Abstract

A simple method is proposed for determining the mode coupling coefficient D in step-index multimode optical fibers. It only requires observation of the far-field output pattern for one fiber length with the input light launched centrally along the fiber axis (θ0=0). For illustration, the coupling coefficient determined by this simple method for a step-index plastic optical fiber was used to calculate the coupling length Lc at which the equilibrium mode distribution is achieved, and length zs at which the steady-state distribution is achieved. Our results are in good agreement with experimental results reported earlier.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Kitayama and M. Ikeda, "Mode coupling measurements in optical fibers," Appl. Opt. 17, 3979-3983 (1978).
    [Crossref] [PubMed]
  2. J. Mateo, M. A. Losada, I. Garcés, and J. Zubía, "Global characterization of optical power propagation in step-index plastic optical fibers," Opt. Express 14, 9028-9035 (2006).
    [Crossref] [PubMed]
  3. J. Dugas and G. Maurel, "Mode-coupling processes in polymethyl methacrylate-core optical fibers," Appl. Opt. 31, 5069-5079 (1992).
    [Crossref] [PubMed]
  4. G. Jiang, R. F. Shi, and F. Garito, "Mode coupling and equilibrium mode distribution conditions in plastic optical fibers," IEEE Photon. Technol. Lett. 9, 1128-1130 (1997).
    [Crossref]
  5. A. F. Garito, J. Wang, and R. Gao, "Effects of random perturbations in plastic optical fibers," Science 281, 962-967 (1998).
    [Crossref] [PubMed]
  6. W. A. Gambling, D. P. Payne, and H. Matsumura, "Mode conversion coefficients in optical fibers," Appl. Opt. 14, 1538-1542 (1975).
    [Crossref] [PubMed]
  7. J. Zubía, G. Durana, G. Aldabaldetreku, J. Arrue, M. A. Losada, and M. Lopez-Higuera, "New method to calculate mode conversion coefficients in SI multimode optical fibers," J. Lightwave Technol. 21, 776-781 (2003).
    [Crossref]
  8. M. Eve and J. H. Hannay, "Ray theory and random mode coupling in an optical fiber waveguide, I.," Opt. Quantum Electron. 8, 503-508 (1976).
    [Crossref]
  9. 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]
  10. D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1783 (1972).
  11. 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]
  12. 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]
  13. S. Savović and A. Djordjevich, "Optical power flow in plastic clad silica fibers," Appl. Opt. 41, 7588-7591 (2002).
    [Crossref]
  14. 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]
  15. L. Jeunhomme, M. Fraise, and J. P. Pocholle, "Propagation model for long step-index optical fibers," Appl. Opt. 15, 3040-3046 (1976).
    [Crossref] [PubMed]
  16. 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]
  17. M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, "Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers," J. Lightwave Technol. 20, 1160-1164 (2002).
    [Crossref]
  18. H. Risken, The Fokker-Planck Equation (Springer-Verlag, 1989).
  19. S. Zheng, X. Jin, and X. Zhang, "Analysis of the effects of mode coupling on the bandwidth characteristics of step-index optical fiber," Microwave Opt. Technol. Lett. 48, 432-435 (2006).
    [Crossref]
  20. M. J. Yadlowsky and A. R. Mickelson, "Distributed loss and mode coupling and their effect on time-dependent propagation in multimode fibers," Appl. Opt. 32, 6664-6677 (1993).
    [Crossref] [PubMed]

2006 (2)

J. Mateo, M. A. Losada, I. Garcés, and J. Zubía, "Global characterization of optical power propagation in step-index plastic optical fibers," Opt. Express 14, 9028-9035 (2006).
[Crossref] [PubMed]

S. Zheng, X. Jin, and X. Zhang, "Analysis of the effects of mode coupling on the bandwidth characteristics of step-index optical fiber," Microwave Opt. Technol. Lett. 48, 432-435 (2006).
[Crossref]

2005 (1)

2004 (1)

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]

2003 (1)

2002 (3)

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 (1)

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

1997 (1)

G. Jiang, R. F. Shi, and F. Garito, "Mode coupling and equilibrium mode distribution conditions in plastic optical fibers," IEEE Photon. Technol. Lett. 9, 1128-1130 (1997).
[Crossref]

1993 (1)

1992 (1)

1978 (1)

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 fiber waveguide, I.," Opt. Quantum Electron. 8, 503-508 (1976).
[Crossref]

1975 (1)

1972 (1)

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

Aldabaldetreku, G.

Arrue, J.

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]

Djordjevich, A.

Dugas, J.

Durana, G.

Eve, M.

M. Eve and J. H. Hannay, "Ray theory and random mode coupling in an optical fiber waveguide, I.," Opt. Quantum Electron. 8, 503-508 (1976).
[Crossref]

Fraise, M.

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]

Garito, F.

G. Jiang, R. F. Shi, and 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).

Hannay, J. H.

M. Eve and J. H. Hannay, "Ray theory and random mode coupling in an optical fiber waveguide, I.," Opt. Quantum Electron. 8, 503-508 (1976).
[Crossref]

Ikeda, M.

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 F. Garito, "Mode coupling and equilibrium mode distribution conditions in plastic optical fibers," IEEE Photon. Technol. Lett. 9, 1128-1130 (1997).
[Crossref]

Jiménez, F.

Jin, X.

S. Zheng, X. Jin, and X. Zhang, "Analysis of the effects of mode coupling on the bandwidth characteristics of step-index optical fiber," Microwave Opt. Technol. Lett. 48, 432-435 (2006).
[Crossref]

Kitayama, K.

Lopez-Higuera, M.

Losada, M. A.

Lou, J.

Mateo, J.

Matsumura, H.

Maurel, G.

Mickelson, A. R.

Payne, D. P.

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.

Risken, H.

H. Risken, The Fokker-Planck Equation (Springer-Verlag, 1989).

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]

Salinas, I.

Savovic, S.

Shi, R. F.

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

Yadlowsky, M. J.

Zhang, X.

S. Zheng, X. Jin, and X. Zhang, "Analysis of the effects of mode coupling on the bandwidth characteristics of step-index optical fiber," Microwave Opt. Technol. Lett. 48, 432-435 (2006).
[Crossref]

Zheng, S.

S. Zheng, X. Jin, and X. Zhang, "Analysis of the effects of mode coupling on the bandwidth characteristics of step-index optical fiber," Microwave Opt. Technol. Lett. 48, 432-435 (2006).
[Crossref]

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).

IEEE Photon. Technol. Lett. (3)

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

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]

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. (3)

Microwave Opt. Technol. Lett. (1)

S. Zheng, X. Jin, and X. Zhang, "Analysis of the effects of mode coupling on the bandwidth characteristics of step-index optical fiber," Microwave Opt. Technol. Lett. 48, 432-435 (2006).
[Crossref]

Opt. Express (1)

Opt. Quantum Electron. (1)

M. Eve and J. H. Hannay, "Ray theory and random mode coupling in an optical fiber 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 (1)

H. Risken, The Fokker-Planck Equation (Springer-Verlag, 1989).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Normalized output angular power distribution as a function of the fiber length for a light beam launched centrally ( θ 0 = 0 ° ) along the fiber axis, as observed experimentally by Zheng et al. (Ref. [19]).

Fig. 2
Fig. 2

Numerically determined normalized output angular power distribution for four Gaussian input angles θ 0 = 0 ° (solid curve), 7.5° (dashed curve), 15° (dotted curve), and 22.7° (dashed-dotted curve) with FWHM = 7.5 ° at different locations along the SI POF: z = (a) 5, (b) 12, (c) 13, and (d) 30 m (squares represent the analytical steady-state solution).

Equations (8)

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 ) z = D 2 P ( θ , z ) θ 2 .
P ( θ , z ) = 1 2 π σ z exp [ θ 2 2 σ z 2 ] .
σ z 2 = σ z = 0 2 + 2 D z ,
D = σ z 2 σ z = 0 2 2 z .
D = σ z 2 2 σ z 1 2 2 ( z 2 z 1 ) ,

Metrics