Abstract

We propose a method for phase, time-delay, and impulse-response reconstruction from spectral power reflectance or reflectivity and apply it to uniform fiber Bragg gratings. This method is based on causality conditions and uses Hilbert and Wiener–Lee transforms. Results show a good agreement between exact and reconstructed functions.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. J. Brooks, G. L. Vossler, and K. A. Winick, Appl. Phys. Lett. 66, 2168 (1995).
    [CrossRef]
  2. S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
    [CrossRef]
  3. M. Volanthen, H. Geiger, M. J. Cole, R. I. Laming, and J. P. Dakin, Electron. Lett. 32, 757 (1996).
    [CrossRef]
  4. M. A. Muriel and A. Carballar, in LEOS’96 (Institute of Electrical and Electronic Engineers, 1996), paper TuCC5.
  5. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  6. M. Yamada and K. Sakuda, Appl. Opt. 26, 3474 (1987).
    [CrossRef] [PubMed]
  7. G. Björk and O. Nilson, J. Lightwave Technol. 5, 140 (1987).
    [CrossRef]
  8. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).
  9. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

1996

M. Volanthen, H. Geiger, M. J. Cole, R. I. Laming, and J. P. Dakin, Electron. Lett. 32, 757 (1996).
[CrossRef]

1995

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

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

1987

M. Yamada and K. Sakuda, Appl. Opt. 26, 3474 (1987).
[CrossRef] [PubMed]

G. Björk and O. Nilson, J. Lightwave Technol. 5, 140 (1987).
[CrossRef]

Barcelos, S.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Björk, G.

G. Björk and O. Nilson, J. Lightwave Technol. 5, 140 (1987).
[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, in LEOS’96 (Institute of Electrical and Electronic Engineers, 1996), paper TuCC5.

Cole, M. J.

M. Volanthen, H. Geiger, M. J. Cole, R. I. Laming, and J. P. Dakin, Electron. Lett. 32, 757 (1996).
[CrossRef]

Dakin, J. P.

M. Volanthen, H. Geiger, M. J. Cole, R. I. Laming, and J. P. Dakin, Electron. Lett. 32, 757 (1996).
[CrossRef]

Geiger, H.

M. Volanthen, H. Geiger, M. J. Cole, R. I. Laming, and J. P. Dakin, Electron. Lett. 32, 757 (1996).
[CrossRef]

Kashyap, R.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Laming, R. I.

M. Volanthen, H. Geiger, M. J. Cole, R. I. Laming, and J. P. Dakin, Electron. Lett. 32, 757 (1996).
[CrossRef]

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Mckee, P. F.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Muriel, M. A.

M. A. Muriel and A. Carballar, in LEOS’96 (Institute of Electrical and Electronic Engineers, 1996), paper TuCC5.

Nilson, O.

G. Björk and O. Nilson, J. Lightwave Technol. 5, 140 (1987).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).

Payne, D. N.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Reekie, L.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Sakuda, K.

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Sladen, F.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Tucknott, J. A.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Volanthen, M.

M. Volanthen, H. Geiger, M. J. Cole, R. I. Laming, and J. P. Dakin, Electron. Lett. 32, 757 (1996).
[CrossRef]

Vossler, G. L.

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

Winick, K. A.

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

Wojciechowicz, B.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Yamada, M.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Zervas, M. N.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

Electron. Lett.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Mckee, F. Sladen, and B. Wojciechowicz, Electron. Lett. 31, 1280 (1995).
[CrossRef]

M. Volanthen, H. Geiger, M. J. Cole, R. I. Laming, and J. P. Dakin, Electron. Lett. 32, 757 (1996).
[CrossRef]

J. Lightwave Technol.

G. Björk and O. Nilson, J. Lightwave Technol. 5, 140 (1987).
[CrossRef]

Other

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

M. A. Muriel and A. Carballar, in LEOS’96 (Institute of Electrical and Electronic Engineers, 1996), paper TuCC5.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Block diagram of the reconstruction algorithm: FFT’s, fast Fourier transforms.

Fig. 2
Fig. 2

UFBG1: (a) Reflectivity (top curve), along with the exact (dashed curve) and the reconstructed (solid curve) phase. (b) Exact (dashed curve) and reconstructed (solid curve) time delay. (c) Detail of the exact (dashed curve) and the reconstructed (solid curve) impulse response, which are practically superimposed upon each other. Vertical dotted line, end reflection time.

Fig. 3
Fig. 3

UFBG2, with the same definitions as for Fig. 2.

Fig. 4
Fig. 4

ht,L, impulse response versus time and FBG (device) length.

Equations (6)

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

ϕω=ωπPV-lnHΩΩ2-ω2dΩ,
α̲δ=d0+d1 cosδ+d2 cos2δ+,
ϕ̲δ=c1 sinδ+c2 sin2δ+.
dn=-cn.
n1z=1.452+Δnsin2πz/Λ,
n2z=1.452+ΔnTzsin2πz/Λ,

Metrics