Abstract

We propose a technique for performing a real-time Fourier transformation simultaneously over all the channels of a multiwavelength signal traveling in a single optical fiber. The technique requires only the reflection of the original signal in an appropriately designed structure of superimposed chirped fiber gratings. The potential and the limitations of superimposed fiber-grating structures for implementing known applications of fiber gratings over various multiwavelength channels (including the application proposed herein) are analytically and numerically studied. To demonstrate our proposal we design a real-time optical spectrum analyzer operating on three different wavelength channels. Numerical calculations show that the design works properly, and we use joint time–frequency signal representations to get a better understanding of the physical processes that determine the behavior of the system.

© 2001 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  2. T. Jannson, “Real-time Fourier transformation in dispersive optical fibers,” Opt. Lett. 8, 232–234 (1983).
    [CrossRef] [PubMed]
  3. Y. C. Tong, L. Y. Chan, K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33, 983–985 (1997).
    [CrossRef]
  4. H. Hakimi, F. Hakimi, K. L. Hall, K. A. Rauschenbach, “A new wide-band pulse-restoration technique for digital fiber-optic communication systems using temporal gratings,” IEEE Photon. Technol. Lett. 11, 1048–1050 (1999).
    [CrossRef]
  5. K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson, K. A. Rauschenbach, “An ultrafast variable optical delay technique,” IEEE Photon. Technol. Lett. 12, 208–210 (2000).
    [CrossRef]
  6. M. A. Muriel, J. Azaña, A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett. 24, 1–3 (1999).
    [CrossRef]
  7. J. Azaña, L. R. Chen, M. A. Muriel, P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
    [CrossRef]
  8. J. Azaña, M. A. Muriel, “Real-time optical spectrum analysis based on the time–space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36, 517–526 (2000).
    [CrossRef]
  9. B. H. Kolner, “Space–time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
    [CrossRef]
  10. M. S. Borella, J. P. Jue, D. Banerjee, B. Ramamurthy, B. Mukherjee, “Optical components for WDM lightwave networks,” Proc. IEEE 85, 1274–1307 (1997).
    [CrossRef]
  11. J. Azaña, M. A. Muriel, “Superimposed in-fiber grating structures for optical signal processing in wavelength-division-multiplexing systems,” in OFC’2000 (25th Conference on Optical Fiber Communication, T. Li, ed., Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 233–235, paper WM8.
  12. A. Othonos, X. Lee, R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
    [CrossRef]
  13. L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
    [CrossRef]
  14. L. A. Everall, K. Sugden, J. A. R. Williams, I. Bennion, X. Liu, J. S. Aitchison, S. Thoms, R. M. Rue, “Fabrication of multipassband moiré resonators in fibers by the dual-phase-mask exposure method,” Opt. Lett. 22, 1473–1475 (1997).
    [CrossRef]
  15. L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
    [CrossRef]
  16. M. Ibsen, M. K. Durkin, R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photon. Technol. Lett. 10, 84–86 (1998).
    [CrossRef]
  17. F. Ouellette, “Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,” Opt. Lett. 12, 847–849 (1987).
    [CrossRef] [PubMed]
  18. F. Oullette, J.-F. Cliche, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
    [CrossRef]
  19. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]
  20. M. A. Muriel, A. Carballar, J. Azaña, “Field distributions inside fiber gratings,” IEEE J. Quantum Electron. 35, 548–558 (1999).
    [CrossRef]
  21. D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Martí, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
    [CrossRef]
  22. K. Ennser, M. N. Zervas, R. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
    [CrossRef]
  23. K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, M. Durkin, “Effects of non-ideal group delay and reflection characteristics of fibre grating dispersion compensators,” in Proceedings of the 23rd European Conference on Optical Communications, 1997 (ECOC’97) (Institute of Electrical Engineers, London, 1977), Vol. 2, pp. 45–48.
  24. L. Cohen, Time-Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1995).

2000 (2)

K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson, K. A. Rauschenbach, “An ultrafast variable optical delay technique,” IEEE Photon. Technol. Lett. 12, 208–210 (2000).
[CrossRef]

J. Azaña, M. A. Muriel, “Real-time optical spectrum analysis based on the time–space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36, 517–526 (2000).
[CrossRef]

1999 (5)

J. Azaña, L. R. Chen, M. A. Muriel, P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

H. Hakimi, F. Hakimi, K. L. Hall, K. A. Rauschenbach, “A new wide-band pulse-restoration technique for digital fiber-optic communication systems using temporal gratings,” IEEE Photon. Technol. Lett. 11, 1048–1050 (1999).
[CrossRef]

M. A. Muriel, A. Carballar, J. Azaña, “Field distributions inside fiber gratings,” IEEE J. Quantum Electron. 35, 548–558 (1999).
[CrossRef]

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
[CrossRef]

M. A. Muriel, J. Azaña, A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett. 24, 1–3 (1999).
[CrossRef]

1998 (2)

M. Ibsen, M. K. Durkin, R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photon. Technol. Lett. 10, 84–86 (1998).
[CrossRef]

K. Ennser, M. N. Zervas, R. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
[CrossRef]

1997 (4)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Y. C. Tong, L. Y. Chan, K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33, 983–985 (1997).
[CrossRef]

M. S. Borella, J. P. Jue, D. Banerjee, B. Ramamurthy, B. Mukherjee, “Optical components for WDM lightwave networks,” Proc. IEEE 85, 1274–1307 (1997).
[CrossRef]

L. A. Everall, K. Sugden, J. A. R. Williams, I. Bennion, X. Liu, J. S. Aitchison, S. Thoms, R. M. Rue, “Fabrication of multipassband moiré resonators in fibers by the dual-phase-mask exposure method,” Opt. Lett. 22, 1473–1475 (1997).
[CrossRef]

1996 (1)

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Martí, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

1995 (1)

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

1994 (3)

F. Oullette, J.-F. Cliche, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

A. Othonos, X. Lee, R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

B. H. Kolner, “Space–time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

1987 (1)

1983 (1)

Aitchison, J. S.

Azaña, J.

J. Azaña, M. A. Muriel, “Real-time optical spectrum analysis based on the time–space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36, 517–526 (2000).
[CrossRef]

J. Azaña, L. R. Chen, M. A. Muriel, P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

M. A. Muriel, A. Carballar, J. Azaña, “Field distributions inside fiber gratings,” IEEE J. Quantum Electron. 35, 548–558 (1999).
[CrossRef]

M. A. Muriel, J. Azaña, A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett. 24, 1–3 (1999).
[CrossRef]

J. Azaña, M. A. Muriel, “Superimposed in-fiber grating structures for optical signal processing in wavelength-division-multiplexing systems,” in OFC’2000 (25th Conference on Optical Fiber Communication, T. Li, ed., Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 233–235, paper WM8.

Banerjee, D.

M. S. Borella, J. P. Jue, D. Banerjee, B. Ramamurthy, B. Mukherjee, “Optical components for WDM lightwave networks,” Proc. IEEE 85, 1274–1307 (1997).
[CrossRef]

Bennion, I.

Borella, M. S.

M. S. Borella, J. P. Jue, D. Banerjee, B. Ramamurthy, B. Mukherjee, “Optical components for WDM lightwave networks,” Proc. IEEE 85, 1274–1307 (1997).
[CrossRef]

Capmany, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Martí, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Carballar, A.

M. A. Muriel, A. Carballar, J. Azaña, “Field distributions inside fiber gratings,” IEEE J. Quantum Electron. 35, 548–558 (1999).
[CrossRef]

M. A. Muriel, J. Azaña, A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett. 24, 1–3 (1999).
[CrossRef]

Chan, L. Y.

Y. C. Tong, L. Y. Chan, K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33, 983–985 (1997).
[CrossRef]

Chen, L. R.

J. Azaña, L. R. Chen, M. A. Muriel, P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
[CrossRef]

Cliche, J.-F.

F. Oullette, J.-F. Cliche, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

Cohen, L.

L. Cohen, Time-Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1995).

Cooper, D. J. F.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
[CrossRef]

Durkin, M.

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, M. Durkin, “Effects of non-ideal group delay and reflection characteristics of fibre grating dispersion compensators,” in Proceedings of the 23rd European Conference on Optical Communications, 1997 (ECOC’97) (Institute of Electrical Engineers, London, 1977), Vol. 2, pp. 45–48.

Durkin, M. K.

M. Ibsen, M. K. Durkin, R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photon. Technol. Lett. 10, 84–86 (1998).
[CrossRef]

Ennser, K.

K. Ennser, M. N. Zervas, R. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
[CrossRef]

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, M. Durkin, “Effects of non-ideal group delay and reflection characteristics of fibre grating dispersion compensators,” in Proceedings of the 23rd European Conference on Optical Communications, 1997 (ECOC’97) (Institute of Electrical Engineers, London, 1977), Vol. 2, pp. 45–48.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Everall, L. A.

Gagnon, S.

F. Oullette, J.-F. Cliche, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Gu, X.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
[CrossRef]

Hakimi, F.

K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson, K. A. Rauschenbach, “An ultrafast variable optical delay technique,” IEEE Photon. Technol. Lett. 12, 208–210 (2000).
[CrossRef]

H. Hakimi, F. Hakimi, K. L. Hall, K. A. Rauschenbach, “A new wide-band pulse-restoration technique for digital fiber-optic communication systems using temporal gratings,” IEEE Photon. Technol. Lett. 11, 1048–1050 (1999).
[CrossRef]

Hakimi, H.

K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson, K. A. Rauschenbach, “An ultrafast variable optical delay technique,” IEEE Photon. Technol. Lett. 12, 208–210 (2000).
[CrossRef]

H. Hakimi, F. Hakimi, K. L. Hall, K. A. Rauschenbach, “A new wide-band pulse-restoration technique for digital fiber-optic communication systems using temporal gratings,” IEEE Photon. Technol. Lett. 11, 1048–1050 (1999).
[CrossRef]

Hall, K. L.

K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson, K. A. Rauschenbach, “An ultrafast variable optical delay technique,” IEEE Photon. Technol. Lett. 12, 208–210 (2000).
[CrossRef]

H. Hakimi, F. Hakimi, K. L. Hall, K. A. Rauschenbach, “A new wide-band pulse-restoration technique for digital fiber-optic communication systems using temporal gratings,” IEEE Photon. Technol. Lett. 11, 1048–1050 (1999).
[CrossRef]

Ibsen, M.

M. Ibsen, M. K. Durkin, R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photon. Technol. Lett. 10, 84–86 (1998).
[CrossRef]

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, M. Durkin, “Effects of non-ideal group delay and reflection characteristics of fibre grating dispersion compensators,” in Proceedings of the 23rd European Conference on Optical Communications, 1997 (ECOC’97) (Institute of Electrical Engineers, London, 1977), Vol. 2, pp. 45–48.

Jannson, T.

Jue, J. P.

M. S. Borella, J. P. Jue, D. Banerjee, B. Ramamurthy, B. Mukherjee, “Optical components for WDM lightwave networks,” Proc. IEEE 85, 1274–1307 (1997).
[CrossRef]

Kolner, B. H.

B. H. Kolner, “Space–time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

Laming, R.

K. Ennser, M. N. Zervas, R. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
[CrossRef]

Laming, R. I.

M. Ibsen, M. K. Durkin, R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photon. Technol. Lett. 10, 84–86 (1998).
[CrossRef]

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, M. Durkin, “Effects of non-ideal group delay and reflection characteristics of fibre grating dispersion compensators,” in Proceedings of the 23rd European Conference on Optical Communications, 1997 (ECOC’97) (Institute of Electrical Engineers, London, 1977), Vol. 2, pp. 45–48.

Lee, X.

A. Othonos, X. Lee, R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

Liu, X.

Loka, H. S.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
[CrossRef]

Martí, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Martí, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Measures, R. M.

A. Othonos, X. Lee, R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

Molony, A.

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

Moriarty, D. T.

K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson, K. A. Rauschenbach, “An ultrafast variable optical delay technique,” IEEE Photon. Technol. Lett. 12, 208–210 (2000).
[CrossRef]

Mukherjee, B.

M. S. Borella, J. P. Jue, D. Banerjee, B. Ramamurthy, B. Mukherjee, “Optical components for WDM lightwave networks,” Proc. IEEE 85, 1274–1307 (1997).
[CrossRef]

Muriel, M. A.

J. Azaña, M. A. Muriel, “Real-time optical spectrum analysis based on the time–space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36, 517–526 (2000).
[CrossRef]

J. Azaña, L. R. Chen, M. A. Muriel, P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

M. A. Muriel, A. Carballar, J. Azaña, “Field distributions inside fiber gratings,” IEEE J. Quantum Electron. 35, 548–558 (1999).
[CrossRef]

M. A. Muriel, J. Azaña, A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett. 24, 1–3 (1999).
[CrossRef]

J. Azaña, M. A. Muriel, “Superimposed in-fiber grating structures for optical signal processing in wavelength-division-multiplexing systems,” in OFC’2000 (25th Conference on Optical Fiber Communication, T. Li, ed., Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 233–235, paper WM8.

Ortega, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Martí, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Othonos, A.

A. Othonos, X. Lee, R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

Ouellette, F.

Oullette, F.

F. Oullette, J.-F. Cliche, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

Pastor, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Martí, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Ramamurthy, B.

M. S. Borella, J. P. Jue, D. Banerjee, B. Ramamurthy, B. Mukherjee, “Optical components for WDM lightwave networks,” Proc. IEEE 85, 1274–1307 (1997).
[CrossRef]

Rauschenbach, K. A.

K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson, K. A. Rauschenbach, “An ultrafast variable optical delay technique,” IEEE Photon. Technol. Lett. 12, 208–210 (2000).
[CrossRef]

H. Hakimi, F. Hakimi, K. L. Hall, K. A. Rauschenbach, “A new wide-band pulse-restoration technique for digital fiber-optic communication systems using temporal gratings,” IEEE Photon. Technol. Lett. 11, 1048–1050 (1999).
[CrossRef]

Robinson, B. S.

K. L. Hall, D. T. Moriarty, H. Hakimi, F. Hakimi, B. S. Robinson, K. A. Rauschenbach, “An ultrafast variable optical delay technique,” IEEE Photon. Technol. Lett. 12, 208–210 (2000).
[CrossRef]

Rue, R. M.

Smith, P. W. E.

J. Azaña, L. R. Chen, M. A. Muriel, P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
[CrossRef]

Sugden, K.

Tam, R.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
[CrossRef]

Tatay, V.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Martí, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Thoms, S.

Tong, Y. C.

Y. C. Tong, L. Y. Chan, K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33, 983–985 (1997).
[CrossRef]

Tsang, K.

Y. C. Tong, L. Y. Chan, K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33, 983–985 (1997).
[CrossRef]

Williams, J. A. R.

Zervas, M. N.

K. Ennser, M. N. Zervas, R. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
[CrossRef]

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, M. Durkin, “Effects of non-ideal group delay and reflection characteristics of fibre grating dispersion compensators,” in Proceedings of the 23rd European Conference on Optical Communications, 1997 (ECOC’97) (Institute of Electrical Engineers, London, 1977), Vol. 2, pp. 45–48.

Zhang, L.

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

Electron. Lett. (5)

J. Azaña, L. R. Chen, M. A. Muriel, P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

A. Othonos, X. Lee, R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

Y. C. Tong, L. Y. Chan, K. Tsang, “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33, 983–985 (1997).
[CrossRef]

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings,” Electron. Lett. 35, 584–585 (1999).
[CrossRef]

IEEE J. Quantum Electron. (4)

M. A. Muriel, A. Carballar, J. Azaña, “Field distributions inside fiber gratings,” IEEE J. Quantum Electron. 35, 548–558 (1999).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the multichannel real-time optical spectrum analyzer. λ i (i = 1, 2, 3, … ) refers to the central wavelength within each WDM channel.

Fig. 2
Fig. 2

Duality between the spatial Fresnel diffraction and the temporal distortion of pulses reflected from a LCFG. Under spatial (temporal) Fraunhofer conditions the output field distribution (output temporal pulse) is proportional to the Fourier transform of the input field distribution (input temporal pulse).

Fig. 3
Fig. 3

(a) Solid curve, reflectivity of a superimposed FG structure consisting of a strong-coupling uniform grating (FG#1) and a weak-coupling uniform grating (FG#2). Dotted and dotted–dashed curves, reflectivity of the individual grating perturbations, FG#1 and FG#2. (b) Solid curves, reflection group delay of the superimposed FG structure. Dotted curves, reflection group delay of individual grating perturbations FG#1 and FG#2. The reflection spectra of the individual gratings do not overlap, and, as a result, each one of these gratings retains its individual behavior.

Fig. 4
Fig. 4

(a) Solid curve, reflectivity of a superimposed FG structure. The structure comprises a strong-coupling uniform grating (FG#1) and a weak-coupling uniform grating (FG#2). Dotted curves, reflectivity of the individual grating perturbations FG#1 and FG#2. (b) Solid curves, reflection group delay of the superimposed FG structure. Dotted curves, reflection group delay of the individual grating perturbations FG#1 and FG#2. The reflection spectra of the individual gratings partially overlap, which causes an interaction between gratings and the associated deviation in the spectral response with respect to that of the individual gratings.

Fig. 5
Fig. 5

(a) Solid curve, reflectivity of a SLCFG composed of strong-coupling (LCFG#1) and weak-coupling (LCFG#2). Dotted and dotted–dashed curves, reflectivity of the individual grating perturbations LCFG#1 and LCFG#2. (b) Solid curves, reflection group delay of the SLCFG. Dotted curves, reflection group delay of the individual grating perturbations LCFG#1 and LCFG#2. The reflection spectra of the individual gratings do not overlap, and, as a result, each one of these gratings retains its individual behavior.

Fig. 6
Fig. 6

Effective bandwidth versus design bandwidth (from 1 GHz to 1 THz) for unapodized LCFGs. The effective bandwidth is estimated for different lengths (L = 5 mm, 1 cm, 10 cm) and different coupling strengths (Δn max = 1 × 10-5, 2 × 10-4, 2 × 10-3).

Fig. 7
Fig. 7

(a) Local grating period variation along the fiber length for the designed SLCFG. (b) SLCFG reflectivity and reflection group delay, both as a function of the optical frequency.

Fig. 8
Fig. 8

Signal incident upon the SLCFG. (a) Energy spectrum of the total input signal. (b) Joint TF energy distribution of the total input signal. (c) Temporal waveform (average optical power) of the total input signal. (d)–(f) Normalized average optical power of the input signal within each wavelength channel.

Fig. 9
Fig. 9

Signal reflected from the SLCFG. (a) Energy spectrum of the total input signal. (b) Joint TF energy distribution of the total input signal. (c) Temporal waveform (average optical power) of the total input signal. (d)–(f) Solid curves, normalized average optical power of the reflected signal within each wavelength channel. Dashed curves, normalized energy spectrum of the input signal within each wavelength channel, with t [ps] = ν [THz] × 104.

Equations (23)

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Δt22π|Φ¨|  1,
yˆt  expj 12Φ¨ t2Xˆωω=t/ϕ¨,
Xˆω=Fxˆt,
nz=neff+Δn¯effz+ΔnmaxTzcosφz,-L/2zL/2,
φz=-L/2z Ωzdz,
Ωz=CΩz+Ω0,
|CΩ|  8πnav2c2Δt2,
L  cΔt2Δω4πnav,
dAzdz=-jKzAz-jKzexpj2βzBz,
dBzdz=jKzBz+jKzexp-j2βzAz,
Kz=ω2μ02β Δεz,
nz=neff+Δn¯effz+i=1N Δnmax,iTizcosφiz,-L/2zL/2,
εz=ε0n2z=ε0neff2+Δεz,
Δεz2ε0neffΔn¯effz+i=1N Δnmax,iTizcosφiz.
Δn¯effz+i=1N Δnmax,i  neff.
Kz=σz+κz,
σz=ωc Δn¯effz
κz=ωci=1N Δnmax,iTizcosφiz
κz=i=1N κiz,
κiz=ωc Δnmax,iTizcosφiz=κmax,izcosφiz.
2β-ϕpzz0,
dAzdz=-jσzAz-j κmax,pz2×expj2βz-φpzBz,
dBzdz=jσzBz+j κmax,pz2×exp-j2βz-φpzAz.

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