Abstract

An optical-feedback semiconductor laser Michelson interferometer (OSMI) is presented for measuring microscopic linear displacements without ambiguity in the direction of motion. The two waves from the interferometer arms, one from the reference mirror and the other from the reflecting moving target, are fed back into the lasing medium (λ = 830 nm), causing variations in the laser output power. We model the OSMI into an equivalent Fabry–Perot resonator and derive the dependence of the output power (and the junction voltage) on the path difference between the two interferometer arms. Numerical and experimental results consistently show that the laser output power varies periodically (period, λ/2) with path difference. The output power variation exhibits an asymmetric behavior with the direction of motion, which is used to measure, at subwavelength resolution, the displacement vector (both amplitude and direction) of the moving sample. Two samples are considered in the experiments: (i) a piezoelectric transducer and (ii) an audio speaker.

© 2001 Optical Society of America

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  1. R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  2. D. Lenstra, M. Van Vaalen, B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
    [CrossRef]
  3. H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
    [CrossRef]
  4. M. Pan, B. Shi, G. Gray, “Semiconductor laser dynamics subject to strong optical feedback,” Opt. Lett. 22, 166–168 (1997).
    [CrossRef] [PubMed]
  5. Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
    [CrossRef]
  6. M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
    [CrossRef]
  7. I. Fischer, O. Hess, W. Elsässer, E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
    [CrossRef] [PubMed]
  8. S. Donati, G. Giuliani, S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113–119 (1995).
    [CrossRef]
  9. W. Wang, K. Grattan, A. Palmer, W. Boyle, “Self-mixing interference inside a single-mode diode for optical sensing applications,” IEEE J. Lightwave Technol. 12, 1577–1586 (1994).
    [CrossRef]
  10. F. Gouaux, N. Servagent, T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37, 6684–6689 (1998).
    [CrossRef]
  11. S. Donati, L. Falzoni, S. Merlo, “A pc-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45, 942–947 (1996).
    [CrossRef]
  12. T. Gharbi, A. Courteville, A. Chebbour, “Backscatter-modulated laser diode for low-frequency small-amplitude vibration measurement,” Appl. Opt. 36, 8233–8237 (1997).
    [CrossRef]
  13. A. Chebbour, C. Gorecki, G. Tribillon, “Range finding and velocimetry with directional discrimination using a modulated laser diode Michelson interferometer,” Opt. Commun. 111, 1–5 (1994).
    [CrossRef]
  14. R. Juskaitis, N. P. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
    [CrossRef] [PubMed]
  15. R. Juskaitis, N. P. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy using laser detection,” Opt. Commun. 99, 105–113 (1994).
    [CrossRef]
  16. T. Zhang, Y. Hashimoto, M. Yonemura, “Theory behind and experimentation on the spectral control of a laser diode with a Michelson external cavity,” Jpn. J. Appl. Phys. 35, 6095–6101 (1996).
    [CrossRef]

1999 (1)

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

1998 (1)

1997 (3)

1996 (2)

S. Donati, L. Falzoni, S. Merlo, “A pc-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45, 942–947 (1996).
[CrossRef]

T. Zhang, Y. Hashimoto, M. Yonemura, “Theory behind and experimentation on the spectral control of a laser diode with a Michelson external cavity,” Jpn. J. Appl. Phys. 35, 6095–6101 (1996).
[CrossRef]

1995 (1)

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

1994 (6)

W. Wang, K. Grattan, A. Palmer, W. Boyle, “Self-mixing interference inside a single-mode diode for optical sensing applications,” IEEE J. Lightwave Technol. 12, 1577–1586 (1994).
[CrossRef]

I. Fischer, O. Hess, W. Elsässer, E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
[CrossRef]

A. Chebbour, C. Gorecki, G. Tribillon, “Range finding and velocimetry with directional discrimination using a modulated laser diode Michelson interferometer,” Opt. Commun. 111, 1–5 (1994).
[CrossRef]

R. Juskaitis, N. P. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
[CrossRef] [PubMed]

R. Juskaitis, N. P. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy using laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

1984 (1)

D. Lenstra, M. Van Vaalen, B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

1980 (1)

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

Bosch, T.

Boyle, W.

W. Wang, K. Grattan, A. Palmer, W. Boyle, “Self-mixing interference inside a single-mode diode for optical sensing applications,” IEEE J. Lightwave Technol. 12, 1577–1586 (1994).
[CrossRef]

Chebbour, A.

T. Gharbi, A. Courteville, A. Chebbour, “Backscatter-modulated laser diode for low-frequency small-amplitude vibration measurement,” Appl. Opt. 36, 8233–8237 (1997).
[CrossRef]

A. Chebbour, C. Gorecki, G. Tribillon, “Range finding and velocimetry with directional discrimination using a modulated laser diode Michelson interferometer,” Opt. Commun. 111, 1–5 (1994).
[CrossRef]

Courteville, A.

Daza, M.

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Donati, S.

S. Donati, L. Falzoni, S. Merlo, “A pc-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45, 942–947 (1996).
[CrossRef]

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

Elsässer, W.

I. Fischer, O. Hess, W. Elsässer, E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Falzoni, L.

S. Donati, L. Falzoni, S. Merlo, “A pc-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45, 942–947 (1996).
[CrossRef]

Fischer, I.

I. Fischer, O. Hess, W. Elsässer, E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Fujita, K.

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Gharbi, T.

Giuliani, G.

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

Göbel, E.

I. Fischer, O. Hess, W. Elsässer, E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Gorecki, C.

A. Chebbour, C. Gorecki, G. Tribillon, “Range finding and velocimetry with directional discrimination using a modulated laser diode Michelson interferometer,” Opt. Commun. 111, 1–5 (1994).
[CrossRef]

Gouaux, F.

Grattan, K.

W. Wang, K. Grattan, A. Palmer, W. Boyle, “Self-mixing interference inside a single-mode diode for optical sensing applications,” IEEE J. Lightwave Technol. 12, 1577–1586 (1994).
[CrossRef]

Gray, G.

Hashimoto, Y.

T. Zhang, Y. Hashimoto, M. Yonemura, “Theory behind and experimentation on the spectral control of a laser diode with a Michelson external cavity,” Jpn. J. Appl. Phys. 35, 6095–6101 (1996).
[CrossRef]

Hess, O.

I. Fischer, O. Hess, W. Elsässer, E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Jaskorzynska, B.

D. Lenstra, M. Van Vaalen, B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

Juskaitis, R.

R. Juskaitis, N. P. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
[CrossRef] [PubMed]

R. Juskaitis, N. P. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy using laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

Kakiuchida, H.

H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
[CrossRef]

Kobayashi, K.

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

Lang, R.

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

Lenstra, D.

D. Lenstra, M. Van Vaalen, B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

Liu, Y.

Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
[CrossRef]

Merlo, S.

S. Donati, L. Falzoni, S. Merlo, “A pc-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45, 942–947 (1996).
[CrossRef]

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

Ohtsubo, J.

Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
[CrossRef]

H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
[CrossRef]

Palmer, A.

W. Wang, K. Grattan, A. Palmer, W. Boyle, “Self-mixing interference inside a single-mode diode for optical sensing applications,” IEEE J. Lightwave Technol. 12, 1577–1586 (1994).
[CrossRef]

Pan, M.

Rea, N. P.

R. Juskaitis, N. P. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
[CrossRef] [PubMed]

R. Juskaitis, N. P. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy using laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

Saloma, C.

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Servagent, N.

Shi, B.

Tarun, A.

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Tribillon, G.

A. Chebbour, C. Gorecki, G. Tribillon, “Range finding and velocimetry with directional discrimination using a modulated laser diode Michelson interferometer,” Opt. Commun. 111, 1–5 (1994).
[CrossRef]

Van Vaalen, M.

D. Lenstra, M. Van Vaalen, B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

Wang, W.

W. Wang, K. Grattan, A. Palmer, W. Boyle, “Self-mixing interference inside a single-mode diode for optical sensing applications,” IEEE J. Lightwave Technol. 12, 1577–1586 (1994).
[CrossRef]

Wilson, T.

R. Juskaitis, N. P. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy using laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

R. Juskaitis, N. P. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
[CrossRef] [PubMed]

Yonemura, M.

T. Zhang, Y. Hashimoto, M. Yonemura, “Theory behind and experimentation on the spectral control of a laser diode with a Michelson external cavity,” Jpn. J. Appl. Phys. 35, 6095–6101 (1996).
[CrossRef]

Zhang, T.

T. Zhang, Y. Hashimoto, M. Yonemura, “Theory behind and experimentation on the spectral control of a laser diode with a Michelson external cavity,” Jpn. J. Appl. Phys. 35, 6095–6101 (1996).
[CrossRef]

Appl. Opt. (3)

IEEE J. Lightwave Technol. (1)

W. Wang, K. Grattan, A. Palmer, W. Boyle, “Self-mixing interference inside a single-mode diode for optical sensing applications,” IEEE J. Lightwave Technol. 12, 1577–1586 (1994).
[CrossRef]

IEEE J. Quantum Electron. (4)

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

Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
[CrossRef]

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

H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

S. Donati, L. Falzoni, S. Merlo, “A pc-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45, 942–947 (1996).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Zhang, Y. Hashimoto, M. Yonemura, “Theory behind and experimentation on the spectral control of a laser diode with a Michelson external cavity,” Jpn. J. Appl. Phys. 35, 6095–6101 (1996).
[CrossRef]

Opt. Commun. (3)

R. Juskaitis, N. P. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy using laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

A. Chebbour, C. Gorecki, G. Tribillon, “Range finding and velocimetry with directional discrimination using a modulated laser diode Michelson interferometer,” Opt. Commun. 111, 1–5 (1994).
[CrossRef]

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

I. Fischer, O. Hess, W. Elsässer, E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Physica C (1)

D. Lenstra, M. Van Vaalen, B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Theoretical model. The OSMI consists of a SL in a Michelson interferometer configuration. It is reduced into an equivalent Fabry–Perot resonator for theoretical calculation of the change r b1 in front-facet amplitude reflectivity. An equivalent mirror Meff replaces the optical system that consists of the front facet M b , beam splitter BS, and the two mirrors M1 and M2.

Fig. 2
Fig. 2

Experimental setup. The moving M1 in the OSMI is mounted on two possible test targets (M2 is stationary): (i) PZT-driven stage and (ii) audio speaker diaphragm. Each target provides displacement to mirror M1 along the optical axis of the SL and the objective lens C. A precision diode controller provides injection current I 0 to SL and monitors I PD and V.

Fig. 3
Fig. 3

L - I curves of SL for different OF strengths. The OF increases the SL output power and reduces its threshold current. Also shown are two kinds of OF from the two mirrors M1 and M2 in the OSMI: (a) maximum feedback (pulses) due to constructive interference and (b) minimum feedback (crosses) due to destructive interference.

Fig. 4
Fig. 4

Junction voltage versus injection current plots for different OF levels. The effect of OF is to decrease the junction voltage. The uncertainty in the junction voltage measurements is ±0.5 mV.

Fig. 5
Fig. 5

Numerical (solid curve) and experimental SL output power as a function of path difference between M1 and M2 where the position of M2 is fixed at (a) L 2 = 11.3 cm, (b) L 1 = 11.4 cm (c), 11.5 cm, (d) 11.6 cm, and (e) 11.7 cm. Moving mirror M1 is centered at x = 0 when L 1 = 11.1 cm.

Fig. 6
Fig. 6

SL output power as function of relative displacement of M1 and for SL injection current I 0 = 45 mA (a), (b) 50 mA, (c) 55 mA, (d) 60 mA, (e) 65 mA, and (f) 70 mA. Mirror M1 is mounted on a PZT-driven stage that linearly displaces the mirror towards the SL, whereas M2 is held stationary.

Fig. 7
Fig. 7

SL output power variation and its derivative with a 1.0-Hz driving signal for the two test targets. Plots (a) and (b) are for the PZT sample with 4.0-V (p–p) triangular and sinusoidal driving signals, respectively. Plots (c) and (d) are for the audio speaker with 2.0-V (p–p) triangular and sinusoidal signals, respectively.

Fig. 8
Fig. 8

Amplitudes of vibration of the two test targets versus driving voltage V d . Points were obtained by means of counting the spikes of the differentiated power variation where the interval between adjacent spikes is equal to λ/2. The uncertainty in the measured amplitude is ±λ/4 ≈ ±0.2075 µm.

Tables (1)

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Table 1 Summary of Parameters

Equations (13)

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dndt=iqD-nτe-gp,
dpdt=gp-pτp.
i0qD-n0τe-g0p0=0,
g0p0-p0τph=0.
g0=σ+2τln1ra+ln1rb,
1τph1-1τpho=2τlnrbrb+rb1.
E=E0rb+n=1tb2t02nr1nrbn-1 expj2nkL0+L1+E0n=1tb2r02nr22nrbn-1 expj2nkL0+L2,
EE0=rb+tb2t02r1 expj2kL0+L11-rbt02r1 expj2kL0+L1+tb2r02r2 expj2kL0+L21-rbr02r2 expj2kL0+L2.
i1qD-n1τe-g0p1+g1p0=0,
g1+2τlnrb+rb1rb=0.
p1=2n1g1g02τn0qDlnrb+rb1rbg0-n0g1n1ith+n0g1n1i0.
p1=2n1g1g02τn0qDlnrb+|rb1|rbg0-n0g1n1ith+n0g1n1i0,
V1=-4kBTn1g1qn0τlnrb+|rb1|rb.

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