Abstract

We discuss the analytical expressions that describe the displacement field resulting from the inscription of a Bragg grating in a Ge-doped optical fiber. The equations stem from a phenomenological approach and allow calculation of the induced stresses. Our model provides an efficient tool to analyze the effects of radiation-induced density variations on the properties of fiber Bragg gratings.

© 1999 Optical Society of America

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References

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  1. D. P. Hand and P. St. J. Russell, Opt. Lett. 15, 102 (1990).
    [CrossRef]
  2. J. P. Bernardin and N. M. Lawandy, Opt. Commun. 79, 194 (1990).
    [CrossRef]
  3. M. G. Sceats, G. R. Atkins, and S. B. Poole, Annu. Rev. Mater. Sci. 23, 381 (1993).
    [CrossRef]
  4. B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
    [CrossRef]
  5. M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
    [CrossRef]
  6. P. Y. Fonjallaz, H. G. Limberger, R. P. Salathé, F. Cochet, and B. Leuenberger, Opt. Lett. 20, 1346 (1995).
    [CrossRef] [PubMed]
  7. B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, J. Phys. D 29, 1842 (1996).
    [CrossRef]
  8. S. Chen, B. Liu, J. Sirkis, M. K. Park, and S. Singh, Proc. SPIE 3746, 478 (1999).
  9. J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
    [CrossRef]
  10. J. D. Eshelby, in Solid State Physics, F. Seitz and D. Turnbull, eds. (Academic, New York, 1956), Vol. 3, p. 79.
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    [CrossRef]

1999 (2)

S. Chen, B. Liu, J. Sirkis, M. K. Park, and S. Singh, Proc. SPIE 3746, 478 (1999).

J. Canning and M. Åslund, Opt. Lett. 24, 463 (1999).
[CrossRef]

1997 (1)

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

1996 (1)

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, J. Phys. D 29, 1842 (1996).
[CrossRef]

1995 (3)

P. Y. Fonjallaz, H. G. Limberger, R. P. Salathé, F. Cochet, and B. Leuenberger, Opt. Lett. 20, 1346 (1995).
[CrossRef] [PubMed]

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
[CrossRef]

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

1993 (1)

M. G. Sceats, G. R. Atkins, and S. B. Poole, Annu. Rev. Mater. Sci. 23, 381 (1993).
[CrossRef]

1990 (2)

D. P. Hand and P. St. J. Russell, Opt. Lett. 15, 102 (1990).
[CrossRef]

J. P. Bernardin and N. M. Lawandy, Opt. Commun. 79, 194 (1990).
[CrossRef]

Albert, J.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
[CrossRef]

Åslund, M.

Atkins, G. R.

M. G. Sceats, G. R. Atkins, and S. B. Poole, Annu. Rev. Mater. Sci. 23, 381 (1993).
[CrossRef]

Bayon, J. F.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, J. Phys. D 29, 1842 (1996).
[CrossRef]

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

Bernage, P.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

Bernardin, J. P.

J. P. Bernardin and N. M. Lawandy, Opt. Commun. 79, 194 (1990).
[CrossRef]

Bilodeau, F.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
[CrossRef]

Canning, J.

Chen, S.

S. Chen, B. Liu, J. Sirkis, M. K. Park, and S. Singh, Proc. SPIE 3746, 478 (1999).

Cochet, F.

Cordier, P.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

Delevaque, E.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

Dong, L.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

Douay, M.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, J. Phys. D 29, 1842 (1996).
[CrossRef]

Eshelby, J. D.

J. D. Eshelby, in Solid State Physics, F. Seitz and D. Turnbull, eds. (Academic, New York, 1956), Vol. 3, p. 79.

Fonjallaz, P. Y.

Guenot, P.

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

Hand, D. P.

Hill, K. O.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
[CrossRef]

Johnson, D. C.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
[CrossRef]

Lawandy, N. M.

J. P. Bernardin and N. M. Lawandy, Opt. Commun. 79, 194 (1990).
[CrossRef]

Leuenberger, B.

Limberger, H. G.

Liu, B.

S. Chen, B. Liu, J. Sirkis, M. K. Park, and S. Singh, Proc. SPIE 3746, 478 (1999).

Malo, B.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
[CrossRef]

Niay, P.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, J. Phys. D 29, 1842 (1996).
[CrossRef]

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

Park, M. K.

S. Chen, B. Liu, J. Sirkis, M. K. Park, and S. Singh, Proc. SPIE 3746, 478 (1999).

Poignant, H.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

Poole, S. B.

M. G. Sceats, G. R. Atkins, and S. B. Poole, Annu. Rev. Mater. Sci. 23, 381 (1993).
[CrossRef]

Poumellec, B.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, J. Phys. D 29, 1842 (1996).
[CrossRef]

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

Riant, I.

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

Russell, P. St. J.

Salathé, R. P.

Sansonetti, P.

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

Sceats, M. G.

M. G. Sceats, G. R. Atkins, and S. B. Poole, Annu. Rev. Mater. Sci. 23, 381 (1993).
[CrossRef]

Singh, S.

S. Chen, B. Liu, J. Sirkis, M. K. Park, and S. Singh, Proc. SPIE 3746, 478 (1999).

Sirkis, J.

S. Chen, B. Liu, J. Sirkis, M. K. Park, and S. Singh, Proc. SPIE 3746, 478 (1999).

Taunnay, T.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

Thériault, S.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
[CrossRef]

Xie, W. X.

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

M. G. Sceats, G. R. Atkins, and S. B. Poole, Annu. Rev. Mater. Sci. 23, 381 (1993).
[CrossRef]

Appl. Phys. Lett. (1)

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, Appl. Phys. Lett. 67, 3529 (1995).
[CrossRef]

J. Lightwave Technol. (1)

M. Douay, W. X. Xie, T. Taunnay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, and E. Delevaque, J. Lightwave Technol. 15, 1329 (1997).
[CrossRef]

J. Phys. D (1)

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, J. Phys. D 29, 1842 (1996).
[CrossRef]

Opt. Commun. (1)

J. P. Bernardin and N. M. Lawandy, Opt. Commun. 79, 194 (1990).
[CrossRef]

Opt. Lett. (3)

Opt. Mater. (1)

B. Poumellec, P. Guenot, I. Riant, P. Sansonetti, P. Niay, P. Bernage, and J. F. Bayon, Opt. Mater. 4, 441 (1995).
[CrossRef]

Proc. SPIE (1)

S. Chen, B. Liu, J. Sirkis, M. K. Park, and S. Singh, Proc. SPIE 3746, 478 (1999).

Other (1)

J. D. Eshelby, in Solid State Physics, F. Seitz and D. Turnbull, eds. (Academic, New York, 1956), Vol. 3, p. 79.

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Figures (2)

Fig. 1
Fig. 1

Computed distribution of the stress induced by a grating inscription with a period of 0.4 µm in a fiber with a 4.0µm core radius: (a) axial stress σzzr,z, (b) radial stress σrrr,z, (c) tangential stress σφφr,z.

Fig. 2
Fig. 2

Computed axial stress distribution σzzr,z induced by a grating inscription with a period equal to the fiber-core radius 4.0 µm.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Δρ/ρ=-fDr,
μ2u+λ+μ·u=KfDr,K=λ+μ,
λ+2 µ2Φ-Kfr+μ2w+λ+μ·w=0.
fz=NzΘR-r,
Nz=½N01+b cosaz,  a=2π/Λ,
Φr,z=-γFr+b cosazPr,γ=N0K/2λ+2µ
Pr=a-2-R/aI0arK1aRr<RR/aK0arI1aRr>R,Fr=R0dαα-2J0αrJ1αR,

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