Abstract

The author considers the resonant-mode structure of a three-wall Fabry–Perot laser-diode cavity in the context of multiple-color interferometric techniques for determining absolute distance. It is found that the theoretical emission spectrum for a dispersive gain medium such as GaAlAs in such a cavity can be used to generate synthetic wavelengths from less than 200 μm to more than a meter with a single laser diode. The emission characteristics and their use in distance measurements are then illustrated experimentally by using a commercially available short-external-cavity device operated near threshold.

© 1993 Optical Society of America

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References

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  1. N. A. Massie, H. J. Caulfield, “Absolute distance interferometry,” in Interferometric Metrology (Critical Reviews), N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 149–157 (1987).
  2. G. L. Bourdet, A. G. Orszag, “Absolute distance measurements by CO2 laser multiwavelength interferometry,” Appl. Opt. 18, 225–227 (1979).
    [CrossRef] [PubMed]
  3. C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).
  4. H. Matsumoto, “Length measurement using infrared two-wavelength He–Xe laser interferometer,” Rev. Sci. Instrum. 53, 641–643 (1983).
    [CrossRef]
  5. A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
    [CrossRef] [PubMed]
  6. A. S. Gerges, T. P. Newson, D. A. Jackson, “Coherence tuned fiber optic sensing system, with self-initialization, based on a multimode laser diode,” Appl. Opt. 29, 4473–4480 (1990).
    [CrossRef] [PubMed]
  7. P. de Groot, “Interferometric laser profilometer for rough surfaces,” Opt. Lett. 16, 357–359 (1991).
    [CrossRef] [PubMed]
  8. P. de Groot, “Three-color laser-diode interferometer,” Appl. Opt. 30, 3612–3616 (1991).
    [CrossRef] [PubMed]
  9. O. Svelto, Principles of Lasers (Plenum, New York, 1982), p. 162.
  10. K. R. Preston, K. C. Woolard, K. H. Cameron, “External cavity controlled single longitudinal mode laser transmitter module,” Electron. Lett. 17, 931–932 (1981).
    [CrossRef]
  11. D. T. Cassidy, D. M. Bruce, B. F. Ventrudo, “Short external cavity module for enhanced single-mode tuning of InGaAsP and AlGaAs semiconductor diode lasers,” Rev. Sci. Instrum. 62, 2385–2388 (1991).
    [CrossRef]
  12. J. P. van der Ziel, R. M. Mikulyak, “Single-mode operation of 1.3 μm InGaAsP/InP buried crescent lasers using a short external optical cavity,” IEEE J. Quantum Electron. QE-20, 223–229 (1984).
    [CrossRef]
  13. D. T. Cassidy, L. J. Bonnell, “Trace gas detection with short-external-cavity InGaAsP diode laser transmitter modules operating at 1.58 μm,” Appl. Opt. 27, 2688–2693 (1988).
    [CrossRef] [PubMed]
  14. Laser Diode User’s Manual (Sharp Corporation, Osaka, Japan, 1988), p. 19.
  15. C. Voumard, R. Salathe’, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external resonators,” Appl. Phys. 12, 369–378 (1977).
    [CrossRef]
  16. R. Dändliker, R. Thalmann, D. Prongue, “Two-wavelength laser interferometry using superheterodyne detection,” Opt. Lett. 13, 339–341 (1988).
    [CrossRef] [PubMed]
  17. Z. Zoran, E. Fischer, T. Ittner, H. J. Tiziani, “Two-wavelength double heterodyne interferometry using a matched grating technique,” Appl. Opt. 30, 3139–3144 (1991).
    [CrossRef]
  18. C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16, 1857–1860 (1977).
    [CrossRef] [PubMed]
  19. C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
    [CrossRef]
  20. K. R. Preston, “Simple spectral control technique for external cavity laser transmitters,” Electron. Lett. 18, 1092–1094 (1982).
    [CrossRef]
  21. A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
    [CrossRef]
  22. P. de Groot, “Range dependent optical feedback effects on the multimode spectrum of laser diodes,” J. Mod. Opt. 37, 1199–1214 (1990).
    [CrossRef]
  23. J. P. Van Der Ziel, “Dispersion of the group velocity refractive index in GaAs double heterostructure lasers,” IEEE J. Quantum Electron. QE-19, 164–169 (1983).
    [CrossRef]
  24. O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
    [CrossRef] [PubMed]
  25. P. de Groot, S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
    [CrossRef] [PubMed]

1991 (6)

1990 (2)

1989 (1)

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

1988 (2)

1986 (1)

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

1985 (1)

1984 (1)

J. P. van der Ziel, R. M. Mikulyak, “Single-mode operation of 1.3 μm InGaAsP/InP buried crescent lasers using a short external optical cavity,” IEEE J. Quantum Electron. QE-20, 223–229 (1984).
[CrossRef]

1983 (3)

C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).

H. Matsumoto, “Length measurement using infrared two-wavelength He–Xe laser interferometer,” Rev. Sci. Instrum. 53, 641–643 (1983).
[CrossRef]

J. P. Van Der Ziel, “Dispersion of the group velocity refractive index in GaAs double heterostructure lasers,” IEEE J. Quantum Electron. QE-19, 164–169 (1983).
[CrossRef]

1982 (1)

K. R. Preston, “Simple spectral control technique for external cavity laser transmitters,” Electron. Lett. 18, 1092–1094 (1982).
[CrossRef]

1981 (1)

K. R. Preston, K. C. Woolard, K. H. Cameron, “External cavity controlled single longitudinal mode laser transmitter module,” Electron. Lett. 17, 931–932 (1981).
[CrossRef]

1979 (1)

1977 (2)

C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16, 1857–1860 (1977).
[CrossRef] [PubMed]

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

Bonnell, L. J.

Bourdet, G. L.

Bruce, D. M.

D. T. Cassidy, D. M. Bruce, B. F. Ventrudo, “Short external cavity module for enhanced single-mode tuning of InGaAsP and AlGaAs semiconductor diode lasers,” Rev. Sci. Instrum. 62, 2385–2388 (1991).
[CrossRef]

Buholz, N. E.

C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).

Cameron, K. H.

K. R. Preston, K. C. Woolard, K. H. Cameron, “External cavity controlled single longitudinal mode laser transmitter module,” Electron. Lett. 17, 931–932 (1981).
[CrossRef]

Cassidy, D. T.

D. T. Cassidy, D. M. Bruce, B. F. Ventrudo, “Short external cavity module for enhanced single-mode tuning of InGaAsP and AlGaAs semiconductor diode lasers,” Rev. Sci. Instrum. 62, 2385–2388 (1991).
[CrossRef]

D. T. Cassidy, L. J. Bonnell, “Trace gas detection with short-external-cavity InGaAsP diode laser transmitter modules operating at 1.58 μm,” Appl. Opt. 27, 2688–2693 (1988).
[CrossRef] [PubMed]

Caulfield, H. J.

N. A. Massie, H. J. Caulfield, “Absolute distance interferometry,” in Interferometric Metrology (Critical Reviews), N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 149–157 (1987).

Dändliker, R.

de Groot, P.

Fercher, A. F.

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
[CrossRef] [PubMed]

Fischer, E.

Gerges, A. S.

Gillard, C. W.

C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).

Hu, H. Z.

Ittner, T.

Jackson, D. A.

Kishner, S.

Massie, N. A.

N. A. Massie, H. J. Caulfield, “Absolute distance interferometry,” in Interferometric Metrology (Critical Reviews), N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 149–157 (1987).

Matsumoto, H.

H. Matsumoto, “Length measurement using infrared two-wavelength He–Xe laser interferometer,” Rev. Sci. Instrum. 53, 641–643 (1983).
[CrossRef]

Mikulyak, R. M.

J. P. van der Ziel, R. M. Mikulyak, “Single-mode operation of 1.3 μm InGaAsP/InP buried crescent lasers using a short external optical cavity,” IEEE J. Quantum Electron. QE-20, 223–229 (1984).
[CrossRef]

Newson, T. P.

Orszag, A. G.

Preston, K. R.

K. R. Preston, “Simple spectral control technique for external cavity laser transmitters,” Electron. Lett. 18, 1092–1094 (1982).
[CrossRef]

K. R. Preston, K. C. Woolard, K. H. Cameron, “External cavity controlled single longitudinal mode laser transmitter module,” Electron. Lett. 17, 931–932 (1981).
[CrossRef]

Prongue, D.

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]

Sasaki, O.

Sasazaki, H.

Suzuki, T.

Svelto, O.

O. Svelto, Principles of Lasers (Plenum, New York, 1982), p. 162.

Thalmann, R.

Tilford, C. R.

Tiziani, H. J.

van der Ziel, J. P.

J. P. van der Ziel, R. M. Mikulyak, “Single-mode operation of 1.3 μm InGaAsP/InP buried crescent lasers using a short external optical cavity,” IEEE J. Quantum Electron. QE-20, 223–229 (1984).
[CrossRef]

J. P. Van Der Ziel, “Dispersion of the group velocity refractive index in GaAs double heterostructure lasers,” IEEE J. Quantum Electron. QE-19, 164–169 (1983).
[CrossRef]

Ventrudo, B. F.

D. T. Cassidy, D. M. Bruce, B. F. Ventrudo, “Short external cavity module for enhanced single-mode tuning of InGaAsP and AlGaAs semiconductor diode lasers,” Rev. Sci. Instrum. 62, 2385–2388 (1991).
[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]

Vry, U.

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
[CrossRef] [PubMed]

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]

Werner, W.

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

Wickramasinghe, H. K.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Williams, C. C.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Woolard, K. C.

K. R. Preston, K. C. Woolard, K. H. Cameron, “External cavity controlled single longitudinal mode laser transmitter module,” Electron. Lett. 17, 931–932 (1981).
[CrossRef]

Zoran, Z.

Appl. Opt. (9)

G. L. Bourdet, A. G. Orszag, “Absolute distance measurements by CO2 laser multiwavelength interferometry,” Appl. Opt. 18, 225–227 (1979).
[CrossRef] [PubMed]

A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
[CrossRef] [PubMed]

A. S. Gerges, T. P. Newson, D. A. Jackson, “Coherence tuned fiber optic sensing system, with self-initialization, based on a multimode laser diode,” Appl. Opt. 29, 4473–4480 (1990).
[CrossRef] [PubMed]

P. de Groot, “Three-color laser-diode interferometer,” Appl. Opt. 30, 3612–3616 (1991).
[CrossRef] [PubMed]

D. T. Cassidy, L. J. Bonnell, “Trace gas detection with short-external-cavity InGaAsP diode laser transmitter modules operating at 1.58 μm,” Appl. Opt. 27, 2688–2693 (1988).
[CrossRef] [PubMed]

Z. Zoran, E. Fischer, T. Ittner, H. J. Tiziani, “Two-wavelength double heterodyne interferometry using a matched grating technique,” Appl. Opt. 30, 3139–3144 (1991).
[CrossRef]

C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16, 1857–1860 (1977).
[CrossRef] [PubMed]

O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
[CrossRef] [PubMed]

P. de Groot, S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
[CrossRef] [PubMed]

Appl. Phys. (1)

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

Electron. Lett. (2)

K. R. Preston, K. C. Woolard, K. H. Cameron, “External cavity controlled single longitudinal mode laser transmitter module,” Electron. Lett. 17, 931–932 (1981).
[CrossRef]

K. R. Preston, “Simple spectral control technique for external cavity laser transmitters,” Electron. Lett. 18, 1092–1094 (1982).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. P. Van Der Ziel, “Dispersion of the group velocity refractive index in GaAs double heterostructure lasers,” IEEE J. Quantum Electron. QE-19, 164–169 (1983).
[CrossRef]

J. P. van der Ziel, R. M. Mikulyak, “Single-mode operation of 1.3 μm InGaAsP/InP buried crescent lasers using a short external optical cavity,” IEEE J. Quantum Electron. QE-20, 223–229 (1984).
[CrossRef]

J. Appl. Phys. (1)

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

J. Mod. Opt. (1)

P. de Groot, “Range dependent optical feedback effects on the multimode spectrum of laser diodes,” J. Mod. Opt. 37, 1199–1214 (1990).
[CrossRef]

Opt. Eng. (1)

C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).

Opt. Lasers Eng. (1)

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

Opt. Lett. (2)

Rev. Sci. Instrum. (2)

H. Matsumoto, “Length measurement using infrared two-wavelength He–Xe laser interferometer,” Rev. Sci. Instrum. 53, 641–643 (1983).
[CrossRef]

D. T. Cassidy, D. M. Bruce, B. F. Ventrudo, “Short external cavity module for enhanced single-mode tuning of InGaAsP and AlGaAs semiconductor diode lasers,” Rev. Sci. Instrum. 62, 2385–2388 (1991).
[CrossRef]

Other (3)

O. Svelto, Principles of Lasers (Plenum, New York, 1982), p. 162.

N. A. Massie, H. J. Caulfield, “Absolute distance interferometry,” in Interferometric Metrology (Critical Reviews), N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 149–157 (1987).

Laser Diode User’s Manual (Sharp Corporation, Osaka, Japan, 1988), p. 19.

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Figures (9)

Fig. 1
Fig. 1

One-dimensional model of the proposed multimode SXC laser diode. The addition of the weakly reflecting third wall R3 a distance xe < xd from the two-walled Fabry–Perot cavity of length xd introduces variations in the intermode wave-number separation and the threshold gain that are useful for multiple-color interferometry.

Fig. 2
Fig. 2

Separation of resonant modes of the resonator shown in Fig. 1 as a function of wave number. The quasi-periodic variation is due to the three-wall resonator structure, while the overall decrease in intermode separation with increasing wave number is due to second-order chromatic dispersion in the gain medium.

Fig. 3
Fig. 3

Variation of the threshold gain with wave number for the resonator model shown in Fig. 1. In an ordinary two-walled Fabry–Perot laser cavity, the threshold gain is independent of wave number, and the lasing mode is determined only by the peak of the gain curve. In a three-walled resonator it is possible to have simultaneous emission in two widely spaced spectral regions defined by the minima in the threshold-gain curve shown above.

Fig. 4
Fig. 4

Optical spectrum of a Shapr LTO80 laser diode operated near threshold to effect multimode oscillations. The peak in the gain curve has been temperature tuned to a position between the threshold-gain minima shown in Fig. 3. The lasing action is in this way divided between two widely spaced spectral regions at 780 and 784 nm.

Fig. 5
Fig. 5

Apparatus for measuring the relative wave numbers of the peaks in the spectrum shown in Fig. 4. A diffraction grating was used to separate the various spectral components of the interferometer output, and two detectors selected the phase-modulation signals that correspond to different lasing modes. The same apparatus was used for demonstrating synthetic wavelength interferometry.

Fig. 6
Fig. 6

Experimental measurement of mode separation as a function of wave number for the LTO80 laser. Each data point represents the wave-number difference of two adjacent peaks in the optical spectrum. The solid curve is a least-squares polynomial fit for comparison with the theoretical calculation of Fig. 2. The measurement accuracy, which may be inferred from the scatter in the data, was best for the strong emission modes near the minima in the curve.

Fig. 7
Fig. 7

Experimental range dependence of the interferometric phase difference that corresponds to two different lasing modes having a wave-number separation of 62.5 cm−1. These modes correspond to the two principal spectral peaks near 780 and 784 nm that appear in Fig. 4. The synthetic wavelength was 0.16 mm.

Fig. 8
Fig. 8

Experimental range dependence of the interferometric phase difference that corresponds to two different lasing modes having a wave-number separation of 4.95 cm−1. These lasing modes correspond to neighboring peaks near 784 nm in the spectrum shown in Fig. 4. The synthetic wavelength was 2.02 mm.

Fig. 9
Fig. 9

Experimental range dependence of the net interferometric phase that corresponds to four different lasing modes of the SXC laser, resulting in a compound synthetic wavelength of 355 nm.

Equations (13)

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2 π m = 4 π x d σ + arg ( Z ) ,
Z = R 2 + R 3 exp ( 4 π i σ x e ) 1 + R 2 R 3 exp ( 4 π i σ x e ) ,
σ = σ / n .
σ m = m 2 x d 1 4 π x d arg ( Z ) .
σ = σ 0 + ( σ σ 0 ) d σ d σ + 1 2 ( σ σ 0 ) 2 d 2 σ d σ 2 ,
σ = σ 0 + ( σ σ 0 ) N α ( σ σ 0 ) 2 2 N 2 ,
α = d N d σ = 1 N d N d σ
G t = 1 | Z R 1 | ,
Λ i j = 1 σ i σ j , σ i > σ j .
ϕ i = 4 π L σ i ,
L = Λ i j ( ϕ i ϕ j ) 4 π .
Λ i j = 1 ( σ i + 1 σ i σ j + 1 + σ j ) , σ i + 1 > σ i > σ j + 1 > σ j ,
L = Λ i j 4 π ( ϕ i + 1 ϕ i ϕ j + 1 + ϕ j ) .

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