Abstract

We propose a theoretical model for analyzing the dynamics of a periodically driven semiconductor laser subject to optical feedback from a microcantilever. We numerically investigate the temporal evolution of the light intensity of the semiconductor laser, and we show the interspikes of the light intensity. These interspikes of light intensity are also demonstrated in our experiment. The validity of the theoretical model is verified. The observed phenomenon has a potential application for resonant sensing.

© 2008 Optical Society of America

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References

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  1. D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (Wiley, 2005).
    [CrossRef]
  2. Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697-R2700 (1995).
    [CrossRef]
  3. Y. Takiguchi, Y. Liu, and J. Ohtsubo, “Low-frequency fluctuation induced by injection-current modulation in semiconductor lasers with optical feedback,” Opt. Lett. 23, 1369-1371 (1998).
    [CrossRef]
  4. J. M. Buldú, J. Garciá-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
    [CrossRef]
  5. J. M. Mendez, R. Lajie, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
    [CrossRef]
  6. M. S. Torre, G. Masoller, P. Mandel, and K. A. Shore, “Enhanced sensitivity to current modulation near dynamic instability in semiconductor lasers with optical feedback and optical injection,” J. Opt. Soc. Am. B 21, 302-306 (2004).
    [CrossRef]
  7. G. Guiliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4, S283-S294 (2002).
    [CrossRef]
  8. G. Plantier, C. Bes, T. Bosch, and F. Bony, “Auto adaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Instrument and Measurement Technology Conference (IEEE, 2005), pp. 1013-1017.
  9. G. Plantier, C. Bes, and T. Bosch, “Behavioral model of a self-mixing displacement sensor,” IEEE J. Quantum Electron. 41, 1157-1167 (2005).
    [CrossRef]
  10. C. J. Welham, J. W. Gardner, and J. Greenwood, “A laterally driven micromachined resonant pressure sensor,” Sens. Actuators, A 52, 86-91 (1996).
    [CrossRef]
  11. N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett. 82, 2697-2699 (2003).
    [CrossRef]
  12. T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
    [CrossRef] [PubMed]
  13. T. Heil, I. Fischer, and W. Elsäβer, “Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback,” Phys. Rev. A 60, 634-641 (1999).
    [CrossRef]
  14. R. Lang and L. Lobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347-355 (1980).
    [CrossRef]
  15. A. V. Churenkov, “Photothermal excitation and self-excitation of silicon microresonators,” Sens. Actuators, A 39, 141-148 (1993).
    [CrossRef]
  16. R. Sandberg, K. Mølhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng. 15, 2249-2253 (2005).
    [CrossRef]
  17. S. Rast, C. Wattinger, U. Gysin, and E. Meyer, “Dynamics of damped cantilevers,” Rev. Sci. Instrum. 71, 2772-2775 (2000).
    [CrossRef]
  18. Y. M. Liu, X. Z. Wang, and X. F. Wang, “Study on silicon micro-resonators by using a novel optical excitation and detection apparatus,” Chin. Opt. Lett. 4, 309-310, (2006).
  19. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 16th ed. (Longman, 1995).
  20. R. W. Tkach and A. R. Charplyvy, “Regimes of feedback regimes in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. LT-4, 1655-1661 (1986).
    [CrossRef]
  21. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

2007

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

2006

2005

R. Sandberg, K. Mølhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng. 15, 2249-2253 (2005).
[CrossRef]

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

2004

2003

N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett. 82, 2697-2699 (2003).
[CrossRef]

2002

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

J. M. Buldú, J. Garciá-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[CrossRef]

2001

J. M. Mendez, R. Lajie, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[CrossRef]

2000

S. Rast, C. Wattinger, U. Gysin, and E. Meyer, “Dynamics of damped cantilevers,” Rev. Sci. Instrum. 71, 2772-2775 (2000).
[CrossRef]

1999

T. Heil, I. Fischer, and W. Elsäβer, “Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback,” Phys. Rev. A 60, 634-641 (1999).
[CrossRef]

1998

1996

C. J. Welham, J. W. Gardner, and J. Greenwood, “A laterally driven micromachined resonant pressure sensor,” Sens. Actuators, A 52, 86-91 (1996).
[CrossRef]

1995

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697-R2700 (1995).
[CrossRef]

1993

A. V. Churenkov, “Photothermal excitation and self-excitation of silicon microresonators,” Sens. Actuators, A 39, 141-148 (1993).
[CrossRef]

1986

R. W. Tkach and A. R. Charplyvy, “Regimes of feedback regimes in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. LT-4, 1655-1661 (1986).
[CrossRef]

1980

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

Agrawal, G. P.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

Aliaga, J.

J. M. Mendez, R. Lajie, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[CrossRef]

Babcock, K.

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Bes, C.

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

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Auto adaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Instrument and Measurement Technology Conference (IEEE, 2005), pp. 1013-1017.

Boisen, A.

R. Sandberg, K. Mølhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng. 15, 2249-2253 (2005).
[CrossRef]

Bony, F.

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Auto adaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Instrument and Measurement Technology Conference (IEEE, 2005), pp. 1013-1017.

Bosch, T.

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

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

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Auto adaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Instrument and Measurement Technology Conference (IEEE, 2005), pp. 1013-1017.

Buldú, J. M.

J. M. Buldú, J. Garciá-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[CrossRef]

Burg, T. P.

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Carlson, G.

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Charplyvy, A. R.

R. W. Tkach and A. R. Charplyvy, “Regimes of feedback regimes in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. LT-4, 1655-1661 (1986).
[CrossRef]

Churenkov, A. V.

A. V. Churenkov, “Photothermal excitation and self-excitation of silicon microresonators,” Sens. Actuators, A 39, 141-148 (1993).
[CrossRef]

Datskos, P. G.

N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett. 82, 2697-2699 (2003).
[CrossRef]

Donati, S.

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

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

Elsäßer, W.

T. Heil, I. Fischer, and W. Elsäβer, “Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback,” Phys. Rev. A 60, 634-641 (1999).
[CrossRef]

Fischer, I.

T. Heil, I. Fischer, and W. Elsäβer, “Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback,” Phys. Rev. A 60, 634-641 (1999).
[CrossRef]

Foster, J. S.

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Garciá-Ojalvo, J.

J. M. Buldú, J. Garciá-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[CrossRef]

Gardner, J. W.

C. J. Welham, J. W. Gardner, and J. Greenwood, “A laterally driven micromachined resonant pressure sensor,” Sens. Actuators, A 52, 86-91 (1996).
[CrossRef]

Giudici, M.

J. M. Mendez, R. Lajie, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[CrossRef]

Godin, M.

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Greenwood, J.

C. J. Welham, J. W. Gardner, and J. Greenwood, “A laterally driven micromachined resonant pressure sensor,” Sens. Actuators, A 52, 86-91 (1996).
[CrossRef]

Guiliani, G.

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

Gysin, U.

S. Rast, C. Wattinger, U. Gysin, and E. Meyer, “Dynamics of damped cantilevers,” Rev. Sci. Instrum. 71, 2772-2775 (2000).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, and W. Elsäβer, “Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback,” Phys. Rev. A 60, 634-641 (1999).
[CrossRef]

Kane, D. M.

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (Wiley, 2005).
[CrossRef]

Kaye, W. C.

W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 16th ed. (Longman, 1995).

Kikuchi, N.

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697-R2700 (1995).
[CrossRef]

Knudsen, S. M.

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Laby, T. H.

W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 16th ed. (Longman, 1995).

Lajie, R.

J. M. Mendez, R. Lajie, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[CrossRef]

Lang, R.

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

Lavrik, N. V.

N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett. 82, 2697-2699 (2003).
[CrossRef]

Liu, Y.

Y. Takiguchi, Y. Liu, and J. Ohtsubo, “Low-frequency fluctuation induced by injection-current modulation in semiconductor lasers with optical feedback,” Opt. Lett. 23, 1369-1371 (1998).
[CrossRef]

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697-R2700 (1995).
[CrossRef]

Liu, Y. M.

Lobayashi, L.

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

Manalis, S. R.

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Mandel, P.

Masoller, G.

Mendez, J. M.

J. M. Mendez, R. Lajie, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[CrossRef]

Meyer, E.

S. Rast, C. Wattinger, U. Gysin, and E. Meyer, “Dynamics of damped cantilevers,” Rev. Sci. Instrum. 71, 2772-2775 (2000).
[CrossRef]

Mindlin, G. B.

J. M. Mendez, R. Lajie, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[CrossRef]

Mirasso, C. R.

J. M. Buldú, J. Garciá-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[CrossRef]

Mølhave, K.

R. Sandberg, K. Mølhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng. 15, 2249-2253 (2005).
[CrossRef]

Norgia, M.

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

Ohtsubo, J.

Y. Takiguchi, Y. Liu, and J. Ohtsubo, “Low-frequency fluctuation induced by injection-current modulation in semiconductor lasers with optical feedback,” Opt. Lett. 23, 1369-1371 (1998).
[CrossRef]

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697-R2700 (1995).
[CrossRef]

Plantier, G.

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

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Auto adaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Instrument and Measurement Technology Conference (IEEE, 2005), pp. 1013-1017.

Rast, S.

S. Rast, C. Wattinger, U. Gysin, and E. Meyer, “Dynamics of damped cantilevers,” Rev. Sci. Instrum. 71, 2772-2775 (2000).
[CrossRef]

Sandberg, R.

R. Sandberg, K. Mølhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng. 15, 2249-2253 (2005).
[CrossRef]

Shen, W. J.

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Shore, K. A.

Svendsen, W.

R. Sandberg, K. Mølhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng. 15, 2249-2253 (2005).
[CrossRef]

Takiguchi, Y.

Tkach, R. W.

R. W. Tkach and A. R. Charplyvy, “Regimes of feedback regimes in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. LT-4, 1655-1661 (1986).
[CrossRef]

Torre, M. S.

Torrent, M. C.

J. M. Buldú, J. Garciá-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[CrossRef]

Wang, X. F.

Wang, X. Z.

Wattinger, C.

S. Rast, C. Wattinger, U. Gysin, and E. Meyer, “Dynamics of damped cantilevers,” Rev. Sci. Instrum. 71, 2772-2775 (2000).
[CrossRef]

Welham, C. J.

C. J. Welham, J. W. Gardner, and J. Greenwood, “A laterally driven micromachined resonant pressure sensor,” Sens. Actuators, A 52, 86-91 (1996).
[CrossRef]

Appl. Phys. Lett.

N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett. 82, 2697-2699 (2003).
[CrossRef]

Chin. Opt. Lett.

IEEE J. Quantum Electron.

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

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

J. Lightwave Technol.

R. W. Tkach and A. R. Charplyvy, “Regimes of feedback regimes in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. LT-4, 1655-1661 (1986).
[CrossRef]

J. Micromech. Microeng.

R. Sandberg, K. Mølhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng. 15, 2249-2253 (2005).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

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

J. Opt. Soc. Am. B

Nature

T. P. Burg, M. Godin, S. M. Knudsen, W. J. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446, 1066-1069 (2007).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

T. Heil, I. Fischer, and W. Elsäβer, “Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback,” Phys. Rev. A 60, 634-641 (1999).
[CrossRef]

Phys. Rev. E

J. M. Buldú, J. Garciá-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[CrossRef]

J. M. Mendez, R. Lajie, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[CrossRef]

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697-R2700 (1995).
[CrossRef]

Rev. Sci. Instrum.

S. Rast, C. Wattinger, U. Gysin, and E. Meyer, “Dynamics of damped cantilevers,” Rev. Sci. Instrum. 71, 2772-2775 (2000).
[CrossRef]

Sens. Actuators, A

A. V. Churenkov, “Photothermal excitation and self-excitation of silicon microresonators,” Sens. Actuators, A 39, 141-148 (1993).
[CrossRef]

C. J. Welham, J. W. Gardner, and J. Greenwood, “A laterally driven micromachined resonant pressure sensor,” Sens. Actuators, A 52, 86-91 (1996).
[CrossRef]

Other

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Auto adaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Instrument and Measurement Technology Conference (IEEE, 2005), pp. 1013-1017.

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (Wiley, 2005).
[CrossRef]

W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 16th ed. (Longman, 1995).

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

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Figures (5)

Fig. 1
Fig. 1

(a) Experimental setup: MCL, microcantilever; C, convergent lens; PS, power supply; S, signal generator; SL, semiconductor laser; PD, photodiode; TEC, thermoelectric cooler; OSC, oscilloscope. (b)–(d) The first-, second-, and third-order resonant vibration state of the microcantilever.

Fig. 2
Fig. 2

Frequency response of the microcantilever. The solid curve denotes the theoretically calculated results. The dots denote the experimental results. The dashed curve denotes the fitting results of the experimental results.

Fig. 3
Fig. 3

Mapping of the normalized N H F at different I d c in the I m - k space: (a) I d c = 1.25 I th , (b) I d c = 1.5 I t h , (c) I d c = 2 I t h , (d) I d c = 2.5 I t h .

Fig. 4
Fig. 4

(a) Numerically calculated temporal evolution of the light intensity. (b)–(d) Schematic depictions of the competition of the ECMs.

Fig. 5
Fig. 5

Experimentally detected intensity time series of the semiconductor laser.

Tables (1)

Tables Icon

Table 1 Parameters of Microcantilever’s Material [19]

Equations (11)

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

K 2 Δ T ( x ) x 2 = i ω I Δ T ( x ) ,
Δ T ( x ) = P 1 δ th η W mc ( d 1 k t e 1 + d 2 k t e 2 ) { exp [ ( x x 0 ) δ th ] cos [ ( x x 0 ) δ th ] + exp [ ( x + x 0 2 L mc ) δ th ] cos [ ( x + x 0 2 L mc ) δ th ] } , for x x 0
Δ T ( x ) = P 1 δ th η W mc ( d 1 k t e 1 + d 2 k t e 2 ) { exp [ ( x x 0 ) δ th ] cos [ ( x x 0 ) δ th ] + exp [ ( x + x 0 2 L mc ) δ th ] cos [ ( x + x 0 2 L mc ) δ th ] } , for x > x 0
A ( x , t ) = ϕ m eff ( ω n 2 ω I 2 ) 2 + ( ω n ω I Q ) 2 ψ ( x ) sin ( ω I t + θ ) ,
ω n = ( k m L mc ) 2 L mc 2 [ d 1 0 E y m 1 ( z z 0 ) 2 d z + 0 d 2 E y m 2 ( z z 0 ) 2 d z d 1 ρ 1 + d 2 ρ 2 ] 1 2 ,
ψ ( x ) = A m { sin ( k m x ) sinh ( k m x ) + cos ( k m L mc ) + cosh ( k m L mc ) sin ( k m L mc ) sinh ( k m L mc ) [ cos ( k m x ) cosh ( k m x ) ] } .
ϕ = 0 L mc f ( x ) ψ ( x ) d x 0 L mc ψ ( x ) d x 2 .
A ( x ) = Q Θ ψ ( x ) m eff ( ω n 2 ω I 2 ) 2 + ( ω n ω I Q ) 2 0 L mc Δ T ( x 0 ) d 2 ψ ( x 0 ) d x 0 2 d x 0 0 L mc ψ ( x ) d x 2 .
Δ τ = 2 Θ ψ ( x 0 ) m eff c ( ω n 2 ω I 2 ) 2 + ( ω n ω I Q ) 2 0 L m c Δ T ( x 0 , t ) d 2 ψ ( x 0 ) d x 0 2 d x 0 0 L m c ψ ( x ) d x 2 ,
d E ( t ) d t = 1 2 ( 1 + i α ) [ G ( N ( t ) N 0 ) 1 τ p ] E ( t ) + k E ( t τ ) exp ( i ω s o τ ) ,
d N ( t ) d t = I d c e V + I a c e V cos ( ω I t ) N ( t ) τ s G [ N ( t ) N 0 ] E 2 ( t ) ,

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