Abstract

We have analyzed the effects of various normally distributed nonuniformities of sampled fiber Bragg gratings on the reflective spectra and group time delay. Through numerical simulations we have drawn the following conclusions: (1) the magnitude of nonuniformity with normal distribution of the fiber’s average refractive-index modulation δ̅ n eff greatly influences the characteristics of both reflective spectra and group time delay, whose suggested precision varies from 20% to 10%; (2) the nonuniformities of sampling periods P and sampling lengths L are important factors that influence the characteristics of the group time delay, and the accepted tolerance of dimensional precision of both P and L are ±4 μm; and (3) the tolerance of nonuniformity of the sampling period’s chirp coefficient is high, and its precision can be as great as 100% with few adverse effects.

© 2004 Optical Society of America

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  1. F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, B. Eggleton, “Broadband and WDM dispersion compensation using chirped sample fiber Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
    [CrossRef]
  2. W. H. Loh, F. Q. Zhou, J. J. Pan, “Novel designs for sampled grating-based multiplexers–demultiplexers,” Opt. Lett. 24, 1457–1459 (1999).
    [CrossRef]
  3. Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
    [CrossRef]
  4. C.-H. Wang, L. R. Chen, P. W. E. Smith, “Analysis of chirped-sampled and sampled-chirped fiber Bragg gratings,” Appl. Opt. 41, 1654–1660 (2002).
    [CrossRef] [PubMed]
  5. W. H. Loh, F. Q. Zhou, J. J. Pan, “Sampled fiber grating based-dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280–1282 (1999).
    [CrossRef]
  6. X.-F. Chen, Y. Luo, C.-C. Fan, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period in its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett. 12, 1013–1015 (2000).
    [CrossRef]

2002 (1)

2000 (2)

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

X.-F. Chen, Y. Luo, C.-C. Fan, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period in its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett. 12, 1013–1015 (2000).
[CrossRef]

1999 (2)

W. H. Loh, F. Q. Zhou, J. J. Pan, “Novel designs for sampled grating-based multiplexers–demultiplexers,” Opt. Lett. 24, 1457–1459 (1999).
[CrossRef]

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

1995 (1)

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

Cai, J.-X.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Chen, L. R.

Chen, X.-F.

X.-F. Chen, Y. Luo, C.-C. Fan, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period in its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett. 12, 1013–1015 (2000).
[CrossRef]

Dhosi, G.

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

Eggleton, B.

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

Fan, C.-C.

X.-F. Chen, Y. Luo, C.-C. Fan, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period in its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett. 12, 1013–1015 (2000).
[CrossRef]

Feinberg, J.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Grubsky, V.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Krug, P. A.

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

Lee, S.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Loh, W. H.

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

W. H. Loh, F. Q. Zhou, J. J. Pan, “Novel designs for sampled grating-based multiplexers–demultiplexers,” Opt. Lett. 24, 1457–1459 (1999).
[CrossRef]

Luo, Y.

X.-F. Chen, Y. Luo, C.-C. Fan, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period in its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett. 12, 1013–1015 (2000).
[CrossRef]

Ouellette, F.

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

Pan, J. J.

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

W. H. Loh, F. Q. Zhou, J. J. Pan, “Novel designs for sampled grating-based multiplexers–demultiplexers,” Opt. Lett. 24, 1457–1459 (1999).
[CrossRef]

Pan, Z.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Salik, E.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Smith, P. W. E.

Starodubov, D. S.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Stephens, T.

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

Wang, C.-H.

Willner, A. E.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Xie, S.-Z.

X.-F. Chen, Y. Luo, C.-C. Fan, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period in its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett. 12, 1013–1015 (2000).
[CrossRef]

Xie, Y.

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Zhou, F. Q.

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

W. H. Loh, F. Q. Zhou, J. J. Pan, “Novel designs for sampled grating-based multiplexers–demultiplexers,” Opt. Lett. 24, 1457–1459 (1999).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

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

IEEE Photon. Technol. Lett. (3)

Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

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

X.-F. Chen, Y. Luo, C.-C. Fan, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period in its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett. 12, 1013–1015 (2000).
[CrossRef]

Opt. Lett. (1)

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Figures (9)

Fig. 1
Fig. 1

Various nonuniformities of the SFBGs.

Fig. 2
Fig. 2

Spectral reflection responses of SFBGs with uniform grating periods that have different values of average refractive-index modulation nonuniform factor α. Other parameters are n eff = 1.447, δ̅ n eff0 = 5 × 10-4, Λ g = 0.5355909 μm, N = 50, P 0 = 1 mm, L = 0.15 mm, and c = c s = 0.

Fig. 3
Fig. 3

Spectral reflection and group time delay responses of SFBGs with chirped grating periods that have different values of average refractive-index modulation nonuniform factor α. Other parameters are n eff = 1.447, δ̅ n eff0 = 5 × 10-4, Λ g = 0.5355909 μm, N = 100, P 0 = 1 mm, L = 0.15 mm, c = 4 × 10-6 mm-1, and c s = 0.

Fig. 4
Fig. 4

Deviations from linear group time delay of channels 4, 7, and 10 versus different values of average refractive-index modulation nonuniform factor α. Other parameters are n eff = 1.447, δ̅ n eff = 5 × 10-4, Λ g = 0.5355909 μm, N = 100, P 0 = 1 mm, L = 0.15 mm, c = 4 × 10-6 mm-1, and c s = 0.

Fig. 5
Fig. 5

Effects of varying random value δ1 and δ2 on spectral reflection and group time delay responses of SFBGs with chirped grating periods. Other parameters are n eff = 1.447, δ̅ n eff = 5 × 10-4, Λ g = 0.5355909 μm, N = 100, P 0 = 1 mm, L 0 = 0.15 mm, c = 4 × 10-6 mm-1, and c s = 0.

Fig. 6
Fig. 6

Deviations from linear group time delay of channels 4, 6, and 10 versus random values δ1 and δ2. Other parameters are n eff = 1.447, δ̅ n eff = 5 × 10-4, Λ g = 0.5355909 μm, N = 100, P 0 = 1 mm, L 0 = 0.15 mm, c = 4 × 10-6 mm-1, and c s = 0.

Fig. 7
Fig. 7

Spectral reflection and group time delay responses of SFBGs with chirped grating periods that have different values of chirped sampling periods’ coefficient nonuniform factor β. Other parameters are n eff = 1.447, δ̅ n eff = 5 × 10-4, Λ g = 0.5355909 μm, N = 100, P 0 = 1 mm, L = 0.15 mm, c = 4 × 10-6 mm-1, and c s = 5 × 10-4.

Fig. 8
Fig. 8

Deviations from linear group time delay of channels 4, 6, and 10 versus different values of chirped sampling periods’ coefficient nonuniform factor β. Other parameters are n eff = 1.447, δ̅ n eff = 5 × 10-4, Λ g = 0.5355909 μm, N = 100, P 0 = 1 mm, L 0 = 0.15 mm, c = 4 × 10-6 mm-1, and c s = 5 × 10-4.

Fig. 9
Fig. 9

Effects of varying nonuniform coefficient β on both the reflective spectrum’s 3-dB bandwidth and the chromatic dispersion of channels 4–10. Other parameters are n eff = 1.447, δ̅ n eff = 5 × 10-4, Λ g = 0.5355909 μm, N = 100, P 0 = 1 mm, L 0 = 0.15 mm, c = 4 × 10-6 mm-1, and c s = 5 × 10-4.

Equations (7)

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δneffz=δ¯neffzi=0NrectzL * δz-iPi×1+v cos2πΛz z,
Λz=Λg1+cz,
Pi=Pi-1+P0cs, i=1, 2N,
δ¯neffz=δ¯neff01+αz,
Pi=P0+δ1i, i=0, 1, 2N,
Li=L0+δ2i, i=0, 1, 2N,
csi=cs01+βi, i=0, 1, 2N,

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