Abstract

We propose a method to reconstruct the grating period in fiber grating structures from the field reflection coefficient or the related impulse response. The method is based on the joint time–frequency signal analysis and uses the Wigner–Ville and the spectrogram distributions. Results show good agreement between exact and reconstructed functions.

© 1998 Optical Society of America

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References

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  1. K. O. Hill and G. Meltz, IEEE J. Lightwave Technol. 15, 1263 (1997).
    [CrossRef]
  2. C. R. Giles, IEEE J. Lightwave Technol. 15, 1391 (1997).
    [CrossRef]
  3. S. Qian and D. Chen, Joint Time–Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1996).
  4. P. J. Loughlin, ed., special issue on time–frequency analysis, Proc. IEEE 84(9) (1996).
  5. M. A. Muriel, J. Azaña, and A. Carballar, presented at the 24th European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.
  6. M. A. Muriel and A. Carballar, Opt. Lett. 22, 93 (1997).
    [CrossRef] [PubMed]
  7. C. J. Brooks, G. L. Vossler, and K. A. Winick, Appl. Phys. Lett. 66, 2168 (1995).
    [CrossRef]
  8. G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, IEEE Photon. Technol. Lett. 7, 78 (1995).
    [CrossRef]
  9. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  10. M. A. Muriel and A. Carballar, IEEE Photon. Technol. Lett. 9, 955 (1997).
    [CrossRef]

1997 (4)

K. O. Hill and G. Meltz, IEEE J. Lightwave Technol. 15, 1263 (1997).
[CrossRef]

C. R. Giles, IEEE J. Lightwave Technol. 15, 1391 (1997).
[CrossRef]

M. A. Muriel and A. Carballar, IEEE Photon. Technol. Lett. 9, 955 (1997).
[CrossRef]

M. A. Muriel and A. Carballar, Opt. Lett. 22, 93 (1997).
[CrossRef] [PubMed]

1996 (1)

P. J. Loughlin, ed., special issue on time–frequency analysis, Proc. IEEE 84(9) (1996).

1995 (2)

C. J. Brooks, G. L. Vossler, and K. A. Winick, Appl. Phys. Lett. 66, 2168 (1995).
[CrossRef]

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, IEEE Photon. Technol. Lett. 7, 78 (1995).
[CrossRef]

Azaña, J.

M. A. Muriel, J. Azaña, and A. Carballar, presented at the 24th European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.

Bennion, I.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, IEEE Photon. Technol. Lett. 7, 78 (1995).
[CrossRef]

Brooks, C. J.

C. J. Brooks, G. L. Vossler, and K. A. Winick, Appl. Phys. Lett. 66, 2168 (1995).
[CrossRef]

Carballar, A.

M. A. Muriel and A. Carballar, IEEE Photon. Technol. Lett. 9, 955 (1997).
[CrossRef]

M. A. Muriel and A. Carballar, Opt. Lett. 22, 93 (1997).
[CrossRef] [PubMed]

M. A. Muriel, J. Azaña, and A. Carballar, presented at the 24th European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.

Chen, D.

S. Qian and D. Chen, Joint Time–Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1996).

Giles, C. R.

C. R. Giles, IEEE J. Lightwave Technol. 15, 1391 (1997).
[CrossRef]

Hill, K. O.

K. O. Hill and G. Meltz, IEEE J. Lightwave Technol. 15, 1263 (1997).
[CrossRef]

Meltz, G.

K. O. Hill and G. Meltz, IEEE J. Lightwave Technol. 15, 1263 (1997).
[CrossRef]

Muriel, M. A.

M. A. Muriel and A. Carballar, Opt. Lett. 22, 93 (1997).
[CrossRef] [PubMed]

M. A. Muriel and A. Carballar, IEEE Photon. Technol. Lett. 9, 955 (1997).
[CrossRef]

M. A. Muriel, J. Azaña, and A. Carballar, presented at the 24th European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.

Poole, S. B.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, IEEE Photon. Technol. Lett. 7, 78 (1995).
[CrossRef]

Qian, S.

S. Qian and D. Chen, Joint Time–Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1996).

Sugden, K.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, IEEE Photon. Technol. Lett. 7, 78 (1995).
[CrossRef]

Town, G. E.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, IEEE Photon. Technol. Lett. 7, 78 (1995).
[CrossRef]

Vossler, G. L.

C. J. Brooks, G. L. Vossler, and K. A. Winick, Appl. Phys. Lett. 66, 2168 (1995).
[CrossRef]

Williams, J. A. R.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, IEEE Photon. Technol. Lett. 7, 78 (1995).
[CrossRef]

Winick, K. A.

C. J. Brooks, G. L. Vossler, and K. A. Winick, Appl. Phys. Lett. 66, 2168 (1995).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Appl. Phys. Lett. (1)

C. J. Brooks, G. L. Vossler, and K. A. Winick, Appl. Phys. Lett. 66, 2168 (1995).
[CrossRef]

IEEE J. Lightwave Technol. (2)

K. O. Hill and G. Meltz, IEEE J. Lightwave Technol. 15, 1263 (1997).
[CrossRef]

C. R. Giles, IEEE J. Lightwave Technol. 15, 1391 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, IEEE Photon. Technol. Lett. 7, 78 (1995).
[CrossRef]

M. A. Muriel and A. Carballar, IEEE Photon. Technol. Lett. 9, 955 (1997).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

P. J. Loughlin, ed., special issue on time–frequency analysis, Proc. IEEE 84(9) (1996).

Other (3)

M. A. Muriel, J. Azaña, and A. Carballar, presented at the 24th European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.

S. Qian and D. Chen, Joint Time–Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1996).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

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Figures (3)

Fig. 1
Fig. 1

Block diagram of the period reconstruction algorithm, with the notation defined in the text.

Fig. 2
Fig. 2

FG1: (a) Reflectivity Rω=rω2. (b) Reflection impulse response, calculated as the inverse Fourier transform of rω. (c) WV distribution of rω. Dashed curve, SP distribution used as a mask to isolate useful patterns. (d) Reconstructed grating period (solid curve) and initial data period (dashed curve) along the structure.

Fig. 3
Fig. 3

FG2 with the same definitions as for Fig. 2.

Equations (3)

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WVt,ω=-+rω-12Ωr*ω+12Ω×exp-jΩtdΩ,
SPt,ω=-+rΩGω-ΩexpjΩtdΩ2,
ω¯t=-+ωWVSt,ωdω-+WVSt,ωdω.

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