Abstract

We report the measurement of the frequency noise power spectral density of a quantum cascade laser emitting at 2.5THz. The technique is based on heterodyning the laser emission frequency with a harmonic of the repetition rate of a near-infrared laser comb. This generates a beatnote in the radio frequency range that is demodulated using a tracking oscillator allowing measurement of the frequency noise. We find that the latter is strongly affected by the level of optical feedback, and obtain an intrinsic linewidth of ~230Hz, for an output power of 2mW.

© 2012 OSA

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  1. B. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics1(9), 517–525 (2007).
    [CrossRef]
  2. S. Kumar, Q. Hu, and J. Reno, “186K operation of terahertz quantum cascade lasers based on diagonal design,” Appl. Phys. Lett.94(13), 131105 (2009).
    [CrossRef]
  3. S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics5(5), 306–313 (2011).
    [CrossRef]
  4. 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]
  5. 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]
  6. 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. Photonics4(9), 636–640 (2010).
    [CrossRef]
  7. M. Ravaro, C. Manquest, C. Sirtori, S. Barbieri, G. Santarelli, K. Blary, J.-F. Lampin, S. P. Khanna, and E. H. Linfield, “Phase-locking of a 2.5 THz quantum cascade laser to a frequency comb using a GaAs photomixer,” Opt. Lett.36(20), 3969–3971 (2011).
    [CrossRef] [PubMed]
  8. R. Paiella, Intersubband Transitions in Quantum Structures (McGraw Hill Nanoscience and Technology, 2006)
  9. R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett.92(7), 071106 (2008).
    [CrossRef]
  10. M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a THz laser,” Nat. Photonics6(8), 525–528 (2012).
    [CrossRef]
  11. 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]
  12. F. Rhiele, Frequency Standards (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004).
  13. W. P. Robins, Phase Noise in Signal Sources (IEE Telecommunications series, 1992).
  14. L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, and R. O. Miles, “Spectral characteristics of semiconductor lasers with optical feedback,” IEEE J. Quantum Electron.18(4), 555–564 (1982).
    [CrossRef]
  15. G. P. Agrawal, “Line narrowing in a single-mode injection laser due to external optical feedback,” IEEE J. Quantum Electron.20(5), 468–471 (1984).
    [CrossRef]
  16. G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on the longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
    [CrossRef]
  17. R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol.11(4), 1655–1661 (1986).
    [CrossRef]
  18. The ratio 2.6x10−3/0.08 = 0.032 between the ε coefficients at minimum and maximum isolation corresponds to the field amplitude isolation, i.e. to a power isolation of 1x10−3, or 30dB. By directly measuring the performance of our isolator using a power detector we found instead an isolation of 16dB. There are several possible explanations for this large difference. The most likely is related to the thickness of the quartz wave plate (3.1+/−0.005mm) being much larger that the QCL wavelength. Therefore, given the QCL large free spectral range of 16GHz, the amount of isolation is strongly dependent on the Fabry-Perot lasing mode number, which can change depending on the feedback conditions. For technical reasons the direct measurement was performed with the QCL operating in pulsed mode, thus lasing on several longitudinal modes, which underestimates the isolation. Instead the QCL was lasing in continuous wave on a single-mode when we measured the frequency pulling.
  19. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron.18(2), 259–264 (1982).
    [CrossRef]
  20. 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. Express18(20), 20799–20816 (2010).
    [CrossRef] [PubMed]
  21. M. Yamanishi, T. Edamura, K. Fujita, N. Akikusa, and H. Kan, “Theory of the intrinsic linewidth of quantum cascade lasers: hidden reason for the narrow linewidth and line broadening by therma photons,” IEEE J. Quantum Electron.44(1), 12–29 (2008).
    [CrossRef]

2012 (1)

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

2011 (2)

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

M. Ravaro, C. Manquest, C. Sirtori, S. Barbieri, G. Santarelli, K. Blary, J.-F. Lampin, S. P. Khanna, and E. H. Linfield, “Phase-locking of a 2.5 THz quantum cascade laser to a frequency comb using a GaAs photomixer,” Opt. Lett.36(20), 3969–3971 (2011).
[CrossRef] [PubMed]

2010 (2)

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. Express18(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. Photonics4(9), 636–640 (2010).
[CrossRef]

2009 (1)

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

2008 (2)

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

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

2007 (1)

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

2004 (3)

1986 (1)

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

1984 (2)

G. P. Agrawal, “Line narrowing in a single-mode injection laser due to external optical feedback,” IEEE J. Quantum Electron.20(5), 468–471 (1984).
[CrossRef]

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on the longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

1982 (2)

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, and R. O. Miles, “Spectral characteristics of semiconductor lasers with optical feedback,” IEEE J. Quantum Electron.18(4), 555–564 (1982).
[CrossRef]

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

Acket, G.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on the longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, “Line narrowing in a single-mode injection laser due to external optical feedback,” IEEE J. Quantum Electron.20(5), 468–471 (1984).
[CrossRef]

Ajili, L.

Akikusa, N.

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

Alton, 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]

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]

Barbieri, S.

M. Ravaro, C. Manquest, C. Sirtori, S. Barbieri, G. Santarelli, K. Blary, J.-F. Lampin, S. P. Khanna, and E. H. Linfield, “Phase-locking of a 2.5 THz quantum cascade laser to a frequency comb using a GaAs photomixer,” Opt. Lett.36(20), 3969–3971 (2011).
[CrossRef] [PubMed]

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

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. Express18(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. Photonics4(9), 636–640 (2010).
[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]

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]

Barkan, A.

Bartalini, S.

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

Beere, H.

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. Photonics4(9), 636–640 (2010).
[CrossRef]

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

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]

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, 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]

Beltram, F.

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

Blary, K.

Chraplyvy, A. R.

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

Colombelli, R.

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. Photonics4(9), 636–640 (2010).
[CrossRef]

Consolino, L.

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

Dandridge, A.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, and R. O. Miles, “Spectral characteristics of semiconductor lasers with optical feedback,” IEEE J. Quantum Electron.18(4), 555–564 (1982).
[CrossRef]

Davies, A. G.

De Natale, P.

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

Den Boef, A.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on the longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Dengler, R.

Ding, L.

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. Photonics4(9), 636–640 (2010).
[CrossRef]

Edamura, T.

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

Faist, J.

Filloux, P.

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]

Fujita, K.

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

Gellie, P.

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

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. Express18(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. Photonics4(9), 636–640 (2010).
[CrossRef]

Giuliani, G.

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

Goldberg, L.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, and R. O. Miles, “Spectral characteristics of semiconductor lasers with optical feedback,” IEEE J. Quantum Electron.18(4), 555–564 (1982).
[CrossRef]

Green, R. P.

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

Henry, C. H.

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

Hu, Q.

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

Inguscio, M.

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

Kan, H.

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

Khanna, S. P.

Kumar, S.

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

Lampin, J.-F.

Lenstra, D.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on the longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Linfield, E. H.

Linfield, H.

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

Mahler, L.

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

Maineult, W.

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. Photonics4(9), 636–640 (2010).
[CrossRef]

Manquest, C.

Miles, R. O.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, and R. O. Miles, “Spectral characteristics of semiconductor lasers with optical feedback,” IEEE J. Quantum Electron.18(4), 555–564 (1982).
[CrossRef]

Mittleman, D. M.

Ravaro, M.

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

M. Ravaro, C. Manquest, C. Sirtori, S. Barbieri, G. Santarelli, K. Blary, J.-F. Lampin, S. P. Khanna, and E. H. Linfield, “Phase-locking of a 2.5 THz quantum cascade laser to a frequency comb using a GaAs photomixer,” Opt. Lett.36(20), 3969–3971 (2011).
[CrossRef] [PubMed]

Reno, J.

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

Ritchie, D.

Ritchie, D. A.

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. Photonics4(9), 636–640 (2010).
[CrossRef]

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

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]

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, 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]

Sagnes, I.

Santarelli, G.

M. Ravaro, C. Manquest, C. Sirtori, S. Barbieri, G. Santarelli, K. Blary, J.-F. Lampin, S. P. Khanna, and E. H. Linfield, “Phase-locking of a 2.5 THz quantum cascade laser to a frequency comb using a GaAs photomixer,” Opt. Lett.36(20), 3969–3971 (2011).
[CrossRef] [PubMed]

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

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. Photonics4(9), 636–640 (2010).
[CrossRef]

Scalari, G.

Siegel, P. H.

Sirtori, C.

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

M. Ravaro, C. Manquest, C. Sirtori, S. Barbieri, G. Santarelli, K. Blary, J.-F. Lampin, S. P. Khanna, and E. H. Linfield, “Phase-locking of a 2.5 THz quantum cascade laser to a frequency comb using a GaAs photomixer,” Opt. Lett.36(20), 3969–3971 (2011).
[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. Express18(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. Photonics4(9), 636–640 (2010).
[CrossRef]

Taschin, A.

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

Taylor, H. F.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, and R. O. Miles, “Spectral characteristics of semiconductor lasers with optical feedback,” IEEE J. Quantum Electron.18(4), 555–564 (1982).
[CrossRef]

Tittel, F. K.

Tkach, R. W.

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

Tredicucci, A.

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

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

Verbeek, B.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on the longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Vitiello, M. S.

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

Weller, J. F.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, and R. O. Miles, “Spectral characteristics of semiconductor lasers with optical feedback,” IEEE J. Quantum Electron.18(4), 555–564 (1982).
[CrossRef]

Williams, B.

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

Withington, S.

Xu, J. H.

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

Yamanishi, M.

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

Appl. Phys. Lett. (3)

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

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]

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

IEEE J. Quantum Electron. (5)

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

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

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, and R. O. Miles, “Spectral characteristics of semiconductor lasers with optical feedback,” IEEE J. Quantum Electron.18(4), 555–564 (1982).
[CrossRef]

G. P. Agrawal, “Line narrowing in a single-mode injection laser due to external optical feedback,” IEEE J. Quantum Electron.20(5), 468–471 (1984).
[CrossRef]

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on the longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

J. Lightwave Technol. (1)

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

Nat. Photonics (4)

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

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

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

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. Photonics4(9), 636–640 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Other (4)

F. Rhiele, Frequency Standards (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004).

W. P. Robins, Phase Noise in Signal Sources (IEE Telecommunications series, 1992).

The ratio 2.6x10−3/0.08 = 0.032 between the ε coefficients at minimum and maximum isolation corresponds to the field amplitude isolation, i.e. to a power isolation of 1x10−3, or 30dB. By directly measuring the performance of our isolator using a power detector we found instead an isolation of 16dB. There are several possible explanations for this large difference. The most likely is related to the thickness of the quartz wave plate (3.1+/−0.005mm) being much larger that the QCL wavelength. Therefore, given the QCL large free spectral range of 16GHz, the amount of isolation is strongly dependent on the Fabry-Perot lasing mode number, which can change depending on the feedback conditions. For technical reasons the direct measurement was performed with the QCL operating in pulsed mode, thus lasing on several longitudinal modes, which underestimates the isolation. Instead the QCL was lasing in continuous wave on a single-mode when we measured the frequency pulling.

R. Paiella, Intersubband Transitions in Quantum Structures (McGraw Hill Nanoscience and Technology, 2006)

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Figures (3)

Fig. 1
Fig. 1

Experimental setup (see text). At the output of the balanced detection fbeat is of the order of a few tens of MHz. Before the band pass filter (labeled BP) fbeat is summed to the frequency of an RF synthesiser (not shown) in order to bring it close to 140MHz, the frequency of operation of the VCO. THz optical isolation is obtained as follows. A wire-grid polarizer is oriented parallel to the TM-polarized light from the QCL. Next a quartz quarter-waveplate is oriented with its fast-axis at 45deg with respect to the polarizer, so that at its output the THz light is left circularly polarized. The polarization is changed from left to right circular after reflection from the ZnTe crystal, producing, after the quarter-waveplate, a linearly polarized beam ideally oriented at 90deg with respect to the wire grid polarizer.

Fig. 2
Fig. 2

FNSD (Sν(f)) traces measured with the FFT analyser of the QCL (red), the RF generator (blue), and of n × frep ~104 × frep (green). The black line is obtained by dividing the red line by the blue line, and represents the FNSD of the QCL normalised to the frequency noise produced by the detection system noise floor (see text). The black dotted lines are given by the relation Sν(f) = (2/SNR) × f 2, for SNRs of 80, 89, 100, and 110dB in 1Hz bandwidth. The horizontal grey line is a guide to the eye indicating the quantum noise limited QCL FNSD. Shaded grey areas correspond to regions where the black line does not correspond to the QCL FNSD. We attribute the peak close to 167kHz in the green curve to a spurious frequency noise of the near-IR comb produced by stray oscillations of the power-supply. The level of the peak is mode-locking state dependent. This explains the discrepancy between the peaks in the black and green curves.

Fig. 3
Fig. 3

FNSD curves of the QCL for output powers/currents of 2mW/1.3A (black) and 0.8mW/1.12A (blue), and maximum (solid) and minimum isolation (dotted). The output power corresponds to the power emitted by one QCL facet and was measured with a calibrated THz power meter. All the curves were normalised to the FNSD produced by the detection system noise floor (see text and the caption of Fig. 2). The solid black trace is the same as the black trace of Fig. 2.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

f beat (t)= v QCL (t)n × f rep (t)
v QCL v 0 = cK 4π L ext [sin(4π v QCL L ext /c)+ α H cos(4π v QCL L ext /c)]
K=ε(1- R QCL ) R ZnTe R QCL L ext L QCL n eff
Δv= Δ v 0 { 1+ 1+ α H 2 Kcos[(4π v QCL L ext /c)+t g -1 α H )] } 2
Δ v 0 = ( c n ' eff ) 2 h v QCL α t α m (1+ α H 2 ) 8πP

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