Abstract

We present a theoretical analysis of the mode coupling effects at a microbend along a graded-index (GI) multimode fiber (MMF). By matching the incident and excited mode fields at the microbend, we obtain the coupling coefficients among the guided modes at different microbending conditions. The theoretical results compare well with the experimental results from near-field measurements on a GI MMF subject to microbending. The usefulness of our theory is demonstrated with two applications: (i) an explanation of the operation principle of a wavelength-switchable fiber laser that contains a fiber Bragg grating in a GI MMF and (ii) quantification of the function of a microbend-based mode scrambler.

© 2005 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  15. T. Mizunami, T. V. Djambova, T. Niiho, S. Gupta, “Bragg gratings in multimode and few-mode optical fibers,” J. Lightwave Technol. 18, 230–235 (2000).
    [CrossRef]

2005 (1)

L. Su, C. Lu, “Wavelength-switching fiber laser based on multimode fiber Bragg gratings,” Electron. Lett. 41, 11–13 (2005).
[CrossRef]

2000 (1)

1997 (1)

1995 (1)

J. W. Berthold, “Historical review of microbend fiber-optic sensors,” J. Lightwave Technol. 13, 1193–1199 (1995).
[CrossRef]

1987 (2)

J. W. Berthold, W. L. Ghering, D. Varshneya, “Design and characterization of a high-temperature fiber-optic pressure transducer,” J. Lightwave Technol. LT-5, 870–876 (1987).
[CrossRef]

N. Lagakos, J. H. Cole, J. A. Bucaro, “Microbend fiber-optic sensor,” Appl. Opt. 26, 2171–2180 (1987).
[CrossRef] [PubMed]

1986 (2)

1984 (1)

H. F. Taylor, “Bending effects in optical fibers,” J. Lightwave Technol. LT-2, 617–628 (1984).
[CrossRef]

1980 (2)

1977 (1)

1975 (1)

1974 (1)

1973 (1)

Berthold, J. W.

J. W. Berthold, “Historical review of microbend fiber-optic sensors,” J. Lightwave Technol. 13, 1193–1199 (1995).
[CrossRef]

J. W. Berthold, W. L. Ghering, D. Varshneya, “Design and characterization of a high-temperature fiber-optic pressure transducer,” J. Lightwave Technol. LT-5, 870–876 (1987).
[CrossRef]

Blake, J. N.

Bucaro, J. A.

Cole, J. H.

Djambova, T. V.

Donlagic, D.

Field, J. N.

Ghering, W. L.

J. W. Berthold, W. L. Ghering, D. Varshneya, “Design and characterization of a high-temperature fiber-optic pressure transducer,” J. Lightwave Technol. LT-5, 870–876 (1987).
[CrossRef]

Gupta, S.

Halme, S. J.

Kim, B. Y.

Lagakos, N.

Lu, C.

L. Su, C. Lu, “Wavelength-switching fiber laser based on multimode fiber Bragg gratings,” Electron. Lett. 41, 11–13 (2005).
[CrossRef]

Mizunami, T.

Niiho, T.

Olshansky, R.

Saijonmaa, J.

Sharma, A. B.

Shaw, H. J.

Siegman, A. E.

Su, L.

L. Su, C. Lu, “Wavelength-switching fiber laser based on multimode fiber Bragg gratings,” Electron. Lett. 41, 11–13 (2005).
[CrossRef]

Taylor, H. F.

Varshneya, D.

J. W. Berthold, W. L. Ghering, D. Varshneya, “Design and characterization of a high-temperature fiber-optic pressure transducer,” J. Lightwave Technol. LT-5, 870–876 (1987).
[CrossRef]

Zauderer, E.

Zavrsnik, M.

Appl. Opt. (6)

Electron. Lett. (1)

L. Su, C. Lu, “Wavelength-switching fiber laser based on multimode fiber Bragg gratings,” Electron. Lett. 41, 11–13 (2005).
[CrossRef]

J. Lightwave Technol. (4)

T. Mizunami, T. V. Djambova, T. Niiho, S. Gupta, “Bragg gratings in multimode and few-mode optical fibers,” J. Lightwave Technol. 18, 230–235 (2000).
[CrossRef]

H. F. Taylor, “Bending effects in optical fibers,” J. Lightwave Technol. LT-2, 617–628 (1984).
[CrossRef]

J. W. Berthold, W. L. Ghering, D. Varshneya, “Design and characterization of a high-temperature fiber-optic pressure transducer,” J. Lightwave Technol. LT-5, 870–876 (1987).
[CrossRef]

J. W. Berthold, “Historical review of microbend fiber-optic sensors,” J. Lightwave Technol. 13, 1193–1199 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Lett. (2)

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Figures (8)

Fig. 1
Fig. 1

(a) A periodic microbend with a pitch Λ and a microbending angle θ. (b) Model of a single microbend showing the local coordinate systems.

Fig. 2
Fig. 2

Dependence of the normalized modal power on the microbending displacement δ for (a) a single microbend and (b) a three-tooth microbend deformer with a pitch of 1 mm, when the input light contains only the HG00 mode. (c) Dependence of the microbending displacement δ required for dominantly coupling to a particular mode on the number of microbends.

Fig. 3
Fig. 3

Dependence of the normalized modal power on the microbending displacement δ for a single microbend when the input light contains only the HG30 mode.

Fig. 4
Fig. 4

Experimental setup for examining the near-field pattern from a GI MMF.

Fig. 5
Fig. 5

Near-field patterns from the GI MMF measured at δ = (a) 0, (b) 10, (c) 15, (d) 19, (e) 23, and (f) δ = 30 µm.

Fig. 6
Fig. 6

Dependence of the mode order p of the dominantly coupled mode on the microbending displacement when only the HG00 mode is launched into a three-tooth microbending deformer with a pitch of 1 mm.

Fig. 7
Fig. 7

Variation of the modal power distribution with the number of microbends for δ = (a) 4, (b) 8, and (c) δ = 12 µm. (d) The corresponding power losses.

Fig. 8
Fig. 8

Reflection spectra of the fiber subject to microbending measured with a FBG introduced at the other end of the fiber for δ = (a) 0, (b) 16, (c) 22, and (d) 28 µm.

Equations (23)

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U m ( x , y , z ) = a m u m ( x , y ) exp ( i ω t i β m z ) ,
+ + u k · u m * d x d y = { 0 , k m 1 , k = m .
x ( n ) = x ( n + 1 ) = X cos θ ,
z ( n ) = X sin θ ,
z ( n + 1 ) = X sin θ .
U ( n ) ( X cos θ , y , X sin θ ) = U ( n + 1 ) ( X cos θ , y , X sin θ ) .
m = 1 N a m ( n ) u m ( X cos θ , y ) exp ( i ω t + i β m X sin θ ) = k = 1 N a k ( n + 1 ) u k ( X cos θ , y ) exp ( i ω t i β k X sin θ ) .
a k ( n + 1 ) = m = 1 N a m ( n ) u m ( x , y ) u k * ( x , y ) × exp ( i γ m , k x ) d x d y ,
γ m , k = ( β m + β k ) tan θ .
c m , k = u m ( x , y ) u k * ( x , y ) exp ( i γ m , k x ) d x d y .
M n + 1 ( θ ) = [ c 00 c 01 c 0 , N 1 c 10 c 11 c 1 , N 1 c N 1 , 0 c N 1 , 1 c N 1 , N 1 ] .
A ( n + 1 ) = M n + 1 ( θ ) A ( n ) ,
A ( n + 1 ) = M ( n + 1 ) ( θ ) M n ( θ ) M 2 ( θ ) M 1 ( θ ) A ( 0 ) .
ψ p q ( x , y , z ) = [ ω 0 2 π 2 ( p + q 1 ) p ! q ! ] 1 / 2 H p ( 2 x ω 0 ) H q ( 2 y ω 0 ) × exp [ ( x 2 + y 2 ) / ω 0 2 ] exp ( i β p , q z ) ,
ω 0 = 2 a / [ k n co ( 2 Δ ) 1 / 2 ] ,
M = N = 1 2 a 2 k 2 n co 2 Δ .
β m = n co k [ 1 2 Δ ( m / M ) ] 1 / 2 .
u m ( x , y ) = [ ω 0 2 π 2 ( p + q 1 ) p ! q ! ] 1 / 2 H p ( 2 x ω 0 ) H q ( 2 y ω 0 ) × exp [ ( x 2 + y 2 ) / ω 0 2 ] .
P g ( n ) = ( A ( n ) ) · [ ( A ( n ) ) * ] T = | a 0 ( n ) | 2 + | a 1 ( n ) | 2 + + | a N 1 ( n ) | 2 .
A ( 0 ) = [ 1 , 0 , , 0 ] T .
A ( 1 ) = M ( θ ) · A ( 0 ) = [ c 0 , 0 , c 0 , 1 , , c 0 , M 1 ] T ,
c 0 , k = 2 ω 0 2 π [ 2 ( p + q ) p ! q ! ] 1 / 2 H p ( 2 x ω 0 ) × exp ( 2 x 2 ω 0 2 + i γ 0 , k x ) d x H q ( 2 y ω 0 ) × exp ( 2 y 2 ω 0 2 ) d y ,
c 0 , k = ( 2 p · p ! ) 1 / 2 ( i γ ) p exp ( γ 2 4 ) .

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