Abstract

The relationship between group-delay ripple and the apodization profile of chirped Bragg gratings is analyzed. Simple physical explanations are given for departures from ideal linear group delay by use of only the concepts of reflection at discontinuities and band gaps and the optical path lengths of cavities. Quantitative expressions are obtained for the amplitudes, phases, and periods of both the fast and slow components of the ripple.

© 2000 Optical Society of America

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References

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  1. N. M. Litchinitser, D. B. Patterson, “Analysis of fiber Bragg gratings for dispersion compensation in reflective and transmissive geometries,” J. Lightwave Technol. 15, 1323–1328 (1997).
    [CrossRef]
  2. S. Thibault, J. Lauzon, J.-F. Cliche, J. Martin, M. A. Duguay, M. Tetu, “Numerical analysis of the optimal-length and profile of a linearly chirped fiber Bragg grating for dispersion compensation,” Opt. Lett. 20, 647–649 (1995).
    [CrossRef] [PubMed]
  3. M. Ibsen, R. I. Laming, “Fibre non-uniformity caused Bragg grating imperfections,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper FA1–1, pp. 2–4.
  4. L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E 48, 4758–4767 (1993).
    [CrossRef]
  5. A. Arraf, L. Poladian, C. M. de Sterke, T. G. Brown, “Effective-medium approach for counterpropagating waves in nonuniform Bragg gratings,” J. Opt. Soc. Am. A 14, 1137–1143 (1997).
    [CrossRef]

1997 (2)

N. M. Litchinitser, D. B. Patterson, “Analysis of fiber Bragg gratings for dispersion compensation in reflective and transmissive geometries,” J. Lightwave Technol. 15, 1323–1328 (1997).
[CrossRef]

A. Arraf, L. Poladian, C. M. de Sterke, T. G. Brown, “Effective-medium approach for counterpropagating waves in nonuniform Bragg gratings,” J. Opt. Soc. Am. A 14, 1137–1143 (1997).
[CrossRef]

1995 (1)

1993 (1)

L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E 48, 4758–4767 (1993).
[CrossRef]

Arraf, A.

Brown, T. G.

Cliche, J.-F.

de Sterke, C. M.

Duguay, M. A.

Ibsen, M.

M. Ibsen, R. I. Laming, “Fibre non-uniformity caused Bragg grating imperfections,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper FA1–1, pp. 2–4.

Laming, R. I.

M. Ibsen, R. I. Laming, “Fibre non-uniformity caused Bragg grating imperfections,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper FA1–1, pp. 2–4.

Lauzon, J.

Litchinitser, N. M.

N. M. Litchinitser, D. B. Patterson, “Analysis of fiber Bragg gratings for dispersion compensation in reflective and transmissive geometries,” J. Lightwave Technol. 15, 1323–1328 (1997).
[CrossRef]

Martin, J.

Patterson, D. B.

N. M. Litchinitser, D. B. Patterson, “Analysis of fiber Bragg gratings for dispersion compensation in reflective and transmissive geometries,” J. Lightwave Technol. 15, 1323–1328 (1997).
[CrossRef]

Poladian, L.

Tetu, M.

Thibault, S.

J. Lightwave Technol. (1)

N. M. Litchinitser, D. B. Patterson, “Analysis of fiber Bragg gratings for dispersion compensation in reflective and transmissive geometries,” J. Lightwave Technol. 15, 1323–1328 (1997).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. E (1)

L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E 48, 4758–4767 (1993).
[CrossRef]

Other (1)

M. Ibsen, R. I. Laming, “Fibre non-uniformity caused Bragg grating imperfections,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper FA1–1, pp. 2–4.

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Figures (2)

Fig. 1
Fig. 1

Deviation in group delay (solid curve) for various apodized chirped gratings and the simple physical model (dashed curve). Apodization profile with (a) nonzero at the grating ends, (b) zero at the grating ends (but a nonzero slope), (c) slope zero at the grating ends.

Fig. 2
Fig. 2

Schematic of reflection from a local photonic band gap in a chirped grating.

Equations (13)

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κz=κ0 exp-3.52zL4.
κz=κ01-4z2L2.
κz=κ0 cos2π24z2L2.
rtotalrbarrier expiϕfront+rfront+rˆfrontrbarrier2 exp2iϕfront+rbacktbarrier2 expiϕfront+iϕback,
τ=dϕtotaldω=Imddω lnrtotal,
ϕfront=2 zfz1δz2-κz21/2dz.
rbarrieri tanhκLbarrier,
κLbarrierz1z2κz2-δz21/2 dz+ln2,
redge-Δκ2δ-i Δκ4δ2,
rδi  κzexp2iδzdz.
rtotal=i tanhκLbarrierexpiϕfront-Δκfront2δ+i Δκfront4δ2-Δκfront2δ-i Δκfront4δ2tanh2κLbarrier×exp2iϕfront-Δκback2δ-i Δκback4δ2sech2×κLbarrierexpiϕfront+iϕback.
rtotali expiϕfront1+i Δκfrontδ cos ϕfront+i Δκfront2δ2 sin ϕfront.
ϕtotalπ2+ϕfront+Δκδ cosϕfront+Δκ2δ2 sinϕfront.

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