Abstract

Using the power-flow equation, we have examined the state of mode coupling in step-index plastic optical fibers with different numerical apertures. Our results confirm that the coupling rates vary with the coupling coefficient of the fibers as the dominant parameter, especially in the early stage of coupling near the input fiber end. However, we show that the fiber’s numerical aperture has a significant influence on later stages of this process. Consequently, equilibrium mode distribution and steady-state distribution are achieved at overall fiber lengths that depend on both of these factors. As one of our examples demonstrates, it is possible for the coupling length of a high-aperture fiber to be similar to that of a low-aperture fiber despite the three-times-larger coupling coefficient of the former.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2003 (1)

2002 (3)

2001 (1)

A. Djordjevich, M. Fung, R. Y. K. Fung, “Principles of deflection-curvature measurement,” Meas. Sci. Technol. 12, 1983–1989 (2001).
[CrossRef]

2000 (1)

A. Djordjevich, 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 (1)

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

1997 (1)

G. Jiang, R. F. Shi, A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photon. Technol. Lett. 9, 1128–1130 (1997).
[CrossRef]

1995 (1)

1993 (1)

1977 (1)

M. Rousseau, 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 (2)

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

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

1975 (1)

1973 (1)

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, D. B. Keck, “The length dependence of pulse spreading in the CGW-Bell-10 optical fiber,” Proc. IEEE 61, 1499–1500 (1973).
[CrossRef]

1972 (1)

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

Aldabaldetreku, G.

Anderson, J. D.

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

Arrue, J.

Chinnock, E. L.

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, D. B. Keck, “The length dependence of pulse spreading in the CGW-Bell-10 optical fiber,” Proc. IEEE 61, 1499–1500 (1973).
[CrossRef]

Cohen, L. G.

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, D. B. Keck, “The length dependence of pulse spreading in the CGW-Bell-10 optical fiber,” Proc. IEEE 61, 1499–1500 (1973).
[CrossRef]

Djordjevich, A.

S. Savović, 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]

S. Savović, A. Djordjevich, “Optical power flow in plastic clad silica fibers,” Appl. Opt. 41, 7588–7591 (2002).
[CrossRef]

A. Djordjevich, M. Fung, R. Y. K. Fung, “Principles of deflection-curvature measurement,” Meas. Sci. Technol. 12, 1983–1989 (2001).
[CrossRef]

A. Djordjevich, 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]

Durana, G.

Eve, M.

M. Eve, 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.

Fung, M.

A. Djordjevich, M. Fung, R. Y. K. Fung, “Principles of deflection-curvature measurement,” Meas. Sci. Technol. 12, 1983–1989 (2001).
[CrossRef]

Fung, R. Y. K.

A. Djordjevich, M. Fung, R. Y. K. Fung, “Principles of deflection-curvature measurement,” Meas. Sci. Technol. 12, 1983–1989 (2001).
[CrossRef]

Gambling, W. A.

Gao, R.

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

Garcés, I.

Garito, A. F.

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

G. Jiang, R. F. Shi, A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photon. Technol. Lett. 9, 1128–1130 (1997).
[CrossRef]

Gloge, D.

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

Hannay, J. H.

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

Holden, W. S.

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, D. B. Keck, “The length dependence of pulse spreading in the CGW-Bell-10 optical fiber,” Proc. IEEE 61, 1499–1500 (1973).
[CrossRef]

Jeunhomme, L.

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

Jiang, G.

G. Jiang, R. F. Shi, A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photon. Technol. Lett. 9, 1128–1130 (1997).
[CrossRef]

Keck, D. B.

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, D. B. Keck, “The length dependence of pulse spreading in the CGW-Bell-10 optical fiber,” Proc. IEEE 61, 1499–1500 (1973).
[CrossRef]

Lopez-Higuera, M.

Losada, M. A.

Lou, J.

Mateo, J.

Matsumura, H.

Mickelson, A. R.

Payne, D. N.

Pocholle, J. P.

Rousseau, M.

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

Ruddy, V.

Salinas, I.

Savovic, S.

Shaw, G.

Shi, R. F.

G. Jiang, R. F. Shi, A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photon. Technol. Lett. 9, 1128–1130 (1997).
[CrossRef]

Standley, R. D.

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, D. B. Keck, “The length dependence of pulse spreading in the CGW-Bell-10 optical fiber,” Proc. IEEE 61, 1499–1500 (1973).
[CrossRef]

Wang, J.

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

Yadlowsky, M. J.

Zubia, J.

Zubía, J.

Appl. Opt. (6)

Bell Syst. Tech. J. (1)

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

IEEE Photon. Technol. Lett. (2)

A. Djordjevich, 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]

G. Jiang, R. F. Shi, A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photon. Technol. Lett. 9, 1128–1130 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. Rousseau, 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. (2)

Meas. Sci. Technol. (1)

A. Djordjevich, M. Fung, R. Y. K. Fung, “Principles of deflection-curvature measurement,” Meas. Sci. Technol. 12, 1983–1989 (2001).
[CrossRef]

Opt. Quantum Electron. (1)

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

Proc. IEEE (1)

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, D. B. Keck, “The length dependence of pulse spreading in the CGW-Bell-10 optical fiber,” Proc. IEEE 61, 1499–1500 (1973).
[CrossRef]

Science (1)

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

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

Normalized output angular power distribution at several locations along the S-HNA fiber calculated for four Gaussian input angles θ0: 0° (solid curves), 5° (dashed curves), 10° (dotted curves), and 15° (dashed-dotted curves) with a FWHM of 2.5° for z = 4, 10, 15, 45 m (squares represent the analytical steady-state solution).

Fig. 2
Fig. 2

Normalized output angular power distribution at several locations along the LNA fiber calculated for three Gaussian input angles θ0: 0° (solid curves), 5° (dashed curves), and 10° (dotted curves) with a FWHM of 2.5° for z = 4, 10, 18, 50 m (squares represent the analytical steady-state solution).

Fig. 3
Fig. 3

Normalized output angular power distribution at several locations along the U-HNA fiber calculated for four Gaussian input angles θ0: 0° (solid curves), 5° (dashed curves), 10° (dotted curves), and 15° (dashed-dotted curves) with a FWHM of 2.5° for z = 4, 15, 35, 100 m (squares represent the analytical steady-state solution).

Fig. 4
Fig. 4

Variation of a fiber’s coupling length with its NA. (Filled markers represent the actual POFs. Lines are drawn for visual aid.)

Tables (1)

Tables Icon

Table 1 Coupling Length Lc and Length zs for Achieving Steady-State Mode Distribution for Fibers with Several NAs and Mode Coupling Coefficients D

Equations (4)

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

Pθ, zz=-αθPθ, z+Dθθθ Pθ, zθ,
Pθ, zz=DθPθ, zθ+D 2Pθ, zθ2.
Pθ, z=J02.405 θθcexp-γ0z,
Pθ, z=exp-θ-θ02σ2,

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