Abstract

Group-delay ripple (GDR) introduced by systematic and random errors in chirped fiber Bragg grating fabrication is the most significant impediment to application of these devices in optical communication systems. We suggest and demonstrate a novel iterative procedure for GDR correction by subsequent UV exposure by use of a simple solution of the inverse problem for the coupled-wave equation. Our method is partly based but does not fully rely on the accuracy of this solution. In the experiment we achieved substantial reduction of the low-frequency group-delay ripple, from ±15 to ±2 ps, which resulted in dramatic improvement of the optical signal-to-noise-ratio system penalty, from 7 to less than 1 dB, for a chirped fiber Bragg grating used as a dispersion compensator in a 40-Gbit/s carrier-suppressed return-to-zero system.

© 2003 Optical Society of America

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References

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  1. R. Kashyap, Fiber Bragg Gratings (Academic, San Diego, Calif., 1999).
  2. B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, J. Lightwave Technol. 18, 1418 (2000).
    [CrossRef]
  3. I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
    [CrossRef]
  4. S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, and A. S. Holmes, Appl. Opt. 39, 3670 (2000).
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  6. A. V. Buryak and D. Yu. Stepanov, Opt. Lett. 27, 1099 (2002).
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    [CrossRef] [PubMed]

2002 (3)

2001 (1)

T. Komukai, T. Inui, and M. Nakazawa, Electron. Lett. 37, 449 (2001).
[CrossRef]

2000 (2)

1999 (1)

I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
[CrossRef]

1998 (1)

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 1476 (1998).
[CrossRef]

Ahuja, A.

Albert, J.

Bilodeau, F.

Bungarzeanu, C.

I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
[CrossRef]

Buryak, A. V.

de Sterke, C. M.

Durkin, M.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 1476 (1998).
[CrossRef]

Eggleton, B. J.

Ennser, K.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 1476 (1998).
[CrossRef]

Feced, R.

Gourhant, J.

I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
[CrossRef]

Gurib, S.

I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
[CrossRef]

Hill, K. O.

Holmes, A. S.

Ibsen, M.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 1476 (1998).
[CrossRef]

Inui, T.

T. Komukai, T. Inui, and M. Nakazawa, Electron. Lett. 37, 449 (2001).
[CrossRef]

Johnson, D. C.

Kashyap, R.

I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
[CrossRef]

R. Kashyap, Fiber Bragg Gratings (Academic, San Diego, Calif., 1999).

Komukai, T.

T. Komukai, T. Inui, and M. Nakazawa, Electron. Lett. 37, 449 (2001).
[CrossRef]

Kuo, P.

Laming, R. I.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 1476 (1998).
[CrossRef]

Mihailov, S. J.

Mikkelsen, B.

Nakazawa, M.

T. Komukai, T. Inui, and M. Nakazawa, Electron. Lett. 37, 449 (2001).
[CrossRef]

Nielsen, T. N.

Riant, I.

I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
[CrossRef]

Rogers, J. A.

Sansonetti, P.

I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
[CrossRef]

Skaar, J.

Stepanov, D. Yu.

Sumetsky, M.

Westbrook, P. S.

Zervas, M. N.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 1476 (1998).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

T. Komukai, T. Inui, and M. Nakazawa, Electron. Lett. 37, 449 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, IEEE J. Sel. Top. Quantum Electron. 5, 1312 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, IEEE Photon. Technol. Lett. 10, 1476 (1998).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Lett. (1)

Other (1)

R. Kashyap, Fiber Bragg Gratings (Academic, San Diego, Calif., 1999).

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Figures (3)

Fig. 1
Fig. 1

Iterative CFBG correction: a, group delay and GDR of the initial CFBG; b, the result of low-frequency filtering of the GDR shown in a; c, determination of the corrective dc index and introduction of it into the CFBG by direct UV exposure; d, group delay and GDR after the first correction.

Fig. 2
Fig. 2

a, Gaussian peak dc index perturbations and b, corresponding GDR obtained by numerical solution of the coupled-wave equation for peak widths equal to 1, 1 mm; 2, 2 mm; 3, 5 mm; and 4, 10 mm (solid curves) compared with the desired Gaussian GDR peaks obtained from Eq. (1) (dashed curves). c, dc index perturbation profiles corresponding to Gaussian peaks in the GDR computed with Eq. (3). d, GDR found by numerical solution of the coupled-wave equation by use of the dc index perturbation profiles of c (solid curves). The peaks in d are close to the desired Gaussian GDR peaks (dashed curves).

Fig. 3
Fig. 3

a, Iterative process of grating correction: GDR (finer curves) and GDR averaged over 0.1 nm (bolder curves) after several correction steps, from 1 (initial step) to 5 (final step). b, Computed OSNR penalties for initial (1) and final corrected (5) gratings.

Equations (3)

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δndcx=const cCgrΛgrδτ2neffCgrx,
δndcx=-dλδτλΦx,λ,Φx,λ=constcCgr1/223/2π2ΛgrΔnac0dq×cosx-λ2neffCgrq+Λgr24πCgrq2,
δndcx=constcCgr1/2λwδτ02π3/2Δnac×0dq exp-λw2q216neff2Cgr2×cosx-λ02neffCgrq+Λgr2q24πCgr.

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