Abstract

Using the power flow equation, the state of mode coupling in 100400μm core step-index silica optical fibers is investigated in this article. Results show the coupling length Lc at which the equilibrium mode distribution is achieved and the length zs of the fiber required for achieving the steady-state mode distribution. Functional dependences of these lengths on the core radius and wavelength are also given. Results agree well with those obtained using a long-established calculation method. Since large core silica optical fibers are used at short distances (usually at lengths of up to 10m), the light they transmit is at the stage of coupling that is far from the equilibrium and steady-state mode distributions.

© 2011 Optical Society of America

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    [CrossRef]
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2011 (2)

2007 (1)

2006 (1)

2005 (1)

2004 (2)

M. A. Losada, J. Mateo, I. Garcés, J. Zubía. J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photon. 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 (1)

2002 (2)

2000 (1)

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

1998 (2)

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 behaviour when bending plastic optical fibres,” IEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

1995 (1)

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

1977 (1)

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

1976 (2)

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 (1)

1974 (1)

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

1972 (1)

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).

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 behaviour when bending plastic optical fibres,” 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 Photon. Technol. Lett. 16, 1513–1515 (2004).
[CrossRef]

Chauny, L.-A.

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.

El-Rabii, H.

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 behaviour when bending plastic optical fibres,” 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 Photon. 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]

Gloge, D.

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).

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]

Hurand, S.

Jeunhomme, L.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theor. 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.

Joshi, S.

Kalymnios, D.

J. Arrúe, J. Zubía, G. Fuster, and D. Kalymnios, “Light power behaviour when bending plastic optical fibres,” 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 Photon. 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 Photon. 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 Photon. 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 Theor. 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]

Yalin, A.

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 Photon. 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 behaviour when bending plastic optical fibres,” IEE Proc. Optoelectron. 145, 313–318 (1998).
[CrossRef]

Appl. Opt. (7)

Bell Syst. Tech. J. (1)

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).

IEE Proc. Optoelectron. (1)

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

IEEE Photon. Technol. Lett. (2)

M. A. Losada, J. Mateo, I. Garcés, J. Zubía. J. A. Casao, and P. Peréz-Vela, “Analysis of strained plastic optical fibers,” IEEE Photon. 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 Photon. Technol. Lett. 12, 1489–1491 (2000).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (1)

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

J. Lightwave Technol. (2)

Opt. Commun. (1)

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

Opt. Lasers Eng. (1)

S. Savović and A. Djordjevich, “Mode coupling in chalcogenide-glass optical fibers,” Opt. Lasers Eng. 49, 855–858 (2011).
[CrossRef]

Opt. Quantum Electron. (1)

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 (1)

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

Other (2)

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 (1)

Fig. 1
Fig. 1

Normalized output angular power distribution at different locations along the 200 / 745 silica fiber calculated for three Gaussian input angles θ 0 = 0 ° (solid curve), 4 ° (dashed curve), and 8 ° (dotted–dashed curve) with ( FWHM ) z = 0 = 0.127 ° for (a)  z = 500 m , (b)  z = 900 m , (c)  z = 1380 m , and (d)  z = 2470 m (solid squares represent the analytical steady-state solution).

Tables (2)

Tables Icon

Table 1 Core Diameter, Clad Diameter, Coupling Coefficient D, Coupling Length L c , and Length z s for Silica Fibers at λ = 633 nm a

Tables Icon

Table 2 Coupling Coefficient D, Coupling Length L c , and Length z s at Different Wavelengths λ for 200 / 745 Silica Fiber a

Equations (5)

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 ) ,
z s = 0.2 D ( NA n ) 2 ,
P ( θ , z ) = exp [ ( θ θ 0 ) 2 σ 2 ] ,

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