Abstract

An optical feedback laser diode (OFLD) operating in period-one oscillation (POO) with a moving external target is investigated by exploring its potential sensing capability. First, the modeling of an OFLD-POO sensing system is presented. An analytical expression is derived for OFLD-POO sensing signal, from which a new displacement measurement method is developed. The proposed sensing model is verified by the well-known Lang-Kobayashi equations used to describe the dynamic behavior of a laser with optical feedback. Then, an experimental OFLD-POO system is built in order to demonstrate an application example for displacement sensing. The measurement results show that the OFLD-POO sensing system can achieve displacement measurement with large measurement range, high sensitivity, and resolution.

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

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References

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2018 (2)

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

Y. Ruan, B. Liu, Y. Yu, J. Xi, Q. Guo, and J. Tong, “Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback,” Sensors (Basel) 18(11), 4004 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (3)

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

S. Zhang, S. Zhang, L. Sun, and Y. Tan, “Fiber self-mixing interferometer with orthogonally polarized light compensation,” Opt. Express 24(23), 26558–26564 (2016).
[Crossref] [PubMed]

2015 (1)

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

2014 (2)

2013 (3)

D. Lenstra, “Relaxation oscillation dynamics in semiconductor diode lasers with optical feedback,” IEEE Photonics Technol. Lett. 25(6), 591–593 (2013).
[Crossref]

U. Zabit, O. D. Bernal, and T. Bosch, “Self-mixing laser sensor for large displacements: Signal recovery in the presence of speckle,” IEEE J. Sensors 13(2), 824–831 (2013).
[Crossref]

M. Nikolić, E. Hicks, Y. L. Lim, K. Bertling, and A. D. Rakić, “Self-mixing laser Doppler flow sensor: an optofluidic implementation,” Appl. Opt. 52(33), 8128–8133 (2013).
[Crossref] [PubMed]

2012 (2)

M. Norgia, A. Pesatori, and L. Rovati, “Self-mixing laser Doppler spectra of extracorporeal blood flow: a theoretical and experimental study,” IEEE J. Sensors 12(3), 552–557 (2012).
[Crossref]

R. Teysseyre, F. Bony, J. Perchoux, and T. Bosch, “Laser dynamics in sawtooth-like self-mixing signals,” Opt. Lett. 37(18), 3771–3773 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

U. Zabit, F. Bony, T. Bosch, and A. D. Rakic, “A self-mixing displacement sensor with fringe-loss compensation for harmonic vibrations,” IEEE Photonics Technol. Lett. 22(6), 410–412 (2010).
[Crossref]

2005 (1)

2004 (2)

M. Wang and G. Lai, “Self-mixing microscopic interferometer for the measurement of microprofile,” Opt. Commun. 238(4–6), 237–244 (2004).
[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 Photonics Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

2002 (1)

L. Scalise and N. Paone, “Laser Doppler vibrometry based on self-mixing effect,” Opt. Lasers Eng. 38(3–4), 173–184 (2002).
[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]

1993 (1)

1984 (1)

B. Tromborg, J. H. 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.

U. Zabit, O. D. Bernal, and T. Bosch, “Self-mixing laser sensor for large displacements: Signal recovery in the presence of speckle,” IEEE J. Sensors 13(2), 824–831 (2013).
[Crossref]

Bertling, K.

Bony, F.

R. Teysseyre, F. Bony, J. Perchoux, and T. Bosch, “Laser dynamics in sawtooth-like self-mixing signals,” Opt. Lett. 37(18), 3771–3773 (2012).
[Crossref] [PubMed]

U. Zabit, F. Bony, T. Bosch, and A. D. Rakic, “A self-mixing displacement sensor with fringe-loss compensation for harmonic vibrations,” IEEE Photonics Technol. Lett. 22(6), 410–412 (2010).
[Crossref]

Bosch, T.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

K. Bertling, J. Perchoux, T. Taimre, R. Malkin, D. Robert, A. D. Rakić, and T. Bosch, “Imaging of acoustic fields using optical feedback interferometry,” Opt. Express 22(24), 30346–30356 (2014).
[Crossref] [PubMed]

U. Zabit, O. D. Bernal, and T. Bosch, “Self-mixing laser sensor for large displacements: Signal recovery in the presence of speckle,” IEEE J. Sensors 13(2), 824–831 (2013).
[Crossref]

R. Teysseyre, F. Bony, J. Perchoux, and T. Bosch, “Laser dynamics in sawtooth-like self-mixing signals,” Opt. Lett. 37(18), 3771–3773 (2012).
[Crossref] [PubMed]

U. Zabit, F. Bony, T. Bosch, and A. D. Rakic, “A self-mixing displacement sensor with fringe-loss compensation for harmonic vibrations,” IEEE Photonics Technol. Lett. 22(6), 410–412 (2010).
[Crossref]

Chicharo, J. F.

Dabbicco, M.

Donati, S.

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 Photonics Technol. Lett. 16(4), 990–992 (2004).
[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.

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

Y. Fan, Y. Yu, J. Xi, and Q. Guo, “Dynamic stability analysis for a self-mixing interferometry system,” Opt. Express 22(23), 29260–29269 (2014).
[Crossref] [PubMed]

Giuliani, G.

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 Photonics Technol. Lett. 16(4), 990–992 (2004).
[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]

Guo, D.

Guo, Q.

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

Y. Ruan, B. Liu, Y. Yu, J. Xi, Q. Guo, and J. Tong, “Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback,” Sensors (Basel) 18(11), 4004 (2018).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Q. Guo, J. Tong, and R. A. Lewis, “Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback,” Appl. Opt. 56(24), 6962–6966 (2017).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

Y. Fan, Y. Yu, J. Xi, and Q. Guo, “Dynamic stability analysis for a self-mixing interferometry system,” Opt. Express 22(23), 29260–29269 (2014).
[Crossref] [PubMed]

Haug, H.

Hicks, E.

Intermite, A.

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]

Lai, G.

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

Lenstra, D.

D. Lenstra, “Relaxation oscillation dynamics in semiconductor diode lasers with optical feedback,” IEEE Photonics Technol. Lett. 25(6), 591–593 (2013).
[Crossref]

Lewis, R. A.

B. Liu, Y. Yu, J. Xi, Q. Guo, J. Tong, and R. A. Lewis, “Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback,” Appl. Opt. 56(24), 6962–6966 (2017).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

Li, H.

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

Lim, Y. L.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

M. Nikolić, E. Hicks, Y. L. Lim, K. Bertling, and A. D. Rakić, “Self-mixing laser Doppler flow sensor: an optofluidic implementation,” Appl. Opt. 52(33), 8128–8133 (2013).
[Crossref] [PubMed]

Lin, K.

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

Liu, B.

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

Y. Ruan, B. Liu, Y. Yu, J. Xi, Q. Guo, and J. Tong, “Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback,” Sensors (Basel) 18(11), 4004 (2018).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Q. Guo, J. Tong, and R. A. Lewis, “Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback,” Appl. Opt. 56(24), 6962–6966 (2017).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

Malkin, R.

Merlo, S.

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]

Nikolic, M.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

M. Nikolić, E. Hicks, Y. L. Lim, K. Bertling, and A. D. Rakić, “Self-mixing laser Doppler flow sensor: an optofluidic implementation,” Appl. Opt. 52(33), 8128–8133 (2013).
[Crossref] [PubMed]

Norgia, M.

M. Norgia, A. Pesatori, and L. Rovati, “Self-mixing laser Doppler spectra of extracorporeal blood flow: a theoretical and experimental study,” IEEE J. Sensors 12(3), 552–557 (2012).
[Crossref]

Olesen, H.

B. Tromborg, J. H. 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. H.

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

Paone, N.

L. Scalise and N. Paone, “Laser Doppler vibrometry based on self-mixing effect,” Opt. Lasers Eng. 38(3–4), 173–184 (2002).
[Crossref]

Perchoux, J.

Pesatori, A.

M. Norgia, A. Pesatori, and L. Rovati, “Self-mixing laser Doppler spectra of extracorporeal blood flow: a theoretical and experimental study,” IEEE J. Sensors 12(3), 552–557 (2012).
[Crossref]

Rajan, G.

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

Rakic, A. D.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

K. Bertling, J. Perchoux, T. Taimre, R. Malkin, D. Robert, A. D. Rakić, and T. Bosch, “Imaging of acoustic fields using optical feedback interferometry,” Opt. Express 22(24), 30346–30356 (2014).
[Crossref] [PubMed]

M. Nikolić, E. Hicks, Y. L. Lim, K. Bertling, and A. D. Rakić, “Self-mixing laser Doppler flow sensor: an optofluidic implementation,” Appl. Opt. 52(33), 8128–8133 (2013).
[Crossref] [PubMed]

U. Zabit, F. Bony, T. Bosch, and A. D. Rakic, “A self-mixing displacement sensor with fringe-loss compensation for harmonic vibrations,” IEEE Photonics Technol. Lett. 22(6), 410–412 (2010).
[Crossref]

Ritter, A.

Robert, D.

Rovati, L.

M. Norgia, A. Pesatori, and L. Rovati, “Self-mixing laser Doppler spectra of extracorporeal blood flow: a theoretical and experimental study,” IEEE J. Sensors 12(3), 552–557 (2012).
[Crossref]

Ruan, Y.

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

Y. Ruan, B. Liu, Y. Yu, J. Xi, Q. Guo, and J. Tong, “Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback,” Sensors (Basel) 18(11), 4004 (2018).
[Crossref] [PubMed]

Scalise, L.

L. Scalise and N. Paone, “Laser Doppler vibrometry based on self-mixing effect,” Opt. Lasers Eng. 38(3–4), 173–184 (2002).
[Crossref]

Scamarcio, G.

Su, L.

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

Sun, L.

Taimre, T.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

K. Bertling, J. Perchoux, T. Taimre, R. Malkin, D. Robert, A. D. Rakić, and T. Bosch, “Imaging of acoustic fields using optical feedback interferometry,” Opt. Express 22(24), 30346–30356 (2014).
[Crossref] [PubMed]

Tan, S.

Tan, Y.

Teysseyre, R.

Tong, J.

Y. Ruan, B. Liu, Y. Yu, J. Xi, Q. Guo, and J. Tong, “Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback,” Sensors (Basel) 18(11), 4004 (2018).
[Crossref] [PubMed]

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Q. Guo, J. Tong, and R. A. Lewis, “Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback,” Appl. Opt. 56(24), 6962–6966 (2017).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

Tromborg, B.

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

Wang, M.

D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13(5), 1537–1543 (2005).
[Crossref] [PubMed]

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

Xi, J.

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

Y. Ruan, B. Liu, Y. Yu, J. Xi, Q. Guo, and J. Tong, “Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback,” Sensors (Basel) 18(11), 4004 (2018).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Q. Guo, J. Tong, and R. A. Lewis, “Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback,” Appl. Opt. 56(24), 6962–6966 (2017).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

Y. Fan, Y. Yu, J. Xi, and Q. Guo, “Dynamic stability analysis for a self-mixing interferometry system,” Opt. Express 22(23), 29260–29269 (2014).
[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]

Yu, Y.

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

Y. Ruan, B. Liu, Y. Yu, J. Xi, Q. Guo, and J. Tong, “Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback,” Sensors (Basel) 18(11), 4004 (2018).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Q. Guo, J. Tong, and R. A. Lewis, “Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback,” Appl. Opt. 56(24), 6962–6966 (2017).
[Crossref] [PubMed]

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

Y. Fan, Y. Yu, J. Xi, and Q. Guo, “Dynamic stability analysis for a self-mixing interferometry system,” Opt. Express 22(23), 29260–29269 (2014).
[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, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photonics Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

Zabit, U.

U. Zabit, O. D. Bernal, and T. Bosch, “Self-mixing laser sensor for large displacements: Signal recovery in the presence of speckle,” IEEE J. Sensors 13(2), 824–831 (2013).
[Crossref]

U. Zabit, F. Bony, T. Bosch, and A. D. Rakic, “A self-mixing displacement sensor with fringe-loss compensation for harmonic vibrations,” IEEE Photonics Technol. Lett. 22(6), 410–412 (2010).
[Crossref]

Zhang, S.

Adv. Opt. Photonics (1)

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

Appl. Opt. (2)

IEEE J. Quantum Electron. (3)

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

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

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[Crossref]

IEEE J. Sensors (2)

M. Norgia, A. Pesatori, and L. Rovati, “Self-mixing laser Doppler spectra of extracorporeal blood flow: a theoretical and experimental study,” IEEE J. Sensors 12(3), 552–557 (2012).
[Crossref]

U. Zabit, O. D. Bernal, and T. Bosch, “Self-mixing laser sensor for large displacements: Signal recovery in the presence of speckle,” IEEE J. Sensors 13(2), 824–831 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (3)

U. Zabit, F. Bony, T. Bosch, and A. D. Rakic, “A self-mixing displacement sensor with fringe-loss compensation for harmonic vibrations,” IEEE Photonics Technol. Lett. 22(6), 410–412 (2010).
[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 Photonics Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

D. Lenstra, “Relaxation oscillation dynamics in semiconductor diode lasers with optical feedback,” IEEE Photonics Technol. Lett. 25(6), 591–593 (2013).
[Crossref]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

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

Opt. Express (5)

Opt. Lasers Eng. (1)

L. Scalise and N. Paone, “Laser Doppler vibrometry based on self-mixing effect,” Opt. Lasers Eng. 38(3–4), 173–184 (2002).
[Crossref]

Opt. Lett. (1)

Sensors (Basel) (4)

B. Liu, Y. Yu, J. Xi, Y. Fan, Q. Guo, J. Tong, and R. A. Lewis, “Features of a self-mixing laser diode operating near relaxation oscillation,” Sensors (Basel) 16(9), 1546 (2016).
[Crossref] [PubMed]

Y. Ruan, B. Liu, Y. Yu, J. Xi, Q. Guo, and J. Tong, “Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback,” Sensors (Basel) 18(11), 4004 (2018).
[Crossref] [PubMed]

K. Lin, Y. Yu, J. Xi, H. Li, Q. Guo, J. Tong, and L. Su, “A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young’s Modulus,” Sensors (Basel) 16(6), 928 (2016).
[Crossref] [PubMed]

B. Liu, Y. Ruan, Y. Yu, J. Xi, Q. Guo, J. Tong, and G. Rajan, “Laser self-mixing fiber Bragg grating sensor for acoustic emission measurement,” Sensors (Basel) 18(6), 1956 (2018).
[Crossref] [PubMed]

Other (2)

J. Ohtsubo, Semiconductor lasers: stability, instability and chaos (Springer, 2012), Vol. 111.

A. Uchida, Optical communication with chaotic lasers: applications of nonlinear dynamics and synchronization (John Wiley & Sons, 2012).

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Figures (8)

Fig. 1
Fig. 1 (a) Relationship between RO frequency and displacement of external cavity, (b) waveform of Δ P OFLDPOO-Ep for a change of external cavity length when L 0 =24cm, I=1.3 I th and C=4.5.
Fig. 2
Fig. 2 Verification of OFLD-POO signal expressed in Eq. (40) by the numerical results from L-K equations. (a) displacement of the external target; (b) and (c) results from L-K equations with C = 2.8 and C = 4.5 respectively; (d) and (e) results from Eq. (40) when C = 2.8 and C = 4.5 respectively.
Fig. 3
Fig. 3 OFLD-POO signal and displacement corresponding to Δ L t and Δ L f .
Fig. 4
Fig. 4 Displacement reconstruction procedure from the OFLD-POO signal, (a) the pre-set displacement, (b) corresponding OFLD-POO signal, (c) upper envelope of OFLD-POO signal, (d) envelope differentiation.
Fig. 5
Fig. 5 Experiment setup, where LD, BS and PZT represent laser diode, beam splitter, and piezoelectric transducer.
Fig. 6
Fig. 6 Experimental results of laser intensity when I=50 mA, L 0 =18 cm,and ΔL=300 nm.
Fig. 7
Fig. 7 RO frequency variation for different displacements when I=50 mA, and L 0 =18 cm.
Fig. 8
Fig. 8 (a) PZT controlling signal, (b) corresponding OFLD-POO signal.

Tables (2)

Tables Icon

Table 1 Meanings of the symbols in the L-K equations

Tables Icon

Table 2 Displacement results by PZT sensor and OFLD-POO

Equations (47)

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dE(t) dt = 1 2 { G[ N(t),E(t) ] 1 τ p }E(t)+ κ τ in E(tτ)cos[ ω 0 τ+ϕ(t)ϕ(tτ) ].
dϕ(t) dt = 1 2 α{ G[ N(t),E(t) ] 1 τ p } κ τ in E(tτ) E(t) sin[ ω 0 τ+ϕ(t)ϕ(tτ) ].
dN(t) dt =I N(t) τ s G[ N(t),E(t) ] E 2 (t).
E(t)= E ¯ +ΔEcos( ω r t+ θ e ).
N(t)= N ¯ +ΔNcos( ω r t+ θ n ).
ϕ(t)=( ω ¯ ω 0 )t+(Δϕ/2)cos ω r t.
E ¯ 2 = I N ¯ / τ s G N ( N ¯ N 0 ) .
N ¯ = N 0 + 1 G N τ p 2kcos( ω s τ) τ in G N .
ω s = ω 0 k 1+ α 2 τ in sin( ω s τ+arctanα).
2 G N ( N ¯ N 0 ) E ¯ ΔEcos( ω r t+ θ e ) =I N ¯ / τ s G N ( N ¯ N 0 ) E ¯ 2 +ΔN ω r 2 + (1/ τ s + G N E ¯ 2 ) 2 cos{ ω r t+ θ n arctan[(1/ τ s + G N E ¯ 2 )/ ω r ]π/2}.
2 G N ( N ¯ N 0 ) E ¯ ΔE=ΔN ω r 2 + (1/ τ s + G N E ¯ 2 ) 2 .
θ e = θ n arctan[(1/ τ s + G N E ¯ 2 )/ ω r ]π/2.
I N ¯ / τ s G N ( N ¯ N 0 ) E ¯ 2 =0.
- ω r ΔEsin( ω r t+ θ e ) ={ 1 2 [ G N ( N ¯ +ΔNcos( ω r t+ θ n )- N 0 ) 1 τ p ] }[ E ¯ +ΔEcos( ω r t+ θ e )] + κ τ in [ E ¯ -ΔEcos( ω r t+ θ e )]cos[ ω s τ+Δϕcos( ω r t)].
- ω r ΔEsin( ω r t+ θ e )= 1 2 [ G N ( N ¯ - N 0 )1/ τ p ] E ¯ + κ τ in E ¯ cos ω s τ J 0 (Δϕ) + 1 2 G N E ¯ ΔNcos( ω r t+ θ n )+ 1 2 [ G N ( N s - N 0 ) 1 τ p ]ΔEcos( ω r t+ θ e ) 2 κ τ in E ¯ sin ω s τ J 1 (Δϕ)cos ω r t.
1 2 [ G N ( N ¯ - N 0 )1/ τ p ]+ κ τ in cos ω s τ J 0 (Δϕ)=0.
ω r ΔEsin( ω r t+ θ e )=2 κ τ in E ¯ sin ω s τ J 1 (Δϕ)cos ω r t 1 2 [ G N ( N ¯ - N 0 )1/ τ p ]ΔEcos( ω r t+ θ e ) 1 2 G N E ¯ ΔNcos( ω r t+ θ n ).
ω r ΔEcos θ e sin ω r t+ ω r ΔEsin θ e cos ω r t= { 1 2 [ G N ( N ¯ - N 0 )1/ τ p ]ΔEsin θ e + 1 2 G N E ¯ ΔNsin θ n }sin ω r t +{ 1 2 [ G N ( N ¯ - N 0 )1/ τ p ]ΔEcos θ e 1 2 G N E ¯ ΔNcos θ n +2 κ τ in E ¯ sin ω s τ J 1 (Δϕ) }cos ω r t.
ω r ΔEcos θ e = 1 2 [ G N ( N ¯ N 0 )1/ τ p ]ΔEsin θ e + 1 2 G N E ¯ ΔNsin θ n .
cot θ n = 1 ω r ω r 2 G N 2 E ¯ 2 ( N s N 0 )(1/ τ s + G N E ¯ 2 )(κ/ τ in ) J 0 (Δϕ)cos ω s τ 1/ τ s + G N E ¯ 2 +(κ/ τ in ) J 0 (Δϕ)cos ω s τ .
ω ¯ ω 0 =α κ τ in cos ω ¯ τ J 0 (Δϕ) κ τ in sin ω ¯ τ J 0 (Δϕ).
1 2 α G N ΔNcos θ n 2 κ τ in cos ω ¯ τ J 1 (Δϕ)=0.
Δϕ ω r =α G N ΔNsin θ n .
cos ω ¯ τ J 0 (Δϕ)=cos ω s τ.
cot θ n = 1 ω r ω r 2 G N 2 E ¯ 2 ( N s N 0 )( G N E ¯ 2 + 1 τ s ) κ τ in cos ω s τ G N E ¯ 2 + 1 τ s + κ τ in cos ω s τ .
Δϕ=2 ω r τ in cot θ n 2κcos ω s τ ω r τ in cot θ n κcos ω s τ .
ΔN= 2 ω r α G N sin θ n ω r τ in cot θ n 2κcos ω s τ ω r τ in cot θ n κcos ω s τ .
ΔE= ω r α G N sin θ n ω r τ in cot θ n 2κcos ω s τ ω r τ in cot θ n κcos ω s τ ω r 2 + ( G N E ¯ 2 +1/ τ s ) 2 G N ( N ¯ N 0 ) E ¯ .
ΔE= ω r 2 α G N sin θ n ω r τ in cot θ n 2κcos ω s τ ω r τ in cot θ n κcos ω s τ 1 G N ( N ¯ N 0 ) E ¯ .
P(t)= E 2 (t) = E ¯ 2 +2 E ¯ ΔEcos( ω r t+ θ e )+Δ E 2 cos 2 ( ω r t+ θ e ).
P(t) = E ¯ 2 +2 τ p ω r 2 α G N sin θ n ω r τ in cot θ n 2κcos ω s τ ω r τ in cot θ n κcos ω s τ (1+ 2κ τ p τ in cos ω s τ)cos( ω r t+ θ e ).
E ¯ 2 = E S0 2 +2( E S0 2 + 1 G N τ s ) κ τ p τ in cos( ω s τ).
cot θ n = τ s ( ω r 2 ω r0 2 ) κ τ in cos ω s τ ω r .
P(t)= E S0 2 +2( E S0 2 + 1 G N τ s ) κ τ p τ in cos( ω s τ) +2 τ p ω r α G N ω r 2 + [ τ s ( ω r 2 ω r0 2 ) κ τ in cos ω s τ] 2 cos( ω r t+ θ e ).
ΔP(L,t)=P(t) E S0 2 =Δ P OFLD (L)+Δ P OFLDPOO-Ep (L)cos[ ω r (L)t+ θ e ].
Δ P OFLD (L)=2( E S0 2 + 1 G N τ s ) κ τ p τ in cos[ ϕ F (L)].
Δ P OFILDPOOEp (L)=2 τ p ω r (L) α G N ω r 2 (L)+ { τ s [ ω r 2 (L) ω r0 2 ] κ τ in cos[ ϕ F (L)]} 2 .
ω r (ΔL+N λ 0 2 )= ω r0 + ω r-offset + 2( ω rmax ω rmin ) λ 0 ΔL.
Δ P OFLD-POOEp (L+N λ 0 2 ) =2 τ p ω r (L+N λ 0 2 ) α G N ω r 2 (L+N λ 0 2 )+[ τ s ( ω r 2 (L+N λ 0 2 ) ω r0 2 ) κ τ in cos ( ϕ F (L+N λ 0 2 )] 2 . =Δ P OFLD-POOEp (L)
Δ P OFLDPOO (L,t)=Δ P OFLD-POOEp (L)cos[ ω r (L)t+ θ e ].
Δ P OFLDPOOEpmin 2 τ p ω r0 2 α G N .
Δ P OFLDPOOEpmax 2 τ p ω r 0 2 α G N 1+ [2 τ s ( ω r-offset + ω rmax ω rmin )] 2 .
Δ P OFLDPOOEppp =2 τ p ω r 0 2 α G N ( 1+[2 τ s ( ω r-offset + ω rmax ω rmin ) ] 2 -1).
Δ P OFLDPOOEppp Δ P OFLDpp = 2 τ p ω r 0 2 α G N ( 1+ [2 τ s ( ω r-offset + ω rmax ω rmin )] 2 -1) 4( E S0 2 + 1 G N τ s ) κ τ p τ in τ in 2ακ τ p ( 1+ [2 τ s ( ω r-offset + ω rmax ω rmin )] 2 -1).
ΔL=Δ L t +Δ L f .
Δ L f = λ 0 2 ω r2 ω r1 ω rmax ω rmin .

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