Abstract

The group delay in transmission of an arbitrary fiber Bragg grating can be determined uniquely from the amplitude response. The corresponding quantities in reflection are determined uniquely if the grating is symmetric. For nonsymmetric gratings strict minimum and maximum bounds on the group delay in reflection can be obtained. The results are applied to several different chirped or tapered grating profiles that have appeared in the literature.

© 1997 Optical Society of America

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References

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  1. J. Sipe, L. Poladian, and C. M. de Sterke, J. Opt. Soc. Am. A 11, 1307 (1993).
    [CrossRef]
  2. F. Ouellette, Opt. Lett. 12, 847 (1987).
    [CrossRef] [PubMed]
  3. T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
    [CrossRef]
  4. K. Hinton, in Proceedings of the 21st Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1996), pp. 41–44.
  5. L. Poladian, Phys. Rev. E 54, 2963 (1996).
    [CrossRef]
  6. E. Brinkmeyer, Opt. Lett. 20, 810 (1995).
    [CrossRef] [PubMed]
  7. G.-H. Song and S.-Y. Shin, J. Opt. Soc. Am. A 2, 1905 (1985).
    [CrossRef]
  8. G. H. Song, J. Opt. Soc. Am. A 11, 2027 (1994).
    [CrossRef]
  9. J. S. Toll, Phys. Rev. 104, 1760 (1956).
    [CrossRef]
  10. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).
  11. M. A. Muriel and A. Carballar, Opt. Lett. 22, 93 (1997).
    [CrossRef] [PubMed]

1997 (1)

1996 (2)

T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
[CrossRef]

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

1987 (1)

1985 (1)

1956 (1)

J. S. Toll, Phys. Rev. 104, 1760 (1956).
[CrossRef]

Brinkmeyer, E.

Brodzelli, Z.

T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
[CrossRef]

Carballar, A.

de Sterke, C. M.

Dhosi, G.

T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
[CrossRef]

Hinton, K.

K. Hinton, in Proceedings of the 21st Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1996), pp. 41–44.

Krug, P. A.

T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
[CrossRef]

Muriel, M. A.

Ouellette, F.

T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
[CrossRef]

F. Ouellette, Opt. Lett. 12, 847 (1987).
[CrossRef] [PubMed]

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).

Poladian, L.

T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
[CrossRef]

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

J. Sipe, L. Poladian, and C. M. de Sterke, J. Opt. Soc. Am. A 11, 1307 (1993).
[CrossRef]

Shin, S.-Y.

Sipe, J.

Song, G. H.

Song, G.-H.

Stephens, T.

T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
[CrossRef]

Toll, J. S.

J. S. Toll, Phys. Rev. 104, 1760 (1956).
[CrossRef]

Electron. Lett. (1)

T. Stephens, P. A. Krug, Z. Brodzelli, G. Dhosi, F. Ouellette, and L. Poladian, Electron. Lett. 32, 1599 (1996).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Lett. (3)

Phys. Rev. (1)

J. S. Toll, Phys. Rev. 104, 1760 (1956).
[CrossRef]

Phys. Rev. E (1)

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

Other (2)

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).

K. Hinton, in Proceedings of the 21st Australian Conference on Optical Fibre Technology (Institution of Radio and Electronics Engineers, Sydney, Australia, 1996), pp. 41–44.

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Figures (6)

Fig. 1
Fig. 1

Actual group delay in reflection or transmission (solid curve) and that inferred from the amplitude spectrum (dashed curve) for a symmetric self-chirped Gaussian grating.

Fig. 2
Fig. 2

Actual group delay in reflection or transmission (solid curve) and that inferred from the amplitude spectrum (dashed curve) for a symmetric unchirped grating with a triangular apodization profile.

Fig. 3
Fig. 3

Actual group delay in transmission (solid curve) and that inferred from the amplitude spectrum (dashed curve) for a linearly chirped grating with a Gaussian apodization profile.

Fig. 4
Fig. 4

Actual group delay in transmission (solid curve) and that inferred from the amplitude spectrum (dashed curve) for an unchirped grating with a linearly ramped profile.

Fig. 5
Fig. 5

Forward and backward group delays in reflection (solid curves) and the upper and lower bounds (dashed curves) calculated from the reflectance for the same grating as in Fig.  3.

Fig. 6
Fig. 6

Forward and backward group delays in reflection (solid curves) and the upper and lower bounds (dashed curves) calculated from the reflectance for the same grating as in Fig.  4.

Equations (8)

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r-ω=-r+ω*tωtω*,
DTω=ϕTωω,
DR±ω=ϕR±ωω,
Rω+Tω=1,
1/2DR+ω+DR-ω=DTω.
1tωtωω= logTωω+iDTω,
DTω-D0=-1π- logTωωdωω-ω,
DRminω=-1π- logRωωdωω-ω.

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