Abstract

Self-mixing velocity sensor based on a mutual-injected two-element terahertz quantum cascade laser (THz QCL) array is studied theoretically. The working characteristics of mutual-injected THz QCL array with different frequency detunings and self-mixing feedback strengths, as well as their influences on the self-mixing measurements are discussed in detail. Within the phase-locked range, each laser in the array reaches a stable state rapidly and can be used as a self-mixing detector due to the mutual injection coupling. The array will no longer be phase-locked when the frequency detuning of the lasers is too large, and only the laser that receives the feedback light can still be used for self-mixing velocity measurements. It is also found that even for the case of strong feedback, the THz QCLs will not be completely unstable and the self-mixing velocity measurements could also be possible. In addition, the simulation also shows that the array could measure two independent moving targets simultaneously. These results provide the theoretical support for the future applications of THz QCL arrays in self-mixing sensors.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Basic phase-locking, noise, and modulation properties of optically mutual-injected terahertz quantum cascade lasers

Yuanyuan Li, Ning Yang, Yan Xie, Weidong Chu, Wei Zhang, Suqing Duan, and Jian Wang
Opt. Express 27(3) 3146-3160 (2019)

Injection locking of a terahertz quantum cascade laser to a telecommunications wavelength frequency comb

Joshua R. Freeman, Lalitha Ponnampalam, Haymen Shams, Reshma A. Mohandas, Cyril C. Renaud, Paul Dean, Lianhe Li, A. Giles Davies, Alwyn J. Seeds, and Edmund H. Linfield
Optica 4(9) 1059-1064 (2017)

Origin of terminal voltage variations due to self-mixing in terahertz frequency quantum cascade lasers

Andrew Grier, Paul Dean, Alexander Valavanis, James Keeley, Iman Kundu, Jonathan D. Cooper, Gary Agnew, Thomas Taimre, Yah Leng Lim, Karl Bertling, Aleksandar D. Rakić, Lianhe H. Li, Paul Harrison, Edmund H. Linfield, Zoran Ikonić, A. Giles Davies, and Dragan Indjin
Opt. Express 24(19) 21948-21956 (2016)

References

  • View by:
  • |
  • |
  • |

  1. J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
    [Crossref]
  2. P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microwave Theory Tech. 52(10), 2438–2447 (2004).
    [Crossref]
  3. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
    [Crossref]
  4. B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
    [Crossref]
  5. P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
    [Crossref]
  6. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4(6), S283–S294 (2002).
    [Crossref]
  7. F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
    [Crossref]
  8. B. Meng and Q. J. Wang, “Theoretical investigation of injection-locked high modulation bandwidth quantum cascade lasers,” Opt. Express 20(2), 1450–1464 (2012).
    [Crossref]
  9. A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
    [Crossref]
  10. R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
    [Crossref]
  11. F. P. Mezzapesa, L. L. Columbo, M. Dabbicco, M. Brambilla, and G. Scamarcio, “QCL-based nonlinear sensing of independent targets dynamics,” Opt. Express 22(5), 5867–5874 (2014).
    [Crossref]
  12. L. K. Hoffmann, M. Klinkmüller, E. Mujagić, M. P. Semtsiv, W. Schrenk, W. T. Masselink, and G. Strasser, “Tree array quantum cascade laser,” Opt. Express 17(2), 649–657 (2009).
    [Crossref]
  13. Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
    [Crossref]
  14. T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016).
    [Crossref]
  15. Y. Halioua, G. Xu, S. Moumdji, L. Li, J. Zhu, E. H. Linfield, A. G. Davies, H. E. Beere, D. A. Ritchie, and R. Colombelli, “Phase-locked arrays of surface-emitting graded-photonic-heterostructure terahertz semiconductor lasers,” Opt. Express 23(5), 6915–6923 (2015).
    [Crossref]
  16. A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by $\pi$π coupling,” Nat. Photonics 13(1), 47–53 (2019).
    [Crossref]
  17. N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
    [Crossref]
  18. Y. Li, N. Yang, Y. Xie, W. Chu, W. Zhang, S. Duan, and J. Wang, “Basic phase-locking, noise, and modulation properties of optically mutual-injected terahertz quantum cascade lasers,” Opt. Express 27(3), 3146–3160 (2019).
    [Crossref]
  19. E. A. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclassical Opt. 6(2), L9–L12 (2004).
    [Crossref]
  20. F. Rogister and J. García-Ojalvo, “Symmetry breaking and high-frequency periodic oscillations in mutually coupled laser diodes,” Opt. Lett. 28(14), 1176–1178 (2003).
    [Crossref]
  21. L. Junges, A. Gavrielides, and J. A. C. Gallas, “Synchronization properties of two mutually delay-coupled semiconductor lasers,” J. Opt. Soc. Am. B 33(7), C65–C71 (2016).
    [Crossref]
  22. N. Jiang, W. Pan, L. Yan, B. Luo, W. Zhang, S. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
    [Crossref]
  23. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [Crossref]
  24. T. Gensty and W. Elsäßer, “Semiclassical model for the relative intensity noise of intersubband quantum cascade lasers,” Opt. Commun. 256(1-3), 171–183 (2005).
    [Crossref]
  25. Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, “Dynamic modeling of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 22–29 (2011).
    [Crossref]
  26. X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
    [Crossref]
  27. 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]
  28. C. Wang, F. Grillot, V. Kovanis, and J. Even, “Rate equation analysis of injection-locked quantum cascade lasers,” J. Appl. Phys. 113(6), 063104 (2013).
    [Crossref]
  29. S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, “Continuous-wave operation of terahertz quantum cascade lasers above liquid-nitrogen temperature,” Appl. Phys. Lett. 84(14), 2494–2496 (2004).
    [Crossref]
  30. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express 13(9), 3331–3339 (2005).
    [Crossref]

2019 (2)

2017 (2)

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

2016 (2)

T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016).
[Crossref]

L. Junges, A. Gavrielides, and J. A. C. Gallas, “Synchronization properties of two mutually delay-coupled semiconductor lasers,” J. Opt. Soc. Am. B 33(7), C65–C71 (2016).
[Crossref]

2015 (1)

2014 (2)

F. P. Mezzapesa, L. L. Columbo, M. Dabbicco, M. Brambilla, and G. Scamarcio, “QCL-based nonlinear sensing of independent targets dynamics,” Opt. Express 22(5), 5867–5874 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

2013 (4)

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
[Crossref]

C. Wang, F. Grillot, V. Kovanis, and J. Even, “Rate equation analysis of injection-locked quantum cascade lasers,” J. Appl. Phys. 113(6), 063104 (2013).
[Crossref]

2012 (1)

2011 (2)

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, “Dynamic modeling of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 22–29 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

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 (2)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

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

2005 (3)

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

T. Gensty and W. Elsäßer, “Semiclassical model for the relative intensity noise of intersubband quantum cascade lasers,” Opt. Commun. 256(1-3), 171–183 (2005).
[Crossref]

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

2004 (3)

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, “Continuous-wave operation of terahertz quantum cascade lasers above liquid-nitrogen temperature,” Appl. Phys. Lett. 84(14), 2494–2496 (2004).
[Crossref]

E. A. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclassical Opt. 6(2), L9–L12 (2004).
[Crossref]

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microwave Theory Tech. 52(10), 2438–2447 (2004).
[Crossref]

2003 (1)

2002 (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4(6), S283–S294 (2002).
[Crossref]

1980 (1)

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

Agnew, G.

Alhathlool, R.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Bai, Y.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Bandyopadhyay, N.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Barat, R.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Beere, H. E.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Y. Halioua, G. Xu, S. Moumdji, L. Li, J. Zhu, E. H. Linfield, A. G. Davies, H. E. Beere, D. A. Ritchie, and R. Colombelli, “Phase-locked arrays of surface-emitting graded-photonic-heterostructure terahertz semiconductor lasers,” Opt. Express 23(5), 6915–6923 (2015).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[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]

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]

Bertling, K.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

Borri, S.

Bosch, T.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4(6), S283–S294 (2002).
[Crossref]

Brambilla, M.

Burnett, A. D.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

Caffey, D.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Chan, W. L.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Chu, W.

Colombelli, R.

Columbo, L. L.

Dabbicco, M.

Davies, A. G.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

Y. Halioua, G. Xu, S. Moumdji, L. Li, J. Zhu, E. H. Linfield, A. G. Davies, H. E. Beere, D. A. Ritchie, and R. Colombelli, “Phase-locked arrays of surface-emitting graded-photonic-heterostructure terahertz semiconductor lasers,” Opt. Express 23(5), 6915–6923 (2015).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Day, T.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Dean, P.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Degl’Innocenti, R.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Deibel, J.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Destic, F.

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, “Dynamic modeling of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 22–29 (2011).
[Crossref]

Donati, S.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4(6), S283–S294 (2002).
[Crossref]

Duan, S.

Elsäßer, W.

T. Gensty and W. Elsäßer, “Semiclassical model for the relative intensity noise of intersubband quantum cascade lasers,” Opt. Commun. 256(1-3), 171–183 (2005).
[Crossref]

Even, J.

C. Wang, F. Grillot, V. Kovanis, and J. Even, “Rate equation analysis of injection-locked quantum cascade lasers,” J. Appl. Phys. 113(6), 063104 (2013).
[Crossref]

Federici, J. F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Gallas, J. A. C.

García-Ojalvo, J.

Gary, D.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Gavrielides, A.

Gensty, T.

T. Gensty and W. Elsäßer, “Semiclassical model for the relative intensity noise of intersubband quantum cascade lasers,” Opt. Commun. 256(1-3), 171–183 (2005).
[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]

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4(6), S283–S294 (2002).
[Crossref]

Grahn, H. T.

N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
[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]

Grier, A.

Grillot, F.

C. Wang, F. Grillot, V. Kovanis, and J. Even, “Rate equation analysis of injection-locked quantum cascade lasers,” J. Appl. Phys. 113(6), 063104 (2013).
[Crossref]

Halioua, Y.

Hoffmann, L. K.

Hofmann, S.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Hu, Q.

A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by $\pi$π coupling,” Nat. Photonics 13(1), 47–53 (2019).
[Crossref]

T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016).
[Crossref]

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

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, “Continuous-wave operation of terahertz quantum cascade lasers above liquid-nitrogen temperature,” Appl. Phys. Lett. 84(14), 2494–2496 (2004).
[Crossref]

Huang, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Hübers, H.-W.

N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
[Crossref]

Indjin, D.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Jiang, N.

Junges, L.

Kao, T.-Y.

T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016).
[Crossref]

Keeley, J.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

Khalatpour, A.

A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by $\pi$π coupling,” Nat. Photonics 13(1), 47–53 (2019).
[Crossref]

Khanna, S. P.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Kindness, S. J.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Kliese, R.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Klinkmüller, M.

Kobayashi, K.

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

Kohen, S.

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, “Continuous-wave operation of terahertz quantum cascade lasers above liquid-nitrogen temperature,” Appl. Phys. Lett. 84(14), 2494–2496 (2004).
[Crossref]

Kovanis, V.

C. Wang, F. Grillot, V. Kovanis, and J. Even, “Rate equation analysis of injection-locked quantum cascade lasers,” J. Appl. Phys. 113(6), 063104 (2013).
[Crossref]

Kumar, S.

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

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, “Continuous-wave operation of terahertz quantum cascade lasers above liquid-nitrogen temperature,” Appl. Phys. Lett. 84(14), 2494–2496 (2004).
[Crossref]

Kundu, I.

Lang, R.

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

Li, L.

Li, L. H.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

Li, Y.

Lim, Y. L.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Linfield, E. H.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

Y. Halioua, G. Xu, S. Moumdji, L. Li, J. Zhu, E. H. Linfield, A. G. Davies, H. E. Beere, D. A. Ritchie, and R. Colombelli, “Phase-locked arrays of surface-emitting graded-photonic-heterostructure terahertz semiconductor lasers,” Opt. Express 23(5), 6915–6923 (2015).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Lu, Q. Y.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Luo, B.

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]

Mandel, P.

E. A. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclassical Opt. 6(2), L9–L12 (2004).
[Crossref]

Masselink, W. T.

Meng, B.

Mezzapesa, F. P.

Mitrofanov, O.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Mittleman, D. M.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Mollier, J. C.

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, “Dynamic modeling of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 22–29 (2011).
[Crossref]

Moumdji, S.

Mujagic, E.

Nikolic, M.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Norgia, M.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4(6), S283–S294 (2002).
[Crossref]

Oliveira, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Pan, W.

Petitjean, Y.

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, “Dynamic modeling of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 22–29 (2011).
[Crossref]

Pushkarsky, M.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Qi, X.

Rakic, A. D.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Razeghi, M.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Reno, J. L.

A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by $\pi$π coupling,” Nat. Photonics 13(1), 47–53 (2019).
[Crossref]

T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016).
[Crossref]

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

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, “Continuous-wave operation of terahertz quantum cascade lasers above liquid-nitrogen temperature,” Appl. Phys. Lett. 84(14), 2494–2496 (2004).
[Crossref]

Richter, H.

N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
[Crossref]

Ritchie, D. A.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Y. Halioua, G. Xu, S. Moumdji, L. Li, J. Zhu, E. H. Linfield, A. G. Davies, H. E. Beere, D. A. Ritchie, and R. Colombelli, “Phase-locked arrays of surface-emitting graded-photonic-heterostructure terahertz semiconductor lasers,” Opt. Express 23(5), 6915–6923 (2015).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[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]

Rogister, F.

Rothbart, N.

N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
[Crossref]

Scamarcio, G.

Schrenk, W.

Schrottke, L.

N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
[Crossref]

Schulkin, B.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Semtsiv, M. P.

Siegel, P. H.

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microwave Theory Tech. 52(10), 2438–2447 (2004).
[Crossref]

Sirtori, C.

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, “Dynamic modeling of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 22–29 (2011).
[Crossref]

Slivken, S.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Strasser, G.

Taimre, T.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

Tredicucci, A.

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]

Tsao, S.

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

Valavanis, A.

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Viktorov, E. A.

E. A. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclassical Opt. 6(2), L9–L12 (2004).
[Crossref]

Vitiello, M. S.

Wallis, R.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Wang, C.

C. Wang, F. Grillot, V. Kovanis, and J. Even, “Rate equation analysis of injection-locked quantum cascade lasers,” J. Appl. Phys. 113(6), 063104 (2013).
[Crossref]

Wang, J.

Wang, Q. J.

Wei, B.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Weimer, P. B.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Wienold, M.

N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
[Crossref]

Williams, B. S.

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

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

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, “Continuous-wave operation of terahertz quantum cascade lasers above liquid-nitrogen temperature,” Appl. Phys. Lett. 84(14), 2494–2496 (2004).
[Crossref]

Wilson, S. J.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

Xiang, S.

Xiao, L.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Xie, Y.

Xu, G.

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]

Yacomotti, A. M.

E. A. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclassical Opt. 6(2), L9–L12 (2004).
[Crossref]

Yan, L.

Yang, L.

Yang, N.

Zhang, W.

Zheng, D.

Zhu, J.

Zimdars, D.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

ACS Photonics (1)

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. B. Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Appl. Phys. Lett. (3)

Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q. Y. Lu, D. Caffey, M. Pushkarsky, T. Day, and M. Razeghi, “High power, continuous wave, quantum cascade ring laser,” Appl. Phys. Lett. 99(26), 261104 (2011).
[Crossref]

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

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, “Continuous-wave operation of terahertz quantum cascade lasers above liquid-nitrogen temperature,” Appl. Phys. Lett. 84(14), 2494–2496 (2004).
[Crossref]

IEEE J. Quantum Electron. (1)

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

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, “Dynamic modeling of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 22–29 (2011).
[Crossref]

IEEE Sens. J. (1)

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13(1), 37–43 (2013).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microwave Theory Tech. 52(10), 2438–2447 (2004).
[Crossref]

IEEE Trans. Terahertz Sci. Technol. (1)

N. Rothbart, H. Richter, M. Wienold, L. Schrottke, H. T. Grahn, and H.-W. Hübers, “Fast 2-D and 3-D terahertz imaging with a quantum-cascade laser and a scanning mirror,” IEEE Trans. Terahertz Sci. Technol. 3(5), 617–624 (2013).
[Crossref]

J. Appl. Phys. (1)

C. Wang, F. Grillot, V. Kovanis, and J. Even, “Rate equation analysis of injection-locked quantum cascade lasers,” J. Appl. Phys. 113(6), 063104 (2013).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. A: Pure Appl. Opt. (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4(6), S283–S294 (2002).
[Crossref]

J. Opt. B: Quantum Semiclassical Opt. (1)

E. A. Viktorov, A. M. Yacomotti, and P. Mandel, “Semiconductor lasers coupled face-to-face,” J. Opt. B: Quantum Semiclassical Opt. 6(2), L9–L12 (2004).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. D: Appl. Phys. (1)

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers—a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

Nat. Photonics (3)

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

T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016).
[Crossref]

A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by $\pi$π coupling,” Nat. Photonics 13(1), 47–53 (2019).
[Crossref]

Opt. Commun. (1)

T. Gensty and W. Elsäßer, “Semiclassical model for the relative intensity noise of intersubband quantum cascade lasers,” Opt. Commun. 256(1-3), 171–183 (2005).
[Crossref]

Opt. Express (8)

X. Qi, G. Agnew, I. Kundu, T. Taimre, Y. L. Lim, K. Bertling, P. Dean, A. Grier, A. Valavanis, E. H. Linfield, A. G. Davies, D. Indjin, and A. D. Rakić, “Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer,” Opt. Express 25(9), 10153–10165 (2017).
[Crossref]

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

Y. Halioua, G. Xu, S. Moumdji, L. Li, J. Zhu, E. H. Linfield, A. G. Davies, H. E. Beere, D. A. Ritchie, and R. Colombelli, “Phase-locked arrays of surface-emitting graded-photonic-heterostructure terahertz semiconductor lasers,” Opt. Express 23(5), 6915–6923 (2015).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Dabbicco, M. Brambilla, and G. Scamarcio, “QCL-based nonlinear sensing of independent targets dynamics,” Opt. Express 22(5), 5867–5874 (2014).
[Crossref]

L. K. Hoffmann, M. Klinkmüller, E. Mujagić, M. P. Semtsiv, W. Schrenk, W. T. Masselink, and G. Strasser, “Tree array quantum cascade laser,” Opt. Express 17(2), 649–657 (2009).
[Crossref]

Y. Li, N. Yang, Y. Xie, W. Chu, W. Zhang, S. Duan, and J. Wang, “Basic phase-locking, noise, and modulation properties of optically mutual-injected terahertz quantum cascade lasers,” Opt. Express 27(3), 3146–3160 (2019).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref]

B. Meng and Q. J. Wang, “Theoretical investigation of injection-locked high modulation bandwidth quantum cascade lasers,” Opt. Express 20(2), 1450–1464 (2012).
[Crossref]

Opt. Lett. (1)

Rep. Prog. Phys. (1)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Semicond. Sci. Technol. (1)

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons, and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. The schematic diagram of the self-mixing velocity measurements for (a) one target and (b) two targets based on two face-to-face mutual-injected THz QCLs. (c) Two mutual-injected THz QCLs receive feedback lights from two targets at the same time.
Fig. 2.
Fig. 2. The simulation of the phase-locked THz QCL array with frequency detuning $\Delta \Omega /2\pi =0.1$ GHz and feedback strength $\kappa _{OL}=0.1\kappa _c$. (a) Time evolution of $N_{A/B}$ with $\Delta {L_A}=40\mu {m}$ and $120\mu {m}$, (b) the self-mixing signals given by QCLs A and B with moving target $\nu _{TA}=60$ mm/s, (c) spectrums of self-mixing signals.
Fig. 3.
Fig. 3. Out of the phase-locked range, the simulation of THz QCL array with frequency detuning $\Delta \Omega /2\pi =10$ GHz and feedback strength $\kappa _{OL}=0.1\kappa _c$. (a) Time evolution of $N_{A/B}$ with $\Delta {L_A}=40\mu {m}$ and $\Delta {L_A}=120\mu {m}$, (b) the self-mixing signals of QCLs A and B with the moving target $\nu _{TA}=60$ mm/s, (c) spectrums of self-mixing signals.
Fig. 4.
Fig. 4. For the case of strong feedback strength, the simulation with $\kappa _{OL} = 0.4\kappa _c$, $\Delta \Omega /2\pi = 0.16$ GHz. (a) Time evolution of $N_{A/B}$ with $\Delta {L_A} = 40\mu {m}$ and $\Delta {L_A} = 80\mu {m}$, (b) the self-mixing signals with the moving target $\nu _{TA} = 60$ mm/s, (c) spectrums of self-mixing signals.
Fig. 5.
Fig. 5. Self-mixing signals and corresponding spectrums of QCLs A and B with two independent targets. (a)–(d) Simulations for the case in Fig. 1(b). (a) and (b) $\Delta \Omega /2\pi =0.1$GHz, $\kappa _{OL}$=$\kappa _{OR}=0.1\kappa _c$, (c) and (d) $\Delta \Omega /2\pi =10$GHz, $\kappa _{OL}$=$\kappa _{OR}=0.1\kappa _c$. (e)–(f) Simulations for the case in Fig. 1(c) with $\Delta \Omega /2\pi =0.1$GHz, $\kappa _A=0.1\kappa _c$, and $\kappa _B=0.05\kappa _c$.

Tables (1)

Tables Icon

Table 1. Values of key parameters used in the simulations.

Equations (19)

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

d ε A ( t ) d t = i Ω A 0 ε A ( t ) + 1 2 ( 1 + i α ) { Z g [ N A , 3 ( t ) N A , 2 ( t ) ] 1 τ p } ε A ( t ) + κ c τ l ε B ( t τ e x t ) + κ O L τ l ε A ( t τ O L ) ,
d ε B ( t ) d t = i Ω B 0 ε B ( t ) + 1 2 ( 1 + i α ) { Z g [ N B , 3 ( t ) N B , 2 ( t ) ] 1 τ p } ε B ( t ) + κ c τ l ε A ( t τ e x t ) ,
d N A , 3 ( t ) d t = I i n , A q N A , 3 ( t ) τ 32 N A , 3 ( t ) τ 31 g [ N A , 3 ( t ) N A , 2 ( t ) ] | ε A ( t ) | 2 ,
d N B , 3 ( t ) d t = I i n , B q N B , 3 ( t ) τ 32 N B , 3 ( t ) τ 31 g [ N B , 3 ( t ) N B , 2 ( t ) ] | ε B ( t ) | 2 ,
d N A , 2 ( t ) d t = N A , 3 ( t ) τ 32 N A , 2 ( t ) τ 21 + g [ N A , 3 ( t ) N A , 2 ( t ) ] | ε A ( t ) | 2 ,
d N B , 2 ( t ) d t = N B , 3 ( t ) τ 32 N B , 2 ( t ) τ 21 + g [ N B , 3 ( t ) N B , 2 ( t ) ] | ε B ( t ) | 2 ,
d N A , 1 ( t ) d t = N A , 3 ( t ) τ 31 + N A , 2 ( t ) τ 21 N A , 1 ( t ) τ o u t ,
d N B , 1 ( t ) d t = N B , 3 ( t ) τ 31 + N B , 2 ( t ) τ 21 N B , 1 ( t ) τ o u t .
ε A ( t ) = F A exp ( i ω L t ) , ε B ( t ) = F B exp ( i ω L t + i ϕ L ) ,
0 = Ω A 0 ω L κ c τ l F B F A 1 + α 2 sin ( ω L τ e x t ϕ L + arctan α ) κ O L τ l 1 + α 2 sin ( ω L τ O L + arctan α ) ,
0 = Ω B 0 ω L κ c τ l F A F B 1 + α 2 sin ( ω L τ e x t + ϕ L + arctan α ) .
Δ Ω = κ c τ l F A F B 1 + α 2 sin ( ω L τ e x t + ϕ L + arctan α ) κ c τ l F B F A 1 + α 2 sin ( ω L τ e x t ϕ L + arctan α ) κ O L τ l 1 + α 2 sin ( ω L τ O L + arctan α ) .
| Δ Ω | m a x = ( κ c F B F A + κ c F A F B + κ O L ) 1 + α 2 τ l .
| Δ Ω | m a x = ( 2 κ c + κ O L ) 1 + α 2 τ l .
N A = 1 Z g [ 2 κ c τ l F B F A cos ( ω L τ e x t ϕ L ) 2 κ O L τ l cos ( ω L 2 L 0 , O L c + ω T A t ) + 1 τ p ] ,
N B = 1 Z g [ 2 κ c τ l F A F B cos ( ω L τ e x t + ϕ L ) + 1 τ p ] ,
d ε B ( t ) d t = i Ω B 0 ε B ( t ) + 1 2 ( 1 + i α ) { Z g [ N B , 3 ( t ) N B , 2 ( t ) ] 1 τ p } ε B ( t ) + κ c τ l ε A ( t τ e x t ) + κ O R τ l ε B ( t τ O R ) .
d ε A ( t ) d t = i Ω A 0 ε A ( t ) + 1 2 ( 1 + i α ) { Z g [ N A , 3 ( t ) N A , 2 ( t ) ] 1 τ p } ε A ( t ) + κ c τ l ε B ( t τ e x t ) + κ A τ l ε A ( t τ A ) + κ B τ l ε A ( t τ B ) ,
d ε B ( t ) d t = i Ω B 0 ε B ( t ) + 1 2 ( 1 + i α ) { Z g [ N B , 3 ( t ) N B , 2 ( t ) ] 1 τ p } ε B ( t ) + κ c τ l ε A ( t τ e x t ) + κ B τ l ε B ( t τ B ) + κ A τ l ε B ( t τ A ) .

Metrics