Abstract

A self-mixing interferometry (SMI) system is a laser diode (LD) with an external cavity formed by a moving external target. The behavior of an SMI system is governed by the injection current J to the LD and the parameters associated with the external cavity mainly including optical feedback factor C, the initial external cavity length (L0) and the light phase (ϕ0) which is mapped to the movement of the target. In this paper, we investigate the dynamic behavior of an SMI system by using the Lang-Kobayashi model. The stability boundary of such system is presented in the plane of (C, ϕ0), from which a critical C (denoted as Ccritical) is derived. Both simulations and experiments show that the stability can be enhanced by increasing either L0 or J. Furthermore, three regions on the plane of (C, ϕ0) are proposed to characterize the behavior of an SMI system, including stable, semi-stable and unstable regions. We found that the existing SMI model is only valid for the stable region, and the semi-stable region has potential applications on sensing and measurement but needs re-modeling the system by considering the bandwidth of the detection components.

© 2014 Optical Society of America

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References

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  1. N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
    [Crossref]
  2. Y. Yu, X. Qiang, Z. Wei, and X. Sun, “Differential displacement measurement system using laser self-mixing interference effect,” Acta Opt. Sin. 19, 1269–1273 (1999).
  3. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A 4(6), S283–S294 (2002).
    [Crossref]
  4. C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55(4), 1101–1105 (2006).
    [Crossref]
  5. Y. Yu, C. Guo, and H. Ye, “Vibration measurement based on moderate optical feedback self-mixing interference,” Acta Opt. Sin. 27, 1430–1434 (2007).
  6. M. Norgia, G. Giuliani, and S. Donati, “Absolute distance measurement with improved accuracy using laser diode self-mixing interferometry in a closed loop,” IEEE Trans. Instrum. Meas. 56(5), 1894–1900 (2007).
    [Crossref]
  7. M. Norgia, A. Pesatori, M. Tanelli, and M. Lovera, “Frequency compensation for a self-mixing interferometer,” IEEE Trans. Instrum. Meas. 59(5), 1368–1374 (2010).
    [Crossref]
  8. Y. Fan, Y. Yu, J. Xi, and J. F. Chicharo, “Improving the measurement performance for a self-mixing interferometry-based displacement sensing system,” Appl. Opt. 50(26), 5064–5072 (2011).
    [Crossref] [PubMed]
  9. S. Donati, “Developing self-mixing interferometry for instrumentation and measurements,” Laser Photon. Rev. 6(3), 393–417 (2012).
    [Crossref]
  10. A. Magnani, A. Pesatori, and M. Norgia, “Self-mixing vibrometer with real-time digital signal elaboration,” Appl. Opt. 51(21), 5318–5325 (2012).
    [Crossref] [PubMed]
  11. O. D. Bernal, U. Zabit, and T. Bosch, “Study of laser feedback phase under self-mixing leading to improved phase unwrapping for vibration sensing,” IEEE J. Sensors 13(12), 4962–4971 (2013).
    [Crossref]
  12. Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
    [Crossref]
  13. J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41(8), 1058–1064 (2005).
    [Crossref]
  14. Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43(7), 527–534 (2007).
    [Crossref]
  15. L. Wei, J. T. Xi, Y. G. Yu, and J. F. Chicharo, “Linewidth enhancement factor measurement based on optical feedback self-mixing effect: a genetic algorithm approach,” J. Opt. A. 11(4), 045505 (2009).
    [Crossref]
  16. Y. Yu and J. Xi, “Influence of external optical feedback on the alpha factor of semiconductor lasers,” Opt. Lett. 38(11), 1781–1783 (2013).
    [Crossref] [PubMed]
  17. S. Donati and M. T. Fathi, “Transition from short-to-long cavity and from self-mixing to chaos in a delayed optical feedback laser,” IEEE J. Quantum Electron. 48(10), 1352–1359 (2012).
    [Crossref]
  18. K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
    [Crossref]
  19. S. Donati and M. Norgia, “Self-mixing interferometry for biomedical signals sensing,” IEEE J. Sel. Top. Quantum Electron. 20(2), 6900108 (2014).
    [Crossref]
  20. G. Plantier, C. Bes, and T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41(9), 1157–1167 (2005).
    [Crossref]
  21. Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45(7), 840–848 (2009).
    [Crossref]
  22. Y. Yu, J. Xi, and J. F. Chicharo, “Measuring the feedback parameter of a semiconductor laser with external optical feedback,” Opt. Express 19(10), 9582–9593 (2011).
    [Crossref] [PubMed]
  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. J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
    [Crossref]
  25. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
    [Crossref]
  26. W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
    [Crossref]
  27. T. Taimre and A. D. Rakić, “On the nature of Acket’s characteristic parameter C in semiconductor lasers,” Appl. Opt. 53(5), 1001–1006 (2014).
    [Crossref] [PubMed]
  28. B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
    [Crossref]
  29. S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
    [Crossref]
  30. H. Li, J. Ye, and J. G. McInerney, “Detailed analysis of coherence collapse in semiconductor lasers,” IEEE J. Quantum Electron. 29(9), 2421–2432 (1993).
    [Crossref]
  31. S.-Y. Ye and J. Ohtsubo, “Experimental investigation of stability enhancement in semiconductor lasers with optical feedback,” Opt. Rev. 5(5), 280–284 (1998).
    [Crossref]

2014 (2)

S. Donati and M. Norgia, “Self-mixing interferometry for biomedical signals sensing,” IEEE J. Sel. Top. Quantum Electron. 20(2), 6900108 (2014).
[Crossref]

T. Taimre and A. D. Rakić, “On the nature of Acket’s characteristic parameter C in semiconductor lasers,” Appl. Opt. 53(5), 1001–1006 (2014).
[Crossref] [PubMed]

2013 (3)

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

O. D. Bernal, U. Zabit, and T. Bosch, “Study of laser feedback phase under self-mixing leading to improved phase unwrapping for vibration sensing,” IEEE J. Sensors 13(12), 4962–4971 (2013).
[Crossref]

Y. Yu and J. Xi, “Influence of external optical feedback on the alpha factor of semiconductor lasers,” Opt. Lett. 38(11), 1781–1783 (2013).
[Crossref] [PubMed]

2012 (3)

S. Donati and M. T. Fathi, “Transition from short-to-long cavity and from self-mixing to chaos in a delayed optical feedback laser,” IEEE J. Quantum Electron. 48(10), 1352–1359 (2012).
[Crossref]

S. Donati, “Developing self-mixing interferometry for instrumentation and measurements,” Laser Photon. Rev. 6(3), 393–417 (2012).
[Crossref]

A. Magnani, A. Pesatori, and M. Norgia, “Self-mixing vibrometer with real-time digital signal elaboration,” Appl. Opt. 51(21), 5318–5325 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

M. Norgia, A. Pesatori, M. Tanelli, and M. Lovera, “Frequency compensation for a self-mixing interferometer,” IEEE Trans. Instrum. Meas. 59(5), 1368–1374 (2010).
[Crossref]

2009 (2)

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45(7), 840–848 (2009).
[Crossref]

L. Wei, J. T. Xi, Y. G. Yu, and J. F. Chicharo, “Linewidth enhancement factor measurement based on optical feedback self-mixing effect: a genetic algorithm approach,” J. Opt. A. 11(4), 045505 (2009).
[Crossref]

2007 (3)

Y. Yu, C. Guo, and H. Ye, “Vibration measurement based on moderate optical feedback self-mixing interference,” Acta Opt. Sin. 27, 1430–1434 (2007).

M. Norgia, G. Giuliani, and S. Donati, “Absolute distance measurement with improved accuracy using laser diode self-mixing interferometry in a closed loop,” IEEE Trans. Instrum. Meas. 56(5), 1894–1900 (2007).
[Crossref]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43(7), 527–534 (2007).
[Crossref]

2006 (1)

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55(4), 1101–1105 (2006).
[Crossref]

2005 (2)

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41(8), 1058–1064 (2005).
[Crossref]

G. Plantier, C. Bes, and T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41(9), 1157–1167 (2005).
[Crossref]

2004 (1)

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

2002 (1)

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

1999 (1)

Y. Yu, X. Qiang, Z. Wei, and X. Sun, “Differential displacement measurement system using laser self-mixing interference effect,” Acta Opt. Sin. 19, 1269–1273 (1999).

1998 (2)

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

S.-Y. Ye and J. Ohtsubo, “Experimental investigation of stability enhancement in semiconductor lasers with optical feedback,” Opt. Rev. 5(5), 280–284 (1998).
[Crossref]

1997 (1)

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[Crossref]

1995 (1)

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

1994 (1)

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[Crossref]

1993 (1)

H. Li, J. Ye, and J. G. McInerney, “Detailed analysis of coherence collapse in semiconductor lasers,” IEEE J. Quantum Electron. 29(9), 2421–2432 (1993).
[Crossref]

1992 (1)

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[Crossref]

1984 (1)

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[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]

Bernal, O. D.

O. D. Bernal, U. Zabit, and T. Bosch, “Study of laser feedback phase under self-mixing leading to improved phase unwrapping for vibration sensing,” IEEE J. Sensors 13(12), 4962–4971 (2013).
[Crossref]

Bertling, K.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Bes, C.

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55(4), 1101–1105 (2006).
[Crossref]

G. Plantier, C. Bes, and T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41(9), 1157–1167 (2005).
[Crossref]

Bosch, T.

O. D. Bernal, U. Zabit, and T. Bosch, “Study of laser feedback phase under self-mixing leading to improved phase unwrapping for vibration sensing,” IEEE J. Sensors 13(12), 4962–4971 (2013).
[Crossref]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43(7), 527–534 (2007).
[Crossref]

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55(4), 1101–1105 (2006).
[Crossref]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41(8), 1058–1064 (2005).
[Crossref]

G. Plantier, C. Bes, and T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41(9), 1157–1167 (2005).
[Crossref]

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

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

Bosch, T. M.

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45(7), 840–848 (2009).
[Crossref]

Boyle, W. J. O.

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[Crossref]

Chicharo, J. F.

Y. Yu, J. Xi, and J. F. Chicharo, “Measuring the feedback parameter of a semiconductor laser with external optical feedback,” Opt. Express 19(10), 9582–9593 (2011).
[Crossref] [PubMed]

Y. Fan, Y. Yu, J. Xi, and J. F. Chicharo, “Improving the measurement performance for a self-mixing interferometry-based displacement sensing system,” Appl. Opt. 50(26), 5064–5072 (2011).
[Crossref] [PubMed]

L. Wei, J. T. Xi, Y. G. Yu, and J. F. Chicharo, “Linewidth enhancement factor measurement based on optical feedback self-mixing effect: a genetic algorithm approach,” J. Opt. A. 11(4), 045505 (2009).
[Crossref]

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45(7), 840–848 (2009).
[Crossref]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43(7), 527–534 (2007).
[Crossref]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41(8), 1058–1064 (2005).
[Crossref]

Dean, P.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Donati, S.

S. Donati and M. Norgia, “Self-mixing interferometry for biomedical signals sensing,” IEEE J. Sel. Top. Quantum Electron. 20(2), 6900108 (2014).
[Crossref]

S. Donati and M. T. Fathi, “Transition from short-to-long cavity and from self-mixing to chaos in a delayed optical feedback laser,” IEEE J. Quantum Electron. 48(10), 1352–1359 (2012).
[Crossref]

S. Donati, “Developing self-mixing interferometry for instrumentation and measurements,” Laser Photon. Rev. 6(3), 393–417 (2012).
[Crossref]

M. Norgia, G. Giuliani, and S. Donati, “Absolute distance measurement with improved accuracy using laser diode self-mixing interferometry in a closed loop,” IEEE Trans. Instrum. Meas. 56(5), 1894–1900 (2007).
[Crossref]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

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

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Fan, Y.

Fathi, M. T.

S. Donati and M. T. Fathi, “Transition from short-to-long cavity and from self-mixing to chaos in a delayed optical feedback laser,” IEEE J. Quantum Electron. 48(10), 1352–1359 (2012).
[Crossref]

Giuliani, G.

M. Norgia, G. Giuliani, and S. Donati, “Absolute distance measurement with improved accuracy using laser diode self-mixing interferometry in a closed loop,” IEEE Trans. Instrum. Meas. 56(5), 1894–1900 (2007).
[Crossref]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

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

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Gouaux, F.

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

Grattan, K. T. V.

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[Crossref]

Guo, C.

Y. Yu, C. Guo, and H. Ye, “Vibration measurement based on moderate optical feedback self-mixing interference,” Acta Opt. Sin. 27, 1430–1434 (2007).

Höfling, S.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Indjin, D.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Kamp, M.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

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]

Koeth, J.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

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, H.

H. Li, J. Ye, and J. G. McInerney, “Detailed analysis of coherence collapse in semiconductor lasers,” IEEE J. Quantum Electron. 29(9), 2421–2432 (1993).
[Crossref]

Lim, Y. L.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Lovera, M.

M. Norgia, A. Pesatori, M. Tanelli, and M. Lovera, “Frequency compensation for a self-mixing interferometer,” IEEE Trans. Instrum. Meas. 59(5), 1368–1374 (2010).
[Crossref]

Magnani, A.

Mark, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[Crossref]

McInerney, J. G.

H. Li, J. Ye, and J. G. McInerney, “Detailed analysis of coherence collapse in semiconductor lasers,” IEEE J. Quantum Electron. 29(9), 2421–2432 (1993).
[Crossref]

Merlo, S.

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Mork, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[Crossref]

Norgia, M.

S. Donati and M. Norgia, “Self-mixing interferometry for biomedical signals sensing,” IEEE J. Sel. Top. Quantum Electron. 20(2), 6900108 (2014).
[Crossref]

A. Magnani, A. Pesatori, and M. Norgia, “Self-mixing vibrometer with real-time digital signal elaboration,” Appl. Opt. 51(21), 5318–5325 (2012).
[Crossref] [PubMed]

M. Norgia, A. Pesatori, M. Tanelli, and M. Lovera, “Frequency compensation for a self-mixing interferometer,” IEEE Trans. Instrum. Meas. 59(5), 1368–1374 (2010).
[Crossref]

M. Norgia, G. Giuliani, and S. Donati, “Absolute distance measurement with improved accuracy using laser diode self-mixing interferometry in a closed loop,” IEEE Trans. Instrum. Meas. 56(5), 1894–1900 (2007).
[Crossref]

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

Ohtsubo, J.

S.-Y. Ye and J. Ohtsubo, “Experimental investigation of stability enhancement in semiconductor lasers with optical feedback,” Opt. Rev. 5(5), 280–284 (1998).
[Crossref]

Olesen, H.

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[Crossref]

Osmundsen, J.

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[Crossref]

Palmer, A. W.

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[Crossref]

Pesatori, A.

A. Magnani, A. Pesatori, and M. Norgia, “Self-mixing vibrometer with real-time digital signal elaboration,” Appl. Opt. 51(21), 5318–5325 (2012).
[Crossref] [PubMed]

M. Norgia, A. Pesatori, M. Tanelli, and M. Lovera, “Frequency compensation for a self-mixing interferometer,” IEEE Trans. Instrum. Meas. 59(5), 1368–1374 (2010).
[Crossref]

Plantier, G.

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55(4), 1101–1105 (2006).
[Crossref]

G. Plantier, C. Bes, and T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41(9), 1157–1167 (2005).
[Crossref]

Qiang, X.

Y. Yu, X. Qiang, Z. Wei, and X. Sun, “Differential displacement measurement system using laser self-mixing interference effect,” Acta Opt. Sin. 19, 1269–1273 (1999).

Rakic, A. D.

T. Taimre and A. D. Rakić, “On the nature of Acket’s characteristic parameter C in semiconductor lasers,” Appl. Opt. 53(5), 1001–1006 (2014).
[Crossref] [PubMed]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Servagent, N.

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

Sun, X.

Y. Yu, X. Qiang, Z. Wei, and X. Sun, “Differential displacement measurement system using laser self-mixing interference effect,” Acta Opt. Sin. 19, 1269–1273 (1999).

Taimre, T.

T. Taimre and A. D. Rakić, “On the nature of Acket’s characteristic parameter C in semiconductor lasers,” Appl. Opt. 53(5), 1001–1006 (2014).
[Crossref] [PubMed]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Tanelli, M.

M. Norgia, A. Pesatori, M. Tanelli, and M. Lovera, “Frequency compensation for a self-mixing interferometer,” IEEE Trans. Instrum. Meas. 59(5), 1368–1374 (2010).
[Crossref]

Tromborg, B.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[Crossref]

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[Crossref]

von Edlinger, M.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Wang, W. M.

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[Crossref]

Wei, L.

L. Wei, J. T. Xi, Y. G. Yu, and J. F. Chicharo, “Linewidth enhancement factor measurement based on optical feedback self-mixing effect: a genetic algorithm approach,” J. Opt. A. 11(4), 045505 (2009).
[Crossref]

Wei, Z.

Y. Yu, X. Qiang, Z. Wei, and X. Sun, “Differential displacement measurement system using laser self-mixing interference effect,” Acta Opt. Sin. 19, 1269–1273 (1999).

Weih, R.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

Xi, J.

Y. Yu and J. Xi, “Influence of external optical feedback on the alpha factor of semiconductor lasers,” Opt. Lett. 38(11), 1781–1783 (2013).
[Crossref] [PubMed]

Y. Fan, Y. Yu, J. Xi, and J. F. Chicharo, “Improving the measurement performance for a self-mixing interferometry-based displacement sensing system,” Appl. Opt. 50(26), 5064–5072 (2011).
[Crossref] [PubMed]

Y. Yu, J. Xi, and J. F. Chicharo, “Measuring the feedback parameter of a semiconductor laser with external optical feedback,” Opt. Express 19(10), 9582–9593 (2011).
[Crossref] [PubMed]

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45(7), 840–848 (2009).
[Crossref]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43(7), 527–534 (2007).
[Crossref]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41(8), 1058–1064 (2005).
[Crossref]

Xi, J. T.

L. Wei, J. T. Xi, Y. G. Yu, and J. F. Chicharo, “Linewidth enhancement factor measurement based on optical feedback self-mixing effect: a genetic algorithm approach,” J. Opt. A. 11(4), 045505 (2009).
[Crossref]

Ye, H.

Y. Yu, C. Guo, and H. Ye, “Vibration measurement based on moderate optical feedback self-mixing interference,” Acta Opt. Sin. 27, 1430–1434 (2007).

Ye, J.

H. Li, J. Ye, and J. G. McInerney, “Detailed analysis of coherence collapse in semiconductor lasers,” IEEE J. Quantum Electron. 29(9), 2421–2432 (1993).
[Crossref]

Ye, S.-Y.

S.-Y. Ye and J. Ohtsubo, “Experimental investigation of stability enhancement in semiconductor lasers with optical feedback,” Opt. Rev. 5(5), 280–284 (1998).
[Crossref]

Yu, Y.

Y. Yu and J. Xi, “Influence of external optical feedback on the alpha factor of semiconductor lasers,” Opt. Lett. 38(11), 1781–1783 (2013).
[Crossref] [PubMed]

Y. Fan, Y. Yu, J. Xi, and J. F. Chicharo, “Improving the measurement performance for a self-mixing interferometry-based displacement sensing system,” Appl. Opt. 50(26), 5064–5072 (2011).
[Crossref] [PubMed]

Y. Yu, J. Xi, and J. F. Chicharo, “Measuring the feedback parameter of a semiconductor laser with external optical feedback,” Opt. Express 19(10), 9582–9593 (2011).
[Crossref] [PubMed]

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45(7), 840–848 (2009).
[Crossref]

Y. Yu, C. Guo, and H. Ye, “Vibration measurement based on moderate optical feedback self-mixing interference,” Acta Opt. Sin. 27, 1430–1434 (2007).

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43(7), 527–534 (2007).
[Crossref]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41(8), 1058–1064 (2005).
[Crossref]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

Y. Yu, X. Qiang, Z. Wei, and X. Sun, “Differential displacement measurement system using laser self-mixing interference effect,” Acta Opt. Sin. 19, 1269–1273 (1999).

Yu, Y. G.

L. Wei, J. T. Xi, Y. G. Yu, and J. F. Chicharo, “Linewidth enhancement factor measurement based on optical feedback self-mixing effect: a genetic algorithm approach,” J. Opt. A. 11(4), 045505 (2009).
[Crossref]

Zabit, U.

O. D. Bernal, U. Zabit, and T. Bosch, “Study of laser feedback phase under self-mixing leading to improved phase unwrapping for vibration sensing,” IEEE J. Sensors 13(12), 4962–4971 (2013).
[Crossref]

Acta Opt. Sin. (2)

Y. Yu, X. Qiang, Z. Wei, and X. Sun, “Differential displacement measurement system using laser self-mixing interference effect,” Acta Opt. Sin. 19, 1269–1273 (1999).

Y. Yu, C. Guo, and H. Ye, “Vibration measurement based on moderate optical feedback self-mixing interference,” Acta Opt. Sin. 27, 1430–1434 (2007).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103(23), 231107 (2013).
[Crossref]

IEEE J. Quantum Electron. (11)

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41(8), 1058–1064 (2005).
[Crossref]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43(7), 527–534 (2007).
[Crossref]

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[Crossref]

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[Crossref]

H. Li, J. Ye, and J. G. McInerney, “Detailed analysis of coherence collapse in semiconductor lasers,” IEEE J. Quantum Electron. 29(9), 2421–2432 (1993).
[Crossref]

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

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

G. Plantier, C. Bes, and T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41(9), 1157–1167 (2005).
[Crossref]

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45(7), 840–848 (2009).
[Crossref]

S. Donati and M. T. Fathi, “Transition from short-to-long cavity and from self-mixing to chaos in a delayed optical feedback laser,” IEEE J. Quantum Electron. 48(10), 1352–1359 (2012).
[Crossref]

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

S. Donati and M. Norgia, “Self-mixing interferometry for biomedical signals sensing,” IEEE J. Sel. Top. Quantum Electron. 20(2), 6900108 (2014).
[Crossref]

IEEE J. Sensors (1)

O. D. Bernal, U. Zabit, and T. Bosch, “Study of laser feedback phase under self-mixing leading to improved phase unwrapping for vibration sensing,” IEEE J. Sensors 13(12), 4962–4971 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

IEEE Trans. Instrum. Meas. (3)

M. Norgia, G. Giuliani, and S. Donati, “Absolute distance measurement with improved accuracy using laser diode self-mixing interferometry in a closed loop,” IEEE Trans. Instrum. Meas. 56(5), 1894–1900 (2007).
[Crossref]

M. Norgia, A. Pesatori, M. Tanelli, and M. Lovera, “Frequency compensation for a self-mixing interferometer,” IEEE Trans. Instrum. Meas. 59(5), 1368–1374 (2010).
[Crossref]

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55(4), 1101–1105 (2006).
[Crossref]

J. Lightwave Technol. (1)

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[Crossref]

J. Opt. (1)

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

J. Opt. A (1)

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

J. Opt. A. (1)

L. Wei, J. T. Xi, Y. G. Yu, and J. F. Chicharo, “Linewidth enhancement factor measurement based on optical feedback self-mixing effect: a genetic algorithm approach,” J. Opt. A. 11(4), 045505 (2009).
[Crossref]

Laser Photon. Rev. (1)

S. Donati, “Developing self-mixing interferometry for instrumentation and measurements,” Laser Photon. Rev. 6(3), 393–417 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Opt. Rev. (1)

S.-Y. Ye and J. Ohtsubo, “Experimental investigation of stability enhancement in semiconductor lasers with optical feedback,” Opt. Rev. 5(5), 280–284 (1998).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Influence of J and L 0 on the stability boundary of an SMI system. (a) for a fixed L 0 = 0.25 m with different J , (b) for a fixed J = 1.3 J t h with different L 0 .
Fig. 2
Fig. 2 The stability boundary of an SMI system when J = 1.1 J t h and L 0 = 0.35 m .
Fig. 3
Fig. 3 SMI signals predicated by the L-K model and the existing SMI model respectively. (a) and (f): movement trace of the external target, (b)-(e): SMI signals obtained by the L-K model with C = 1.5 , C = 2.5 , C = 4.0 and C = 9.0 respectively. (g)-(j) SMI signals obtained by the existing SMI model with C = 1.5 , C = 2.5 , C = 4.0 and C = 9.0 respectively.
Fig. 4
Fig. 4 Experimental setup for investigating the influence of the external cavity length and the injection current respectively on the critical feedback level
Fig. 5
Fig. 5 Two optical spectra obtained with L 0 = 0.25 m and J = 1.7 J t h for (a) the stable region, (b) the semi-stable region.
Fig. 6
Fig. 6 Experimental results. (a) for a fixed L 0 = 0.25 m , (b) for a fixed J / J t h = 1.3 .

Tables (1)

Tables Icon

Table 1 Physical meanings for the internal cavity parameters in L-K equations [24]

Equations (15)

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

d E ( t ) d t = 1 2 { G [ N ( t ) , E ( t ) ] 1 τ p } E ( t ) + κ τ i n E ( t τ ) cos [ ω 0 τ + ϕ ( t ) ϕ ( t τ ) ]
d ϕ ( t ) d t = 1 2 α { G [ N ( t ) , E ( t ) ] 1 τ p } κ τ i n E ( t τ ) E ( t ) sin [ ω 0 τ + ϕ ( t ) ϕ ( t τ ) ]
d N ( t ) d t = J e V N ( t ) τ s G [ N ( t ) , E ( t ) ] E 2 ( t )
ω 0 τ = ω s τ + κ τ i n τ 1 + α 2 sin ( ω s τ + arc tan α )
N s = N 0 + 1 τ p G N 2 κ cos ( ω s τ ) τ i n G N
E s 2 = J / ( e V ) N s / τ s G N ( N s N 0 )
ϕ 0 = ω 0 τ , ϕ s = ω s τ and C = κ τ i n τ 1 + α 2
ϕ 0 = ϕ s + C sin ( ϕ s + arc tan α )
g = cos ( ϕ s )
α κ sin ( ϕ s ) + κ cos ( ϕ s ) [ 1 2 ( Ω ω R ) 2 ] < ( Ω ω R ) 2 τ i n 2 τ R sin 2 ( Ω τ 0 / 2 )
Ω 2 ω R 2 = Ω τ R cot ( Ω τ 0 2 )
ω R = G N τ p E s 0 , 1 τ R = 1 τ s + ( τ p + ε Γ G N ) ω R 2
C { cos ( ϕ s ) [ 1 2 ( Ω ω R ) 2 ] α sin ( ϕ s ) } ( Ω ω R ) 2 τ 0 1 + α 2 2 τ R sin 2 ( Ω τ 0 / 2 )
ϕ s = arc tan [ α 2 ( Ω / ω R ) 2 1 ] + p π
C c r i t i c a l = ( Ω ω R ) 2 L 0 1 + α 2 τ R c sin 2 ( Ω L 0 / c ) [ 2 ( Ω / ω R ) 2 1 ] 2 + α 2 [ 2 ( Ω / ω R ) 2 1 ] 2 + α 2

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