Abstract

This study performs experimental and numerical investigations into the power losses induced in bent, elongated polymer optical fibers (POFs). The theoretical analysis is based on a three-dimensional elastic–plastic finite-element model and makes the assumption of a planar waveguide. The finite-element model is used to calculate the deformation of the elongated POFs such that the power loss can be analytically derived. The effect of bending on the power loss is examined by considering seven different bend radii ranging from 10 to 50  mm. The results show that bending and elongation have a significant effect on the power loss in POFs. The contribution of skew rays to the overall power loss in bent, elongated POFs is not obvious at large radii of curvature but becomes more significant as the radius is reduced.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. A. W. Snyder and D. J. Mitchell, "Bending losses of multimode optical fibres," Electron. Lett. 10, 11-12 (1974).
    [CrossRef]

2006

2005

2004

M. A. Losada, J. Mateo, I. Garces, J. Zubia, J. A. Casao, and P. Pérez-Vela, "Analysis of strained plastic optical fibers," IEEE Photon. Technol. Lett. 16, 1513-1515 (2004).
[CrossRef]

2003

C. P. Achenbach and J. H. Cobb, "Computational studies of light acceptance and propagation in straight and curved multimode active fibres," J. Opt. A: Pure Appl. Opt. 5, 239-249 (2003).
[CrossRef]

G. Durana, J. Zubia, J. Arrue, G. Aldabaldetreku, and J. Mateo, "Dependence of bending losses on cladding thickness in plastic optical fibers," Appl. Opt. 42, 997-1002 (2003).
[CrossRef] [PubMed]

2002

H. Tai and R. Rogowski, "Optical anisotropy induced by torsion and bending in an optical fiber," Opt. Fiber Technol. 8, 162-169 (2002).
[CrossRef]

1999

A. E. Akinay and T. Tincer, "γ-irradiated poly(tetrafluoroethylene) particle-filled low-density polyethylene. II. UV stability of LDPE in the presence of 2°-PTFE powder and silane coupling agents," J. Appl. Polym. Sci. 74, 877-888 (1999).
[CrossRef]

1998

J. Arrue, J. Zubia, G. Fuster, and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
[CrossRef]

1997

J. Zubia and J. Arrue, "Theoretical analysis of the model dispersion induced by stresses in a multimode plastic optical fiber," IEE Proc. Optoelectron. 144, 397-403 (1997).
[CrossRef]

A. Oshima, S. Ikeda, T. Seguchi, and Y. Tabata, "Improvement of radiation resistance for polytetrafluoroethylene (PTFE) by radiation crosslinking," Radiat. Phys. Chem. 49, 279-284 (1997).
[CrossRef]

1996

J. Arrue and J. Zubia, "Analysis of the decrease in attenuation achieved by poperly bending plastic optical fibres," IEE Proc. Optoelectron. 143, 135-138 (1996).
[CrossRef]

1990

1979

C. Winkler, J. D. Love, and A. K. Ghatak, "Loss calculations in bent multimode optical waveguides," Opt. Quantum Electron. 11, 173-183 (1979).
[CrossRef]

1974

A. W. Snyder and D. J. Mitchell, "Bending losses of multimode optical fibres," Electron. Lett. 10, 11-12 (1974).
[CrossRef]

Appl. Opt.

Electron. Lett.

A. W. Snyder and D. J. Mitchell, "Bending losses of multimode optical fibres," Electron. Lett. 10, 11-12 (1974).
[CrossRef]

IEE Proc. Optoelectron.

J. Arrue, J. Zubia, G. Fuster, and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
[CrossRef]

J. Zubia and J. Arrue, "Theoretical analysis of the model dispersion induced by stresses in a multimode plastic optical fiber," IEE Proc. Optoelectron. 144, 397-403 (1997).
[CrossRef]

J. Arrue and J. Zubia, "Analysis of the decrease in attenuation achieved by poperly bending plastic optical fibres," IEE Proc. Optoelectron. 143, 135-138 (1996).
[CrossRef]

IEEE Photon. Technol. Lett.

M. A. Losada, J. Mateo, I. Garces, J. Zubia, J. A. Casao, and P. Pérez-Vela, "Analysis of strained plastic optical fibers," IEEE Photon. Technol. Lett. 16, 1513-1515 (2004).
[CrossRef]

J. Appl. Polym. Sci.

A. E. Akinay and T. Tincer, "γ-irradiated poly(tetrafluoroethylene) particle-filled low-density polyethylene. II. UV stability of LDPE in the presence of 2°-PTFE powder and silane coupling agents," J. Appl. Polym. Sci. 74, 877-888 (1999).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

C. P. Achenbach and J. H. Cobb, "Computational studies of light acceptance and propagation in straight and curved multimode active fibres," J. Opt. A: Pure Appl. Opt. 5, 239-249 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Fiber Technol.

H. Tai and R. Rogowski, "Optical anisotropy induced by torsion and bending in an optical fiber," Opt. Fiber Technol. 8, 162-169 (2002).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

C. Winkler, J. D. Love, and A. K. Ghatak, "Loss calculations in bent multimode optical waveguides," Opt. Quantum Electron. 11, 173-183 (1979).
[CrossRef]

Radiat. Phys. Chem.

A. Oshima, S. Ikeda, T. Seguchi, and Y. Tabata, "Improvement of radiation resistance for polytetrafluoroethylene (PTFE) by radiation crosslinking," Radiat. Phys. Chem. 49, 279-284 (1997).
[CrossRef]

Other

ABAQUS User's Manual, Version 6.5 (Hibbitt, Karlsson and Sorensen, Inc., 2005).

W. D. Callister, Materials Science and Engineering: An Introduction (Wiley, 2000), Appendix B.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983), Chap. 9.

W. Daum, J. Krauser, P. E. Zamzow, and O. Ziemann, POF--Polymer Optical Fibers for Data Communication (Springer, 2002), pp. 338-339.

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Figures (13)

Fig. 1
Fig. 1

Variation of the power ratio in the bent POF.

Fig. 2
Fig. 2

Ray path in the straight region of the elongated POF core.

Fig. 3
Fig. 3

Ray paths in the bent and elongated POF cores at arbitrary angular position ξ.

Fig. 4
Fig. 4

Experimental setup used to measure power losses in the bent and elongated POF.

Fig. 5
Fig. 5

Geometric configuration of the bent POF.

Fig. 6
Fig. 6

Finite-element model of the bent POF.

Fig. 7
Fig. 7

Load–displacement relationship for the POF subjected to bending and elongation. FEM, finite-element method.

Fig. 8
Fig. 8

Experimental and numerical evidence of necking deformation.

Fig. 9
Fig. 9

Variation of power ratio, P o u t / P i n , with fiber elongation, δ / l .

Fig. 10
Fig. 10

Power losses in the bent and elongated POF.

Fig. 11
Fig. 11

Variation of axial strain, ε z , along the straight region of the fiber core for various bend radii.

Fig. 12
Fig. 12

Variation of tangential strain, ε z , along the curved region of the fiber core for various bend radii.

Fig. 13
Fig. 13

Variation of power loss ratio, P o u t / P i n , with elongation. Experimental results, solid curves; finite-element model, symbols.

Tables (3)

Tables Icon

Table 1 Mechanical Properties of POF Used in the Finite-Element Model

Tables Icon

Table 2 Deformation Results Obtained from Elastic–Plastic Finite-Element Simulations for Bend Radius of R = 50 mm

Tables Icon

Table 3 Deformation Results Obtained from Elastic–Plastic Finite-Element Simulations for Bend Radius of R = 10 mm

Equations (93)

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

50   mm
P o u t / P i n
P o u t P i n = ( P B P A ) L 1 ( P C P B ) R ( P D P C ) L 2 ,
( P B / P A ) L 1
( P D / P C ) L 2
( P C / P B ) R
P ( z m ) = P ( 0 ) exp ( 0 z m T cot α i ( z m ) D c o d z ) ,
P ( 0 )
D c o
α i ( z m )
z m
T = 4 n c o n c l cos α i ( z m ) ( 1 sin 2 α i ( z m ) sin 2 α c ) 1 / 2 [ n c o cos α i ( z m ) + n c l ( 1 sin 2 α i ( z m ) sin 2 α c ) 1 / 2 ] 2 ,
n c o
n c l
α c
sin α c = n c l n c o .
z m
α i ( z m )
α i ( 0 )
cos α i ( z m ) = ( D c o D m ) cos α i ( 0 ) = ( D c o D c o 2 z m tan α m ) cos α i ( 0 ) ,
α m
D m
z m
P ( 0 )
P ( ξ ) = P ( 0 ) exp ( α ξ ) .
α = i = 1 N ln ( 1 T i ) i = 1 N Δ ξ i ,
Δ ξ i
T i
T i
T r = 4 cos α i ( ξ ) [ cos 2 α i ( ξ ) cos 2 α c ] 1 / 2 [ cos α i ( ξ ) + ( cos 2 α i ( ξ ) cos 2 α c ) 1 / 2 ] 2 .
O
R i n
R o u t
R o u t
O Q ¯
D m
Δ O P Q
R i n sin [ α i ( ξ ) + θ n ] = R o u t sin α i ( 0 ) ,
R i n sin [ α i ( ξ ) θ n ] = R o u t sin α i ( 0 ) ,
α i ( ξ )
α i ( 0 )
Δ O O Q
θ n
θ n = cos 1 ( R o u t 2 + R o u t 2 n 2 2 R o u t R o u t ) .
α i ( ξ )
α i ( ξ ) = sin 1 [ ( R i n R i n + D m ) sin α i ( 0 ) ] θ n ,
α i ( ξ ) = sin 1 [ ( R i n R i n + D m ) sin α i ( 0 ) ] + θ n .
P ( 0 ) = P i n
P ( ξ ) = P o u t
P o u t / P i n
P o u t P i n = ( 1 T i ) N ,
( 660   nm )
2.2   mm
1   mm
0 .98   mm
n c o = 1.492
n c l = 1.402
100 200   mm
100 mm / min
100   mm
R = 10
50   mm
50   mm
R = 50   mm
50   mm
100   mm
α i ( 0 )
R o u t ( ξ )
ε z
O A
δ = 50
ε z
O
O
θ = 0 °
α i ( ξ )
R = 50
R = 10   mm
P o u t / P i n
R > 30   mm
R = 10   mm
50   mm
R o u t
R o u t
R i n
R o u t
R o u t
R i n
P o u t / P i n
δ / l
ε z
ε z
P o u t / P i n

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