Abstract

We demonstrate a common-path interferometer to measure the independent displacement of multiple targets through nonlinear frequency mixing in a quantum-cascade laser (QCL). The sensing system exploits the unique stability of QCLs under strong optical feedback to access the intrinsic nonlinearity of the active medium. The experimental results using an external dual cavity are in excellent agreement with the numerical simulations based on the Lang-Kobayashi equations.

© 2014 Optical Society of America

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  1. F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
    [CrossRef] [PubMed]
  2. J. von Staden, T. Gensty, W. Elsässer, G. Giuliani, C. Mann, “Measurements of the alpha factor of a distributed-feedback quantum cascade laser by an optical feedback self-mixing technique,” Opt. Lett. 31(17), 2574–2576 (2006).
    [CrossRef] [PubMed]
  3. R. P. Green, J. H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92(7), 071106 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. F. P. Mezzapesa, V. Spagnolo, A. Antonio, G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett. 101(17), 171107 (2012).
    [CrossRef]
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    [CrossRef]
  8. S. Ottonelli, F. De Lucia, M. Di Vietro, M. Dabbicco, G. Scamarcio, F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20(16), 1360–1362 (2008).
    [CrossRef]
  9. X. Dai, M. Wang, C. Zhou, “Multiplexing self-mixing interference in fiber ring lasers,” IEEE Photon. Technol. Lett. 22(21), 1619–1621 (2010).
    [CrossRef]
  10. Y. L. Lim, R. Kliese, K. Bertling, K. Tanimizu, P. A. Jacobs, A. D. Rakić, “Self-mixing flow sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 18(11), 11720–11727 (2010).
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    [CrossRef] [PubMed]
  12. F. Zhao, “Sub-aperture interferometers: multiple target sub-beams are derived from the same measurement beam,” NASA Tech Briefs. 29–30 (2010).
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  15. R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [CrossRef]
  16. M. Wang, G. Lai, “Self-mixing microscopic interferometer for the measurement of micro-profile,” Opt. Commun. 238(4–6), 237–244 (2004).
    [CrossRef]

2013

2012

M. C. Phillips, M. S. Taubman, “Intracavity sensing via compliance voltage in an external cavity quantum cascade laser,” Opt. Lett. 37(13), 2664–2666 (2012).
[CrossRef] [PubMed]

F. P. Mezzapesa, V. Spagnolo, A. Antonio, G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett. 101(17), 171107 (2012).
[CrossRef]

2011

2010

2008

S. Ottonelli, F. De Lucia, M. Di Vietro, M. Dabbicco, G. Scamarcio, F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20(16), 1360–1362 (2008).
[CrossRef]

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

2006

2004

M. Wang, G. Lai, “Self-mixing microscopic interferometer for the measurement of micro-profile,” Opt. Commun. 238(4–6), 237–244 (2004).
[CrossRef]

1994

1986

1980

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

Ancona, A.

Antonio, A.

F. P. Mezzapesa, V. Spagnolo, A. Antonio, G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett. 101(17), 171107 (2012).
[CrossRef]

Beere, H. E.

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

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

Bertling, K.

Borri, S.

Brambilla, M.

Columbo, L.

Columbo, L. L.

Dabbicco, M.

Dai, X.

X. Dai, M. Wang, C. Zhou, “Multiplexing self-mixing interference in fiber ring lasers,” IEEE Photon. Technol. Lett. 22(21), 1619–1621 (2010).
[CrossRef]

Davies, A. G.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

De Lucia, F.

F. P. Mezzapesa, L. Columbo, M. Brambilla, M. Dabbicco, A. Ancona, T. Sibillano, F. De Lucia, P. M. Lugarà, G. Scamarcio, “Simultaneous measurement of multiple target displacements by self-mixing interferometry in a single laser diode,” Opt. Express 19(17), 16160–16173 (2011).
[CrossRef] [PubMed]

S. Ottonelli, F. De Lucia, M. Di Vietro, M. Dabbicco, G. Scamarcio, F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20(16), 1360–1362 (2008).
[CrossRef]

Dean, P.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

Di Vietro, M.

S. Ottonelli, F. De Lucia, M. Di Vietro, M. Dabbicco, G. Scamarcio, F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20(16), 1360–1362 (2008).
[CrossRef]

Elsässer, W.

Gensty, T.

Giuliani, G.

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

J. von Staden, T. Gensty, W. Elsässer, G. Giuliani, C. Mann, “Measurements of the alpha factor of a distributed-feedback quantum cascade laser by an optical feedback self-mixing technique,” Opt. Lett. 31(17), 2574–2576 (2006).
[CrossRef] [PubMed]

Green, R. P.

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

Harrison, P.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Ikonic, Z.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

Indjin, D.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Jacobs, P. A.

Juskaitis, R.

Khanna, S. P.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

Kliese, R.

Kobayashi, K.

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

Lachab, M.

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

Lai, G.

M. Wang, G. Lai, “Self-mixing microscopic interferometer for the measurement of micro-profile,” Opt. Commun. 238(4–6), 237–244 (2004).
[CrossRef]

Lang, R.

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

Lim, Y. L.

Linfield, E.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

Linfield, E. H.

Lugarà, P. M.

Mahler, L.

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

Mann, C.

Mezzapesa, F. P.

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

F. P. Mezzapesa, V. Spagnolo, A. Antonio, G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett. 101(17), 171107 (2012).
[CrossRef]

F. P. Mezzapesa, L. Columbo, M. Brambilla, M. Dabbicco, A. Ancona, T. Sibillano, F. De Lucia, P. M. Lugarà, G. Scamarcio, “Simultaneous measurement of multiple target displacements by self-mixing interferometry in a single laser diode,” Opt. Express 19(17), 16160–16173 (2011).
[CrossRef] [PubMed]

S. Ottonelli, F. De Lucia, M. Di Vietro, M. Dabbicco, G. Scamarcio, F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20(16), 1360–1362 (2008).
[CrossRef]

Mochizuki, A.

Nikolic, M.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Ottonelli, S.

S. Ottonelli, F. De Lucia, M. Di Vietro, M. Dabbicco, G. Scamarcio, F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20(16), 1360–1362 (2008).
[CrossRef]

Phillips, M. C.

Rakic, A. D.

Rea, N. P.

Ritchie, D. A.

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

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

Scamarcio, G.

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

F. P. Mezzapesa, V. Spagnolo, A. Antonio, G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett. 101(17), 171107 (2012).
[CrossRef]

F. P. Mezzapesa, L. Columbo, M. Brambilla, M. Dabbicco, A. Ancona, T. Sibillano, F. De Lucia, P. M. Lugarà, G. Scamarcio, “Simultaneous measurement of multiple target displacements by self-mixing interferometry in a single laser diode,” Opt. Express 19(17), 16160–16173 (2011).
[CrossRef] [PubMed]

S. Ottonelli, F. De Lucia, M. Di Vietro, M. Dabbicco, G. Scamarcio, F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20(16), 1360–1362 (2008).
[CrossRef]

Shinohara, S.

Sibillano, T.

Spagnolo, V.

F. P. Mezzapesa, V. Spagnolo, A. Antonio, G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett. 101(17), 171107 (2012).
[CrossRef]

Sumi, M.

Tanimizu, K.

Taubman, M. S.

Tredicucci, A.

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

Valavanis, A.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[CrossRef] [PubMed]

Vitiello, M. S.

von Staden, J.

Wang, M.

X. Dai, M. Wang, C. Zhou, “Multiplexing self-mixing interference in fiber ring lasers,” IEEE Photon. Technol. Lett. 22(21), 1619–1621 (2010).
[CrossRef]

M. Wang, G. Lai, “Self-mixing microscopic interferometer for the measurement of micro-profile,” Opt. Commun. 238(4–6), 237–244 (2004).
[CrossRef]

Wilson, S. J.

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

Wilson, T.

Xu, J. H.

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

Yoshida, H.

Zhou, C.

X. Dai, M. Wang, C. Zhou, “Multiplexing self-mixing interference in fiber ring lasers,” IEEE Photon. Technol. Lett. 22(21), 1619–1621 (2010).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

F. P. Mezzapesa, V. Spagnolo, A. Antonio, G. Scamarcio, “Detection of ultrafast laser ablation using quantum cascade laser-based sensing,” Appl. Phys. Lett. 101(17), 171107 (2012).
[CrossRef]

Y. L. Lim, P. Dean, M. Nikolic, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonic, P. Harrison, E. Linfield, A. G. Davies, S. J. Wilson, A. D. Rakic, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99(8), 081108 (2011).
[CrossRef]

IEEE J. Quantum Electron.

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

IEEE Photon. Technol. Lett.

S. Ottonelli, F. De Lucia, M. Di Vietro, M. Dabbicco, G. Scamarcio, F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20(16), 1360–1362 (2008).
[CrossRef]

X. Dai, M. Wang, C. Zhou, “Multiplexing self-mixing interference in fiber ring lasers,” IEEE Photon. Technol. Lett. 22(21), 1619–1621 (2010).
[CrossRef]

Opt. Commun.

M. Wang, G. Lai, “Self-mixing microscopic interferometer for the measurement of micro-profile,” Opt. Commun. 238(4–6), 237–244 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Other

F. Zhao, “Sub-aperture interferometers: multiple target sub-beams are derived from the same measurement beam,” NASA Tech Briefs. 29–30 (2010).

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Figures (5)

Fig. 1
Fig. 1

Schematic layout of the experimental setup, showing two independent targets (T1 and T2) on the translation stages. The two targets are transparent film of polypropylene.

Fig. 2
Fig. 2

(a) Representative oscilloscope traces of the interferometric intensity VQCL, (b) its analogue derivative and (c) normalized power spectra of SM signal detected at the junction terminals of the QCL under CW operation. Scope timebase setting: 200 ms/div; sample rate: 2.5 MS/s. Upper trace (gray curve): target T1 moving in the forward direction at v1 = 0.5 mm/s. Middle trace (light-gray curve): target T2 moving in the backward direction at v2 = –5 mm/s. Lower trace (black curve): T1 and T2 moving in opposite direction at a set velocity of v1 = 0.5 mm/s and v2 = –5 mm/s, respectively.

Fig. 3
Fig. 3

Normalized power spectra of the experimental interferometric signal VQCL for different velocity of target T1: |v1| = 3 – 2 – 1 – 0.5 mm/s from top to bottom, respectively. The target velocity v2 = –5 mm/s. (a) opposite direction of the targets motion, with the main peak at the sum-frequency; (b) same direction of the targets motion, with the main peak at the difference-frequency.

Fig. 4
Fig. 4

Numerical results. (a) Time trace and (b) normalized power spectrum of the interferometric signal VQCL for feedback strength coefficients: k1 = 0.03 and k2 = 0.025, respectively. Target velocity: v1 = 0.5 mm/s; v2 = –5 mm/s. The other parameters are given in the text. The major peak at ≈11 kHz corresponds to the sum-frequency ω1 + ω2 = 4π(v1 + v2)/λF. Inset of Fig. 4(b): same parameters, but the motion direction of the target T2 is reversed (i.e., v1 = 0.5 mm/s and v2 = 5 mm/s). The major peak is now at ω1 – ω2.

Fig. 5
Fig. 5

Numerical results. Normalized power spectrum of the interferometric signal VQCL for feedback strength coefficients: k1 = 0.025 and k2 = 0.03 (upper trace), k1 = 0.012 and k2 = 0.015 (middle trace), k1 = 0.006 and k2 = 0.007 (lower trace), respectively. Target velocity: v1 = 0.5 mm/s; v2 = –5 mm/s. For decreasing feedback strength the spectra show a dominant signature only at the frequency ω1 and ω2. Same holds if the motion direction of the target T2 is reversed (not shown here).

Equations (4)

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Δ N = G τ p ( N N s o l ) = 2 τ p τ c [ k 1 cos ( ω F τ 1 ) + k 2 cos ( ω F τ 2 ) ]
ω F = ω 0 k 1 τ c [ α cos ( ω F τ 1 ) + sin ( ω F τ 1 ) ] k 2 τ c [ α cos ( ω F τ 2 ) + sin ( ω F τ 2 ) ]
Δ N = 2 τ p τ c [ k 1 cos ( A 1 ± ω 1 t ) + k 2 cos ( A 2 ± ω 2 t ) ]
ω i = 2 | v i | c { ω 0 k 1 τ c [ α cos ( A 1 ± ω 1 t ) + sin ( A 1 ± ω 1 t ) ] k 2 τ c [ α cos ( A 2 ± ω 2 t ) + sin ( A 2 ± ω 2 t ) ] }

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