Abstract

We demonstrate a scheme for displacement measurement by use of the photoelectromotive force effect and a frequency-modulated laser diode. The measurement range can be adjusted by a change in the depth of frequency modulation, thus making the measurement method both simple and versatile.

© 2001 Optical Society of America

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References

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  1. H. Kikuta, K. Iwata, and R. Nagata, Appl. Opt. 25, 2976 (1986).
    [CrossRef]
  2. E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, and H. J. Tiziani, Appl. Opt. 34, 5589 (1995).
    [CrossRef] [PubMed]
  3. M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
    [CrossRef]
  4. F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
    [CrossRef]
  5. C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.
  6. F. Jin, J. B. Khurgin, C.-C. Wang, S. Trivedi, Y. Gabay, E. Gad, D. A. Temple, and U. H. Hommerich, Appl. Opt. 39, 3138 (2000).
    [CrossRef]
  7. I. A. Sokolov and S. I. Stepanov, Appl. Opt. 32, 1958 (1993).
    [CrossRef] [PubMed]
  8. G. N. Watson, Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, Cambridge, 1962).
  9. C. Agrawal and N. Dytta, Semiconductor Lasers (Van Nostrand, New York, 1993), pp. 286–290.

2000 (1)

1999 (1)

F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
[CrossRef]

1995 (1)

1993 (1)

1990 (1)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

1986 (1)

Agrawal, C.

C. Agrawal and N. Dytta, Semiconductor Lasers (Van Nostrand, New York, 1993), pp. 286–290.

Dalhoff, E.

Dytta, N.

C. Agrawal and N. Dytta, Semiconductor Lasers (Van Nostrand, New York, 1993), pp. 286–290.

Fischer, E.

Gabay, Y.

Gad, E.

F. Jin, J. B. Khurgin, C.-C. Wang, S. Trivedi, Y. Gabay, E. Gad, D. A. Temple, and U. H. Hommerich, Appl. Opt. 39, 3138 (2000).
[CrossRef]

F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
[CrossRef]

C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.

Heim, S.

Hofbauer, U.

Hommerich, U. H.

F. Jin, J. B. Khurgin, C.-C. Wang, S. Trivedi, Y. Gabay, E. Gad, D. A. Temple, and U. H. Hommerich, Appl. Opt. 39, 3138 (2000).
[CrossRef]

C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.

Iwata, K.

Jin, F.

F. Jin, J. B. Khurgin, C.-C. Wang, S. Trivedi, Y. Gabay, E. Gad, D. A. Temple, and U. H. Hommerich, Appl. Opt. 39, 3138 (2000).
[CrossRef]

F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
[CrossRef]

C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.

Khurgin, J. B.

F. Jin, J. B. Khurgin, C.-C. Wang, S. Trivedi, Y. Gabay, E. Gad, D. A. Temple, and U. H. Hommerich, Appl. Opt. 39, 3138 (2000).
[CrossRef]

F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
[CrossRef]

C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.

Kikuta, H.

Nagata, R.

Petrov, M. P.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Sokolov, I. A.

I. A. Sokolov and S. I. Stepanov, Appl. Opt. 32, 1958 (1993).
[CrossRef] [PubMed]

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Stepanov, S. I.

I. A. Sokolov and S. I. Stepanov, Appl. Opt. 32, 1958 (1993).
[CrossRef] [PubMed]

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Temple, D. A.

F. Jin, J. B. Khurgin, C.-C. Wang, S. Trivedi, Y. Gabay, E. Gad, D. A. Temple, and U. H. Hommerich, Appl. Opt. 39, 3138 (2000).
[CrossRef]

C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.

Tien, R.

F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
[CrossRef]

Tiziani, H. J.

Trivedi, S.

F. Jin, J. B. Khurgin, C.-C. Wang, S. Trivedi, Y. Gabay, E. Gad, D. A. Temple, and U. H. Hommerich, Appl. Opt. 39, 3138 (2000).
[CrossRef]

F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
[CrossRef]

C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.

Trofimov, G. S.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Wang, C.-C.

F. Jin, J. B. Khurgin, C.-C. Wang, S. Trivedi, Y. Gabay, E. Gad, D. A. Temple, and U. H. Hommerich, Appl. Opt. 39, 3138 (2000).
[CrossRef]

F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
[CrossRef]

C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.

Watson, G. N.

G. N. Watson, Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, Cambridge, 1962).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

F. Jin, J. B. Khurgin, S. Trivedi, R. Tien, C.-C. Wang, and E. Gad, Appl. Phys. Lett. 75, 1374 (1999).
[CrossRef]

J. Appl. Phys. (1)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Other (3)

C.-C. Wang, F. Jin, J. B. Khurgin, S. Trivedi, D. A. Temple, U. H. Hommerich, and E. Gad, in Conference on Lasers and Electro-Optics, Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 569–570.

G. N. Watson, Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, Cambridge, 1962).

C. Agrawal and N. Dytta, Semiconductor Lasers (Van Nostrand, New York, 1993), pp. 286–290.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup and operation principle. F-P, Fabry–Perot; BS, beam splitter. (a) Undulation illumination pattern owing to modulation of frequency. (b) Electron density pattern follows illumination closely because of the short lifetime. (c) Electric field lags behind because of the long relaxation time. (d) ac photo-emf current.

Fig. 2
Fig. 2

Photo-emf signal versus the position of the prism. Modulation frequency, 10  kHz; modulation amplitude, 2Vpp; laser intensities, 63 (reference) and 74 (signal) mW/cm2; fringe pitch, 31 μm.

Fig. 3
Fig. 3

Photo-emf signal versus the position of the prism at various modulation amplitudes. Modulation frequency, 20  kHz; laser intensities, 63 (reference) and 74 (signal) mW/cm2; fringe pitch, 31 μm.

Fig. 4
Fig. 4

Responsivity and linear range versus modulation amplitude. Linear range is defined as a range within which the difference between the measured signal and the linear approximation is less than 10%. The ranges for voltages less than 0.4 Vpp are extrapolated since they are larger than the range that was actually measured.

Equations (5)

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

νt=ν0+Δνcos2πfmt,
Φt=2πν0t+Δν/fmsin2πfmt+ϕr,
It,x=I01+mcosΔΦt,x=I0(1+mcos2k0sinθ1+Δν/ν0cos2πfmtx+k0ΔL+2πΔν/cΔLcos2πfmt),
jt=eμReEtn*t,
jνm=eμn0m2KkBT/eJjfc/fmΔL2πΔν/cJ1-jfc/fm×ΔL2πΔν/c/21+K2LD2,

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