Abstract

We analyze sampled fiber Bragg gratings that have chirp in the grating period, in the sampling function, or in both. In the last-named case the sampling period can be chirped, the sample length can be chirped, or both. We explain the features in the spectral and group-delay (dispersion) responses for gratings that have a single chirp parameter. We then show how the response of sampled gratings that have multiple chirp parameters can be explained in terms of the single-chirp parameter cases.

© 2002 Optical Society of America

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References

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  1. B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
    [CrossRef]
  2. F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899–901 (1995).
    [CrossRef]
  3. M. Ibsen, M. K. Durkin, M. J. Cole, R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” Photon. Technol. Lett. 10, 842–844 (1998).
    [CrossRef]
  4. W. H. Loh, F. Q. Zhou, J. J. Pan, “Sampled fiber grating- based dispersion slope compensator,” Photon. Technol. Lett. 11, 1280–1282 (1999).
    [CrossRef]
  5. W. H. Loh, F. Q. Zhou, J. J. Pan, “Novel designs for sampled grating-based multiplexers-demultiplexers,” Opt. Lett. 24, 1457–1459 (1999).
    [CrossRef]
  6. J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinearly chirped fiber Bragg grating,” Photon. Technol. Lett. 11, 1455–1457 (1999).
    [CrossRef]
  7. X.-F. Chen, C.-C. Fan, T. Wu, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system,” Photon. Technol. Lett. 12, 1013–1015 (2000).
    [CrossRef]
  8. 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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
    [CrossRef]
  9. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]

2000 (2)

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

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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

1999 (3)

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,” Photon. Technol. Lett. 11, 1280–1282 (1999).
[CrossRef]

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

1998 (1)

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

1997 (1)

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

1995 (1)

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

1994 (1)

B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
[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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

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

Chen, X.-F.

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

Cole, M. J.

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

Dhosi, G.

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

Durkin, M. K.

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

Eggleton, B.

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

Eggleton, B. J.

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

Erdogan, T.

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

Fan, C.-C.

X.-F. Chen, C.-C. Fan, T. Wu, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system,” 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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinearly chirped fiber Bragg grating,” 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, J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinearly chirped fiber Bragg grating,” Photon. Technol. Lett. 11, 1455–1457 (1999).
[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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

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

Ibsen, M.

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

Krug, P. A.

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

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

Laming, R. I.

M. Ibsen, M. K. Durkin, M. J. Cole, R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” Photon. Technol. Lett. 10, 842–844 (1998).
[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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Loh, W. H.

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,” Photon. Technol. Lett. 11, 1280–1282 (1999).
[CrossRef]

Ouellette, F.

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

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

Pan, J. J.

W. H. Loh, F. Q. Zhou, J. J. Pan, “Sampled fiber grating- based dispersion slope compensator,” 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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Poladian, L.

B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
[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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

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

Stephens, T.

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

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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

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

Wu, T.

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

Xie, S.-Z.

X.-F. Chen, C.-C. Fan, T. Wu, S.-Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system,” 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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

Zhou, F. Q.

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,” Photon. Technol. Lett. 11, 1280–1282 (1999).
[CrossRef]

Electron. Lett. (2)

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

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

J. Lightwave Technol. (1)

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

Opt. Lett. (1)

Photon. Technol. Lett. (5)

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

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

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

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

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 nonlinear chirped FBG,” Photon. Technol. Lett. 12, 1417–1419 (2000).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

The various grating configurations.

Fig. 2
Fig. 2

Comparison of spectral reflection responses of FBGs that have only a chirped grating period, only a chirped sampling function, and only a chirped sample length with FBGs that have a uniform sampling function with a uniform grating period. Grating parameters: n 0 = 1.485, Λ0 = 521.8855 nm (λ0 = 1550 nm), Δn = 5 × 10-4, and N = 100. For FBGs that have only a chirped sampling period, L s is fixed at 0.15 mm and Z 1 = 0.5 mm. For FBGs with a uniform sampling function or only a chirped sample length the grating length is fixed at L g = 50 mm, and L s1 = 0.15 mm. For the FBG that has only a chirped grating period, c p = 3.654 × 10-6 mm-1; for the FBG with only a chirped sampling function, c s = 7 × 10-4; for the FBG with only a chirped sample length, c L = 2 × 10-2. The dotted lines represent the central wavelengths of the reflection peaks for the various orders of the FBG that has a uniform sampling function with a uniform grating period.

Fig. 3
Fig. 3

Effect of varying the chirp parameter on the reflection peaks of the FBGs with a single chirp parameter: top, wavelength shift relative to a uniform sampling function with a uniform grating period; bottom, FWHM BW.

Fig. 4
Fig. 4

Illustrative group delays for FBGs with only a chirped grating period (solid curves), only a chirped sampling period (dashed curves), and only a chirped sample length (dotted curves) for 0th-, +2nd-, and -2nd-order reflection peaks. For the FBG with only a chirped grating period, c p = 3.654 × 10-6 mm-1, for the FBG with only a chirped sampling period, c s = 7 × 10-4; for the FBG with only a chirped sample length, c L = 2 × 10-2.

Fig. 5
Fig. 5

Dispersion of the FBGs that have only a chirped grating period and those that have only a chirped sampling period as a function of the corresponding chirp parameter.

Fig. 6
Fig. 6

Comparison of the spectral reflection responses of FBGs, that have two chirp parameters and the FBG that has a uniform sampling function with a uniform grating period. The basic grating parameters are the same as those in Fig. 2 and are described in the text. For the FBG that has a chirped sampling period with a chirped grating period, c s = 7 × 10-4 and c p = 3.654 × 10-6 mm-1; for the FBG that has a chirped sampling period with a chirped sample length, c s = 7 × 10-4 and c L = 2 × 10-2; for the FBG that has a chirped sample length with a chirped grating period, c L = 2 × 10-2 and c p = 3.654 × 10-6 mm-1. Dotted lines, central wavelengths of the reflection peaks for the various orders of the FBG that has a uniform sampling function with a uniform sampling period.

Fig. 7
Fig. 7

(a) Wavelength shift of reflection peaks (relative to the FBG that has a uniform sampling function with a uniform grating period) and (b) FWHM BW for the FBG with chirp in both the sampling and the grating periods as a function of c s with c p = 3.654 × 10-6 mm-1 (top) and as a function of c p with c s = 7 × 10-4 (bottom).

Fig. 8
Fig. 8

Dispersion of the FBG that has chirp in both the sampling and the grating periods as a function of (a) c p with c s = 7 × 10-4 and (b) c s with c p = 3.654 × 10-6 mm-1.

Fig. 9
Fig. 9

Dispersion for the Fourier orders of the FBG that has chirp in both the sampling and the grating periods: (a) c s = 7 × 10-4 and c p = 0, =52.2, =15.66, =36.54, =57.42 × 10-7 mm-1; (b) c p = 3.654 × 10-6 mm-1 and c s = 0, =3 × 10-4, =7 × 10-4, =11 × 10-4.

Equations (3)

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nz=n0+ΔnFzGzcos2πzΛz,
Zi=Z11+csi-1,
Lsi=Ls11+cLi-1,

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