Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation

Pierre Gellie; Stefano Barbieri; Jean-François Lampin; Pascal Filloux; Christophe Manquest; Carlo Sirtori; Isabelle Sagnes; Suraj P. Khanna; Edmund H. Linfield; A. Giles Davies; Harvey Beere; David Ritchie

doi:10.1364/OE.18.020799

Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation

Pierre Gellie, Stefano Barbieri, Jean-François Lampin, Pascal Filloux, Christophe Manquest, Carlo Sirtori, Isabelle Sagnes, Suraj P. Khanna, Edmund H. Linfield, A. Giles Davies, Harvey Beere, and David Ritchie

Optics Express
Vol. 18,
Issue 20,
pp. 20799-20816
(2010)
•https://doi.org/10.1364/OE.18.020799

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Pierre Gellie, Stefano Barbieri, Jean-François Lampin, Pascal Filloux, Christophe Manquest, Carlo Sirtori, Isabelle Sagnes, Suraj P. Khanna, Edmund H. Linfield, A. Giles Davies, Harvey Beere, and David Ritchie, "Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation," Opt. Express 18, 20799-20816 (2010)

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Related Topics
Table of Contents Category
- Lasers and Laser Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- General science (000.2700)

About this Article
History
- Original Manuscript: June 10, 2010
- Revised Manuscript: July 23, 2010
- Manuscript Accepted: July 26, 2010
- Published: September 16, 2010

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Open Access

Abstract

We demonstrate that the cavity resonance frequency –the round-trip frequency – of Terahertz quantum cascade lasers can be injection-locked by direct modulation of the bias current using an RF source. Metal-metal and single-plasmon waveguide devices with roundtrip frequencies up to 35GHz have been studied, and show locking ranges above 200MHz. Inside this locking range the laser round-trip frequency is phase-locked, with a phase noise determined by the RF-synthesizer. We find a square-root dependence of the locking range with RF-power in agreement with classical injection-locking theory. These results are discussed in the context of mode-locking operation.

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References

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Publication

E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, “Monolithic and multi-GigaHertz mode-locked semiconductor lasers: constructions, experiments, models and applications,” IEE Proc., Optoelectron. 147(4), 251–278 (2000).
[Crossref]
J. E. Bowers, P. A. Morton, A. Mar, and S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25(6), 1426–1439 (1989).
[Crossref]
L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
[Crossref]
D. Y. Kim, D.-S. Seo, and H.-F. Liu, “Observation of very efficeint hybrid mode-locking in InGaAs/InGaAsInP multiple quantum well distributed Bragg reflector laser diode,” Appl. Phys. Lett. 67(21), 3075–3077 (1995).
[Crossref]
S. Arahira and Y. Ogawa, “Synchronous mode-locking in passively mode-locked semiconductor laser diodes using optical short pulses repeated at subharmonics of the cavity round-trip frequency,” IEEE Photon. Technol. Lett. 8(2), 191–193 (1996).
[Crossref]
T. Hoshida, H-F. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic Hybrid Mode-Locking of a Monolithic Semiconductor Laser,” IEEE J. Selected Topics Quantum. Electron.
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[Crossref]
R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode-locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
[Crossref]
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[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]
G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]
B. S. Williams, “Terahertz quantum cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]
W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, J. F. Lampin, T. Akalin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of THz quantum cascade lasers: a transmission–line approach,” Appl. Phys. Lett. 96(2), 021108–021110 (2010).
[Crossref]
S. Barbieri, W. Maineult, S. S. Dhillon, C. Sirtori, J. Alton, N. Breuil, H. E. Beere, and D. A. Ritchie, “13 GHz direct modulation of terahertz quantum cascade lasers,” Appl. Phys. Lett. 91(14), 143510 (2007).
[Crossref]
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[Crossref] [PubMed]
T. Yilmaz, C. M. Depriest, P. J. Delfyett, A. Braun, and J. Abeles, “Measurement of residual phase noise and longitudinal-mode linewidth in a hybridly mode-locked external linear cavity semiconductor laser,” Opt. Lett. 27(10), 872–874 (2002).
[Crossref]
C. Worrall, J. Alton, M. Houghton, S. Barbieri, H. E. Beere, D. Ritchie, and C. Sirtori, “Continuous wave operation of a superlattice quantum cascade laser emitting at 2 THz,” Opt. Express 14(1), 171–181 (2006).
[Crossref] [PubMed]
The origin of these sidebands is not clear. However they are not relevant for this work.
S. Barbieri, J. Alton, C. Baker, T. Lo, H. Beere, and D. Ritchie, “Imaging with THz quantum cascade lasers using a Schottky diode mixer,” Opt. Express 13(17), 6497–6503 (2005).
[Crossref] [PubMed]
S. Barbieri, W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, T. Akalin, J. F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave technology applied to THz quantum cascade lasers,” Proc. SPIE 7608, 76080X (2010).
[Crossref]
A. E. Siegman, “Lasers” University Science Books, Valley Mill (1986).
Z. Ahmed, L. Zhai, A. J. Lowery, N. Onodera, and R. S. Tucker, “Locking bandwidth of actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1714–1721 (1993).
[Crossref]
As mentioned above in the text, the oscillation in the intensity of fRF is produced by the non-ideal directivity of the coupler (Fig. 2(a)).
M. DiDomenico, “Small-signal analysis of internal (coupling-type) modulation of lasers,” J. Appl. Phys. 35(10), 2870–2876 (1964).
[Crossref]
O. P. McDuff and S. E. Harris, “Nonlinear theory of internally loss-modulated lasers,” IEEE J. Quantum Electron. 3(3), 101–111 (1967).
[Crossref]
R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE 61(10), 1380–1385 (1973).
[Crossref]
B. Razavi, “A study of injection-locking and pulling in oscillators,” IEEE J. Sol. State Circuits. 39(9), 1415–1424 (2004).
[Crossref]
S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” Appl. Phys. Lett. 97, 053106–053108 (2005).
S. Barbieri, J. Alton, J. Fowler, H. E. Beere, 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 (2004).
[Crossref]
M. Hajenius, P. Khosropanah, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, S. Barbieri, S. Dhillon, P. Filloux, C. Sirtori, D. A. Ritchie, and H. E. Beere, “Surface plasmon quantum cascade lasers as terahertz local oscillators,” Opt. Lett. 33(4), 312–314 (2008).
[Crossref] [PubMed]
S. Barbieri, J. Alton, H. E. Beere, E. H Linfield, D. A. Ritchie, S. Withington, G. Scalari, L. Ajili, and J. Faist, “Heterodyne mixing of two far-infrared quantum cascade lasers by use of a point-contact Schottky diode,” Opt. Lett. 29(14), 1632–1634 (2004).
[Crossref] [PubMed]
A. Barkan, F. K. Tittel, D. M. Mittleman, R. Dengler, P. H. Siegel, G. Scalari, L. Ajili, J. Faist, H. E. Beere, E. H. Linfield, A. G. Davies, and D. A. Ritchie, “Linewidth and tuning characteristics of terahertz quantum cascade lasers,” Opt. Lett. 29(6), 575–577 (2004).
[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 2.7THz quantum cascade laser to a mode-locked Er-fiber laser,” Nature Photonics 4, 636 - 640 (2010).
[Crossref]
E. E. Orlova, J. N. Hovenier, T. O. Klaassen, I. Ksalynas, A. J. L. Adam, J. R. Gao, T. M. Klapwijk, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, Phys. Rev. Lett. 96, “Antenna model for wire-lasers,” 173904–173906 (2006).
[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. R. Ritchie, “Double metal quantum cascade lasers with micro-TEM horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[Crossref]
Compared to Section 2, for the measurements presented in this Section we used a different SA with a higher resolution (1Hz compared to 10Hz).
We tried using longer devices. Unfortunately the cooling power needed to cool the QCLs was beyond the capability of our cryostat.
R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearities,” Science 290(5497), 1739–1742 (2000).
[Crossref] [PubMed]
C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[Crossref]
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]
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,” N. J. Phys. 11(12), 1–19 (2009).
[Crossref]
C. Walther, G. Scalari, J. Faist, H. Beere, and D. Ritchie, “Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz,” Appl. Phys. Lett. 89(23), 231121 (2006).
[Crossref]
C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]
S. Ramo, J. R. Whinnery, and T. V. Duzer, “Field and waves in communication electronics,” 2nd ed. (Wiley, 1984).

2010 (3)

W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, S. Barbieri, J. F. Lampin, T. Akalin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave modulation of THz quantum cascade lasers: a transmission–line approach,” Appl. Phys. Lett. 96(2), 021108–021110 (2010).
[Crossref]

S. Barbieri, W. Maineult, L. Ding, P. Gellie, P. Filloux, C. Sirtori, T. Akalin, J. F. Lampin, I. Sagnes, H. E. Beere, and D. A. Ritchie, “Microwave technology applied to THz quantum cascade lasers,” Proc. SPIE 7608, 76080X (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 2.7THz quantum cascade laser to a mode-locked Er-fiber laser,” Nature Photonics 4, 636 - 640 (2010).
[Crossref]

2009 (4)

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]

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (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,” N. J. Phys. 11(12), 1–19 (2009).
[Crossref]

2008 (4)

M. Hajenius, P. Khosropanah, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, S. Barbieri, S. Dhillon, P. Filloux, C. Sirtori, D. A. Ritchie, and H. E. Beere, “Surface plasmon quantum cascade lasers as terahertz local oscillators,” Opt. Lett. 33(4), 312–314 (2008).
[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. R. Ritchie, “Double metal quantum cascade lasers with micro-TEM horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[Crossref]

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]

2007 (4)

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75(3), 031802 (2007).
[Crossref]

S. Barbieri, W. Maineult, S. S. Dhillon, C. Sirtori, J. Alton, N. Breuil, H. E. Beere, and D. A. Ritchie, “13 GHz direct modulation of terahertz quantum cascade lasers,” Appl. Phys. Lett. 91(14), 143510 (2007).
[Crossref]

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

C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]

2006 (3)

C. Walther, G. Scalari, J. Faist, H. Beere, and D. Ritchie, “Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz,” Appl. Phys. Lett. 89(23), 231121 (2006).
[Crossref]

C. Worrall, J. Alton, M. Houghton, S. Barbieri, H. E. Beere, D. Ritchie, and C. Sirtori, “Continuous wave operation of a superlattice quantum cascade laser emitting at 2 THz,” Opt. Express 14(1), 171–181 (2006).
[Crossref] [PubMed]

E. E. Orlova, J. N. Hovenier, T. O. Klaassen, I. Ksalynas, A. J. L. Adam, J. R. Gao, T. M. Klapwijk, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, Phys. Rev. Lett. 96, “Antenna model for wire-lasers,” 173904–173906 (2006).
[Crossref] [PubMed]

2005 (2)

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” Appl. Phys. Lett. 97, 053106–053108 (2005).

S. Barbieri, J. Alton, C. Baker, T. Lo, H. Beere, and D. Ritchie, “Imaging with THz quantum cascade lasers using a Schottky diode mixer,” Opt. Express 13(17), 6497–6503 (2005).
[Crossref] [PubMed]

2004 (4)

S. Barbieri, J. Alton, J. Fowler, H. E. Beere, 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 (2004).
[Crossref]

B. Razavi, “A study of injection-locking and pulling in oscillators,” IEEE J. Sol. State Circuits. 39(9), 1415–1424 (2004).
[Crossref]

S. Barbieri, J. Alton, H. E. Beere, E. H Linfield, D. A. Ritchie, S. Withington, G. Scalari, L. Ajili, and J. Faist, “Heterodyne mixing of two far-infrared quantum cascade lasers by use of a point-contact Schottky diode,” Opt. Lett. 29(14), 1632–1634 (2004).
[Crossref] [PubMed]

A. Barkan, F. K. Tittel, D. M. Mittleman, R. Dengler, P. H. Siegel, G. Scalari, L. Ajili, J. Faist, H. E. Beere, E. H. Linfield, A. G. Davies, and D. A. Ritchie, “Linewidth and tuning characteristics of terahertz quantum cascade lasers,” Opt. Lett. 29(6), 575–577 (2004).
[Crossref] [PubMed]

2002 (2)

T. Yilmaz, C. M. Depriest, P. J. Delfyett, A. Braun, and J. Abeles, “Measurement of residual phase noise and longitudinal-mode linewidth in a hybridly mode-locked external linear cavity semiconductor laser,” Opt. Lett. 27(10), 872–874 (2002).
[Crossref]

L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
[Crossref]

2001 (1)

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

2000 (3)

R. Paiella, F. Capasso, C. Gmachl, H. Y. Hwang, D. L. Sivco, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Monolithic active mode-locking of quantum cascade lasers,” Appl. Phys. Lett. 77(2), 169–171 (2000).
[Crossref]

E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, “Monolithic and multi-GigaHertz mode-locked semiconductor lasers: constructions, experiments, models and applications,” IEE Proc., Optoelectron. 147(4), 251–278 (2000).
[Crossref]

R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearities,” Science 290(5497), 1739–1742 (2000).
[Crossref] [PubMed]

1996 (1)

S. Arahira and Y. Ogawa, “Synchronous mode-locking in passively mode-locked semiconductor laser diodes using optical short pulses repeated at subharmonics of the cavity round-trip frequency,” IEEE Photon. Technol. Lett. 8(2), 191–193 (1996).
[Crossref]

1995 (1)

D. Y. Kim, D.-S. Seo, and H.-F. Liu, “Observation of very efficeint hybrid mode-locking in InGaAs/InGaAsInP multiple quantum well distributed Bragg reflector laser diode,” Appl. Phys. Lett. 67(21), 3075–3077 (1995).
[Crossref]

1993 (1)

Z. Ahmed, L. Zhai, A. J. Lowery, N. Onodera, and R. S. Tucker, “Locking bandwidth of actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1714–1721 (1993).
[Crossref]

1989 (1)

J. E. Bowers, P. A. Morton, A. Mar, and S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25(6), 1426–1439 (1989).
[Crossref]

1973 (1)

R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE 61(10), 1380–1385 (1973).
[Crossref]

1967 (1)

O. P. McDuff and S. E. Harris, “Nonlinear theory of internally loss-modulated lasers,” IEEE J. Quantum Electron. 3(3), 101–111 (1967).
[Crossref]

1964 (1)

M. DiDomenico, “Small-signal analysis of internal (coupling-type) modulation of lasers,” J. Appl. Phys. 35(10), 2870–2876 (1964).
[Crossref]

Abeles, J.

Adam, A. J. L.

Adler, R.

R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE 61(10), 1380–1385 (1973).
[Crossref]

Ahmed, Z.

Z. Ahmed, L. Zhai, A. J. Lowery, N. Onodera, and R. S. Tucker, “Locking bandwidth of actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1714–1721 (1993).
[Crossref]

Ajili, L.

Akalin, T.

Alton, J.

Amanti, M.

Andronico, A.

Arahira, S.

Avrutin, E. A.

Baillargeon, J. N.

Baker, C.

Ballargeon, J. N.

Barbieri, S.

Barkan, A.

Beck, M.

Beere, H.

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]

C. Walther, G. Scalari, J. Faist, H. Beere, and D. Ritchie, “Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz,” Appl. Phys. Lett. 89(23), 231121 (2006).
[Crossref]

Beere, H. E.

Belkin, M. A.

Belyanin, A.

Bour, D.

Bowers, J. E.

J. E. Bowers, P. A. Morton, A. Mar, and S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25(6), 1426–1439 (1989).
[Crossref]

Braun, A.

Breuil, N.

Capasso, F.

Cho, A. Y.

Choi, H.

Colombelli, R.

Corzine, S.

Corzine, S. W.

J. E. Bowers, P. A. Morton, A. Mar, and S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25(6), 1426–1439 (1989).
[Crossref]

Davies, A. G.

Delfyett, P. J.

Dengler, R.

Depriest, C. M.

Dhillon, S.

Dhillon, S. S.

DiDomenico, M.

M. DiDomenico, “Small-signal analysis of internal (coupling-type) modulation of lasers,” J. Appl. Phys. 35(10), 2870–2876 (1964).
[Crossref]

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S. Ramo, J. R. Whinnery, and T. V. Duzer, “Field and waves in communication electronics,” 2nd ed. (Wiley, 1984).

Faist, J.

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]

C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]

C. Walther, G. Scalari, J. Faist, H. Beere, and D. Ritchie, “Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz,” Appl. Phys. Lett. 89(23), 231121 (2006).
[Crossref]

Filloux, P.

Fischer, M

Fischer, M.

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]

Fisher, M.

C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]

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Grein, M. E.

L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
[Crossref]

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[Crossref]

Hofler, G.

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T. Hoshida, H-F. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic Hybrid Mode-Locking of a Monolithic Semiconductor Laser,” IEEE J. Selected Topics Quantum. Electron.

Houghton, M.

Hovenier, J. N.

Hoyler, N.

C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]

Hu, Q.

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,” Appl. Phys. Lett. 97, 053106–053108 (2005).

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Hwang, H. Y.

Ippen, E. P.

L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
[Crossref]

Jiang, L. A.

L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
[Crossref]

Jirauschek, C.

Kamiya, T.

T. Hoshida, H-F. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic Hybrid Mode-Locking of a Monolithic Semiconductor Laser,” IEEE J. Selected Topics Quantum. Electron.

Kapon, E.

Kärtner, F. X.

Khosropanah, P.

Kim, D. Y.

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Klapwijk, T. M.

Kohen, S.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” Appl. Phys. Lett. 97, 053106–053108 (2005).

Ksalynas, I.

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]

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Liu, H-F.

T. Hoshida, H-F. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic Hybrid Mode-Locking of a Monolithic Semiconductor Laser,” IEEE J. Selected Topics Quantum. Electron.

Lo, T.

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Z. Ahmed, L. Zhai, A. J. Lowery, N. Onodera, and R. S. Tucker, “Locking bandwidth of actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1714–1721 (1993).
[Crossref]

Maineult, W.

Mar, A.

J. E. Bowers, P. A. Morton, A. Mar, and S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25(6), 1426–1439 (1989).
[Crossref]

Marsh, J. H.

Martini, R.

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O. P. McDuff and S. E. Harris, “Nonlinear theory of internally loss-modulated lasers,” IEEE J. Quantum Electron. 3(3), 101–111 (1967).
[Crossref]

McNeilage, C.

L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
[Crossref]

Mittleman, D. M.

Morton, P. A.

J. E. Bowers, P. A. Morton, A. Mar, and S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25(6), 1426–1439 (1989).
[Crossref]

Norris, T. B.

Ogawa, Y.

T. Hoshida, H-F. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic Hybrid Mode-Locking of a Monolithic Semiconductor Laser,” IEEE J. Selected Topics Quantum. Electron.

Onodera, N.

Z. Ahmed, L. Zhai, A. J. Lowery, N. Onodera, and R. S. Tucker, “Locking bandwidth of actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1714–1721 (1993).
[Crossref]

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Paiella, R.

R. Paiella, “Intersubband transitions in quantum structures” Mc-Graw Hill Nanoscience and Technology, New York (2006)

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S. Ramo, J. R. Whinnery, and T. V. Duzer, “Field and waves in communication electronics,” 2nd ed. (Wiley, 1984).

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B. Razavi, “A study of injection-locking and pulling in oscillators,” IEEE J. Sol. State Circuits. 39(9), 1415–1424 (2004).
[Crossref]

Reno, J. L.

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]

Ritchie, D.

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]

C. Walther, G. Scalari, J. Faist, H. Beere, and D. Ritchie, “Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz,” Appl. Phys. Lett. 89(23), 231121 (2006).
[Crossref]

Ritchie, D. A.

Ritchie, D. R.

Rudra, A.

Sagnes, I.

Santarelli, G.

Scalari, G.

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]

C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]

C. Walther, G. Scalari, J. Faist, H. Beere, and D. Ritchie, “Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz,” Appl. Phys. Lett. 89(23), 231121 (2006).
[Crossref]

Schneider, H.

Searls, J.

L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
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G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]

C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]

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Troccoli, M.

Tsuchiya, M.

T. Hoshida, H-F. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic Hybrid Mode-Locking of a Monolithic Semiconductor Laser,” IEEE J. Selected Topics Quantum. Electron.

Tucker, R. S.

Z. Ahmed, L. Zhai, A. J. Lowery, N. Onodera, and R. S. Tucker, “Locking bandwidth of actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1714–1721 (1993).
[Crossref]

Walther, C.

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]

C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]

C. Walther, G. Scalari, J. Faist, H. Beere, and D. Ritchie, “Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz,” Appl. Phys. Lett. 89(23), 231121 (2006).
[Crossref]

Wang, C. Y.

Wasilewski, Z. R.

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S. Ramo, J. R. Whinnery, and T. V. Duzer, “Field and waves in communication electronics,” 2nd ed. (Wiley, 1984).

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Williams, B. S.

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

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” Appl. Phys. Lett. 97, 053106–053108 (2005).

Withington, S.

Worrall, C.

Wu, Z. K.

Yilmaz, T.

Yokoyama, H.

L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
[Crossref]

Zhai, L.

Z. Ahmed, L. Zhai, A. J. Lowery, N. Onodera, and R. S. Tucker, “Locking bandwidth of actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1714–1721 (1993).
[Crossref]

Appl. Phys. Lett. (11)

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,” Appl. Phys. Lett. 97, 053106–053108 (2005).

C. Walther, G. Scalari, J. Faist, H. Beere, and D. Ritchie, “Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz,” Appl. Phys. Lett. 89(23), 231121 (2006).
[Crossref]

C. Walther, M. Fisher, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade laser operating from 1.2 to 1.6 THz,” Appl. Phys. Lett. 91(13), 131122 (2007).
[Crossref]

IEE Proc., Optoelectron (1)

IEEE J. Quantum Electron (3)

J. E. Bowers, P. A. Morton, A. Mar, and S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25(6), 1426–1439 (1989).
[Crossref]

Z. Ahmed, L. Zhai, A. J. Lowery, N. Onodera, and R. S. Tucker, “Locking bandwidth of actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 29(6), 1714–1721 (1993).
[Crossref]

O. P. McDuff and S. E. Harris, “Nonlinear theory of internally loss-modulated lasers,” IEEE J. Quantum Electron. 3(3), 101–111 (1967).
[Crossref]

IEEE J. Selected Topics Quantum. Electron (1)

T. Hoshida, H-F. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic Hybrid Mode-Locking of a Monolithic Semiconductor Laser,” IEEE J. Selected Topics Quantum. Electron.

IEEE J. Sol. State Circuits (1)

B. Razavi, “A study of injection-locking and pulling in oscillators,” IEEE J. Sol. State Circuits. 39(9), 1415–1424 (2004).
[Crossref]

IEEE Photon. Technol. Lett. (1)

J. Appl. Phys. (1)

M. DiDomenico, “Small-signal analysis of internal (coupling-type) modulation of lasers,” J. Appl. Phys. 35(10), 2870–2876 (1964).
[Crossref]

Laser Photon Rev. (1)

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photon Rev. 3(1-2), 45–66 (2009).
[Crossref]

N. J. Phys. (1)

Nat. Photonics (1)

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

Nature Photonics (1)

Opt. Express (3)

Opt. Lett. (6)

L. A. Jiang, M. E. Grein, E. P. Ippen, C. McNeilage, J. Searls, and H. Yokoyama, “Quantum-limited noise performance of a mode-locked laser diode,” Opt. Lett. 27(1), 49–51 (2002).
[Crossref]

Phys. Rev. A (1)

Phys. Rev. Lett. (2)

Proc. IEEE (1)

R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE 61(10), 1380–1385 (1973).
[Crossref]

Proc. SPIE (1)

Science (1)

Other (7)

S. Ramo, J. R. Whinnery, and T. V. Duzer, “Field and waves in communication electronics,” 2nd ed. (Wiley, 1984).

A. E. Siegman, “Lasers” University Science Books, Valley Mill (1986).

As mentioned above in the text, the oscillation in the intensity of fRF is produced by the non-ideal directivity of the coupler (Fig. 2(a)).

Compared to Section 2, for the measurements presented in this Section we used a different SA with a higher resolution (1Hz compared to 10Hz).

We tried using longer devices. Unfortunately the cooling power needed to cool the QCLs was beyond the capability of our cryostat.

The origin of these sidebands is not clear. However they are not relevant for this work.

R. Paiella, “Intersubband transitions in quantum structures” Mc-Graw Hill Nanoscience and Technology, New York (2006)

Supplementary Material (1)

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Fig. 1 Metal-metal waveguide QCL. The device is 1.0mm-long and 70μm wide. (a) Continuous-wave (CW) Voltage/Current and Optical-power/Current characteristics at a heat-sink temperature of 10K. (b) Representative THz emission spectrum measured at a current of 150mA (black dot in panel(a)). The FP modes are separated by approximately 34.5GHz.

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Fig. 2 (a) Metal-metal QCL. Schematic of the measurement setup for the RF injection-locking. An RF-synthesizer (Agilent E8257D) is connected to the input port (port 1) of a 40GHz directional coupler. Port 2 of the coupler is connected to the ac input of a 60GHz bias-T. The dc input of the bias-T is connected to a power supply that drives the QCL at constant current. The RF and dc-bias signals are brought to the QCL via a 60GHz, 50Ω coplanar probe positioned at one end of the QCL ridge. The signal from the RF generator is partially reflected at the QCL/coplanar probe boundary and, together with the beat-note at f _rt, is monitored on a spectrum analyzer (SA) connected to port 3 of the coupler. The total attenuation from the RF generator to the QCL (including the 1dB transmission loss at the QCL/probe boundary) is of 14dB. (b) RF-spectrum collected with the RF-source switched OFF, and using a RBW of 100kHz, a sweep time of 1s on a 300MHz span, and with the RMS detection mode switched ON. The central peak at 34.637GHz has a resolution-limited 3dB-linewidth of ∼1MHz.

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Fig. 3 Metal-metal QCL. RF injection-locking of f _rt. The spectra were collected with the same settings of Fig. 2(b) (a) The RF-source is switched OFF and f _rt = 34.637GHz. (b) RF-power of −20dBm, (i.e about −34dBm inside the device) and f _RF = 34.706GHz, 68MHz on the right of f _rt. (c) RF-power of −4dBm. f _rt is pulled by ∼27MHz towards f _RF. Two sidebands appear on the left side of f _rt All the lines are separated by f _b = 42MHz. (d) RF-power of −1dBm. f _rt is injection locked by the RF-source.

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Fig. 4 Metal-metal QCL. Spectra at −2dBm RF-power, of the injection-locked roundtrip frequency measured with increasing RBW of the SA from 100kHz (a) to 10Hz (d), the spectral resolution limit of the SA. Spectra where collected in RMS detection mode, with a 50s sweep time. The peak intensity was normalized at 0dBm. In panel (d) the spectrum of the locked f _rt (blue) is shown together with the spectrum of f _RF (red).

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Fig. 5 Metal-metal QCL. Pulling and locking of f _rt. (a) f _RF is fixed at 34.706GHz and the RF-power is increased from −20dBm to −1.1dBm. (b) the RF-power is fixed at −2dBm and f _RF goes from 34.82GHz (bottom) to 34.70GHz (top). All the spectra were collected with the same settings of Fig. 2(b).

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Fig. 6 Metal-metal QCL. ( Media 1) Video sample of the SA screen. The RF-power is of −2dBm. f _RF is swept at constant speed from the low frequency side (from left to right on the screen). The frequency scale is of 100MHz/div. The intensity scale is of 10dB/div. The oscillations of the intensity of the RF signal are the consequence of an interference effect due to the non-ideal directivity of the coupler shown in Fig. 2 (see text).

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Fig. 7 Schematic diagram showing the RF-injection-locking in the optical ((a), (b) and (c)) and the RF ((d), (e) and (f)), after the rectification process, frequency ranges (see the text for a detailed description).

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Fig. 8 Metal-metal QCL. Locking range vs the RF-power transmitted inside the QCL cavity.

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Fig. 9 Single plasmon waveguide QCL. The device is 3mm-long and 240μm wide. (a) CW Volage/Current and Optical-power/Current characteristics at a heat-sink temperature of 20K. Note that the emitted power is more than two orders of magnitude higher compared to the metal-metal QCL of Fig. 1 (b) Representative THz emission spectra measured at a currents of 1.15A (black dot in panel(a)) and 1.46A (blue dot in panel (a)).

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Fig. 10 Single plasmon QCL. (a) Schematic of the measurement setup for the RF injection-locking. The beam from the QCL is coupled on the Schottky mixer using a pair of 90-deg off-axis parabolic mirrors with f-numbers of 1 and 2, for collection and focusing respectively. The mixer is a commercial point-contact Schottky diode with an IF-bandwidth of approximately 40GHz, embedded into a corner-cube retro-reflector. The RF-signal from the mixer is first amplified using two wideband amplifier stages of 20 and 30dB gain and finally fed into the SA. (b) Single-shot RF spectrum collected with a RBW of 100kHz and a sweep time of 4ms. The QCL was driven at 1.46A, at a temperature of 20K. (c) Same spectrum of panel (b) collected with the “peak-hold” function of the SA switched ON. The measurement time was of ∼10s. (d) Injection-locked spectrum normalized to 0dBm maximum amplitude, and collected with a RBW of 1Hz with 100 video averages (blue line). The RF-power is of 0dBm (for clarity the x-axis was offset by the carrier frequency of 13.324GHz). The red line shows the spectrum of the RF-source (Anritsu MG3693B) normalized to 0dB.

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Fig. 11 Single plasmon QCL. RF spectra obtained by sweeping f _RF across the locking range, from 13.251GHz (bottom) to 13.333GHz (top). Spectra were collected with + 6dBm of RF-power, a RBW of 100kHz, and a sweep time of 4ms with 5 video averages. The QCL was driven at a current of 1.46A. Similarly to Fig. 4-6, the f _rt (black arrows) is pulled towards f _RF (red arrows) and a set of sidebands are generated. In the two central spectra f _rt is injection locked. The locking range is of approximately 70MHz.

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Fig. 12 Single plasmon QCL. (a) Optical-power/ Current characteristic at a heat-sink temperature of 20K. (b) Locking range as a function of RF-power from the synthesizer for different operating currents (red, blue and black dots in panel (a)). The solid curves are the results of fits using y = a x^b as fitting function, where y is the locking range, x the injected power, and a, b are fitting parameters. From the lower to the higher current the b-coefficients are 0.57 ± 0.02, 0.42 ± 0.01 and 0.57 ± 0.01, respectively.

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Fig. 13 Single plasmon QCL. (a) Normalized optical-modulation response in the range 100MHz-26GHz. The trace was obtained by sweeping the frequency of the RF-generator at a constant power of 5dBm, and by collecting the signal from the Schottky with the max-hold function of the SA switched ON. The signal from the Shottky mixer was amplified with a 30dB gain, 30GHz bandwidth amplifier. The QCL drive current was of 1.2A. (b) Emission spectra of the QCL at a current of 1.34A, without RF (blue curve), and with an RF-power of 20dBm. The green and red spectra were collected with f _RF outside and inside the locking range respectively.

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Fig. 14 4-mm long single plasmon QCL. (a) Single shot traces measured on a time window of 1ns. The top traces are an expanded section of the middle ones on a time window of 1μs. In the left traces the QCL is injection-locked at f _RF = 10.042GHz and with an RF-power of + 6dBm. In the right traces f _RF = 10.098GHz, i.e. at the edge of the locking range. The RF-power is of + 14dBm. (b) Fourier transforms of the corresponding (left and right) top traces of panel (a). The intensities of the fundamental 2nd and 3^d harmonics of f _rt are reported next to each line. In the right panel a number of sidebands can be seen around each harmonic.

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Equations (3)

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Δ f_{lock} = \frac{2 ν_{0}}{Q} \sqrt{\frac{P_{inj}}{P_{0}}} .

P_{diss} = \frac{δ I_{qcl}^{2} \cdot Re [Z_{qcl}]}{2},

δ I_{qcl} (m A) = 9 \sqrt{P_{R F} (m W)},