Abstract

A multichannel fiber Bragg grating (FBG) design based on a discrete layer-peeling method is described. This novel method enables us to design any kind of multichannel FBG in which the spectrum responses of the channels can be either identical or nonidentical. In particular, a nine-channel dispersion-free FBG and a nine-channel nonlinearly chirped FBG used simultaneously as chromatic dispersion and dispersion slope compensators are described. Unlike the general multichannel FBG designed by a sampling method, these two gratings have ideal flat-topped profiles in both the transmission and the reflection spectra. By optimally detuning the relative phases for the multiple-spectrum channels with an iterative layer-peeling method, we can make maximum use of length-limited photosensitive fiber. Moreover, we show numerically that one can reduce or eliminate the oscillation that inherently exists in the index-change envelope of our multichannel FBG by accepting a decreased extinction ratio of the in-band signal to the out-of-band noises.

© 2004 Optical Society of America

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    [CrossRef]
  3. K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
    [CrossRef]
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    [CrossRef]
  8. W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
    [CrossRef]
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    [CrossRef]
  10. V. Jayaraman, Z. M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
    [CrossRef]
  11. M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
    [CrossRef]
  12. J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
    [CrossRef]
  20. A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the simulated annealing algorithm,” ACM Trans. Math. Software 13, 262–280 (1987).
    [CrossRef]

2003 (5)

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

H. Li, Y. Sheng, Y. Li, and J. E. Rothenber, “Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,” J. Lightwave Technol. 13, 2074–2083 (2003).

H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15, 1252–1254 (2003).
[CrossRef]

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, “Three-stage design optimization for multi-channel fibre Bragg gratings,” Opt. Express 11, 1029–1038 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

2002 (2)

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

2001 (2)

X. Shu, B. A. L. Gwandu, Y. Liu, L. Zhang, and I. Bennion, “Sampled fiber Bragg grating for simultaneous refractive index and temperature measurement,” Opt. Lett. 26, 774–776 (2001).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

1999 (4)

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based-dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280–1282 (1999).
[CrossRef]

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinear chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 1455–1457 (1999).
[CrossRef]

1998 (1)

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

1995 (1)

F. Oullette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
[CrossRef]

1994 (1)

B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

1993 (1)

V. Jayaraman, Z. M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[CrossRef]

1987 (1)

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the simulated annealing algorithm,” ACM Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Bennion, I.

Buryak, A. V.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, “Three-stage design optimization for multi-channel fibre Bragg gratings,” Opt. Express 11, 1029–1038 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Cai, J.-X.

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinear chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 1455–1457 (1999).
[CrossRef]

Caldwell, R.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

Chuang, Z. M.

V. Jayaraman, Z. M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[CrossRef]

Coldren, L. A.

V. Jayaraman, Z. M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[CrossRef]

Cole, M. J.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

Corana, A.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the simulated annealing algorithm,” ACM Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Dhosi, G.

F. Oullette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
[CrossRef]

Durkin, M. K.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

Eggleton, B.

F. Oullette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
[CrossRef]

B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Erdogen, T.

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Feinberg, J.

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinear chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 1455–1457 (1999).
[CrossRef]

Feng, K.-M.

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinear chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 1455–1457 (1999).
[CrossRef]

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

Grubsky, V.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinear chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 1455–1457 (1999).
[CrossRef]

Gwandu, B. A. L.

Hayee, M. I.

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

Ibsen, M.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

Jayaraman, V.

V. Jayaraman, Z. M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[CrossRef]

Jiang, X.

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

Kolossovski, K. Y.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, “Three-stage design optimization for multi-channel fibre Bragg gratings,” Opt. Express 11, 1029–1038 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Krug, P. A.

F. Oullette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
[CrossRef]

B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Laming, R. I.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

Lee, S.

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

Li, H.

H. Li, Y. Sheng, Y. Li, and J. E. Rothenber, “Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,” J. Lightwave Technol. 13, 2074–2083 (2003).

H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15, 1252–1254 (2003).
[CrossRef]

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

Li, Y.

H. Li, Y. Sheng, Y. Li, and J. E. Rothenber, “Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,” J. Lightwave Technol. 13, 2074–2083 (2003).

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

Liu, Y.

Loh, W. H.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based-dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280–1282 (1999).
[CrossRef]

Marchesi, M.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the simulated annealing algorithm,” ACM Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Martini, C.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the simulated annealing algorithm,” ACM Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Motaghian Nezam, S. M. R.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

Muriel, M. A.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Oullette, F.

F. Oullette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
[CrossRef]

B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Pan, J. J.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based-dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280–1282 (1999).
[CrossRef]

Pan, X.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

Pan, Z.

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

Poladian, L.

B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Popelek, J.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

Poplek, J.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

Ridella, S.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the simulated annealing algorithm,” ACM Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Rothenber, J. E.

H. Li, Y. Sheng, Y. Li, and J. E. Rothenber, “Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,” J. Lightwave Technol. 13, 2074–2083 (2003).

Rothenberg, J. E.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

Sammut, R. A.

Sheng, Y.

H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15, 1252–1254 (2003).
[CrossRef]

H. Li, Y. Sheng, Y. Li, and J. E. Rothenber, “Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,” J. Lightwave Technol. 13, 2074–2083 (2003).

Shu, X.

Skaar, J.

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

Song, W.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

Song, Y. W.

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

Starodubov, D.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

Starodubov, D. S.

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinear chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 1455–1457 (1999).
[CrossRef]

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

Stepanov, D. Y.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, “Three-stage design optimization for multi-channel fibre Bragg gratings,” Opt. Express 11, 1029–1038 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Stephens, T.

F. Oullette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
[CrossRef]

Wang, L.

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

Wang, Y.

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

Wilcox, R.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

Wilcox, R. B.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

Willner, A. E.

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinear chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 1455–1457 (1999).
[CrossRef]

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

Yu, C.

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

Yu, Q.

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
[CrossRef]

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R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

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Zhou, F. Q.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based-dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280–1282 (1999).
[CrossRef]

Zweiback, J.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

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[CrossRef]

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B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

F. Oullette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
[CrossRef]

IEEE J. Quantum Electron. (4)

V. Jayaraman, Z. M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[CrossRef]

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (7)

W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E. Rothenberg, X. Pan, H. Li, R. Wilcox, J. Poplek, R. Caldwell, V. Grubsky, and A. E. Willner, “Tunable interchannel broadband dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photon. Technol. Lett. 15, 144–146 (2003).
[CrossRef]

H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15, 1252–1254 (2003).
[CrossRef]

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[CrossRef]

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309–1311 (2002).
[CrossRef]

K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X. Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gb/s optical system using a novel voltage tuned nonlinearly-chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 373–375 (1999).
[CrossRef]

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based-dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280–1282 (1999).
[CrossRef]

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinear chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 1455–1457 (1999).
[CrossRef]

J. Lightwave Technol. (2)

H. Li, Y. Sheng, Y. Li, and J. E. Rothenber, “Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,” J. Lightwave Technol. 13, 2074–2083 (2003).

Z. Pan, Y. W. Song, C. Yu, Y. Wang, Q. Yu, J. Poplek, H. Li, Y. Li, and A. E. Willner, “Tunable chromatic dispersion compensation in 40-Gb/s systems using nonlinearly chirped fiber Bragg gratings,” J. Lightwave Technol. 12, 2239–2245 (2002).
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Figures (10)

Fig. 1
Fig. 1

Design results for a one-channel dispersion-free FBG filter: (a) apodization curve, (b) transmission and dispersion spectra.

Fig. 2
Fig. 2

Nine-channel dispersion-free FBG filter based on sinc sampling function: (a) apodization curve, (b) transmission spectrum, (c) reflection spectrum, (d) dispersion spectrum.

Fig. 3
Fig. 3

Nine-channel dispersion-free FBG filter based on the layer-peeling method with channel phase ϕm=[0, 0, 0, 0, 0, 0, 0, 0, 0]: (a) apodization curve, (b) transmission spectrum, (c) reflection spectrum, (d) dispersion spectrum.

Fig. 4
Fig. 4

Fine structures of the grating profiles for a nine-channel dispersion-free FBG filter based on the sampling and layer-peeling methods: (a) grating profiles, (b) Fourier transforms of the grating profiles.

Fig. 5
Fig. 5

Nine-channel dispersion-free FBG filter based on the layer-peeling method with channel phase ϕm=[-1.04720, 3.14159, 1.0472, 0, 0, 0, 1.0472, 3.14159, -1.04720]: (a) apodization curve, (b) transmission spectrum, (c) reflection spectrum, (d) dispersion spectrum.

Fig. 6
Fig. 6

Nine-channel dispersion-free FBG filter after the smoothing procedure for the index-change envelope: (a) apodization curve, (b) transmission spectrum, (c) reflection spectrum, (d) dispersion spectrum.

Fig. 7
Fig. 7

Flowcharts for the design processes: (a) optimization for the channel phases, (b) optimization for the index-change envelope smoothing.

Fig. 8
Fig. 8

Design results for a linear chirp FBG with chromatic dispersion D2=-1020 ps/nm: (a) apodization and phase profiles, (b) reflection and dispersion spectra.

Fig. 9
Fig. 9

Design results of a nine-channel simultaneous dispersion and dispersion slope compensator with relative channel phase ϕm=[1.116, 2.744, -1.01, 0.43, -0.285, 0.43, -1.01, 2.744, 1.116]: (a) apodization and phase profiles, (b) transmission spectrum, (c) reflection spectrum, (d) dispersion spectrum.

Fig. 10
Fig. 10

Design results based on Fig. 9 with grating amplitude smoothing: (a) apodization and phase profiles, (b) transmission spectrum, (c) reflection spectrum, (d) dispersion spectrum.

Equations (16)

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

Δn(z)=Re([n1(z)/2]exp{i[2πz/Λ+ϕg(z)]}s(z)),
s(z)=m=-sm exp(i2mπz/P)=m=-|sm|exp(i2mπz/P+ϕm),
EFz=-iEBm=-|sm|κ0 exp{i[-2mπz/P+ϕm+2βz-ϕg(z)]},
EBz=-iEFm=-m=|sm|κ0 exp{-i[-2mπz/P+ϕm+2βz-ϕg(z)]},
β-πm/P=0.
rM(λ)=rs(λ)m=-N-1N+1δ(λ-mΔλ0)={R exp[-iΦ(λ)]}m=-N-1N+1δ(λ-mΔλ0),
rM(λ)={R exp[-iΦ(λ)]}m=-N-1N+1δ(λ-mΔλ0)exp(iϕm).
rs(λ)=0.9 exp-ln 2(λ-λ0)0.5×0.6514.
S(z)=m=-44 expi2mπPz,P1,
M(z, ϕ-NϕN)=0L[EM(z, ϕ-NϕN)-2N+1Es(z)]2dz,
r(z, β)=exp(j2βΔ)r(z+Δ, β)-(q*/|q|)tanh(|q|Δ)1-exp(j2βΔ)(q/|q|)tanh(|q|Δ)r(z+Δ, β),
rs(λ)=0.9 exp-ln 2(λ-λ0)0.5×0.6518exp[-iΦs(λ)],
r(λ)=m=-NNrm(λ)=|rs(λ)|m=-NNδ(λ-mΔλ0)exp(iϕm)×exp[-iΦ(λ)],
Φ(λ)=-cm=-NNλm-Δλ0/2λm+Δλ0/2 2πλ2D2(m)(λ-λm)dλ,
D2(m)=(D2+D3mΔλ0),
m=-N,-(N-1),N-1,N,

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