Abstract

This Letter presents a simple mathematical model developed from coupled-mode theory to describe the relationship between Bragg transmission loss (BTL), grating length, coupling coefficients, and bending loss in a bent fiber Bragg grating. In our investigation, the finding indicates that the decrement of BTL can be attributed to the increasing bending loss and degradation of both dc and ac coupling coefficients as the bending radius decreases. Besides, the center wavelength shifts as a result of coupling coefficients degradation. The validity of the proposed model is supported by experimental result.

© 2013 Optical Society of America

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References

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  1. B. O. Guan, L. Jin, Y. Zhang, and H. Y. Tam, J. Lightwave Technol. 30, 1097 (2012).
    [CrossRef]
  2. K. S. Lim, H. Z. Yang, W. Y. Chong, Y. K. Cheong, C. H. Lim, N. M. Ali, and H. Ahmad, Opt. Express 21, 2551 (2013).
    [CrossRef]
  3. H. Z. Yang, K. S. Lim, X. G. Qiao, W. Y. Chong, Y. K. Cheong, W. H. Lim, W. S. Lim, and H. Ahmad, Opt. Express 21, 14808 (2013).
    [CrossRef]
  4. T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
    [CrossRef]
  5. Y. Liu, L. Wei, and J. W. Y. Lit, Appl. Opt. 46, 6770 (2007).
    [CrossRef]
  6. J. Saijonmaa and D. Yevick, J. Opt. Soc. Am. 73, 1785 (1983).
    [CrossRef]
  7. D. Marcuse, J. Opt. Soc. Am. 66, 311(1976).
    [CrossRef]
  8. H. Renner, J. Lightwave Technol. 10, 544 (1992).
    [CrossRef]
  9. A. Rauf, J. Zhao, B. Jiang, Y. Jiang, and W. Jiang, Opt. Lett. 38, 214 (2013).
    [CrossRef]
  10. S. A. Wade, D. F. Robertson, A. C. Thompson, and P. R. Stoddart, Electron. Lett. 47, 558 (2011).
    [CrossRef]
  11. A. C. Thompson, P. J. Cadusch, D. F. Robertson, P. R. Stoddart, and S. A. Wade, J. Lightwave Technol. 30, 3500 (2012).
    [CrossRef]
  12. D. Marcuse, J. Opt. Soc. Am. 66, 216 (1976).
    [CrossRef]
  13. W. A. Gambling, H. Matsumura, C. M. Ragdale, and R. A. Sammut, IEE J. MicroOpt. Acoust. 2, 134 (1978).
    [CrossRef]

2013 (3)

2012 (2)

2011 (1)

S. A. Wade, D. F. Robertson, A. C. Thompson, and P. R. Stoddart, Electron. Lett. 47, 558 (2011).
[CrossRef]

2007 (1)

1997 (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

1992 (1)

H. Renner, J. Lightwave Technol. 10, 544 (1992).
[CrossRef]

1983 (1)

1978 (1)

W. A. Gambling, H. Matsumura, C. M. Ragdale, and R. A. Sammut, IEE J. MicroOpt. Acoust. 2, 134 (1978).
[CrossRef]

1976 (2)

Ahmad, H.

Ali, N. M.

Cadusch, P. J.

Cheong, Y. K.

Chong, W. Y.

Erdogan, T.

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Gambling, W. A.

W. A. Gambling, H. Matsumura, C. M. Ragdale, and R. A. Sammut, IEE J. MicroOpt. Acoust. 2, 134 (1978).
[CrossRef]

Guan, B. O.

Jiang, B.

Jiang, W.

Jiang, Y.

Jin, L.

Lim, C. H.

Lim, K. S.

Lim, W. H.

Lim, W. S.

Lit, J. W. Y.

Liu, Y.

Marcuse, D.

Matsumura, H.

W. A. Gambling, H. Matsumura, C. M. Ragdale, and R. A. Sammut, IEE J. MicroOpt. Acoust. 2, 134 (1978).
[CrossRef]

Qiao, X. G.

Ragdale, C. M.

W. A. Gambling, H. Matsumura, C. M. Ragdale, and R. A. Sammut, IEE J. MicroOpt. Acoust. 2, 134 (1978).
[CrossRef]

Rauf, A.

Renner, H.

H. Renner, J. Lightwave Technol. 10, 544 (1992).
[CrossRef]

Robertson, D. F.

A. C. Thompson, P. J. Cadusch, D. F. Robertson, P. R. Stoddart, and S. A. Wade, J. Lightwave Technol. 30, 3500 (2012).
[CrossRef]

S. A. Wade, D. F. Robertson, A. C. Thompson, and P. R. Stoddart, Electron. Lett. 47, 558 (2011).
[CrossRef]

Saijonmaa, J.

Sammut, R. A.

W. A. Gambling, H. Matsumura, C. M. Ragdale, and R. A. Sammut, IEE J. MicroOpt. Acoust. 2, 134 (1978).
[CrossRef]

Stoddart, P. R.

A. C. Thompson, P. J. Cadusch, D. F. Robertson, P. R. Stoddart, and S. A. Wade, J. Lightwave Technol. 30, 3500 (2012).
[CrossRef]

S. A. Wade, D. F. Robertson, A. C. Thompson, and P. R. Stoddart, Electron. Lett. 47, 558 (2011).
[CrossRef]

Tam, H. Y.

Thompson, A. C.

A. C. Thompson, P. J. Cadusch, D. F. Robertson, P. R. Stoddart, and S. A. Wade, J. Lightwave Technol. 30, 3500 (2012).
[CrossRef]

S. A. Wade, D. F. Robertson, A. C. Thompson, and P. R. Stoddart, Electron. Lett. 47, 558 (2011).
[CrossRef]

Wade, S. A.

A. C. Thompson, P. J. Cadusch, D. F. Robertson, P. R. Stoddart, and S. A. Wade, J. Lightwave Technol. 30, 3500 (2012).
[CrossRef]

S. A. Wade, D. F. Robertson, A. C. Thompson, and P. R. Stoddart, Electron. Lett. 47, 558 (2011).
[CrossRef]

Wei, L.

Yang, H. Z.

Yevick, D.

Zhang, Y.

Zhao, J.

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Figures (5)

Fig. 1.
Fig. 1.

Total losses of three different fibers bent into overhand knot structures. The experimental results are in good agreement with the calculation using Eq. (7).

Fig. 2.
Fig. 2.

(a) Transmission spectra of a grating written in SMF-28 fiber, at different bending radii. The BTL is as defined in the graph. (b) The relationship between BTL and bending radius.

Fig. 3.
Fig. 3.

Relationship between BTL and bending loss 2αBC. The plot shows experimental results for three FBGs (written in SMF-28 fibers) with different κ. The rate of decrement in BTL with increasing bending loss is higher for FBG with larger κ.

Fig. 4.
Fig. 4.

(a) Transmission spectra of 2 cm long grating written in FUD-2300 fibers. (b) Overlaid graph of BTL (black) and center wavelength (blue) against bending radius.

Fig. 5.
Fig. 5.

(a) Values of the LHS (black) and RHS (blue) of Eq. (16) calculated based on the data of the center wavelength shift and BTL variation with varying bending radius. (b) The characteristics of the relative coupling factor with bending radius. Gratings written in FUD-2300 fibers are used.

Equations (17)

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2αB=12(πγ3R)1/2κ2V2K12(γa)exp(2γ3R3β02),
2αBC=2αB2(Z3Z2)1/2(Z3+Z2)(Z3Z2)cos(2Θ0),
Zqk2nq2(1+2b/R)β02,q=2,3,
Θ0=γ3R3k2n22(RcR1)3/2,
Rc=2k2n22b/γ2.
Γ=2PR+2αBCL,
Γ4παBCR.
dA(z)dz=(α+jσ^)A(z)+jκB(z),
dB(z)dz=(αjσ^)B(z)jκ*A(z),
ρ=B(0)/A(0)=jκsinh(γLg)γcosh(γLg)ϕsinh(γLg),
τ=A(L)/A(0)=γγcosh(γLg)ϕsinh(γLg),
λcenter=(1+εδn¯/neff)λB.
τ(λcenter)=γγcosh(γLg)+αBCsinh(γLg).
τbackground=exp(αBCLg).
BTL=20log10(τbackground/τ(λcenter))=20log10[exp(αBCLg)(cosh(γLg)+αBCsinh(γLg)γ)].
λcenter(R=)=(1+δn¯/neff)λB.
1η=(1ε)δn¯/neff,

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