Abstract

We can introduce chirping, or a variation in the periodicity of a Bragg grating, into an optical fiber by writing gratings on curved optical fibers. By precisely specifying the curvature, we can obtain linear, quadratic, and square-root chirped gratings. Experimental and numerical verifications of the relationships between curvature and grating characteristics are presented.

© 1995 Optical Society of America

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References

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  1. K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.
  2. F. Ouellette, Opt. Lett. 12, 847 (1987).
    [CrossRef] [PubMed]
  3. M. Matsuhara, K. O. Hill, A. Watanabe, J. Opt. Soc. Am. 65, 804 (1975).
    [CrossRef]
  4. J. Martin, J. Lauzon, S. Thibault, F. Ouellette, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD29.
  5. K. O. Hill, Appl. Opt. 13, 1853 (1974).
    [CrossRef] [PubMed]
  6. M. C. Farries, C. M. Ragdale, D. C. Reid, Electron. Lett. 28, 487 (1992).
    [CrossRef]
  7. K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, Electron. Lett. 29, 1659 (1993).
    [CrossRef]
  8. K. Sugden, I. Bennion, A. Molony, N. J. Copner, Electron. Lett. 30, 440 (1994).
    [CrossRef]
  9. Q. Zhang, Ph.D. dissertation (Brown University, Providence, R.I., April1994).

1994 (1)

K. Sugden, I. Bennion, A. Molony, N. J. Copner, Electron. Lett. 30, 440 (1994).
[CrossRef]

1993 (1)

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, Electron. Lett. 29, 1659 (1993).
[CrossRef]

1992 (1)

M. C. Farries, C. M. Ragdale, D. C. Reid, Electron. Lett. 28, 487 (1992).
[CrossRef]

1987 (1)

1975 (1)

1974 (1)

Albert, J.

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

Bennion, I.

K. Sugden, I. Bennion, A. Molony, N. J. Copner, Electron. Lett. 30, 440 (1994).
[CrossRef]

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, Electron. Lett. 29, 1659 (1993).
[CrossRef]

Bilodeau, F.

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

Bricheno, T.

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, Electron. Lett. 29, 1659 (1993).
[CrossRef]

Byron, K. C.

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, Electron. Lett. 29, 1659 (1993).
[CrossRef]

Copner, N. J.

K. Sugden, I. Bennion, A. Molony, N. J. Copner, Electron. Lett. 30, 440 (1994).
[CrossRef]

Farries, M. C.

M. C. Farries, C. M. Ragdale, D. C. Reid, Electron. Lett. 28, 487 (1992).
[CrossRef]

Hill, K. O.

M. Matsuhara, K. O. Hill, A. Watanabe, J. Opt. Soc. Am. 65, 804 (1975).
[CrossRef]

K. O. Hill, Appl. Opt. 13, 1853 (1974).
[CrossRef] [PubMed]

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

Johnson, D. C.

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

Kitagawa, T.

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

Lauzon, J.

J. Martin, J. Lauzon, S. Thibault, F. Ouellette, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD29.

Malo, B.

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

Martin, J.

J. Martin, J. Lauzon, S. Thibault, F. Ouellette, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD29.

Matsuhara, M.

Molony, A.

K. Sugden, I. Bennion, A. Molony, N. J. Copner, Electron. Lett. 30, 440 (1994).
[CrossRef]

Ouellette, F.

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

J. Martin, J. Lauzon, S. Thibault, F. Ouellette, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD29.

Ragdale, C. M.

M. C. Farries, C. M. Ragdale, D. C. Reid, Electron. Lett. 28, 487 (1992).
[CrossRef]

Reid, D. C.

M. C. Farries, C. M. Ragdale, D. C. Reid, Electron. Lett. 28, 487 (1992).
[CrossRef]

Sugden, K.

K. Sugden, I. Bennion, A. Molony, N. J. Copner, Electron. Lett. 30, 440 (1994).
[CrossRef]

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, Electron. Lett. 29, 1659 (1993).
[CrossRef]

Takiguchi, K.

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

Theriault, S.

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

Thibault, S.

J. Martin, J. Lauzon, S. Thibault, F. Ouellette, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD29.

Watanabe, A.

Zhang, Q.

Q. Zhang, Ph.D. dissertation (Brown University, Providence, R.I., April1994).

Appl. Opt. (1)

Electron. Lett. (3)

M. C. Farries, C. M. Ragdale, D. C. Reid, Electron. Lett. 28, 487 (1992).
[CrossRef]

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, Electron. Lett. 29, 1659 (1993).
[CrossRef]

K. Sugden, I. Bennion, A. Molony, N. J. Copner, Electron. Lett. 30, 440 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Other (3)

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD2.

J. Martin, J. Lauzon, S. Thibault, F. Ouellette, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), postdeadline paper PD29.

Q. Zhang, Ph.D. dissertation (Brown University, Providence, R.I., April1994).

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Figures (5)

Fig. 1
Fig. 1

Geometrical relationship between a phase mask and the resulting grating periodicity of nonlinearly chirped gratings on curved fibers.

Fig. 2
Fig. 2

Typical curve functions for generating various orders of chirping. The curve functions are normalized by a factor of L for linear and square-root chirping and by r for quadratic chirping.

Fig. 3
Fig. 3

Reflective spectrum of a linearly chirped grating. Dots, experimental; solid curve, numerical solution by the choice of γ = 1, Δn = 5 × 10−4, and α = 4.26 × 10−3.

Fig. 4
Fig. 4

Reflective spectrum of a grating written on a circular looped fiber with a 2.4-cm radius. Dots, experimental; solid curve, numerical solution by the choice of γ = 2, Δn = 3.4 × 10−4, and r = 2.4 cm.

Fig. 5
Fig. 5

Reflective spectrum of a square-root chirped grating. Dots, experimental; solid curve, numerical solution by the choice of γ = 1/2, Δn = 3.1 × 10−4, and α = 3.17 × 10−3.

Tables (1)

Tables Icon

Table 1 Curve Functions for Various Chirping

Equations (4)

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Λ = Λ 0 [ 1 + f ( z ) 2 ] 1 / 2 ,
Λ ( z ) = Λ 0 [ 1 + α ( z L ) γ ] .
f ( z ) = L α [ 1 2 ( 1 + Z ) Z ( Z + 2 ) - ln ( Z + 2 + Z ) + ln 2 ] ,
Λ ( z ) = Λ 0 cos θ ,

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