Abstract

A small displacement sensor for dynamically measuring small forces is presented. Employing a coupled-cavity laser configuration constructed with a moving external mirror, this sensor provides high sensitivity with a minimum detectable displacement of 0.8 nm, independently of the lasing wavelength, while the lasing state is mechanically stabilized by a negative-feedback loop to maintain a constant external-cavity length. The sensor is shown to be of great use for detecting extremely small distortions in a stiff cantilever, reflecting transient variations in small friction forces in mechanical systems.

© 1998 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. QE-16, 347–355 (1980).
    [CrossRef]
  2. M. Fleming, A. Mooradian, “Spectral characteristics of external-cavity controlled semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 44–59 (1981).
    [CrossRef]
  3. C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external resonators,” Appl. Phys. 12, 369–378 (1977).
    [CrossRef]
  4. G. Agrawal, “Line narrowing in a single-mode injection lasers due to external optical feedback,” IEEE J. Quantum Electron. QE-20, 468–471 (1984).
    [CrossRef]
  5. S. Shinohara, A. Mochizuki, H. Yoshida, M. Sumi, “Laser doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1417–1419 (1986).
    [CrossRef] [PubMed]
  6. T. Yoshino, M. Nara, S. Mnatzakanian, B. Lee, T. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 893–897 (1987).
    [CrossRef]
  7. R. Miles, A. Dandrige, A. Tveten, T. Giallorenzi, “An external cavity laser diode sensor,” IEEE J. Lightwave Technol. LT-1, 81–93 (1983).
    [CrossRef]
  8. P. Spano, S. Piazzolla, M. Tamburrini, “Theory of noise in semiconductor lasers in the presence of optical feedback,” IEEE J. Quantum Electron. QE-20, 350–357 (1984).
    [CrossRef]
  9. Y. Katagiri, S. Hara, “Increased spatial frequency in interferential undulations of coupled cavity lasers,” Appl. Opt. 33, 5564–5570 (1994).
    [CrossRef] [PubMed]
  10. G. Acket, D. Lenstra, A. Boef, B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. QE-20, 1163–1169 (1984).
    [CrossRef]
  11. H. Olesen, J. Henrik, B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. QE-22, 762–773 (1986).
    [CrossRef]
  12. Y. Li, D. Trauner, F. E. Talke, “Effect of humidity on stiction and friction of the head/disk interface,” IEEE Trans. Magn. 26, 2487–2489 (1990).
    [CrossRef]
  13. D. Trauner, Y. Li, F. E. Talke, “Frictional behavior of magnetic recording disks,” IEEE Trans. Magn. 26, 150–152 (1990).
    [CrossRef]
  14. H. J. Lee, R. D. Hempstead, J. Weiss, “Study of head and disk interface in contact start stop test,” IEEE Trans. Magn. 25, 3722–3724 (1989).
    [CrossRef]
  15. Y. Hatamura, M. Nakao, H. Miyazaki, T. Shinohara, “A measurement of sliding resistance forces for various heads and disks by highly rigid force sensor,” IEEE Trans. Magn. 24, 2638–2640 (1988).
    [CrossRef]

1994

1990

Y. Li, D. Trauner, F. E. Talke, “Effect of humidity on stiction and friction of the head/disk interface,” IEEE Trans. Magn. 26, 2487–2489 (1990).
[CrossRef]

D. Trauner, Y. Li, F. E. Talke, “Frictional behavior of magnetic recording disks,” IEEE Trans. Magn. 26, 150–152 (1990).
[CrossRef]

1989

H. J. Lee, R. D. Hempstead, J. Weiss, “Study of head and disk interface in contact start stop test,” IEEE Trans. Magn. 25, 3722–3724 (1989).
[CrossRef]

1988

Y. Hatamura, M. Nakao, H. Miyazaki, T. Shinohara, “A measurement of sliding resistance forces for various heads and disks by highly rigid force sensor,” IEEE Trans. Magn. 24, 2638–2640 (1988).
[CrossRef]

1987

T. Yoshino, M. Nara, S. Mnatzakanian, B. Lee, T. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 893–897 (1987).
[CrossRef]

1986

S. Shinohara, A. Mochizuki, H. Yoshida, M. Sumi, “Laser doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1417–1419 (1986).
[CrossRef] [PubMed]

H. Olesen, J. Henrik, B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. QE-22, 762–773 (1986).
[CrossRef]

1984

G. Acket, D. Lenstra, A. Boef, B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. QE-20, 1163–1169 (1984).
[CrossRef]

P. Spano, S. Piazzolla, M. Tamburrini, “Theory of noise in semiconductor lasers in the presence of optical feedback,” IEEE J. Quantum Electron. QE-20, 350–357 (1984).
[CrossRef]

G. Agrawal, “Line narrowing in a single-mode injection lasers due to external optical feedback,” IEEE J. Quantum Electron. QE-20, 468–471 (1984).
[CrossRef]

1983

R. Miles, A. Dandrige, A. Tveten, T. Giallorenzi, “An external cavity laser diode sensor,” IEEE J. Lightwave Technol. LT-1, 81–93 (1983).
[CrossRef]

1981

M. Fleming, A. Mooradian, “Spectral characteristics of external-cavity controlled semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 44–59 (1981).
[CrossRef]

1980

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

1977

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external resonators,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

Acket, G.

G. Acket, D. Lenstra, A. Boef, B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. QE-20, 1163–1169 (1984).
[CrossRef]

Agrawal, G.

G. Agrawal, “Line narrowing in a single-mode injection lasers due to external optical feedback,” IEEE J. Quantum Electron. QE-20, 468–471 (1984).
[CrossRef]

Boef, A.

G. Acket, D. Lenstra, A. Boef, B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. QE-20, 1163–1169 (1984).
[CrossRef]

Dandrige, A.

R. Miles, A. Dandrige, A. Tveten, T. Giallorenzi, “An external cavity laser diode sensor,” IEEE J. Lightwave Technol. LT-1, 81–93 (1983).
[CrossRef]

Fleming, M.

M. Fleming, A. Mooradian, “Spectral characteristics of external-cavity controlled semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 44–59 (1981).
[CrossRef]

Giallorenzi, T.

R. Miles, A. Dandrige, A. Tveten, T. Giallorenzi, “An external cavity laser diode sensor,” IEEE J. Lightwave Technol. LT-1, 81–93 (1983).
[CrossRef]

Hara, S.

Hatamura, Y.

Y. Hatamura, M. Nakao, H. Miyazaki, T. Shinohara, “A measurement of sliding resistance forces for various heads and disks by highly rigid force sensor,” IEEE Trans. Magn. 24, 2638–2640 (1988).
[CrossRef]

Hempstead, R. D.

H. J. Lee, R. D. Hempstead, J. Weiss, “Study of head and disk interface in contact start stop test,” IEEE Trans. Magn. 25, 3722–3724 (1989).
[CrossRef]

Henrik, J.

H. Olesen, J. Henrik, B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. QE-22, 762–773 (1986).
[CrossRef]

Katagiri, Y.

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]

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]

Lee, B.

T. Yoshino, M. Nara, S. Mnatzakanian, B. Lee, T. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 893–897 (1987).
[CrossRef]

Lee, H. J.

H. J. Lee, R. D. Hempstead, J. Weiss, “Study of head and disk interface in contact start stop test,” IEEE Trans. Magn. 25, 3722–3724 (1989).
[CrossRef]

Lenstra, D.

G. Acket, D. Lenstra, A. Boef, B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. QE-20, 1163–1169 (1984).
[CrossRef]

Li, Y.

D. Trauner, Y. Li, F. E. Talke, “Frictional behavior of magnetic recording disks,” IEEE Trans. Magn. 26, 150–152 (1990).
[CrossRef]

Y. Li, D. Trauner, F. E. Talke, “Effect of humidity on stiction and friction of the head/disk interface,” IEEE Trans. Magn. 26, 2487–2489 (1990).
[CrossRef]

Miles, R.

R. Miles, A. Dandrige, A. Tveten, T. Giallorenzi, “An external cavity laser diode sensor,” IEEE J. Lightwave Technol. LT-1, 81–93 (1983).
[CrossRef]

Miyazaki, H.

Y. Hatamura, M. Nakao, H. Miyazaki, T. Shinohara, “A measurement of sliding resistance forces for various heads and disks by highly rigid force sensor,” IEEE Trans. Magn. 24, 2638–2640 (1988).
[CrossRef]

Mnatzakanian, S.

T. Yoshino, M. Nara, S. Mnatzakanian, B. Lee, T. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 893–897 (1987).
[CrossRef]

Mochizuki, A.

Mooradian, A.

M. Fleming, A. Mooradian, “Spectral characteristics of external-cavity controlled semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 44–59 (1981).
[CrossRef]

Nakao, M.

Y. Hatamura, M. Nakao, H. Miyazaki, T. Shinohara, “A measurement of sliding resistance forces for various heads and disks by highly rigid force sensor,” IEEE Trans. Magn. 24, 2638–2640 (1988).
[CrossRef]

Nara, M.

T. Yoshino, M. Nara, S. Mnatzakanian, B. Lee, T. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 893–897 (1987).
[CrossRef]

Olesen, H.

H. Olesen, J. Henrik, B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. QE-22, 762–773 (1986).
[CrossRef]

Piazzolla, S.

P. Spano, S. Piazzolla, M. Tamburrini, “Theory of noise in semiconductor lasers in the presence of optical feedback,” IEEE J. Quantum Electron. QE-20, 350–357 (1984).
[CrossRef]

Salathe, R.

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external resonators,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

Shinohara, S.

Shinohara, T.

Y. Hatamura, M. Nakao, H. Miyazaki, T. Shinohara, “A measurement of sliding resistance forces for various heads and disks by highly rigid force sensor,” IEEE Trans. Magn. 24, 2638–2640 (1988).
[CrossRef]

Spano, P.

P. Spano, S. Piazzolla, M. Tamburrini, “Theory of noise in semiconductor lasers in the presence of optical feedback,” IEEE J. Quantum Electron. QE-20, 350–357 (1984).
[CrossRef]

Strand, T.

T. Yoshino, M. Nara, S. Mnatzakanian, B. Lee, T. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 893–897 (1987).
[CrossRef]

Sumi, M.

Talke, F. E.

Y. Li, D. Trauner, F. E. Talke, “Effect of humidity on stiction and friction of the head/disk interface,” IEEE Trans. Magn. 26, 2487–2489 (1990).
[CrossRef]

D. Trauner, Y. Li, F. E. Talke, “Frictional behavior of magnetic recording disks,” IEEE Trans. Magn. 26, 150–152 (1990).
[CrossRef]

Tamburrini, M.

P. Spano, S. Piazzolla, M. Tamburrini, “Theory of noise in semiconductor lasers in the presence of optical feedback,” IEEE J. Quantum Electron. QE-20, 350–357 (1984).
[CrossRef]

Trauner, D.

D. Trauner, Y. Li, F. E. Talke, “Frictional behavior of magnetic recording disks,” IEEE Trans. Magn. 26, 150–152 (1990).
[CrossRef]

Y. Li, D. Trauner, F. E. Talke, “Effect of humidity on stiction and friction of the head/disk interface,” IEEE Trans. Magn. 26, 2487–2489 (1990).
[CrossRef]

Tromborg, B.

H. Olesen, J. Henrik, B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. QE-22, 762–773 (1986).
[CrossRef]

Tveten, A.

R. Miles, A. Dandrige, A. Tveten, T. Giallorenzi, “An external cavity laser diode sensor,” IEEE J. Lightwave Technol. LT-1, 81–93 (1983).
[CrossRef]

Verbeek, B.

G. Acket, D. Lenstra, A. Boef, B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. QE-20, 1163–1169 (1984).
[CrossRef]

Voumard, C.

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external resonators,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

Weber, H.

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external resonators,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

Weiss, J.

H. J. Lee, R. D. Hempstead, J. Weiss, “Study of head and disk interface in contact start stop test,” IEEE Trans. Magn. 25, 3722–3724 (1989).
[CrossRef]

Yoshida, H.

Yoshino, T.

T. Yoshino, M. Nara, S. Mnatzakanian, B. Lee, T. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 893–897 (1987).
[CrossRef]

Appl. Opt.

Appl. Phys.

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external resonators,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

IEEE J. Lightwave Technol.

R. Miles, A. Dandrige, A. Tveten, T. Giallorenzi, “An external cavity laser diode sensor,” IEEE J. Lightwave Technol. LT-1, 81–93 (1983).
[CrossRef]

IEEE J. Quantum Electron.

P. Spano, S. Piazzolla, M. Tamburrini, “Theory of noise in semiconductor lasers in the presence of optical feedback,” IEEE J. Quantum Electron. QE-20, 350–357 (1984).
[CrossRef]

G. Agrawal, “Line narrowing in a single-mode injection lasers due to external optical feedback,” IEEE J. Quantum Electron. QE-20, 468–471 (1984).
[CrossRef]

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

M. Fleming, A. Mooradian, “Spectral characteristics of external-cavity controlled semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 44–59 (1981).
[CrossRef]

G. Acket, D. Lenstra, A. Boef, B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. QE-20, 1163–1169 (1984).
[CrossRef]

H. Olesen, J. Henrik, B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. QE-22, 762–773 (1986).
[CrossRef]

IEEE Trans. Magn.

Y. Li, D. Trauner, F. E. Talke, “Effect of humidity on stiction and friction of the head/disk interface,” IEEE Trans. Magn. 26, 2487–2489 (1990).
[CrossRef]

D. Trauner, Y. Li, F. E. Talke, “Frictional behavior of magnetic recording disks,” IEEE Trans. Magn. 26, 150–152 (1990).
[CrossRef]

H. J. Lee, R. D. Hempstead, J. Weiss, “Study of head and disk interface in contact start stop test,” IEEE Trans. Magn. 25, 3722–3724 (1989).
[CrossRef]

Y. Hatamura, M. Nakao, H. Miyazaki, T. Shinohara, “A measurement of sliding resistance forces for various heads and disks by highly rigid force sensor,” IEEE Trans. Magn. 24, 2638–2640 (1988).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Schematic configuration of a coupled-cavity laser (r 1, r 2, laser facet reflectivities; r 3, external-mirror reflectivity; η, coupling coefficient; h, external-cavity length).

Fig. 2
Fig. 2

Interference undulations with various spatial frequencies. U 2, undulation with a period of λ/4; U 3, undulation with a period of λ/6 (λ, typical oscillation wavelength; h o , external-cavity length at the initial state; δh, variation in external-cavity length).

Fig. 3
Fig. 3

Schematic diagram of displacement sensing.

Fig. 4
Fig. 4

Mechanical negative-feedback loop for stabilizing external-cavity laser.

Fig. 5
Fig. 5

Schematic structure of displacement sensor.

Fig. 6
Fig. 6

(a) Frequency spectrum of a signal detected for a single-frequency oscillation of the external mirror at 200 Hz and (b) relationship between the square root of signal power and amplitude of the driving signal for mirror oscillation.

Fig. 7
Fig. 7

Dynamic response characteristics of the sensor in the closed loop.

Fig. 8
Fig. 8

Schematic configuration for measuring a microforce (k o , wave vector of light emitted from laser facet; k, wave vector of reflection from external mirror).

Fig. 9
Fig. 9

Relationship between load and signal output for calibration.

Fig. 10
Fig. 10

Friction forces imposed on a small object dragged over a rough surface.

Fig. 11
Fig. 11

(a) Configuration of flying slider on a rotating disk and (b) experimental setup for measuring forces imposed on the slider.

Fig. 12
Fig. 12

Friction force imposed on head and corresponding relative displacement of a disk in a hard-disk system.

Equations (8)

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

E r t = E r   exp i Ω t = r 2   E o   exp i Ω t - η r 3 1 - r 2 2 exp i Ω t - τ × K = 0 r 2 r 3 K   exp - iK Ω τ E o , τ = 2 h c ,
r eff E r E o = r 2 - η   r 3 1 - r 2 2 exp i Ω τ - r 2 r 3 .
Ω ω m = ω o + m π c / nL o ,
d d t   E o t exp i Ω t = i ω m + G N 2 E o t exp i Ω t + κ E o t - τ exp i Ω t - τ , κ = η 1 - r 2 2 r 3 r 2 c 2 nL o ,
ω m = Ω - κ   sin τ Ω .
Γ C f = Γ M f 1 + β H X f A f H L f + β H X f A f H L f 1 + β H X f A f H L f   Γ L f ,
N rms = f min f max L N f Δ f d f 1 / 2 ,
δ X = 3 κ / L 3 F ,

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