Abstract

By using the power flow equation, we have examined the state of mode coupling in strained and unstrained step-index glass optical fibers. Strained fibers show stronger mode coupling than their unstrained counterparts of the same type. As a result, the coupling length where equilibrium mode distribution is achieved and the length of fiber required for achieving the steady-state mode distribution are shorter for strained than for unstrained fibers.

© 2010 Optical Society of America

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References

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  1. W. Daum, J. Krauser, P. E. Zamzow, and O. Ziemann, POF-Polymer Optical Fibers for Data Communications (Springer, 2002).
  2. J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEE Proc. Optoelectron. 145, 313–318 (1998).
    [CrossRef]
  3. M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
    [CrossRef]
  4. L. Jeunhomme and J. P. Pocholle, “Experimental determination of the radiation pattern of optical fibres,” Opt. Commun. 12, 89–92 (1974).
    [CrossRef]
  5. M. Eve and J. H. Hannay, “Ray theory and random mode coupling in an optical fibre waveguide, I,” Opt. Quantum Electron. 8, 503–508 (1976).
    [CrossRef]
  6. J. Arrue, G. Aldabaldetreku, G. Durana, J. Zubía, I. Garcés, and F. Jiménez, “Design of mode scramblers for step-index and graded-index plastic optical fibers,” J. Lightwave Technol. 23, 1253–1260 (2005).
    [CrossRef]
  7. W. A. Gambling, D. N. Payne, and H. Matsumura, “Mode conversion coefficients in optical fibers,” Appl. Opt. 14, 1538–1542 (1975).
    [CrossRef] [PubMed]
  8. J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEEE Proc. Optoelectron. 145, 313–318 (1998).
    [CrossRef]
  9. M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
    [CrossRef]
  10. L. Jeunhomme, M. Fraise, and J. P. Pocholle, “Propagation model for long step-index optical fibers,” Appl. Opt. 15, 3040–3046 (1976).
    [CrossRef] [PubMed]
  11. A. Djordjevich and S. Savović, “Investigation of mode coupling in step index plastic optical fibers using the power flow equation,” IEEE Photonics Technol. Lett. 12, 1489–1491 (2000).
    [CrossRef]
  12. S. Savović and A. Djordjevich, “Solution of mode coupling in step-index optical fibers by the Fokker-Planck equation and the Langevin equation,” Appl. Opt. 41, 2826–2830 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. J. Zubía, G. Durana, G. Aldabaldetreku, J. Arrúe, M. A. Losada, and M. López-Higuera, “New method to calculate mode conversion coefficients in SI multimode optical fibers,” J. Lightwave Technol. 21, 776–781 (2003).
    [CrossRef]
  15. S. Savović and A. Djordjevich, “Method for calculating the coupling coefficient in step index optical fibers,” Appl. Opt. 46, 1477–1481 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. S. Savović and A. Djordjevich, “Calculation of the coupling coefficient in step-index glass optical fibers,” Appl. Opt. 48, 4496–4500 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. J. D. Anderson, Computational Fluid Dynamics (McGraw-Hill, 1995).
  20. S. Savović and A. Djordjevich, “Mode coupling in strained and unstrained step-index plastic optical fibers,” Appl. Opt. 45, 6775–6780 (2006).
    [CrossRef] [PubMed]

2009

2008

2007

2006

2005

2004

M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

S. Savović and A. Djordjevich, “Influence of numerical aperture on mode coupling in step-index plastic optical fibers,” Appl. Opt. 43, 5542–5546 (2004).
[CrossRef] [PubMed]

2003

2002

2000

A. Djordjevich and S. Savović, “Investigation of mode coupling in step index plastic optical fibers using the power flow equation,” IEEE Photonics Technol. Lett. 12, 1489–1491 (2000).
[CrossRef]

1998

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef] [PubMed]

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

1977

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
[CrossRef]

1976

L. Jeunhomme, M. Fraise, and J. P. Pocholle, “Propagation model for long step-index optical fibers,” Appl. Opt. 15, 3040–3046 (1976).
[CrossRef] [PubMed]

M. Eve and J. H. Hannay, “Ray theory and random mode coupling in an optical fibre waveguide, I,” Opt. Quantum Electron. 8, 503–508 (1976).
[CrossRef]

1975

1974

L. Jeunhomme and J. P. Pocholle, “Experimental determination of the radiation pattern of optical fibres,” Opt. Commun. 12, 89–92 (1974).
[CrossRef]

Aldabaldetreku, G.

Anderson, J. D.

J. D. Anderson, Computational Fluid Dynamics (McGraw-Hill, 1995).

Arrue, J.

Arrúe, J.

J. Zubía, G. Durana, G. Aldabaldetreku, J. Arrúe, M. A. Losada, and M. López-Higuera, “New method to calculate mode conversion coefficients in SI multimode optical fibers,” J. Lightwave Technol. 21, 776–781 (2003).
[CrossRef]

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

Casao, J. A.

M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

Daum, W.

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

Djordjevich, A.

Durana, G.

Eve, M.

M. Eve and J. H. Hannay, “Ray theory and random mode coupling in an optical fibre waveguide, I,” Opt. Quantum Electron. 8, 503–508 (1976).
[CrossRef]

Fraise, M.

Fuster, G.

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

Gambling, W. A.

Gao, R.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef] [PubMed]

Garcés, I.

J. Arrue, G. Aldabaldetreku, G. Durana, J. Zubía, I. Garcés, and F. Jiménez, “Design of mode scramblers for step-index and graded-index plastic optical fibers,” J. Lightwave Technol. 23, 1253–1260 (2005).
[CrossRef]

M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

Garito, A. F.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef] [PubMed]

Hannay, J. H.

M. Eve and J. H. Hannay, “Ray theory and random mode coupling in an optical fibre waveguide, I,” Opt. Quantum Electron. 8, 503–508 (1976).
[CrossRef]

Jeunhomme, L.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
[CrossRef]

L. Jeunhomme, M. Fraise, and J. P. Pocholle, “Propagation model for long step-index optical fibers,” Appl. Opt. 15, 3040–3046 (1976).
[CrossRef] [PubMed]

L. Jeunhomme and J. P. Pocholle, “Experimental determination of the radiation pattern of optical fibres,” Opt. Commun. 12, 89–92 (1974).
[CrossRef]

Jiménez, F.

Kalymnios, D.

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

Krauser, J.

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

López-Higuera, M.

Losada, M. A.

M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

J. Zubía, G. Durana, G. Aldabaldetreku, J. Arrúe, M. A. Losada, and M. López-Higuera, “New method to calculate mode conversion coefficients in SI multimode optical fibers,” J. Lightwave Technol. 21, 776–781 (2003).
[CrossRef]

Mateo, J.

M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

Matsumura, H.

Payne, D. N.

Peréz-Vela, P.

M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

Pocholle, J. P.

L. Jeunhomme, M. Fraise, and J. P. Pocholle, “Propagation model for long step-index optical fibers,” Appl. Opt. 15, 3040–3046 (1976).
[CrossRef] [PubMed]

L. Jeunhomme and J. P. Pocholle, “Experimental determination of the radiation pattern of optical fibres,” Opt. Commun. 12, 89–92 (1974).
[CrossRef]

Rousseau, M.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
[CrossRef]

Savovic, S.

Wang, J.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef] [PubMed]

Zamzow, P. E.

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

Ziemann, O.

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

Zubía, J.

J. Arrue, G. Aldabaldetreku, G. Durana, J. Zubía, I. Garcés, and F. Jiménez, “Design of mode scramblers for step-index and graded-index plastic optical fibers,” J. Lightwave Technol. 23, 1253–1260 (2005).
[CrossRef]

M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

J. Zubía, G. Durana, G. Aldabaldetreku, J. Arrúe, M. A. Losada, and M. López-Higuera, “New method to calculate mode conversion coefficients in SI multimode optical fibers,” J. Lightwave Technol. 21, 776–781 (2003).
[CrossRef]

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

Appl. Opt.

IEE Proc. Optoelectron.

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

IEEE Photonics Technol. Lett.

M. A. Losada, J. Mateo, I. Garcés, J. Zubía, J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photonics Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

A. Djordjevich and S. Savović, “Investigation of mode coupling in step index plastic optical fibers using the power flow equation,” IEEE Photonics Technol. Lett. 12, 1489–1491 (2000).
[CrossRef]

IEEE Proc. Optoelectron.

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behavior when bending plastic optical fibers,” IEEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
[CrossRef]

J. Lightwave Technol.

Opt. Commun.

L. Jeunhomme and J. P. Pocholle, “Experimental determination of the radiation pattern of optical fibres,” Opt. Commun. 12, 89–92 (1974).
[CrossRef]

Opt. Quantum Electron.

M. Eve and J. H. Hannay, “Ray theory and random mode coupling in an optical fibre waveguide, I,” Opt. Quantum Electron. 8, 503–508 (1976).
[CrossRef]

Science

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef] [PubMed]

Other

J. D. Anderson, Computational Fluid Dynamics (McGraw-Hill, 1995).

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

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Figures (3)

Fig. 1
Fig. 1

Experimental output angular power distribution at fiber length z = 980 m for strained (solid curve) and unstrained (dashed curve) SI GOFs illuminated with a laser beam ( FWHM ) z = 0 = 0.85 ° parallel to the fiber axis, obtained by Jeunhomme and Pocholle [4].

Fig. 2
Fig. 2

Normalized output angular power distribution at different locations along the unstrained SI GOF calculated for three Gaussian input angles θ 0 = 0 ° (solid curve), 4 ° (dashed curve), and 8 ° (dashed–dotted curve) with ( FWHM ) z = 0 = 0.85 ° for (a) z = 120 m , (b) z = 240 m , (c) z = 340 m , and (d) z = 1040 m (filled squares represent the analytical steady-state solution).

Fig. 3
Fig. 3

Normalized output angular power distribution at different locations along the strained SI GOF calculated for three Gaussian input angles θ 0 = 0 ° (solid curve), 4 ° (dashed curve), and 8 ° (dashed–dotted curve) with ( FWHM ) z = 0 = 0.85 ° for (a) z = 80 m , (b) z = 160 m , (c) z = 300 m , and (d) z = 950 m (filled squares represent the analytical steady-state solution).

Equations (7)

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

P ( θ , z ) z = α ( θ ) P ( θ , z ) + D θ θ ( θ P ( θ , z ) θ ) ,
P ( θ , z ) z = D θ P ( θ , z ) θ + D 2 P ( θ , z ) θ 2 .
P ( θ , z ) = J 0 ( 2.405 θ θ c ) exp ( γ 0 z ) ,
P ( θ , z ) = exp [ ( θ θ 0 ) 2 σ 2 ] ,
σ z 2 = σ 0 2 + 2 D z ,
D = σ z 2 σ 0 2 2 z .
D = σ z 2 2 σ z 1 2 2 ( z 2 z 1 ) ,

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