Y. Dikmelik, P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, and C. F. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009).
[Crossref]

Kocharovsky, V.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

Kocinac, S.

Kohen, S.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).
[Crossref]

Kumar, S.

S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[Crossref]

Kuznetsova, L.

Lee, A. W. M.

D. Burghoff, T.-Y. Kao, D. Ban, A. W. M. Lee, Q. Hu, and J. Reno, “A terahertz pulse emitter monolithically integrated with a quantum cascade laser,” Appl. Phys. Lett. 98(6), 061112 (2011).
[Crossref]

Li, X.

Linfield, E. H.

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]

Lipson, M.

Liu, H. C.

Liu, P. Q.

J. B. Khurgin, Y. Dikmelik, P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, and C. F. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009).
[Crossref]

Luryi, S.

B. Gelmont, V. Gorfinkel, and S. Luryi, “Theory of the spectral line shape and gain in quantum wells with intersubband transitions,” Appl. Phys. Lett. 68(16), 2171–2173 (1996).
[Crossref]

Manquest, C.

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]

Milanovic, V.

Newbury, N. R.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

Norris, T. B.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
[Crossref] [PubMed]

Ochiai, T.

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

Okawachi, Y.

Owschimikow, N.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

Picqué, N.

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Ravaro, M.

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.

D. Burghoff, T.-Y. Kao, D. Ban, A. W. M. Lee, Q. Hu, and J. Reno, “A terahertz pulse emitter monolithically integrated with a quantum cascade laser,” Appl. Phys. Lett. 98(6), 061112 (2011).
[Crossref]

Reno, J. L.

Y. Yang, D. Burghoff, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz multiheterodyne spectroscopy using laser frequency combs,” Optica 3(5), 499–502 (2016).
[Crossref]

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]

D. Burghoff, C. Wang Ivan Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(26), 261111 (2012).
[Crossref]

S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[Crossref]

Rösch, M.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5(2), 272–291 (2016).
[Crossref]

Santarelli, 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]

Scalari, G.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5(2), 272–291 (2016).
[Crossref]

M. S. Vitiello, G. Scalari, B. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 5167–5182 (2015).
[Crossref] [PubMed]

Schliesser, A.

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Schneider, H.

Sibbett, W.

Sirtori, C.

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]

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

Sivco, D. L.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

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

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

Song, C. Y.

Spence, D. E.

Sugiyama, A.

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

Tomic, S.

Tredicucci, A.

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

Udem, T.

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

Villares, G.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5(2), 272–291 (2016).
[Crossref]

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]

Vitiello, M. S.

Wang, C. Y.

Wang Ivan Chan, C.

D. Burghoff, C. Wang Ivan Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(26), 261111 (2012).
[Crossref]

Wasilewski, Z. R.

Williams, B.

Williams, B. S.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).
[Crossref]

Wu, Z.-K.

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
[Crossref] [PubMed]

Yamanishi, M.

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

Yang, Y.

N. Henry, D. Burghoff, Y. Yang, Q. Hu, and J. B. Khurgin, “Pseudorandom dynamics of frequency combs in free-running quantum cascade lasers,” Opt. Eng. 57(1), 011009 (2017).
[Crossref]

Y. Yang, D. Burghoff, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz multiheterodyne spectroscopy using laser frequency combs,” Optica 3(5), 499–502 (2016).
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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).
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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]

Ycas, G.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

Yu, M.

Appl. Phys. Lett. (7)

J. 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).
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D. Burghoff, C. Wang Ivan Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(26), 261111 (2012).
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IEEE J. Quantum Electron. (1)

K. Fujita, S. Furuta, A. Sugiyama, T. Ochiai, T. Edamura, N. Akikusa, M. Yamanishi, and H. Kan, “High-Performance Quantum Cascade Lasers With λ~8.6 μm Single Phonon-Continuum Depopulation Structures,” IEEE J. Quantum Electron. 46(5), 683–688 (2010).
[Crossref]

J. Appl. Phys. (2)

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97(5), 053106 (2005).
[Crossref]

T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. In Al As–In Ga As/ In P midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006).
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J. Opt. Soc. Am. B (1)

Nanophotonics (1)

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5(2), 272–291 (2016).
[Crossref]

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).
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Nat. Photonics (4)

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]

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]

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Nature (2)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[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).
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Opt. Eng. (1)

N. Henry, D. Burghoff, Y. Yang, Q. Hu, and J. B. Khurgin, “Pseudorandom dynamics of frequency combs in free-running quantum cascade lasers,” Opt. Eng. 57(1), 011009 (2017).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Optica (2)

Phys. Rev. Lett. (2)

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90(4), 043902 (2003).
[Crossref] [PubMed]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100(16), 167401 (2008).
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Science (1)

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S. Diddams, “Optical frequency combs: Introduction, sources and applications,” in Proceedings of IEEE International Frequency Control Symposium (IEEE, 2009)
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 (a) Simplified level definitions of our 3-level QCL model. (b) Cavity diagram of two counter-propagating, frequency modulated waves, the background of which illustrates the cladding and active layers. (c) Pseudo random frequency modulation obtained from the model developed in [15], each signal is generated from a separate run. (d) Spectral gain profile of THz and LWIR QCLs with and without FM.
Fig. 2
Fig. 2 Instant frequency deviation, power spectrum, and spatial distribution for an intracavity field with (a) no frequency modulation (b) non-random frequency modulation with a modulation period equal to the cavity round-trip time, (c)non-random frequency modulation with a period equal to the gain recovery time, (d) random frequency modulation, ( δ=0.5) with mean period equal to the gain recovery time, (e) very random frequency ( δ=0.9) modulation. Data presented here are for a QCL at 3 THz with a frequency modulation spanning 2 THz ( A FM = 1THz), further specifications follow that in Table 1 for a THz QCL.
Fig. 3
Fig. 3 Averaged instant gain (a and c) and relaxation current (b and d) versus frequency modulation span and randomness (δ) for an LWIR QCL.
Fig. 4
Fig. 4 Averaged instant gain (a,c) and relaxation current (b,d) versus frequency modulation span and randomness (δ) for a THz QCL.

Tables (1)

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Table 1 Laser specifications

Equations (6)

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I(z,t)= | A 1 (z)E(t+Δt/2) e j(kz ω 0 t) + A 2 (z)E(tΔt/2) e j(kz+ ω 0 t) | 2 ,
E(t)= E 0 exp( i ω FM (t)dt ),
I(z,t τ = E 0 2 [ 1+ J 0 ( A FM τ rt m sinmπz/L )cos(4πz/λ) ]
d dt N 21 (n) (z,t)= 2 N o τ 2 2 N 21 (n) (z,t) τ 2 [ 1+I(z,t)/ I sat (n) (t) ],
γ(z,t)=Γ n f (n) 4π α 0 n eff N D W z 21 2 ω o τ coh N 21 (n) (z,t) 1+ τ coh 2 Δ ω (n) (t) 2 ,
J ¯ rel = q N D τ 2 1 n f n N 2 (n) (z,t) z,t ,

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