Abstract

Compared with conventional optical heterodyne detection, laser optical feedback imaging (LOFI) allows for a several orders of magnitude higher intensity modulation contrast. The maximum contrast amplification is typically 103 for a diode laser in the gigahertz range and 106 for a microchip laser in the megahertz range. To take advantage of the wavelength tunability of a laser diode and of the lower resonant detection frequency of a microchip laser, we used LOFI modulation induced by the frequency-shifted optical feedback in a laser diode as a modulated pumping power for a microchip laser for resonant dynamic amplification. In this way, we were able to transfer the optical feedback sensitivity of the laser diode to the megahertz range. Application to telemetry is also reported.

© 2004 Optical Society of America

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References

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  1. R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
    [CrossRef]
  2. J. Mork, B. Tromborg, J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
    [CrossRef]
  3. B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
    [CrossRef]
  4. R. Gabet, G. M. Stéphan, M. Bondiou, P. Besnard, D. Kilper, “Ultraghigh sensitivity detector for coherent light: the laser,” Opt. Commun. 185, 109–114 (2000).
    [CrossRef]
  5. P. Besnard, B. Meziane, G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
    [CrossRef]
  6. A. Bearden, M. P. O’Neill, L. C. Osborne, T. L. Wong, “Imaging and vibrational analysis with laser-feedback interferometry,” Opt. Lett. 18, 238–240 (1993).
    [CrossRef] [PubMed]
  7. T. Bosch, N. Servagent, S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
    [CrossRef]
  8. L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, A. Le Floch, “Building blocks for a two-frequency laser lidar-radar: a preliminary study,” Appl. Opt. 41, 5702–5712 (2002).
    [CrossRef] [PubMed]
  9. T. Dresel, G. Häusler, H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
    [CrossRef] [PubMed]
  10. E. Lacot, R. Day, J. Pinel, F. Stoeckel, “Laser relaxation-oscillation frequency imaging,” Opt. Lett. 26, 1483–1485 (2001).
    [CrossRef]
  11. E. Lacot, R. Day, F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
    [CrossRef]
  12. K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
    [CrossRef]
  13. S. Okamoto, H. Takeda, F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
    [CrossRef]
  14. E. Lacot, R. Day, F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
    [CrossRef]
  15. E. Lacot, O. Hugon, F. Stoeckel, “Hopf amplification of frequency-shifted optical feedback,” Phys. Rev. A 67, 053806 (2003).
    [CrossRef]
  16. T.-S. Lim, T.-H. Yang, J.-L. Chern, K. Otsuka, “Phase-noise-driven instability in a single-mode microchip Nd:YVO4 laser with feedback,” IEEE J. Quantum Electron. 37, 1215–1225 (2001).
    [CrossRef]
  17. Y. I. Khanin, Principle of Laser Dynamics (Elsevier, Amsterdam, 1995), pp. 57–62.
  18. Equations (5) show that the direct LOFI modulation is at the first order [O( Re)], independent of the phase amplitude coupling parameters α.
  19. N. Servagent, G. Mourat, F. Gouaux, T. Bosch, “Analysis of some intrinsic limitations of a laser range-finder using the self-mixing interference,” in Laser Interferometry IX: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE3479, 76–83 (1998).
    [CrossRef]
  20. J. J. Zayhowski, A. Mooradian, “Single-frequency microchip Nd lasers,” Opt. Lett. 14, 24–26 (1989).
    [CrossRef] [PubMed]
  21. M. Rabarot, J. Marty, L. Fulbert, Ph. Thony, E. Molva, “Very low threshold microchip lasers with stable microcavities,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 483–484.
  22. D. Derozier, S. Bielawski, P. Glorieux, “Dynamical behavior of a doped fiber laser under pump modulation,” Opt. Commun. 83, 97–102 (1991).
    [CrossRef]
  23. A more detailed analysis of the experimental results (not developed in this paper) shows, for particular experimental conditions, an increase of the signal-to-noise ratio of the indirect LOFI modulation compared with the direct LOFI modulation. This study is currently in progress and is still unresolved.

2003 (1)

E. Lacot, O. Hugon, F. Stoeckel, “Hopf amplification of frequency-shifted optical feedback,” Phys. Rev. A 67, 053806 (2003).
[CrossRef]

2002 (2)

B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
[CrossRef]

L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, A. Le Floch, “Building blocks for a two-frequency laser lidar-radar: a preliminary study,” Appl. Opt. 41, 5702–5712 (2002).
[CrossRef] [PubMed]

2001 (4)

T.-S. Lim, T.-H. Yang, J.-L. Chern, K. Otsuka, “Phase-noise-driven instability in a single-mode microchip Nd:YVO4 laser with feedback,” IEEE J. Quantum Electron. 37, 1215–1225 (2001).
[CrossRef]

E. Lacot, R. Day, F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, J. Pinel, F. Stoeckel, “Laser relaxation-oscillation frequency imaging,” Opt. Lett. 26, 1483–1485 (2001).
[CrossRef]

T. Bosch, N. Servagent, S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

2000 (1)

R. Gabet, G. M. Stéphan, M. Bondiou, P. Besnard, D. Kilper, “Ultraghigh sensitivity detector for coherent light: the laser,” Opt. Commun. 185, 109–114 (2000).
[CrossRef]

1999 (1)

1995 (1)

S. Okamoto, H. Takeda, F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

1993 (2)

P. Besnard, B. Meziane, G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

A. Bearden, M. P. O’Neill, L. C. Osborne, T. L. Wong, “Imaging and vibrational analysis with laser-feedback interferometry,” Opt. Lett. 18, 238–240 (1993).
[CrossRef] [PubMed]

1992 (3)

T. Dresel, G. Häusler, H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
[CrossRef] [PubMed]

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

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

1991 (1)

D. Derozier, S. Bielawski, P. Glorieux, “Dynamical behavior of a doped fiber laser under pump modulation,” Opt. Commun. 83, 97–102 (1991).
[CrossRef]

1989 (1)

1980 (1)

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

Bearden, A.

Besnard, P.

R. Gabet, G. M. Stéphan, M. Bondiou, P. Besnard, D. Kilper, “Ultraghigh sensitivity detector for coherent light: the laser,” Opt. Commun. 185, 109–114 (2000).
[CrossRef]

P. Besnard, B. Meziane, G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

Bielawski, S.

D. Derozier, S. Bielawski, P. Glorieux, “Dynamical behavior of a doped fiber laser under pump modulation,” Opt. Commun. 83, 97–102 (1991).
[CrossRef]

Bondiou, M.

R. Gabet, G. M. Stéphan, M. Bondiou, P. Besnard, D. Kilper, “Ultraghigh sensitivity detector for coherent light: the laser,” Opt. Commun. 185, 109–114 (2000).
[CrossRef]

Bosch, T.

T. Bosch, N. Servagent, S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

N. Servagent, G. Mourat, F. Gouaux, T. Bosch, “Analysis of some intrinsic limitations of a laser range-finder using the self-mixing interference,” in Laser Interferometry IX: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE3479, 76–83 (1998).
[CrossRef]

Bretenaker, F.

Brunel, M.

Chern, J.-L.

T.-S. Lim, T.-H. Yang, J.-L. Chern, K. Otsuka, “Phase-noise-driven instability in a single-mode microchip Nd:YVO4 laser with feedback,” IEEE J. Quantum Electron. 37, 1215–1225 (2001).
[CrossRef]

Day, R.

Derozier, D.

D. Derozier, S. Bielawski, P. Glorieux, “Dynamical behavior of a doped fiber laser under pump modulation,” Opt. Commun. 83, 97–102 (1991).
[CrossRef]

Dolfi, D.

Donati, S.

T. Bosch, N. Servagent, S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

Dresel, T.

Engelborghs, K.

B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
[CrossRef]

Erneux, T.

B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
[CrossRef]

Fulbert, L.

M. Rabarot, J. Marty, L. Fulbert, Ph. Thony, E. Molva, “Very low threshold microchip lasers with stable microcavities,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 483–484.

Gabet, R.

R. Gabet, G. M. Stéphan, M. Bondiou, P. Besnard, D. Kilper, “Ultraghigh sensitivity detector for coherent light: the laser,” Opt. Commun. 185, 109–114 (2000).
[CrossRef]

Glorieux, P.

D. Derozier, S. Bielawski, P. Glorieux, “Dynamical behavior of a doped fiber laser under pump modulation,” Opt. Commun. 83, 97–102 (1991).
[CrossRef]

Gouaux, F.

N. Servagent, G. Mourat, F. Gouaux, T. Bosch, “Analysis of some intrinsic limitations of a laser range-finder using the self-mixing interference,” in Laser Interferometry IX: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE3479, 76–83 (1998).
[CrossRef]

Haegeman, B.

B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
[CrossRef]

Häusler, G.

Hugon, O.

E. Lacot, O. Hugon, F. Stoeckel, “Hopf amplification of frequency-shifted optical feedback,” Phys. Rev. A 67, 053806 (2003).
[CrossRef]

Huignard, J.-P.

Kannari, F.

S. Okamoto, H. Takeda, F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Khanin, Y. I.

Y. I. Khanin, Principle of Laser Dynamics (Elsevier, Amsterdam, 1995), pp. 57–62.

Kilper, D.

R. Gabet, G. M. Stéphan, M. Bondiou, P. Besnard, D. Kilper, “Ultraghigh sensitivity detector for coherent light: the laser,” Opt. Commun. 185, 109–114 (2000).
[CrossRef]

Kobayashi, K.

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

Lacot, E.

E. Lacot, O. Hugon, F. Stoeckel, “Hopf amplification of frequency-shifted optical feedback,” Phys. Rev. A 67, 053806 (2003).
[CrossRef]

E. Lacot, R. Day, F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, J. Pinel, F. Stoeckel, “Laser relaxation-oscillation frequency imaging,” Opt. Lett. 26, 1483–1485 (2001).
[CrossRef]

E. Lacot, R. Day, F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

Lai, N. D.

Lang, R.

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

Le Floch, A.

Lim, T.-S.

T.-S. Lim, T.-H. Yang, J.-L. Chern, K. Otsuka, “Phase-noise-driven instability in a single-mode microchip Nd:YVO4 laser with feedback,” IEEE J. Quantum Electron. 37, 1215–1225 (2001).
[CrossRef]

Mark, J.

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

Marty, J.

M. Rabarot, J. Marty, L. Fulbert, Ph. Thony, E. Molva, “Very low threshold microchip lasers with stable microcavities,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 483–484.

Meziane, B.

P. Besnard, B. Meziane, G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

Molva, E.

M. Rabarot, J. Marty, L. Fulbert, Ph. Thony, E. Molva, “Very low threshold microchip lasers with stable microcavities,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 483–484.

Mooradian, A.

Mork, J.

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

Morvan, L.

Mourat, G.

N. Servagent, G. Mourat, F. Gouaux, T. Bosch, “Analysis of some intrinsic limitations of a laser range-finder using the self-mixing interference,” in Laser Interferometry IX: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE3479, 76–83 (1998).
[CrossRef]

O’Neill, M. P.

Okamoto, S.

S. Okamoto, H. Takeda, F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Osborne, L. C.

Otsuka, K.

T.-S. Lim, T.-H. Yang, J.-L. Chern, K. Otsuka, “Phase-noise-driven instability in a single-mode microchip Nd:YVO4 laser with feedback,” IEEE J. Quantum Electron. 37, 1215–1225 (2001).
[CrossRef]

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

Pieroux, D.

B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
[CrossRef]

Pinel, J.

Rabarot, M.

M. Rabarot, J. Marty, L. Fulbert, Ph. Thony, E. Molva, “Very low threshold microchip lasers with stable microcavities,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 483–484.

Roose, D.

B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
[CrossRef]

Servagent, N.

T. Bosch, N. Servagent, S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

N. Servagent, G. Mourat, F. Gouaux, T. Bosch, “Analysis of some intrinsic limitations of a laser range-finder using the self-mixing interference,” in Laser Interferometry IX: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE3479, 76–83 (1998).
[CrossRef]

Stephan, G. M.

P. Besnard, B. Meziane, G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

Stéphan, G. M.

R. Gabet, G. M. Stéphan, M. Bondiou, P. Besnard, D. Kilper, “Ultraghigh sensitivity detector for coherent light: the laser,” Opt. Commun. 185, 109–114 (2000).
[CrossRef]

Stoeckel, F.

E. Lacot, O. Hugon, F. Stoeckel, “Hopf amplification of frequency-shifted optical feedback,” Phys. Rev. A 67, 053806 (2003).
[CrossRef]

E. Lacot, R. Day, F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, J. Pinel, F. Stoeckel, “Laser relaxation-oscillation frequency imaging,” Opt. Lett. 26, 1483–1485 (2001).
[CrossRef]

E. Lacot, R. Day, F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

Takeda, H.

S. Okamoto, H. Takeda, F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Thony, Ph.

M. Rabarot, J. Marty, L. Fulbert, Ph. Thony, E. Molva, “Very low threshold microchip lasers with stable microcavities,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 483–484.

Tromborg, B.

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

Venzke, H.

Wong, T. L.

Yang, T.-H.

T.-S. Lim, T.-H. Yang, J.-L. Chern, K. Otsuka, “Phase-noise-driven instability in a single-mode microchip Nd:YVO4 laser with feedback,” IEEE J. Quantum Electron. 37, 1215–1225 (2001).
[CrossRef]

Zayhowski, J. J.

Appl. Opt. (2)

IEEE J. Quantum Electron. (4)

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

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

P. Besnard, B. Meziane, G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

T.-S. Lim, T.-H. Yang, J.-L. Chern, K. Otsuka, “Phase-noise-driven instability in a single-mode microchip Nd:YVO4 laser with feedback,” IEEE J. Quantum Electron. 37, 1215–1225 (2001).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

Opt. Commun. (2)

R. Gabet, G. M. Stéphan, M. Bondiou, P. Besnard, D. Kilper, “Ultraghigh sensitivity detector for coherent light: the laser,” Opt. Commun. 185, 109–114 (2000).
[CrossRef]

D. Derozier, S. Bielawski, P. Glorieux, “Dynamical behavior of a doped fiber laser under pump modulation,” Opt. Commun. 83, 97–102 (1991).
[CrossRef]

Opt. Eng. (1)

T. Bosch, N. Servagent, S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (2)

E. Lacot, R. Day, F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, O. Hugon, F. Stoeckel, “Hopf amplification of frequency-shifted optical feedback,” Phys. Rev. A 67, 053806 (2003).
[CrossRef]

Phys. Rev. E (1)

B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, T. Erneux, “Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback,” Phys. Rev. E 66, 046216 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Okamoto, H. Takeda, F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Other (5)

Y. I. Khanin, Principle of Laser Dynamics (Elsevier, Amsterdam, 1995), pp. 57–62.

Equations (5) show that the direct LOFI modulation is at the first order [O( Re)], independent of the phase amplitude coupling parameters α.

N. Servagent, G. Mourat, F. Gouaux, T. Bosch, “Analysis of some intrinsic limitations of a laser range-finder using the self-mixing interference,” in Laser Interferometry IX: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE3479, 76–83 (1998).
[CrossRef]

M. Rabarot, J. Marty, L. Fulbert, Ph. Thony, E. Molva, “Very low threshold microchip lasers with stable microcavities,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 483–484.

A more detailed analysis of the experimental results (not developed in this paper) shows, for particular experimental conditions, an increase of the signal-to-noise ratio of the indirect LOFI modulation compared with the direct LOFI modulation. This study is currently in progress and is still unresolved.

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Figures (6)

Fig. 1
Fig. 1

Normalized contrast of the laser output power modulation (1/Re)(ΔP/ P) versus frequency shift Ω e : a, laser diode with direct frequency-shifted optical feedback (cavity loss modulation); b, microchip laser with direct frequency-shifted optical feedback (cavity loss modulation); c, microchip laser with indirect frequency-shifted optical feedback (pump modulation).

Fig. 2
Fig. 2

Schematic diagram of the LOFI experiment with a pumping laser diode: L1–L4, lenses; BS, beam splitter; AOD1, AOD2, acousto-optic deflectors; rf, radio frequency generator; F e , frequency shift; VA, variable attenuator; PD1, PD2, photodiodes.

Fig. 3
Fig. 3

LOFI telemetric sensing with a laser diode: (a) response of a low-finesse Fabry–Perot etalon (free spectral range of 3.9644 GHz) to the optical frequency scanning of a laser diode; (b) variation of the LOFI phase (i.e., the optical phase) induced by optical frequency scanning of a laser diode; (c) small part of trace (b); (d) unwrapped LOFI phase (Φ) versus calibrated optical frequency scanning (Δν).

Fig. 4
Fig. 4

Time evolution of the phase of the output power modulation induced by optical frequency scanning of the laser diode: top curve, microchip laser phase variation; bottom curve, pumping laser diode phase variation.

Fig. 5
Fig. 5

Polar plot of the LOFI output power modulation (amplitude versus phase). Indirect LOFI modulation of a microchip laser (large circle). Direct LOFI modulation of the pumping laser diode (small circle). The optical frequency shift [(Ω e /2π) = 850 kHz] is not exactly resonant with the microchip laser relaxation frequency [(Ω R /2π) = 875 kHz].

Fig. 6
Fig. 6

(a) Output power modulation of a microchip laser (ΔP μ/P μ) induced by the LOFI output power modulation of a pumping laser diode (ΔP d/ P d) for (Ωe/2π = 600 kHz). (b) Contrast enhancement factor (ΔP μ/P μ)/(ΔP d/ P d) versus optical frequency shift (Ω e /2π).

Tables (1)

Tables Icon

Table 1 Typical Laser Parameters

Equations (21)

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

dNtdt=γ1N0-Nt-BNt|Et|2,
dEtdt=12BNt-γcEt+γe cosΩet-ωcτe-Φt+Φt-τeEt-τe,
dΦtdt=12 αBNt-γc+γe sinΩet-ωcτe-Φt+Φt-τeEt-τeEt,
NS=γc/B,
IS=|ES|2=Isatη-1,
ΦS=2π.
Nt, Re=NS+Re1N1t+Re2N2t+,
Et, Re=ES+Re1E1t+Re2E2t+,
Φt, Re=ΦS+Re1Φ1t+Re2Φ2t+,
dN1tdt=-γ1+B|ES|2N1t-2BNSESE1t, dE1tdt=12 BESN1t+γcES cosΩet-ωcτe, dΦ1tdt=12 αBN1+γc sinΩet-ωcτe.
ΔPt, ΩeP=2ReE1t, ΩeES=2γeΓ12+Ωe21/2ΩR2-Ωe22+Γ12Ωe21/2×cosΩet-ωcτe+ϕR,
tanϕR=ΩeΩR2-Ωe2-Γ12Γ1ΩR2.
Φde=ωcτe-ϕR=ωc2dec-ϕR.
ΔPΩRP2γeηγ1=2 γcηγ1Re.
γ1,μN0,μt=γ1,μN0,μ1+βd cosΩet-Φd,
βdΩe, Re=ΔPdPd=2γc,dReΓ1,d2+Ωe21/2ΩR,d2-Ωe22+Γ1,d2Ωe21/2,
Φdde=ωc,d2de,dc-ϕR,d.
ΔPμt, ΩePμ=βdΩe, ReΓ1,μγc,μΩR,μ2-Ωe22+Γ1,μ2Ωe21/2×cosΩet-Φdde+ΨR,μ,
Φμde=Φdde-ΨR,μ=ωc,d2de,dc-ϕR,d-ΨR,μ.
ΔPμΩR,μPμPdΔPdΩR,μ=γc,μγ1,μ1ημ-1=1.4×103.
de,d=c4πΔϕdΔνd.

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