Abstract

The numerical solution of the complete power flow equation is reported and employed to investigate the state of mode coupling along a step-index plastic optical fiber. This solution is based on the explicit finite-difference method and, in contrast to earlier solutions, does not neglect absorption and scattering loss. It is the only solution that can accommodate any input condition throughout the entire range of feasible input angles without the need for restriction to those angles that are sufficiently far away from critical. Our results for the field patterns at different locations along one type of fiber are in agreement with reported measurements earlier. Furthermore, the length of fiber required for achieving a steady-state mode distribution matches the analytical solution that is available for such distribution as a special case. Mode coupling in plastic fibers is known to affect fiber-optic power delivery, data transmission, and sensing systems.

© 2004 Optical Society of America

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References

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2003 (2)

2002 (3)

2001 (1)

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

2000 (3)

T. Ishigure, M. Kano, and Y. Koike, “Which is a more serious factor to the bandwidth of GI POF: differential mode attenuation or mode coupling?” J. Lightwave Technol. 18, 959–965 (2000).
[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]

K. T. V. Grattan and T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–60 (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]

C. Koeppen, R. F. Shi, W. D. Chen, and A. F. Garito, “Properties of plastic optical fibers,” J. Opt. Soc. Am. B 15, 727–739 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

P. E. Green, Jr., “Optical networking update,” IEEE J. Sel. Areas Commun. 14, 764–779 (1996).
[CrossRef]

1995 (1)

1993 (1)

1992 (2)

1977 (1)

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 (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)

1973 (1)

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, and 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.

Arrue, J.

Chen, W. D.

Chinnock, E. L.

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, and 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, and 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 and A. Djordjevich, “Optical power flow in plastic clad silica fibers,” Appl. Opt. 41, 7588–7591 (2002).
[CrossRef]

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]

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

Dugas, J.

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.

Fung, M.

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

C. Koeppen, R. F. Shi, W. D. Chen, and A. F. Garito, “Properties of plastic optical fibers,” J. Opt. Soc. Am. B 15, 727–739 (1998).
[CrossRef]

G. Jiang, R. F. Shi, and A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photonics 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]

Golowich, S. E.

Grattan, K. T. V.

K. T. V. Grattan and T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–60 (2000).
[CrossRef]

Green Jr., P. E.

P. E. Green, Jr., “Optical networking update,” IEEE J. Sel. Areas Commun. 14, 764–779 (1996).
[CrossRef]

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]

Hanson, D.

D. Hanson, “Wiring with plastic,” IEEE Lightwave Commun. Syst. 3, 34–39 (1992).

Holden, W. S.

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

Ishigure, T.

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]

Jiang, G.

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

Kano, M.

Keck, D. B.

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

Knudsen, E.

Koeppen, C.

Koike, Y.

Lopez-Higuera, M.

Losada, M. A.

Lou, J.

Mateo, J.

Matsumura, H.

Maurel, G.

Mickelson, A. R.

Payne, D. N.

Pocholle, J. P.

Reed, W. A.

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]

Ruddy, V.

Salinas, I.

Savovic, S.

Shaw, G.

Shi, R. F.

C. Koeppen, R. F. Shi, W. D. Chen, and A. F. Garito, “Properties of plastic optical fibers,” J. Opt. Soc. Am. B 15, 727–739 (1998).
[CrossRef]

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

Standley, R. D.

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

Sun, T.

K. T. V. Grattan and T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–60 (2000).
[CrossRef]

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]

White, W.

Yadlowsky, M. J.

Zubia, J.

Zubía, J.

Appl. Opt. (7)

Bell Syst. Tech. J. (1)

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

IEEE J. Sel. Areas Commun. (1)

P. E. Green, Jr., “Optical networking update,” IEEE J. Sel. Areas Commun. 14, 764–779 (1996).
[CrossRef]

IEEE Lightwave Commun. Syst. (1)

D. Hanson, “Wiring with plastic,” IEEE Lightwave Commun. Syst. 3, 34–39 (1992).

IEEE Photonics Technol. Lett. (2)

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]

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

IEEE Trans. Microwave Theory Tech. (1)

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. (4)

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

Meas. Sci. Technol. (1)

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

Proc. IEEE (1)

E. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, and 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, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef] [PubMed]

Sens. Actuators (1)

K. T. V. Grattan and T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–60 (2000).
[CrossRef]

Other (2)

S. Savović and A. Djordjevich, “Influence of numerical aperture on mode coupling in step index plastic optical fibers,” submitted to Appl. Opt.

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

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Figures (3)

Fig. 1
Fig. 1

Numerically determined normalized output angular power distribution for a plane wave launched with input angles θ0=0° (solid curves), 5.5° (dashed curves), 16° (dotted curves), and 29° (dashed–dotted curves) at various locations along the SI POF: z=3 m, z=10 m, z=17.6 m, and z=48 m.

Fig. 2
Fig. 2

Analytically determined normalized output angular power distribution for a plane wave launched with input angles θ0=0° (solid curves), 5.5° (dashed curves), 16° (dotted curves), and 29° (dashed–dotted curves) at several locations along the SI POF: z=3 m, z=10 m, z=17.6 m, and z=48 m.

Fig. 3
Fig. 3

Experimentally determined normalized output angular power distribution for launch angles of 5.5° and 16°, 3 m from the input end (data compiled from Ref. 17).

Tables (1)

Tables Icon

Table 1 Coupling Length (Lc) and Length (zs) for Achieving Steady-State Mode Distribution for SI POFs with Different Numerical Apertures N.A. and Mode Coupling Coefficients D

Equations (9)

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

P(θ, z)z=-Aθ2P(θ, z)+Dθ θ θ P(θ, z)θ,
P(θc, z)=0,D Pθθ=0=0,
P(x, z)=exp-x0+x2 1+exp(-bz)1-exp(-bz)×exp(-1/2bz)1-exp(-bz)I0(4x0x)1/2 exp(-1/2bz)1-exp(-bz),
P(θ, z)z=-Aθ2P(θ, z)+Dθ P(θ, z)θ+D 2P(θ, z)θ2.
Pi,j+1=ΔzDΔθ2-ΔzD2θi,jΔθPi-1,j+1-2ΔzDΔθ2-ΔzAθi,j2Pi,j+ΔzD2θi,jΔθ+ΔzDΔθ2Pi+1,j,
PN,j=0,P0,j=P1,j,
limθ0 1θ θ θ Pθ=2 2Pθ2θ=0.
P(θ, 0)=1θ=θ0,
P(θ, 0)=0θθ0,

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